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30(Unit Operations)

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1. With Partial intermediate printout the following information is provided at each iteration ITER 1 E K 1 0717E 01 E ENTH SPEC 1 392E 03 E SUM 3 159E 01 INNER 0 E ENTH SPEC 1 104E 02 INNER 1 E ENTH SPEC 1 854E 04 ALPHA 1 0000 ITER 2 E K 1 137E 02 E ENTH SPEC 1 854E 04 E SUM 2 454E 02 INNER 0 E ENTH SPEC 5 925E 04 INNER 1 E ENTH SPEC 7 476E 06 ALPHA 1 0000 The error EENTH 4 SPEC is the sum of the enthalpy balance and specifica tion errors and is used to determine convergence of the inner loop The inner loop convergence tolerance for EENTH SPEC is Iteration E ENTH SPEC Tolerance 1 0 01 2 0 001 if E ENTH SPEC error from iter 1 was below 0 001 then the tolerance 2 0E 5 3 2 0E 5 E ENTH SPEC is the most important number to watch for column convergence The second most important number to watch for information about column convergence is alpha the damping factor The damping factor alpha is ap plied to the correction to the stripping factors and sidestream withdrawl fac tors An alpha value of 1 0 corresponds to no damping and indicates that convergence is progressing well Low alpha values indicate that the full correction to the stripping factors resulted in an increase in the inner loop en thalpy and specification equations A line search is performed using a pro gressively smaller step size until the inner loop equation errors are reduced This may be due to a poor approxi
2. o a E a G c e c o o is o a E a Zz Particle size m Making a balance on the number density of the crystals in the crystallizer qr qn ova 4 where q volumetric rate of bottoms product slurry m sec q volumetric rate of feed m sec V operating volume of crystallizer m r characteristic length of crystal m Residence time is defined as T q By rearranging equation 4 multiplying by the integrating factor ee integrating we get and PRO II Unit Operations Reference Manual Crystallizer 1 173 Solids Handling Unit Operations Section 2 7 Jalen t pum dr For the k division eek dr Tay t n l e n ry n r 4 Gt q fk Gi Using the initial condition n ro no at ro 0 r n k l n rj n e 2 f e a ro ia gr n k 2 n rj n e Gt uL l e amp o FK F p a 2 q 1 2 2 1 ne CO Mn e e ep l e amp o Pi Leo For any k the generalized expression is Tk q k PE Ta Ty n r ne ir na e C 2g amp Iz For feed containing no solids equation 9 simplifies to n r ne n 5 Tt a 4 MUS q _ ci ff Gt a if Je EMI e Je ui 5 6 7 8 9 10 The magma density Mr the weight concentration of crystals in slurry is cal culated from the third moment of the particle size distribution je 11 M p ok rndr 0 where Pc density of crystals kg crystal m cr
3. American Society of Mechanical Engineers ASME 1965 Power Test Code 10 31 33 May 1994 Section 2 2 Isentropic Calculations 56 GPSA Method This GPSA method is the default method and is more commonly used in the chemical process industry Adiabatic Efficiency Given In this method the adiabatic head is calculated from equations 3 4 and 9 Once this is calculated the isentropic coefficient k is computed by trial and error using 15 HEAD l G 2 2 RT Non i ies io A i where Zp Z compressibility factors at the inlet and outlet conditions R gas constant T temperature at inlet conditions This trial and error method of computing k produces inaccurate results when the compression ratio equal to P2 P1 becomes low PRO II allows the user to switch to another calculation method for k if the compression ratio falls below a certain set value PRO II Note For more information on using the PSWITCH keyword to control the usage of the isentropic calculation equation see Section 56 Compressor of the PRO II Keyword Input Manual If the calculated compression ratio is less than a value set by the user defaulted to 1 15 in PRO ID or if k does not satisfy 1 0 k lt 1 66667 the isentropic coef ficient k is calculated by trial and error based on the following 16 7 7 2 T ies ZP i 16 The polytropic compressor equation is given by n 1 n 17 HEAD e t 2 RT n 1 zi
4. Basic chemicals Ethylbenzene styrene Fatty acids e g tall oil Cyclohexanone ol Caprolactam Vacuum columns in refineries Cs splitter Ca splitter Absorption desorption columns Fine chemicals Isomers Perfumes Favors Pilot columns Increased performance of existing columns Halogenated organic compounds only limited suitability in the presence of aqueous mineral acid lay and aqueous solutions Sulzer structured packings available in PRO II include 9 types of corrugated sheet metal known as MELLAPAK 2 types of metal gauze known as BX and CY and a ceramic KERAPAK packing PRO II Note For more information on using Sulzer structured packings see Section 77 Column Hydraulics of the PRO II Keyword Input Manual PRO II Unit Operations Reference Manual Column Hydraulics 11 81 Distillation and Liquid Liquid Extraction Columns Section 2 4 Il 82 Column Hydraulics Capacity The capacity of a packed column is generally limited by the onset of flooding or maximum column vapor load The flooding point however is difficult to meas ure For structured packing the limit of capacity is generally used to indicate the flood point The limit of capacity 100 capacity is defined as the vapor load that corresponds to a column pressure drop of 20 mbar m Furthermore the column capacity is expressed in terms of the capacity fac tor The capacity factor or load factor cG of the vapor phase is defin
5. From equations 1 4 5 and 6 the overall objective function for the minimization of Gibbs free energy can be expressed as equation 7 NP NC 7 F n G n RT Ys b Jnd YY mrp k 1 j l p 1 j l NR NS E m S Y a nj nj L aj Y E r 1 jel p l SFIX NCFIX NP su LG Yn j l p In equation 7 above T s are the Lagrange multipliers for the conservation of elemental groups and various mass balance equations Solution of Gibbs Free Energy Minimization The necessary conditions for a minimum value of F n are IV 8 9D ig j 1 NS 8 on or 0 j l NC pL NP an HS E k 1 NE k S u r 1 NR xt 0 jal NSFIX i OF n 1 NCFIX On i J NC J May 1994 Section 2 6 Reactors Note that since these are the necessary but not the sufficient conditions for Gibbs free energy minimization a local minimum Gibbs free energy can be obtained Multiple solutions may be found when multiple fluid phases coex ist in the mixture Providing different initial estimates for different runs can be used as a way to check whether solution corresponding to a local mini mum Gibbs free energy has been reached The new solution point in each calculation iteration is determined by N n A N n 9 where n the solution point from previous iteration N the new solution point from equation 8 A step size parameter The parameter A is adjusted to ensure the new solution point N will fu
6. If the flowsheet solution at x is not a sufficient improvement as com pared to the flowsheet solution at x reduce the search step amp and return to step 4 Let x be the new base case Set k k J and return to step 2 Various tests are included after the solution of the quadratic approximation step 3 and after each non derivative flowsheet solution step 4 to deter mine whether the convergence tolerances are satisfied Il 234 Flowsheet Optimization May 1994 Section 2 10 Flowsheet Solution Algorithms The quadratic programming algorithm used in step 3 automatically deter mines which of the constraints are binding or active i e which of the inequal ity constraints g x lt 0 are satisfied as equality constraints g A x 0 at the current value of the optimizer variables In addition the quadratic program ming algorithm ensures that the optimizer variables do not exceed their bounds and determines which variables are exactly at a bound e g X X1 maxi Note that each optimizer cycle includes steps 2 through 6 If the algorithm has to return to step 4 this is referred to as a line search iteration Line search iterations are common initially if line search iterations are necessary close to the solution this frequently indicates that the error in the first order derivatives is too large and the algorithm is having difficulties meeting the convergence tolerances Calculation of First order Deriv
7. upper case letters refer to total flows or transformed variables The unknowns alternatively referred to as iteration or primitive variables X Y L V Tj where i 1 NT are solved for directly using an augmented Newton Raphson method Specifi cation equations involving the iteration variables are added directly to the above equations and solved simultaneously The modifications of the Newton Raphson method are twofold The first is a line search procedure that will when possible decrease the sum of the errors along the Newton correction If this is not possible the size of the increase will be limited to a prescribed amount The second modification limits the changes in the individual iteration variables Both of these modifications can result in a fractional step in the Newton direction The fractional step size is reported in the iteration summary of the column output Note that an o of 1 indicates that the solution procedure is progressing well and that as the solu tion is approached should become one In the case of very non linear sys tems which may oscillate the user can restrict the step size by specifying a damping factor which reduces the changes in the composition variables A cutoff value is used by the algorithm so that when the value of the sum of the errors drops below the given level the full Newton correction is used This serves to speed the final convergence PRO II Note For more information on using the
8. III Heat control governed by a further equation In this case we have to consider the physical form of the cooling or heating supplied If Tc z is the coolant temperature at position z the heat transfer equation can be written as Q h Te T which leads to another series of sub cases Il 146 Plug Flow Reactor PFR May 1994 Section 2 6 Reactors a Tc constant In this case the differential equations for amp and T can be integrated together This could also be done if Tc were specified as a function of z b Tc governed by a further differential equation Here the issues to be considered are the form of coolant flow cocurrent or countercurrent and whether the cold feed itself is to be used as the coolant PFR Operation PRO II allows for the following modes of plug flow reactor operation Modes adiabatic with or without heat addition removal thermal with the option of indicating temperature and pressure profiles cocurrent flow countercurrent flow the outlet temperature of the cooling stream is required The thermal mode of operation is the default There are two methods of numerical integration available in PRO II The Runge Kutta method is the default method and is preferred in most cases When sharply varying gradients are expected within the reactor the Gear method which has a variable integration step size may be preferred For exothermic reactions two valid solutions the low conversion and the hi
9. Section 2 7 Solids Handling Unit Operations zm Filtering Centrifuge General An alternate solid liquid separating unit to the rotary drum filter is the filtering Information centrifuge In this type of unit the solid liquid mixture is fed to a rotating perfo rated basket lined with a cloth or mesh insert Liquid is forced through the bas ket by centrifugal force while the solids are retained in the basket PRO II contains five types of filtering centrifuges as indicated in Table 2 7 3 1 Table 2 7 3 1 Types of Filtering Centrifuges Available in PRO II Type Description WIDE Wide angle Half angle of basket cone gt angle of repose of solids DIFF Differential scroll Movement of solids from filter basket controlled by a screw AXIAL Axial vibration High frequency force applied to the axis of rotation TORSION Torsional vibration High frequency force applied around the drive shaft OSCIL Oscillating A low frequency force is applied to a pivot supporting the drive shaft 103 dum PRO II Note For more information on specifying the type of filtering centri fuge in PRO II see Section 103 Filtering Centrifuge of the PRO II Keyword Input Manual Calculation For rating applications the basket diameter rotational speed in revolutions Methods per minute and centrifuge type are specified The centrifugal force is then computed using P 1 Scent P where
10. W CVP P Hal where 2 80 C Von s air For subsonic flow the pressure drop across the valve must satisfy AP lt 0 5C P 12 The valve rate for subsonic flow is given by W 322C NAPP G 13 Again substituting equations 9 and 10 into 13 the valve rate for sub sonic flow becomes W C VAPp 14a where C 3 22C DDR reo MW i The constant C has units of weight time pressure weight volume Alternatively the user can specify a constant discharge rate W Constant 15 The user may also specify a more general valve rate formula W AC C Y VPIP 16 where A a constant with units of weight volume pressure time 2 May 1994 Section 2 11 Depressuring Unit Heat Input Equations Values for the constant in equation 16 in English SI or Metric units are given in Table 2 11 1 Table 2 11 1 Value of Constant A Dimensional Value of A Units English 38 84 SI 1 6752 Metric 16 601 Y and Y are given by Y Y 0 148 17 and im AP 0 5 18 Y NES C If Y gt 1 5 Yris not calculated by equation 17 but is instead set equal to 1 0 The control valve coefficient Cy is defined as the number of gallons per minute of water which will pass through a given flow restriction with a pres sure drop of 1 psi This means that the value of C is independent of the problem input units The heat flow between the depressuring vessel and a heat source or sink m
11. bypassed streams or streams which are not well mixed F factors have been derived by Bowman et al to account for these non ideal flow patterns and are used in PRO II to correct equa tions 3 and 4 For multipass heat exchangers where the ratio of shell passes to tube passes given is not 1 2 e g for a 2 shell and 6 tubepass exchanger the F factors actually used are those computed for exchangers with the ratio of one shell to two tubepasses 1 e for 2 shell and 4 tubepasses PRO II Unit Operations Reference Manual Simple Heat Exchangers l 107 Heat Exchangers Section 2 5 The method used by PRO II to determine the heat transferred when using utility streams is given by m For water and air cooling utility streams the only heat transfer consid ered is sensible heat i e Q How Hin hA Tou Tn 5 where h sensible heat transfer coefficient H enthalpy of utility stream m For steam or refrigerant utilities only latent heat is considered in the heat transfer Either the saturation temperature Tsat or saturation pres sure Psat must be supplied Q m 6 where m mass flowrate of utility stream A latent heat at Tsat Any one of the following specifications may be made in PRO II m Overall exchanger heat duty m Product stream temperature hot or cold side m Product stream liquid fraction hot or cold side m Product stream temperature approach to the bubble or dew point hot and co
12. no slip condition applies Generally however the no slip condition will not hold and the mixture velocity Vm is computed from the sum of the phase superficial velocities Vin Yst Vel 5 where Vs superficial liquid velocity volumetric liquid flowrate cross sectional area of pipe Vgl superficial gas velocity 2 volumetric gas flowrate cross sectional area of pipe Equations 2 3 and 4 are therefore rewritten to account for these phase property differences dP dD 7 fry Pip Vip 28 d 6 dP dL sp sino 7 AP AL ge Pip Yip 8c dv dL 8 PRO II Unit Operations Reference Manual Pipes Il 33 Pressure Calculations Section 2 3 Pressure Drop Correlations Il 34 Pipes where Ptp fluid density pyHL pgHg Hy Hg liquid and gas holdup terms subscript tp refers to the two phases The hybrid pressure drop methods available in PRO II each uses a separate method to compute each contributing term in the total pressure drop equation 1 These methods are described below Beggs Brill Moody BBM This method is the default method used by PRO II and is the recommended method for most systems especially single phase systems For the pressure drop elevation term the friction factor f is computed from the relationship f f fp f exps 9 The exponent s is given by s y 0 0523 3 182y 0 8725y 0 01853y 10 s In22e 12 1 e 12 11 y InQ H ve wher
13. 1 IMTP 51 41 24 18 12 Metal TM 2 Hy Pak 45 29 26 16 Metal 3 Super Intalox 60 30 Saddles Ceram 4 Super Intalox 40 28 18 Saddles Ceram 5 Pall Rings 95 55 40 26 17 Plastic 6 Pall Rings 81 56 40 27 18 Metal 7 Intalox Saddles 725 1000 580 145 92 52 40 22 Ceramic 8 Raschig Rings 1600 1000 580 380 255 179 125 93 65 37 Ceramic 9 Raschig Rings 700 390 300 170 155 115 1 32 Metal 10 Raschig Rings 410 300 220 144 110 83 57 32 1 16 Metal 11 Berl Saddles 900 240 170 110 65 45 Ceramic IMTP and Intalox are registered marks of Norton Company Hy Pak is a trademark of Norton Company PRO II Unit Operations Reference Manual Column Hydraulics Il 77 Distillation and Liquid Liquid Extraction Columns Section 2 4 Il 78 Column Hydraulics Capacity The capacity of a randomly packed column is determined by its flood point The flood point is defined as the point at which the slope of the pressure drop curve goes to infinity or the column efficiency goes to zero For ran dom packings the flood point as given by the superficial vapor velocity at flood vcr is determined by Eckart s correlation vor Fp 9 Mp Pg Dp 7 function r G pg pp 8 where vGf superficial vapor velocity at flood Fp packing factor Pw PL Pw density of water PG density of vapor PL density of liquid c gravita
14. 11 223 1 222 11 157 Il 4 1 221 1 215 1 178 1 130 1 130 11 136 11 196 1 193 11 196 11 193 11 195 11 105 Il 5 Il 5 Il 6 K K value generator L Lagrange multipliers See Shadow prices LNG heat exchanger cells zones analysis M Melter Mixer See Equilibrium unit operations MSMPR crystallizer See Crystallizer Multivariable controller algorithm 0 Optimizer objective function recommendations shadow prices P PFR See Plug flow reactor Phase envelope Pipe Beggs Brill Moody correlation Beggs Brill Moody Palmer correlation Dukler Eaton Flanigan correlation Gray correlation Hagedorn Brown correlation Moody friction factor Mukherjee Brill correlation Oliemens correlation thermodynamic generators Plug flow reactor design principles operation models Pump GPSA equation R Random packed column hydraulics capacity Eckart flood point correlation efficiency HETP flood point Norton pressure drop correlation Il 11 I 122 11 124 11 178 11 226 II 227 11 231 11 234 11 238 Il 190 Il 32 Il 34 Il 35 Il 35 I 38 Il 39 Il 34 Il 36 Il 39 Il 32 11 145 1 145 1 147 Il 41 Il 41 Il 76 Il 78 Il 78 Il 79 Il 78 Il 78 May 1994 packing factors Il 77 relative volatility Il 86 packing types Il 76 thermal condition of feed Il 87 Tsai pressure drop correlation Il 79 troubleshooting complex columns Il 97 Reactive distillation troubleshooting simple columns Il 96
15. E 120 12 j Summation y 1 SYn E um 1 0 13 J Li References 1 Shah V B Bondy R W A New Approach to Solving Electrolyte Distillation Problems paper presented at 1991 AIChE annual meeting 2 OLISystems Inc 1991 PROCHEM User s Manuals Version 9 Morris Plains NJ Il 72 ELDIST Algorithm May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns EXE Column Hydraulics General PRO II contains calculation methods for rating and sizing trayed distillation Information columns and for modeling columns packed with random or structured pack ings Trayed columns are preferable to packed columns for applications where liquid rates are high while packed columns are generally preferable to trayed columns for vacuum distillations and for corrosive applications All tray rating and packed column calculations require viscosity data A thermodynamic method for generating viscosity data from Table 2 4 3 1 should therefore be se lected by the user for these applications Table 2 4 3 1 Thermodynamic Generators for Viscosity Method Phase PURE VL PETRO VL TRAPP VL API L SIMSCI L KVIS L Tray Rating Columns containing valve sieve or bubble cap trays may be modeled by and Sizing PRO II using a number of proven methods Methods developed by Glitsch are used to compute the capacity or flood point and the pressure drop for valve trays For sieve or bubble cap trays the ca
16. L total liquid 1 flow from tray i L total liquid 2 flow from tray i Qi heat added to tray i Ti temperatures of tray i x nok natural log of the liquid 1 mole fractions Xina natural log of the liquid 2 mole fractions Kij liquid liquid equilibrium constant for component j on tray i NC number of components NT number of trays subscripts i refers to the tray index j refers to the component index superscripts D refers to a draw L refers to a liquid 1 property L refers to a liquid 2 property I refers to a liquid 1 phase II refers to a liquid 2 phase The unknowns alternatively referred to as iteration or primitive variables x Xl LL LE Ty where i 1 NT are solved for directly using an augmented Newton Raphson method Specifi cation equations involving the iteration variables are added directly to the above equations and solved simultaneously PRO II Unit Operations Reference Manual Liquid Liquid Extractor Il 101 Section 2 4 Distillation and Liquid Liquid Extraction Columns The modifications of the Newton Raphson method are twofold The first is a line search procedure that will when possible decrease the sum of the errors along the Newton correction If this is not possible the size of the increase will be limited to a prescribed amount 70 m PRO II Note See Section 70 Column Input in the PRO II Keyword Input Manual for more information The second modification limits th
17. Rigorous Heat Exchanger General PRO II contains a shell and tube heat exchanger module which will rigor Information ously rate most standard heat exchangers defined by the Tubular Exchanger Manufacturers Association TEMA Shell and tubeside heat transfer coeffi cients pressure drops and fouling factors are calculated The TEMA types available in PRO II are given in Figure 2 5 3 1 Il 112 Rigorous Heat Exchanger May 1994 Section 2 5 Heat Exchangers Figure 2 5 3 1 TEMA Heat Exchanger Types Front End Stationary Head Types Shell Types Rear End Head Types Channel and removable cover One pass shell HERO L Fixed tubesheet like A stationary head m Bonnet Integral cover Two pass shell with longitudinal baffle C Fixed tubesheet like B stationary head only Removable tube bundle Channel integral with tubesheet and removable cover Split flow Double split flow Channel integral with tubesheet and removable cover Divided flow Special high pressure closure PRO II Unit Operations Reference Manual Kettle type reboiler Cross flow e Fixed tubesheet like N sta
18. Scent centrifugal force r radius of centrifuge basket 20 RP O ae rotational speed rad s RPM rotational speed of basket in revolutions min 8c acceleration due to gravity PRO II Unit Operations Reference Manual Filtering Centrifuge 157 Solids Handling Unit Operations Section 2 7 The amount of solids remaining the basket is computed from Men o rae Jhs a o A where Ms mass of solids remaining in the basket lcake radius of inner surface of filter cake h height of basket Ps solid density average filter cake porosity The thickness of the filter cake is given by Leake F Take 3 The surface area of the filter basket and the log mean and arithmetic mean area of the filter cake are given by 2Tht cake cake lIm 7 In r Toake A A Toake h cake mean A fitter 20h 4 6 where Acake lm log mean surface area of filter cake Acake mean arithmetic mean surface area of filter cake Afilter surface area of filter basket The drainage of liquid through the filter cake of granular solids in a filtering centrifuge is a result of two forces the gravitational force and the centrifu gal force in the basket and is given by K fi an 7 where K permeability of filter cake dp diameter of cake particle A B are constants a The values of the constants A and B in equation 7 are a function of e the ratio of the cake sphericity to the cake porosity
19. 167 Particle Size Distribution Il 168 Material and Heat Balances and Phase Equilibria 1l 168 Solution Procedure Il 170 Crystallizer 1l 171 General Information Il 171 Crystallization Kinetics and Population Balance Equations Il 172 Material and Heat Balances and Phase Equilibria Il 175 Solution Procedure Il 176 Table of Contents TOC 3 General Information Il 178 Calculation Methods Il 178 General Information 11 183 Feed Blending Considerations 11 183 Stream Splitting Considerations 11 184 Stream Synthesis Considerations 11 185 D CO O Flowsheet Solution Algorithms Il 21 TOC 4 Table of Contents Phase Envelope ll 190 General Information Il 190 Calculation Methods Il 190 Heating Cooling Curves 11 192 General Information Il 192 Calculation Options Il 192 Critical Point and Retrograde Region Calculations 1I 193 VLE VLLE and Decant Considerations Il 194 Water and Dry Basis Properties 11 194 GAMMA and KPRINT Options 11 194 Availability of Results 11 195 Binary VLE VLLE Data 1l 198 General Information Il 198 Input Considerations Il 198 Output Considerations 11 199 Hydrates Il 200 General Information 11 200 Theory 11 200 Exergy 2 06 General Information 11 206 Interpreting Exergy Reports 11 206 Sequential Modular Solution Technique 11 212 General Information Il 212 Methodology Il 212 Process Unit Grouping II 213 Calculation Sequence and Convergence Il 215 General Information Il 215 Tearing Algorithms Il 215
20. 2 1 Possible Calculation Sequences Order of Units Entered Calculation Sequence Tear Streams by the User a U1 U2 U3 U4 U1 U2 U3 U4 R1 R2 b U1 U3 U2 U4 U1 U3 U2 U4 R1 83 c U2 U1 U3 U4 U2 U1 U3 U4 S2 R2 R1 d U2 U3 U1 U4 U2 U3 U1 U4 S2 R2 e U3 U1 U2 U4 U3 U1 U2 U4 S3 f U3 U2 U1 U4 U3 U2 U1 U4 3 S2 g U4 U3 U2 U1 U3 U2 U1 U4 3 S2 h U3 U4 U2 U1 U3 U2 U1 U4 3 S2 w Note The Process Method always preserves the user input sequence of units of a loop U1 U2 U3 in this case picking the tear streams accordingly and placing units not belonging to loops before or after them as needed see cases g and h in Table 2 10 2 1 Reference Motard R L and Westerberg A W 1979 DRC 06 7 79 Il 216 Calculation Sequence and Convergence May 1994 Section 2 10 Flowsheet Solution Algorithms Convergence Criteria Convergence is defined as being met when the following three requirements are achieved for two successive determinations of the recycle streams Component flow convergence test n l n 1 ge in flow qm m zg Component 1 z Te f component i n c low tolerance where m and m current and last values of the flow of component i in the recycle streams Only components with mole fractions greater than a threshold value default is 0 01 are considered for the above test The component tolerance and threshold value may be set by the user using the TOLERANCE statement i
21. 4 j j where l the component liquid rate moles time v the component vapor rate moles time f the component feed rate moles time PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms 1 51 Distillation and Liquid Liquid Extraction Columns Section 2 4 Given the equilibrium relationship yi Ki xij it is possible to remove v from equation 4 This is done as follows K v l 5 v y v K x y 5 Hoo cup J Ho J L where K is the vapor liquid equilibrium fugacity ratio Now the component mass balance can be written as 1 Kil Via 6 ij L LSS K V VSS mape E 8 j j If K is assumed constant equation 5 results in a linear system of equations for component i which form a tridiagonal system B Cii li 2 1 B Gr la fi2 EE Cis lis fia al Bij Cina ln fini l Bin li fin J where B and C are given by EEEE i K V 9 B ijt ji Li Sidestream withdrawal factors are defined as LSS Rij 1 F Ry 1 ca 10 The vapor equilibrium K value simple model is given by K Oi K b 1 1 where 0 is the relative volatility for component i on stage j and Kp is the base component K value modeled by 1 12 RAP are 12 Il 52 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns In equation 12 T is a reference temperature Using this definition of the simple K v
22. Columns containing various structured packings manufactured by Sulzer Brothers of Switzerland can be simulated using PRO II Column pressure drop capacity and efficiency for the 12 different types of Sulzer packings given in Table 2 4 3 4 are computed using correlations supplied by Sulzer May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Table 2 4 3 4 Types of Sulzer Packings Available in PRO II Type Description Applications M125X M125Y M170Y M250X M250Y M350X M350Y M500X M500Y BX CY KERA 125 m m sheet metal very high capacity Suitable for extremely high liquid loads where separation efficiency requirements are low Configuration angle of X types 30 degree to vertical Y types 45 Use X types for higher capacity Y types for higher separation efficiency 170 m m sheet metal high capacity moderate separation efficiency 250 m m sheet metal moderate capacity high separation efficiency 350 m m sheet metal moderate capacity high separation efficiency 500 m m sheet metal limited capacity very high separation efficiency Suitable where column weight is of overriding importance Metal wire gauze high capacity high separation efficiency even at small liquid loads CY offers maximum separation efficiency lower capacity than BX Thin walled ceramic KERAPAK packing for corrosive and or high temperature applications
23. Convergence Criteria I 217 General Information 11 218 Wegstein Acceleration 11 218 Broyden Acceleration Il 219 Flowsheet Control 11 221 General Information 11 221 Feedback Controller 11 222 General Information Il 222 May 1994 Multivariable Feedback Controller 11 226 General Information 11 226 Flowsheet Optimization 11 229 General Information 1 229 Solution Algorithm 11 234 General Information 11 241 Theory 11 241 Calculating the Vessel Volume I 242 Valve Rate Equations 11 243 Heat Input Equations 11 245 PRO II Unit Operations Reference Manual Table of Contents TOC 5 List of Tables 2 3 1 1 Thermodynamic Generators for Viscosity and Surface Tension Il 32 2 4 3 2 2 4 3 3 Random Packing Types Sizes and Built in Packing Factors Il 77 2 4 8 4 2 4 4 2 Effect of Cut Ranges on Crude Unit Yields Incremental Yields from Base 2 9 2 1 2 9 2 3 2 9 4 2 2 10 4 1 TOC 6 Table of Contents May 1994 List of Figures 2 6 1 1 Reaction Path for Known Outlet Temperature and Pressure II 128 PRO II Unit Operations Reference Manual Table of Contents TOC 7 Functional RelationshipBetween Control Variable and Specification TOC 8 Table of Contents May 1994 Introduction General The PRO II Unit Operations Reference Manual provides details on the basic Information equations and calculation techniques used in the PRO II simulation program It is intended as a complement to the PRO II Keyword Input Ma
24. Conversion C y Cu T CT 2 1 where T is in problem temperature units Co C1 C2 are constants The fractional conversion could be based either on the amount of base component in the feed to the reactor feed based conversion or on the amount of base component available for a particular reaction reaction based conver sion The former concept is suitable for specifying conversions in a system of parallel reactions whereas the latter definition is more appropriate for sequential or series reactions PRO II will select feed based conversion as the default con version basis for single parallel and series parallel reactions Reaction based conversion is the default conversion basis for series reactions If specified explic itly the method FEED or REACTION selected with the CBASIS keyword will be used In any case the fractional conversion value input with the CONVER SION statement will be understood to have as its basis the default or input CBASIS whichever is applicable The reactor may be operated isothermally at a given temperature adiabatically with or without heat duty specified or at the feed temperature For adiabatic reactors heat of reaction data must be given or should be calculable from the heat of formation data available in the component library databank Tempera ture constraints can be specified For isothermal reactors the heat of reaction data is optional If supplied the required heat duty will be calculated
25. II could interpolate the temperature liquid and vapor rates and phase compositions estimates if the end point values for these variables are avail able These end point values could either be provided by the user or esti mated by PRO II When these values are provided by the user we require that the user provide at least two endpoint values first and last theoretical stage The first theoretical stage is the condenser or the top tray for the no condenser case The last theoretical stage is the reboiler or the bottom tray for the no reboiler case Temperatures Tray temperatures are relatively easy to estimate The reboiler and con denser temperatures represent the bubble points and or dew points for the products These may be estimated by the user or calculated using the short cut fractionator model The top and bottom tray temperatures may be estimated by addition or sub traction of a reasonable temperature difference from the condenser and re boiler temperatures For complex fractionators the product draw temperatures are usually known or can be estimated from the product ASTM distillations Liquid and Vapor Profiles For most columns the vapor and or liquid profiles are more difficult to esti mate Moreover they are generally more influential than temperatures in aid ing or hindering the solution Estimates for the overhead or the bottoms products are provided with the product information in addition rates fo
26. Inclined Pipe Two Phase Liquid Holdup Correlations Using Experimental Data 1975 M S Thesis U of Tulsa Mukherjee H K An Experimental Study of Inclined Two Phase Flow 1979 Ph D Dissertation U of Tulsa Gray H E Vertical Flow Correlation in Gas Wells 1974 in User Manual API 14B Subsurface Controlled Safety Valve Sizing Computer Program Flanigan O Effect of Uphill Flow on Pressure Drop in Design of Two Phase Gathering Systems 1958 Oil amp Gas J March 10 56 Eaton B A The Prediction of flow Patterns Liquid Holdup and Pressure Losses Occurring During Continuous Two Phase Flow in Horizontal Pipes 1966 Ph D Dissertation U of Texas Dukler A E et al Gas Liquid Flow in Pipelines Part 1 Research Results Monograph NX 28 U of Houston Hagedorn A R and Brown K E Experimental Study of Pressure Gradients Occuring During Continuous Two Phase Flow in Small Diameter Vertical Conduits 1965 J Petr Tech Apr 475 484 May 1994 Section 2 3 Pressure Calculations zem PED Pumps General The PUMP unit operation in PRO II contains methods to calculate the Information pressure and temperature changes resulting from pumping an incompressible fluid 52 dm PRO II Note For more information on using the PUMP unit operation see Section 52 Pump of the PRO II Keyword Input Manual Basic The GPSA pump equation is used to relate the horsepower required by the Calculations pu
27. May 1994 Section 2 2 Isentropic Calculations Basic Calculations For a compression process the system pressure P is related to the volume V by PV Constant 1 where n exponent Figure 2 2 1 1 shows a series of these pressure versus volume curves as a function of n Figure 2 2 1 1 Polytropic Compression Curve P2 n 1 isothermal P n k Cp C adiabatic Pressure n gt k P V Volume The curve denoted by n 1 is an isothermal compression curve For an ideal gas undergoing adiabatic compression n is the ratio of specific heat at con stant pressure to that at constant volume i e n k c c 2 where k ideal gas isentropic coefficient Cp specific heat at constant pressure Cy specific heat at constant volume For a real gas n k The Mollier chart Figure 2 2 1 2 plots the pressure versus the enthalpy as a function of entropy and temperature This chart is used to show the methods used to calculate the outlet conditions for the compressor as follows PRO II Unit Operations Reference Manual Compressor I 19 Isentropic Calculations Section 2 2 Figure 2 2 1 2 Typical Mollier Chart for Compression Il 20 Compressor Pi Pressure H Enthalpy A flash is performed on the inlet feed at pressure P1 and temperature T1 using a suitable K value and enthalpy method and one of the en tropy calculation methods in Table 2 2 1 1 The entropy S1 and en t
28. Packed Column Y Y Y N Y Tray Rating Sizing Y Y Y N Y Two Liquids on any tray N Y Y N Free Water Decant Y Y N N Tray Efficiency Y N yl N yl Solids Y Y Y N 1 LS Components N N N N Y Electrolytes N N N N Y Kinetic Reaction N N Y Y N Equilibrium Reaction N N Y Y N Conversion Reaction N N Y Y N 1 Eldist predicts solids precipitation on stages but does not allow solid formation for mass balance purposes 2 Only vaporization efficiencies available Il 48 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Side draws may be either liquid or vapor and the location and phase of each must be specified Solid side draws are not allowed There may be an unlim ited number of products from each stage Feed tray locations are given as the tray number upon which the feed is intro duced A feed may be liquid vapor or mixed phase PRO II also allows for different conventions for mixed phase vapor liquid feeds The default con vention NOTSEPARATE introduces both the liquid and the vapor to the same stage SEPARATE places the liquid portion of the feed on the desig nated feed tray and the vapor portion of the feed on the tray above the desig nated feed tray A pumparound is defined as a liquid or vapor stream from one tray to an other The return tray can be either above or below the pumparound draw tray The pumparound flowrate can be specifie
29. Pure component fugacity coefficient Component Poynting correction x XxX XxX X XxX X XxX XxX XxX XxX XxX XxX X Component vapor fugacity coefficient Heating Cooling units always perform their calculations during the output pass of the flowsheet convergence module whenever PRO II executes This means that HCURVE modules are not considered until after the completion of all calculations needed to solve the flowsheet For this reason the follow ing applies to data generated by HCURVE units m HCURVE data are not available to CONTROLLERs or OPTIMIZERs to control or modify flowsheet calculations m HCURVE data are not accessible through the SPECIFICATION feature m HCURVE data cannot be used to affect flowsheet convergence calculations However HCURVE results are stored in the problem database files and ap pear in the standard output reports of the simulation In addition HCURVE results may be retrieved through facilities of the PRO II Data Transfer Sys tem PDTS for use in user written applications see the PRO II Data Trans fer System User s Guide Also a small subset of the HCURVE data is included in the export file created by using the DBASE option PRO II Note See Chapter 5 General Data in the PRO II Keyword Input Man ual for more information on the DBASE option PRO II Unit Operations Reference Manual Heating Cooling Curves I 195 Utilities Section 2 9 The DBASE DATA PCI option creates an ASCII databas
30. a number of thermodynamic calculation methods such as Soave Redlich K wong or Peng Robinson Note The free water decant option may only be used with the Soave Redlich Kwong Peng Robinson Grayson Streed Grayson Streed Erbar Chao Seader Chao Seader Erbar Improved Grayson Streed Braun K10 or Benedict Webb Rubin Starling methods Note that water decant is automatically activated when any one of these methods is selected PRO II Unit Operations Reference Manual Basic Principles 9 Flash Calculations Section 2 1 20 6 q LL Il 10 Basic Principles The water decant flash method as implemented in PRO II follows these steps L Water vapor is assumed to form an ideal mixture with the hydrocarbon va por phase Once either the system temperature or pressure is specified the initial value of the iteration variable V F is selected and the water partial pres sure is calculated using one of two methods The pressure of the system P is calculated on a water free basis by subtracting the water partial pressure A pure water liquid phase is formed when the partial pressure of water reaches its saturation pressure at that temperature A two phase flash calculation is done to determine the hydrocarbon vapor and liquid phase conditions The amount of water dissolved in the hydrocarbon rich liquid phase is computed using one of a number of water solubility correlations Steps 2 through 6 are repeated until the iter
31. between trays unless the rate expression was determined from pilot plant data and the entire volume was used to charac terize the rate equation Similarly if the reaction is catalyzed by a metal on a ceramic support and the rate equation was based on the entire cylindrical vol ume of the packed bed holding the catalyst then this should be used Since the enthalpy basis in PRO II is on a pure chemical basis it is unsuit able for keeping track of enthalpy changes due to reactions Therefore reac tive distillation converts chemical enthalpies to an elemental basis before simulating the tower After the simulation is complete the product stream en thalpies are recalculated using the standard PRO II basis While this is mostly hidden from the user it does impact the reporting overall column en thalpy balance and is the reason for reporting multiple enthalpy balances This does not impact the accuracy of the solution Chemdist and LLEX support any type of reaction which can be entered through the Reaction Data section or described using an in line procedure Various reaction parameters may be varied from the flowsheet using calcula tors and DEFINE statements Any set of mixed reactions may be assigned to trays in the distillation column Chemdist and LLEX support single tray distillation columns By using this feature Chemdist may be used as a two phase reactor model which produces vapor and liquid streams in equilibrium In addition the bo
32. conductivity of liquid phase The Grashof and Prandtl numbers are given by the following relationships 3 2 33 rp P AT NS a 2 Hi May 1994 Section 2 11 Depressuring Unit Cp y 34 Pr k where u viscosity of liquid cp heat capacity of liquid The change in the wall temperature AT war is determined from the isentropic enthalpy change and the heat transferred to the gas from the wall i e AT Du At A fuia lisen My 35 ull Wisess Press where A uia Change in specific enthalpy of the fluid BTU Ib mole AG en isentropic specific enthalpy change as the gas expands Mar moles of gas depressured in time period At Ib mole Wvess weight of depressuring vessel lb CPvess heat capacity of depressuring vessel BTU Ib F References ae 1 Masoneilan Handbook 1977 6th Ed Masoneilan Ltd London GB 2 Perry R H and Green D W 1984 Chemical Engineering Handbook 6th Ed McGraw Hill N Y pg 10 13 PRO II Unit Operations Reference Manual Il 249 Depressuring Unit Section 2 11 This page intentionally left blank Il 250 Depressuring May 1994 Index A Adiabatic flash calculations Il 9 Availability function See Exergy B Binary VLE VLLE data Il 198 distribution coefficient Il 199 XVALUE entry ll 198 Il 199 Bubble point flash calculations Il 8 BVLE See Binary VLE VLLE data C Chemdist See Distillation rigorous Column hydraulics Il 73 See Ra
33. d 23 where Sfr factor calculated from a correlation May 1994 Section 2 3 Pressure Calculations For bubble slug and mist flows the elevation pressure drop is computed us ing equation 7 but for stratified flows the fluid density used is the gas phase density The acceleration pressure drop term is given by dPdD v Y ep 8 Jap 4D 24 where Vs slip velocity The density Ptp is equal to the gas density for stratified flows only A separate expression is used to calculate the holdup for each flow pattern These are given as lt 0 Bubble Slug Mist flow Dm 25 H e H H 2 DE THS 1 0393962 LV H 0 51664 0 789805 sind 0 551627 sin 15 519214 N7 26 Q lt 0 Stratified flow 0 079961 27 H e H H 1 0 604887 Ny H 1 330282 4 808139 sino 4 171584 sin 56 262268 N 28 0 all flow patterns NO475686 29 H GV H e H H 288657 LV H 0 380113 0 129875 sind 0 119788 sin 2 343227 N 30 where NL liquid viscosity number PRO II Unit Operations Reference Manual Pipes 37 Pressure Calculations Section 2 3 Il 38 Pipes Gray The Gray method has been especially developed for gas condensate wells and should not be used for horizontal piping The recommended ranges for use are m Angle of inclination 0 2 70 degrees m Velocity v 50 ft s m Pipe diameter d 3 5 inches m Liquid c
34. damping factor and setting the size of the error increase see Section 74 Chemdist of the PRO II Keyword In put Manual The iteration history also reports the largest errors in the mass balance the energy balance and the vapor liquid equilibrium equations Given a good in itial estimate these should decrease from iteration to iteration However for some systems the errors will temporarily increase before decreasing on the way to finding a solution The user can limit the size of the increase in the sum of the errors All derivatives for the Jacobian matrix are calculated analytically User added thermodynamic options that are used by Chemdist must provide par tial derivatives with respect to component mole fractions and temperature Chemdist uses the chain rule to convert these to the needed form 58 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Vapor Liquid Liquid Algorithm The equations describing the VLLE system are derived by substituting the bulk liquid flows and transformed bulk liquid mole fractions Li and X for the single liquid phase flows and the transformed liquid mole fractions Li and Xi in the above equations 22 26 That is Li becomes Li and Xi j becomes Xij where X 2n e jr TI f 27 Lat tl 28 and L L total liquid flows of the first and second liquid phases respectively lij L ij component liquid flows in the first and sec
35. for example to incorrect column initialization or poorly cho sen design parameters it can be easily identified confined and corrected To calculate a flowsheet of interconnected units a sequence of unit calcula tions is determined automatically or optionally provided by the user If recycles are present an iterative scheme is set up where recycle streams are torn and a succession of convergent guesses is created These guesses are obtained by directly substituting the values calculated in the previous pass through the flowsheet the Direct Substitution technique or by applying special recycle acceleration techniques see Section 2 10 3 Acceleration Techniques For example consider the following schematic flowsheet Figure 2 10 1 1 Flowsheet with Recycle Il 212 Sequential Modular Solution Technique May 1994 Section 2 10 Flowsheet Solution Algorithms One possible solution sequence for this flowsheet is U1 U2 U3 U4 US In this sequence there are two recycle streams R1 and R2 The subsequence U2 U3 U4 is a recycle loop and is solved repeatedly until convergence of the recycle streams is achieved Ww Note The Sequential Modular Solution Technique provides physically mean ingful solution strategies therefore allowing a process simulation to be easily constructed debugged analyzed and interpreted Recently the Simultaneous Modular Solution concept has been coined for the art of flexibly solving simulati
36. from an equilibrium model for the shift reaction PRO II has incorporated the National Bureau of Standards data for equilibrium constants This can be rep resented by eg 7 In K A 5 where A and B are functions of temperature T absolute temperature R and p p 8 where p partial pressure in any units If desired users may override the NBS data and supply their own con stants A and B in the above equation The approach to equilibrium can also be indicated either on a fractional conversion basis or by a temperature approach Methanators are used to convert the excess CO from the shift reaction into methane The reactor model is similar to the shift reactor but both the metha nation and shift reactions take place simultaneously It can also be used to model the reverse reaction viz steam reforming of methane to yield hydro gen These are CO 3H CH H0 9 CO H 0 CO 4H Just as for the shift reaction the National Bureau of Standards data are available for methanation reaction The methanation equilibrium is given by K Peg Pu O 10 eq 3 Poo Py where p partial pressure in psia May 1994 Section 2 6 Reactors Calculation For adiabatic equilibrium models the calculation procedure is as follows Procedure for 1 Equilibrium 2 Assume an outlet temperature Determine the equilibrium constant at the assumed temperature plus the approach to equilibrium Calculate the produc
37. in the cake is a function of the filter pressure drop as well as cake characteristics such as the cake drain number drain height and thickness The cake drain number and height are calculated from the cake permeability and the liquid density and surface tension No VK PL o n 9275 13 14 D7 Np PRO II Unit Operations Reference Manual Rotary Drum Filter 1 155 Solids Handling Unit Operations Section 2 7 Il 156 Rotary Drum Filter The average cake saturation is given by fs exp 2 993 0 036z y 0 0552 0 274z 0 756 zy 0 099zy 0 500y 0 1723 15 where 2 16 17 AP y In 0 453K 3 f p Aaa p For design calculations an iterative method solution method is used in com bination with the equations given above to calculate the filter diameter and width required to produce a specified pressure drop PRO II Note For more information on using a rotary drum filter in PRO II see Section 102 Rotary Drum Filter of the PRO II Keyword Input Manual References Treybal R E 1980 Mass Transfer Operations 3rd Ed McGraw Hill N Y 2 Dahlstrom D H and Silverblatt C E 1977 Solid Liquid Separation Equipment Scale Up Uplands Press 3 Brownell L E and Katz D I 1947 Chem Eng Prog 43 11 601 4 Dombrowski H S and Brownell L E 1954 Ind Eng Chem 46 6 1207 5 Silverblatt C E Risbud H and Tiller F M 1974 Chem Eng 127 Apr 27 May 1994
38. isothermal ISO heating cool ing curve generated by HCURVE unit HC00 for stream F100 The remain ing entries on this line are included for use by PRO II utility functions such as IMPORT and are not described here The subsequent lines of information in Table 2 9 2 2 present a limited subset of data generated for this stream by the HCURVE calculations Each point of the curve is summarized on two lines of the listing Table 2 9 2 3 inter prets the data for a typical point of the curve Table 2 9 2 3 Data For an HCURVE Point Enthalpy K Kcal h 7 Temp C Pres mmHg liquid vapor water decant total 228 00 1000 00 281 89 108 45 0 00000E 00 390 34 mole rate Kg mole hr Mole Fraction wet liquid vapor water decant liquid vapor water decant 21 325 4 7685 0 00000E 00 0 81725 0 18275 0 00000E 00 ll 196 Heating Cooling Curves May 1994 Section 2 9 Utilities All the data are expressed in the dimensional units used to supply input data in the original problem definition For example Table 2 9 2 3 indicates tem perature is presented in degrees Celsius Alternitively if the dimensional unit of temperature in the original input file had been for example Rankine then the temperatures presented in Tables 2 9 2 2 and 2 9 2 3 would repre sent Rankine temperatures This reasoning also applies to the enthalpy and rate data Ww Note The information available in the ASC file always is limited to the data shown in Table 2 9 2
39. located somewhere between the reboiler and condenser Obvi ously absorbers and strippers do not meet these criteria and it is recom mended that only the rigorous distillation method see Section 2 4 1 Rigorous Distillation Algorithms be used for these types of columns Moreover it is not possible to predict extractive distillation or any separation in which K values vary widely with composition since such columns vio late the Fenske and Underwood assumptions For example calculation of the stages and reflux for a propylene propane splitter by shortcut methods will give very poor results since for this type of column the relative volatil ity varies from 1 25 in the reboiler to 1 07 in the condenser Thus the Fenske method will greatly under predict the minimum trays required and the Un derwood method will under predict the minimum reflux required for the separation For simple columns in which the relative volatilities do not vary greatly and in which equal molal overflow is approached the shortcut calculations allow bracketing a reasonable design base May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 An operating point expressed as either fraction of minimum reflux or trays may be selected by the user This is a design parameter and usually a matter of per sonal preference or company standards However a value of 1 5 times mini mum reflux or two times minimum trays will usually give a reasonable basis f
40. m This is the default correlation used in the dissolver model for calculating the mass transfer coefficient If detailed mass transfer data are available the following correlation can be selected by specifying the parameters a b and dcut For dp lt cut a b 8 k gt 0 1733 L d d where a b are mass transfer coefficient parameters deut solid particle cut off diameter m When the mass transfer coefficient is a function of particle size equation 4 can be integrated as 9 9 JZ 70 S O7P using numerical quadrature PRO II Unit Operations Reference Manual Dissolver l 167 Solids Handling Unit Operations Section 2 7 iu Particle Size Distribution Material and Heat Balances and Phase Equilibria Il 168 Dissolver Note Both r radius and dp diameter are used for particle size here but in terconversion between r and dp is done in the program For a solid represented by a discrete particle size distribution rif rof rit and mif mof mirare the particle sizes and mass flowrates of the feed solids and rip r2p Gu rip is the particle size distribution of the solids in the product For the case of constant kr from equation 5 k 10 rim rg p CR p and the rate of dissolution is E wo 0n p 1 Te Dus i fr S o 9 E 1 1 CI p 1 if p if Material and heat balances around the dissolver as well as vapor liquid equi librium have
41. method which is the default method used by PRO II uses the following procedure First the pressure drop for an ideal window section is calculated using the following correlations For Nre lt 100 Wi 0 5 2 0 5 muU P U Do Dy eS P mw Ap c 28 New 3 Ww 11 Il 116 Rigorous Heat Exchanger May 1994 Section 2 5 Heat Exchangers For NRe gt 100 _W 2406 7 12 cw 2g mw p AP wi The pressure drop for an ideal crossflow section is then calculated AFW N oy 13 5 20g Ho where fk the friction factor for the ideal tube bank calculated at the shellside Reynolds number c gravitational force conversion factor 4 18 x 10 Ibm ft Ibf hr Nc number of tubes in one crossflow section cw number of crossflow rows in each window m minimum cross sectional area between rows of tubes for flow normal to tube direction Sw cross sectional area of flow through window Do outside exchanger diameter Dw equivalent diameter of a window p tube pitch center to center spacing of tubes in tube bundle p fluid density The actual shellside pressure drop is obtained by accounting for the effects of bypasses and leakages and is given by N 14 AP ov DAP R N A P R 2A P4R amp R i where APs actual shellside pressure drop Np number of segmental baffles Ry bundle bypass flow correction factor Ri baffle leakage effects correction factor Rs correction factor f
42. phase split and again handles all liquid as a single phase In both of these cases the reported sin gle liquid phase always includes all of the liquid water that is present This means that properties of the decant liquid are meaningless and typically are reported as zero missing or N A i e not applicable The PROPERTY statement allows the user to stipulate sets of properties that will be reported for every heating cooling curve generated in an HCURVE module The GAMMA and KPRINT options allow the user to request property reports for individual heating cooling curves The GAMMA option is a superset of the KVALUE option that is GAMMA prints all the same information as the KVALUE option and adds more data to the report For this reason there is no benefit to including both options for a single heating cooling curve Both GAMMA and KVALUE generate a report for each component in the stream at each point of the heating cooling curve Table 2 9 2 1 summarizes the information reported at each point Il 194 Heating Cooling Curves May 1994 Section 2 9 Utilities Availability of Results Table 2 9 2 1 GAMMA and KPRINT Report Information Property GAMMA KPRINT Point ID number Temperature Pressure Component name Component composition in vapor Component composition in liquid x XxX XxX XxX X X X Component equilibrium K value Component name Component gamma activity coefficient Component vapor pressure
43. region I exhibit local maxima or minima region II or are invariant region IV may cause convergence problems Frequently these difficulties can be overcome by including upper and or lower bounds on the control variable to restrict its range for example VMINI and VMAx1 in Figure 2 10 4 1 2 Figure 2 10 4 1 2 Functional Relationship Between Control Variable and Specification discontinuous local monotonically invariant minimum increasing f V va specified value The PRO II sequencer automatically determines an appropriate calculation sequence for the CONTROLLER loop When recycle loops are also pre sent PRO II determines the loop ordering which allows for most effective flowsheet convergence To override the default ordering the desired se quence must be specified explicitly using a SEQUENCE statement The user should be aware that control loops can significantly increase computational time PRO II Unit Operations Reference Manual Feedback Controller 223 Flowsheet Solution Algorithms Section 2 10 Figure 2 10 4 1 3 Feedback Controller in Recycle Loop l 224 Feedback Controller When controllers are placed within recycle loops careful selection of the controller variable and specification can greatly reduce interference caused by the simultaneous convergence of the two loops Consider for example the flowsheet shown in Figure 2 10 4 1 3 where stream 2 contains pure reactant A The rate of st
44. sb z i The adiabatic head is related to the polytropic head by HEAD Yaq HEAD Y 18 The polytropic efficiency n is calculated by Y 7 n n 1 k 1 19 PRO II Unit Operations Reference Manual Compressor Il 23 Isentropic Calculations Section 2 2 Il 24 Compressor The polytropic coefficient n the polytropic efficiency Yp and the polytropic head are determined by trial and error using equations 17 18 and 19 above The polytropic gas horsepower which is reported as work in PRO II is then given by GHP HEAD F 33000 20 Polytropic Efficiency Given A trial and error method is used to compute the adiabatic efficiency once the polytropic efficiency is given The following calculation path is used 1 The adiabatic head is computed using equations 3 4 and 9 2 The isentropic coefficient k is determined using equations 15 or 16 3 The polytropic coefficient n is then calculated from equation 19 4 The polytropic head is then computed using equation 17 5 The adiabatic efficiency is then obtained from equation 18 Reference GPSA 1979 Engineering Data Book Chapter 4 5 9 5 10 May 1994 Section 2 2 Isentropic Calculations E EX Expander General Information Basic Calculations Figure 2 2 2 1 Typical Mollier Chart for Expansion The methods used in PRO II to model expander unit operations are similar to those described p
45. technique to vary the value of the control variable until the specification is satisfied within tolerance PRO II automatically creates the computational loop for the CONTROL LER the units inside this loop are solved repeatedly until the CONTROL LER has converged For the example in Figure 2 10 4 1 1 units C1 D1 V1 and D2 are solved each time the CONTROLLER varies the cooler duty The calculations terminate successfully when the flowrate of stream 6 has reached the desired value May 1994 Section 2 10 Flowsheet Solution Algorithms Recommendations When defining control variables and specifications it is important to note that the value of a control variable must remain fixed unless it is changed by the CONTROLLER Typical control variables include inlet feedrates speci fied heat duties of heat exchangers and adiabatic flash drums as well as speci fied reflux ratios of distillation columns Conversely the CONTROLLER specifications must be defined as calculated results of the flowsheet simula tion e g outlet flowrates column heat duties or temperatures of intermediate streams However it is meaningless for the CONTROLLER to specify the temperature of an isothermal flash For best performance the functional relationship between the control vari able and the controller specification should be continuous and monotonically increasing or decreasing as illustrated in region III of Figure 2 10 4 1 2 Functions that are discontinuous
46. the most volatile component For a feed where some components are found in very small concentrations the light key component is the most volatile one found at important concentrations The heavy key component is similarly found to be the least volatile component or the least volatile component found at significant concentrations The relative volatility of each component can therefore be expressed in terms of the volatility of the heavy key i e K 4 J Ky where J refers to any component and hk refers to the heavy key component For components lighter that the heavy key a gt 1 and for components heavier than the heavy key o4 lt 1 for the heavy key component itself o 1 The Underwood method is used to determine the reflux ratio requiring an in finite number of trays to separate the key components For a column with in finite trays the distillate will exclude all components heavier than the heavy key component Similarly the bottoms product will exclude all components lighter than the light key Components whose volatilities lie between the heavy and light keys will distribute between the distillate and bottoms prod ucts An equation developed by Shiras et al can be used to determine if the selected keys are correct At minimum reflux ratio XIDD Q lxypD Ak A x 5D 5 Xz pF Ag 1 Xip rE Qj 1 Xi rE If the value of the ratio given by equation 5 is less than 0 01 or greater than 1 01 for any
47. the MVC prints a detailed convergence history and a series of diagnostic plots These are intended to help the user determine what correc tive action to take when the MVC fails to reach the solution Multivariable Feedback Controller May 1994 Section 2 10 Flowsheet Solution Algorithms PAD Flowsheet Optimization General Information The optimization algorithm within PRO II is a powerful tool which allows the operating conditions of a single unit or an entire process flowsheet to be optimized Typical applications are the minimization of heat duty or the maximization of profit Most generally the optimization problem can be formulated as 1 minimize f x x5 x objective function such that hi 4 X5 x 20 2 1 m specifications gi G4 Xp X S 0i 1 73 constraints X mini Xi SXi maxi bounds where n is the number of variables m is the number of specifications and mz is the number of constraints Note Maximizing f is equivalent to minimizing PRO II requires an objective function and at least one variable to be defined in the OPTIMIZER unit In addition upper and lower bounds must be speci fied for each variable If specifications are included m can be at most equal to the number of variables The number of constraints which can be defined is independent of the number of variables There is no hard upper limit on the size of the optimization problem which ca
48. the outlet conditions m The isentropic expander work Ws is computed from W H Hj J2 AH J 4 where J mechanical equivalent of energy In units of horsepower the isentropic expander power output is GHP AH 4 778 F 33000 7 GHP AH 778 F 33000 GHP 4 Yaa 8 HEAD AH 778 9 where GHP work hP AH enthalpy change BTU Ib F mass flow rate Ib min HEADaq Adiabatic Head ft The factor 33000 is used to convert from units of ft Ib min to units of hP Adiabatic Efficiency Given If an adiabatic efficiency other than 100 is given the adiabatic head is cal culated from equations 3 4 and 9 Once this is calculated the isen tropic coefficient k is computed by trial and error using z 10 HEAD fe z 2 RT k 1 Ah ie jy 1 where Zp Z2 compressibility factors at the inlet and outlet conditions R gas constant Tij temperature at inlet conditions The polytropic expander equation is given by 11 HEAD e tz 2 RT n 1 zi Ies p m _ i May 1994 Section 2 2 Isentropic Calculations The adiabatic head is related to the polytropic head by HEAD 4g 4 47 HEAD Y 12 The polytropic efficiency n is calculated by Y In Q1 k 1 13 The polytropic coefficient n the polytropic efficiency yp and the polytropic head are determined by trial and error using equations 11 12 and 13 above The polytropic gas horsepower output by the
49. the recycle streams and the loops of units with which they are associated Then tear streams and a solving sequence are determined The user can override all these calculations and define his her own calculation sequence Initial esti mates for the tear streams are desirable but not mandatory If good estimates are provided convergence will be achieved faster Two calculation sequence methods are available Minimum Tear Streams SimSci Method This default sequencing method uses improved algorithms developed by Sim Sci to determine the best sequence for calculation purposes This method pro vides a calculation sequence featuring a minimum number of tear streams Alternate Method Process Method This method determines the sequence based partially on the order in which the unit operations were placed during the construction of the flowsheet The units which were placed first are likely to be solved earlier than the units which were placed at a later time Both methods determine the independent calculation loops in the flowsheet moving all calculations not affected by the recycle streams outside these inde pendent loops These units will not be calculated until the loops are solved Then for each loop a tear set is determined In the case of the SimSci Method a minimum tear set based on the algorithm developed by Motard and Westerberg 1979 is used If more than one choice is available for the tear set the Simsci Method will pick
50. the temperature and liquid phase concentration in the dissolver are uniform and all the solid particles have the same residence time m The dissolution of a single solid component only is modeled and the pres ence of inert components has no effect on the dissolution process OVHD PRODUCT BTMS PRODUCT PRO II Note For information on using dissolvers in PRO II see Section 105 Dissolver of the PRO II Keyword Input Manual and the PRO II Applications Briefs Manual S1 p Xylene Crystallization May 1994 Section 2 7 Solids Handling Unit Operations Mass Transfer The liquid phase mass transfer coefficient k is a function of various quanti Coefficient ties such as diffusivity of solute in liquid solution impeller power and Correlations diameter and physical properties of the solid component and liquid For large particles the coefficient has been found to be independent of particle size whereas for smaller particles the coefficient increases with decreasing particle size The following correlation has been proposed by Treybal for liquid phase mass transfer in solid liquid slurries For dp 2 mm 0 17 6 d 0 62 0 36 Sh 2 0 47 Re 9 Sc For dp gt 2 mm Sh 0222 Rej Sc 7 where dp solid particle diameter m Shy liquid phase Sherwood number dimensionless Rep particle Reynolds number dimensionless di impeller diameter m dt dissolver tank diameter m Scu liquid phase Schmidt number
51. the un derflow from the tank is transferred to the next tank in the series The feed to the first tank in the series therefore consists of the slurry feed and the over flow from the second tank while the feed to the last tank consists of the liq uid wash typically water and the underflow slurry from the second to last tank If the purpose of the CCD unit is to obtain a clear overflow then the tank is referred to as a clarifier A typical stage of the countercurrent decantation system is shown in Figure 2 7 4 1 N 1 U o l l Stage N u o l E v N 1 PRO II Unit Operations Reference Manual Countercurrent Decanter I 161 Solids Handling Unit Operations Section 2 7 Il 162 The equations describing the model are as developed below Total Mass Balance Uy T PS Oy Uy Ons 7 Uy 1 2 where decanter underflow rate from a stage PS solid fraction in underflow TS total solids flow through CCD total overflow rate from a stage subscripts N N 1 N 1 refer to stage N and the stages below and above stage N Component Balance U o U o inet Un 1 Xi yia Ona Un Xin ONXiN 3 where x composition of underflow from a stage x composition of overflow from a stage The mixing efficiency for each stage En is given by U 4 E Xi N 1 4 N O iN The mixing efficiency is generally a function of temperature and composition However in PRO II it is assumed that the mixing efficiency
52. these bounds should be chosen to reflect the actual range within which the flowsheet values are expected to lie For exam ple while 0 and 100 degrees Celsius may be a physically valid temperature range for water 15 and 25 degrees Celsius provide a more meaningful range for the expected temperatures of a cooling water stream 232 Flowsheet Optimization May 1994 Section 2 10 Flowsheet Solution Algorithms A4 43 Specifications and Constraints Constraints define the domain of acceptable solutions to the optimization problem that is they define ranges into which certain flowsheet values must fall within tolerance to represent an acceptable solution to the optimization problem Specifications define specific values within the flowsheet which must be met within tolerance to obtain an acceptable solution to the optimi zation problem Constraints and specifications may be made on design or performance val ues including values defined by a CALCULATOR unit operation PRO II Note Section 44 Specs Constraints and Objectives of the PRO II Keyword Input Manual discusses the format used to define constraints and specifications Section 43 Flowsheet Parameters of the PRO II Keyword In put Manual lists all the stream and unit operation variables that can be included in OPTIMIZER constraints and specifications Cycles Trials and Iterations The optimizer introduces an outer iterative loop in the flowsheet calculation Fo
53. to be satisfied The equilibrium solid solutility S is also deter mined These equations many of them in simplified form are given below Material and Heat Balance Equations Overall F E B 12 where F mass rate of feed kg sec E mass rate of overhead product kg sec B mass rate of bottoms product kg sec Component solute F sotute 7 Esolute Bsotute 13 solvent F solvent Esolvent Bsotvent 14 inerts FjRESB 12 N 15 where solute refers to the solute component solvent refers to the solvent component i refers to the inert component May 1994 Section 2 7 Solids Handling Unit Operations Solid liquid Solute Balance Per ret Pp 16 solute solute Liq solute 17 P uan B P where FLA mass rate of solute component in feed liquid kg sec Pr mass rate of solid in feed kg sec Bud te mass rate of solute component in bottoms product liquid kg sec P mass rate of solid in bottoms product kg sec Solute Vapor Balance E 18 E solute x one ii ju solute vapor where MWisolue molecular weight of solute component kg kgmol MWyapor molecular weight of overhead product kg kgmol E mass rate of overhead product kg sec Y mole fraction in overhead product Heat Balance Equation Heat Duty Product Enthalpy Feed Enthalpy 19 Phase Equilibrium Equations Solid liquid Equilibrium X oue f temperature 20 Vapor liquid Equilibrium Y f X 21 Residen
54. user may input the valve flow characteristics This unit operation also finds application for problems relating to refrigeration requirements in storage vessels Product streams may be generated as a user option but the calculations are not performed until output time A heat input may also be described by the user to simulate the pressuring of the vessel by a fire or other means The depressuring unit is shown in Figure 2 11 1 The depressuring calcula tions begin by mixing the feed streams adiabatically to give the composition Xi 0 temperature To and pressure Po of the vessel at time t 0 The initial composition of the liquid and vapor inside the vessel is calculated following the guidelines below If a liquid holdup is specified m Fora mixed phase feed the composition of the liquid phase will be set equal to the composition of the liquid portion of the feed and the vapor phase composition set equal to the feed vapor composition m Fora liquid phase feed then the initial vapor composition in the vessel will be set equal to the vapor in equilibrium with the feed liquid at its bubble point temperature Note For a vapor only feed PRO II will give an error message if a liquid hold up is specified After the initial composition of the vapor and liquid portion of the vessel con tents is determined the initial total number of moles for each component Fio in the vessel is calculated using PRO II Unit Operations Reference Man
55. zero while the elevation pressure drop term is computed using dP dL p g sind g 144 43 p p H p H 0 gt 0 P P gt OandH lt 1 0 P P lt Oand Hj 1 44 where d angle of inclination subscripts or L and g or G refer to the liquid and gas phases respectively Hagedorn Brown HB This method is recommended for vertical liquid pipelines and should not be used for horizontal pipes The liquid holdup term is calculated from a correla tion of the form H function af Nv Nov e 45 where Niv Nev Np are the dimensionless liquid velocity number gas velocity number and diameter number PRO II Unit Operations Reference Manual Pipes Il 39 Pressure Calculations Section 2 3 The friction factor is obtained from the Moody diagrams and the friction pressure term is computed using equations 2 or 6 depending on whether there is single or two phase flow 58 E PRO II Note For more information on using these pressure drop correlation methods in the PIPE unit operation see Section 58 Pipe of the PRO II Key word Input Manual LI References 1 Il 40 Pipes Beggs H D An Experimental Study of Two Phase Flow in Inclined Pipes 1972 Ph D Dissertation U of Tulsa Beggs H D and Brill J P A Study of Two Phase Flow in Inclined Pipes 1973 Trans AIME 607 Moody L F Friction Factors for Pipe Flow 1944 Trans ASME 66 671 Palmer C M Evaluation of
56. 3 regardless of the type of heating cooling curve or the printout options included in the HCURVE unit PRO II Unit Operations Reference Manual Heating Cooling Curves l 197 Utilities Section 2 9 AER Binary VLE VLLE Data General Information we em Input Considerations The Binary VLE VLLE Data module BVLE may be used to validate binary vapor liquid or vapor liquid liquid equilibrium data for any given pair of components This unit operation generates tables and plots of K values and fugacity coefficients versus liquid and vapor composition at a specified tem perature or pressure A number of plot options are available Any thermodynamic VLE or VLLE K value method may be used to validate the VLE or VLLE data For liquid activity thermodynamic methods the fol lowing are calculated by the BVLE module K values Liquid activity coefficients Vapor fugacity coefficients Vapor pressures Poynting correction For non liquid activity methods such as the SRK cubic equation of state the following are calculated by the BVLE module gm K values m Liquid fugacity coefficients m Vapor fugacity coefficients Only selected input and output features of the Binary VLE VLLE Data mod ule are discussed in this reference manual PRO II Note See Chapter 126 Binary VLE VLLE Data of the PRO II Key word Input Manual for information on all features and options available for this module The BVLE unit operation do
57. 5 MAX TRAY 3 2 182E 04 TEMP CHANGE AVG 257E 01 MAX TRAY 1 2 431E 01 ITER 2 E K 1 137E 02 E ENTH SPEC 1 854E 04 E SUM 2 454E 02 COMPONENT ERROR AVG 5 068E 03 MAX T 1 1 026e 02 ENTHALPY ERROR AVG 0 000E 00 MAX T 4 LIQ 0 999EF 00 K VALUE ERROR AVG 1 137E 02 MAX T 1 C 2 2 268E 02 INNER 0 E ENTH SPEC 5 9253E 04 SPEC ERROR AVG 6 25E 04 MAX SPEC 1 1 247E 03 HBAL ERROR AVG 2 799E 04 MAX TRAY 2 5 961E 04 TEMP CHANGE AVG 3 719E 02 MAX TRAY 1 8 621E 02 INNER 1 E ENTH SPEC 7 476E 06 ALPHA 1 0000 SPEC ERROR AVG 8 569E 06 MAX SPEC 1 1 587E 05 HBAL ERROR AVG 3 191E 06 MAX TRAY 2 9 271E 06 TEMP CHANGE AVG 7 271E 03 MAX TRAY 1 1 253E 02 Reference aa Russell R A A Flexible and Reliable Method Solves Single tower and a ma Crude distillation column Problems 1983 Chem Eng 90 Oct 17 53 9 Chemdist The Chemdist algorithm in PRO II is a Newton based method which is suited to Algorithm solving non ideal distillation problems involving a smaller number 10 vs 100 of chemical species These conditions are generally encountered in chemical distilla tions as opposed to crude fractionation where the I O algorithm would be a better choice Chemdist is designed to handle both vapor liquid and vapor liquid liquid equilibrium problems as well as chemical reactions Figure 2 4 1 3 Schematic of a Simple Stage for Chemdist Il 56
58. A New Distillation Algorithm for Non Ideal System paper presented at AIChE 1990 Annual Meeting 2 Shah V B and Kovach J W III Bluck D A Structural Approach to Solving Multistage Separations paper presented at 1994 AIChE Spring meeting 102 Liquid Liquid Extractor May 1994 Section 2 5 Heat Exchangers IEEE Heat Exchangers Process heat transfer equipment may be simulated in PRO II using one of three heat exchanger models m Simple heat exchanger m Rigorous heat exchanger m Liquified Natural Gas LNG heat exchanger PRO II Unit Operations Reference Manual 1 105 Heat Exchangers Section 2 5 EE Simple Heat Exchangers General Information Calculation Methods Heat exchangers are used to transfer heat between two process streams or be tween a process stream and a utility stream such as air or steam For all three heat exchanger models the following basic design equation holds q U ATOA 1 where dq heat transferred in elemental length of exchanger dz Uo overall heat transfer coefficient AT overall bulk temperature difference between the two streams 6A element of surface area in exchanger length dz Once an appropriate mean heat transfer coefficient and temperature differ ence is defined equation 1 may be re written for the entire exchanger as follows Q U AAT Aout Hin 2 where Q total exchanger heat duty Uom overall mean heat tra
59. A and B are given by Il 158 Filtering Centrifuge May 1994 Section 2 7 Solids Handling Unit Operations For gt 1 5 A exp 2 49160 0 20996 B exp 1 74456 0 20850 8 9 For 1 5 A exp Pon Es Bep 10 11 The residual cake saturation a result of small amounts of liquid held be tween the cake particles by surface tension forces is a function of a dimen sionless group known as the capillary number Nc The capillary number is given by N 2 Kp Scent 12 8 0 where PL liquid density o liquid surface tension The residual cake saturation so is then calculated based on the value of the capillary number For 0 002 Nc 0 03 m 10 1 8 02991og N 13 For Nc 0 03 is 10627590957 log N 14 For Nc 0 002 s 0 072 15 The cake drain number and height are calculated from the cake permeability centrifugal force and the liquid density and surface tension Np K P Scent Vg c _ 0 275 16 17 Np hg PRO II Unit Operations Reference Manual Filtering Centrifuge 159 Solids Handling Unit Operations Section 2 7 11 160 LL Filtering Centrifuge The average cake saturation is then given by Lake T hp hp 18 Sw 7 50 l Lake cake where Sav average filter cake saturation The corresponding moisture content of the filter cake Xcake is calculated using 19 X cake Say ES P 1 E p Finally the actual rate of filtrate thro
60. An unlimited number of simultaneous reactions may be considered The conversion reactor can also be used to model shift and methanation reactors In this case fractional conversions can be specified for the shift and methanation reactions Il 130 Conversion Reactor May 1994 Section 2 6 Reactors Shift Reactor Model Methanation Reactor Model The purpose of the shift reactor model is to simulate the shift conversion of carbon monoxide into carbon dioxide and hydrogen with steam CO H 0 CO H 2 Methanators are used to convert the excess CO from the shift reaction into methane The reactor model is similar to the shift reactor but both the metha nation and shift reactions take place simultaneously CH H 0 3 CO 3H CO H O CO 4H PRO II Unit Operations Reference Manual Conversion Reactor 131 Reactors Section 2 6 Bg Equilibrium Reactor 132 Equilibrium Reactor The EQUREACTOR unit operation is a simple equilibrium reactor No kinetic information is needed nor are any reactor sizing calculations per formed Equilibrium compositions are calculated based on equilibrium constant data Approach data if specified are used to compute approach to equilibrium The reactor may be operated isothermally at a given temperature adiabati cally with or without heat duty specified or at the feed temperature For adiabatic reactors heat of reaction data must be given or should b
61. Calculation Methods Il 109 Example Il 110 Rigorous Heat Exchanger i112 General Information Il 112 Heat Transfer Correlations Il 114 Pressure Drop Correlations Il 116 Fouling Factors Il 120 General Information Il 122 Calculation Methods 11 122 Zones Analysis 11 124 TOC 2 Table of Contents May 1994 PRO II Unit Operations Reference Manual Reactor Heat Balances 1 128 Heat of Reaction Il 129 Conversion Reactor 11 130 Shift Reactor Model 1 134 Methanation Reactor Model Il 131 Equilibrium Reactor 1 132 Shift Reactor Model Il 134 Methanation Reactor Model Il 134 Calculation Procedure for Equilibrium 11 135 Gibbs Reactor 11 136 General Information Il 136 Mathematics of Free Energy Minimization 11 136 Continuous Stirred Tank Reactor CSTR 11 141 Design Principles 1 141 Multiple Steady States 11 143 Boiling Pot Model 11 144 CSTR Operation Modes 11 144 Plug Flow Reactor PFR 11 145 Design Principles 11 145 PFR Operation Modes Il 147 Dryer 11 152 General Information Il 152 Calculation Methods Il 152 lRoaryDrumFilter 1 1 4 153 General Information Il 153 Calculation Methods II 153 Filtering Centrifuge 11 157 General Information Il 157 Calculation Methods I 157 Countercurrent Decanter 1 161 General Information Il 161 Calculation Methods 11 161 Calculation Scheme Il 163 Dissolver 11 165 General Information 11 165 Development of the Dissolver Model 11 165 Mass Transfer Coefficient Correlations Il
62. Data 1I 199 Utilities Section 2 9 EXX9 Hydrates General PRO II contains calculation methods to predict the occurrence of hydrates in Information mixtures of water and hydrocarbons or other small compounds PRO II can identify the temperature pressure conditions under which the hydrate will form as well as identify the type of hydrate that will form type I or type II The effect of adding an inhibitor either methanol sodium chloride ethylene glycol di ethylene glycol or tri ethylene glycol on hydrate formation can also be predicted by PRO II Theory Hydrates are formed when water acts as a host solid lattice to guest molecules which occupy a certain portion of the lattice cavity Only mole cules which are small in size and of a certain geometry may occupy these guest cavities These hydrates are a form of an inclusion compound known as clathrates and no chemical bonds form between the water lattice and en closed gas molecules Two different types of hydrates can be identified Their characteristics are given in Table 2 9 4 1 Table 2 9 4 2 lists the gas molecules which may occupy the cavities of these hydrates Note Water does not have to be specifically defined by the user as a compo nent in the system for hydrate calculations to proceed PRO II will assume the presence of free water when hydrate calculations are requested Table 2 9 4 1 Properties of Hydrate Types and II Property Typel Type
63. II Number of water molecules per 46 136 unit cell Number of small cavities per cell 2 16 Number of large cavities per cell 6 8 Cavity diameter A Small 7 95 7 82 Large 8 60 9 46 I 200 Hydrates May 1994 Section 2 9 Utilities Table 2 9 4 2 Hydrate forming Gases Methane Ethane Propane N butane Isobutane Carbon dioxide Hydrogen sulfide Nitrogen Ethylene Propylene Argon Krypton Xenon Cyclopropane Sulfur hexafluoride The hydrates formed are stabilized by forces between the host water and guest gas molecules Figure 2 9 4 1 Unit Cell of Hydrate Types I and Il Statistical thermodynamic techniques are used to represent the properties of these hydrates At equilibrium the chemical potential of the water in the hy drate phase is equal to the chemical potential of water in any other phase pre sent e g gaseous ice or liquid In 1958 van der Waals and Platteeuw derived the following equation relating the chemical potential of water in the hydrates to the lattice molecular parameters uu DE 1 i k L i 12 N a cav kz12 N comp where A ua difference in chemical potential between the filled gas hydrate lattice and the empty hydrate lattice v number of cavities of type i in the hydrate Yki probability of cavity i being occupied by a hydrate forming molecule of type k PRO II Unit Operations Reference Manual Hydrates ll 201 Utilities Section 2 9 The pr
64. Increase Increase Bbls Day Overhead 23159 24 0 3 Naphtha 23285 16 2 0 4 0 3 Kerosene 16232 8 2 0 3 1 7 j 0 7 Diesel 19149 0 2 0 6 0 2 0 9 2 1 Gas Oil 11002 11 2 15 4 16 5 16 9 6 4 Topped Crude 42173 1 8 3 6 3 8 4 0 2 3 Total 135000 No Comps 46 36 49 45 39 37 No of Cuts 100 600 20 600 800 5 100 800 28 15 38 34 28 800 1200 8 4 4 4 5 800 1500 15 1000 1500 5 1 1 1 1200 1500 4 E 1 Note For all cases yields were predicted based on product 95 points and 5 95 gaps Standard cuts May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 It is recommended that a systematic approach be taken when debugging shortcut columns Trial printouts will often reveal clues to the limiting speci fication Increasing the number of calculation trials is never a good strategy since solution will normally be reached well within the default number of tri als 20 References LI 1 Treybal R E Mass Transfer Operations 3rd Ed Chapt 9 McGraw Hill N Y 2 Fenske M R 1932 Ind Eng Chem 24 482 3 Underwood A J V 1948 Chem Eng Prog 44 603 4 Gilliland E R 1940 Ind Eng Chem 32 1220 5 Ludwig E E 1964 Process Design for Chemical and Petrochemical Plants Vol 2 pp 26 27 Gulf Publishing 6 Kirkbride C G 1944 Petrol Refiner 23 p 32 PRO II Unit Operations Reference Manual Shortcut Dist
65. LE calculations For most methods a single set of binary interaction parameters is inadequate for handling both VLE and LLE equili bria The PRO II databanks contain separate sets of binary interaction pa rameters for VLE and LLE equilibria for many of the thermodynamic methods available in PRO II including the NRTL and UNIQUAC liquid ac tivity methods For best results the user should always ensure that separate binary interaction parameters for VLE and LLE equilibria are provided for the simulation Table 2 1 1 1 VLLE Predefined Systems and K value Generators K value Method System SRK AMINE SRK NRTL SRKM NRTL SRKM UNIQUAC SRKKD UNIQUAC SRKKD UNIFAC SRKH UNIFAC SRKH UFT1 SRKP UFT1 SRKP UFT2 SRKS UFT2 SRKS UFT3 PR UFT3 PR UNFV PRM UNFV PRM VANLAAR PRH VANLAAR PRH MARGULES PRP MARGULES PRP REGULAR UNIWAALS REGULAR UNIWAALS FLORY IGS FLORY IGS ALCOHOL GSE SOUR GSE GLYCOL CSE GPSWATER CSE SOUR HEXAMER LKP AMINE GPSWATER HEXAMER LKP VLLE available but not recommended PRO II Unit Operations Reference Manual Basic Principles 11 Flash Calculations Section 2 1 m EXE Equilibrium Unit Operations Flash Drum Il 12 Equilibrium Unit Operations The flash drum unit can be operated under a number of different fixed condi tions isothermal temperature and pressure specified adiabatic duty speci fied dew point saturated vapor bubble point saturated liquid or ise
66. Manual Multivariable Feedback Controller 11 227 Flowsheet Solution Algorithms Section 2 10 11 228 For two variables the algorithm involves the following steps 1 Solve the flowsheet at the basecase values of control variables V1 and V2 2 Increase V1 by 10 or set V1 equal to EST2 if supplied by the user and resolve the flowsheet Compare the value of the objective function at the basecase and at the new point Move to the new point if the objective func tion is lower here point 2 in Figure 2 10 4 2 2 3 Repeat step 2 for control variable V2 4 Using the basecase flowsheet solution and those from steps 1 and 2 esti mate the derivatives of the objective function with respect to variables V1 and V2 using finite differences 5 Determine a new search direction using the derivative information at the current point Here a hybrid method is used which combines features from Newton Raphson Steepest descent and Marquardt methods Resolve the flowsheet at the new point 6 Ifthe MVC specifications are not met within tolerance update the matrix of first derivatives using Broyden s method and return to step 5 The search step determined by the optimizer step 5 of the above algorithm is adjusted if it exceeds the user defined STEPSIZES on the variables or if it fails to improve the objective function sufficiently For the example in Figure 2 10 4 2 2 a total of 5 MVC cycles is required to reach the solution If requested
67. P For bubble point pressure calculations where the temperature and feed compositions have been given the equation to be solved can be written as L Kz 1 0 18 May 1994 Section 2 1 Flash Calculations Dew Point Flash Calculations Two phase Adiabatic Flash Calculations Water Decant iu A similar technique is used to solve a dew point flash The amount of vapor V is equal to 1 0 Simplification of the mass balance equations result in the following relationship b z K x 10 19 For dew point pressure calculations equation 19 can be linearized by writ ing it as 20 In For dew point temperature calculations equation 19 may be rewritten as 21 Lx I The dew point temperature or pressure is then found by trial and error New ton Raphson calculations using equations 20 or 21 For a two phase adiabatic Q 0 system the heat balance equation 8 can be rewritten as H y AH 22 1 1 lt TOL H dr An iterative Newton Raphson technique is used to solve the Rachford Rice equation 12 simultaneously with equation 22 using V F and temperature as the iteration variables The water decant option in PRO II is a special case of a three phase flash If this option is chosen and water is present in the system a pure water phase is decanted as the second liquid phase and this phase is not considered in the equilibrium flash computations This option is available for
68. PRO II Unit Operations Reference Manual Copyright Notice Trademarks Credits The software described in this manual is furnished under a license agreement and may be used only in accordance with the terms of that agreement Information in this document is subject to change without notice Simulation Sciences Inc assumes no liability for any damage to any hardware or software component or any loss of data that may occur as a result of the use of the information contained in this manual Copyright 1994 Simulation Sciences Inc All Rights Reserved No part of this publication may be copied and or distributed without the express written permission of Simulation Sciences Inc 601 S Valencia Avenue Brea CA 92621 USA PROIII is a registered mark of Simulation Sciences Inc PROVvisION is a trademark of Simulation Sciences Inc SIMSCI is a service mark of Simulation Sciences Inc Printed in the United States of America Contributors Miguel Bagajewicz Ph D Ron Bondy Bruce Cathcart Althea Champagnie Ph D Joe Kovach Ph D Grace Leung Raj Parikh Ph D Claudia Schmid Ph D Vasant Shah Ph D Richard Yu Ph D Table of Contents ntroduction 1 What is in This Manual Who Should Use This Manual Finding What You Need 1 1 T Flash Calculations Basic Principles Il 4 MESH Equations Il 4 Two phase Isothermal Flash Calculations Il 5 Flash Tolerances Il 8 Bubble Point Flash Calcu
69. Reactor which can operate at a desired conversion level Equilibrium Reactor Gibbs Free Energy Minimization Reactor Ideal Mixed Flow Reactor Continuous Stirred Tank Reactor or CSTR Ideal Tubular Reactor Plug Flow Reactor or PFR PRO II Unit Operations Reference Manual II 127 Reactors Section 2 6 D Reactor Heat Balances The heats of reaction for all reactors are determined in one of two ways m The user may supply the heat of reaction for each stoichiometric reac tion in the Reaction Data section This heat must be given at a reference temperature and phase either vapor or liquid PRO II will not accept a mixed phase reference basis m Ifthe heat of reaction is not supplied the heat of reaction will be calcu lated from heat of formation data PRO II has heat of formation data available for all library components at 25 C vapor phase PRO II will estimate the heats of formation for all PETRO components The heat of formation data may be overridden for all LIBID and PETRO compo nents If NONLIB components are used the heat of formation data should be provided by the user at the same reference conditions as all other components Once the heat of reaction data are supplied PRO II can calculate the total en thalpy change along the reaction path as shown in Figure 2 6 1 1 Figure 2 6 1 1 Reaction Path for pas Known Outlet Temperature O H4 To and Pressure Reactants H4 Ty Reference Reference
70. Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Basic Algorithm Figure 2 4 1 3 shows a schematic of an equilibrium stage for the case of two phase distillation with no chemical reaction The equations which describe the interior trays of the column are as follows Component Mass Balance M exp X L exp Y V expQX 4 i zir 1 22 V i exp Yp p Yen Vin fij fia L NT j 1 NC Energy Balance E LH vH t B L Vin i Viet Hi fes 0 F Hi Fi He i l NT Vapor Liquid Equilibrium Q Yj X InK i LNTandj LNC 24 Summation of Mole Fractions NL 25 21 exp X i 1 NT jel NC 26 S 1 expY i2 LNT jel where Fiz total feed flow to tray i Li total liquid flow from tray i Vi total vapor flow from tray i Qi heat added to tray i Ti temperatures of tray i Xij In xij natural log of the liquid mole fractions Yij ln yij natural log of the vapor mole fractions NC number of components NT number of trays subscripts i tray index j component index PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms Il 57 Distillation and Liquid Liquid Extraction Columns Section 2 4 superscripts Fz refers to a feed D refers to a draw L refers to a liquid property V refers to a vapor property other refers to properties on a molar basis lower case letters refer to component flows
71. S efficiency NTSM 11 83 Sequencing flood point Il 82 PROCESS Il 215 limit of capacity Il 82 Sim Sci 11 215 pressure drop correlations I 83 Sequential modular solution technique 1 212 Souder diagram 1 82 Shadow prices Sulzer packing types Il 80 See Optimizer Sulzer packing Shortcut distillation Il 85 See Structured packed column hydraulics average relative volatility Il 85 column models Il 90 T column specifications Il 92 Tear streams Fenske method Il 85 See also Flowsheet solution algorithms fractionation index Il 95 See Sequencing Gilliland correlation Il 89 Three phase flash calculations key component identification Il 86 See Vapor liquid liquid equilibrium VLLE Kirkbride method 11 89 Two phase flash calculations Il 5 minimum number of trays Il 86 minimum reflux ratio Il 87 optimum feed tray location 1 89 PRO II Unit Operations Reference Manual Index Idx 3 Unit grouping See also Simultaneous modular solution technique V Valve See Equilibrium unit operations Vapor liquid liquid equilibrium VLLE flash calculations predefined systems VLE See Two phase flash calculations Idx 4 Index 1 213 Il 11 Il 11 Il 11 W Water decant 4 Zones analysis example weighted log mean temperature difference Il 9 11 109 Il 111 1 110 11 109 May 1994
72. See Distillation rigorous Underwood method Il 86 Reactors Simple heat exchangers 11 106 Il 108 boiling pot 11 144 basic design equation 11 106 conversion Il 130 log mean temperature difference LMTD 1I 107 CSTR II 141 specifications II 108 equilibrium Il 132 Simultaneous modular solution technique 11 213 general 1 130 Solids handling units Gibbs 1 136 See also Countercurrent decanter heat balances Il 128 See also Crystallizer PFR Il 145 See Dryer shift and methanation models Il 131 Il 134 See also Filtering centrifuge Recycle acceleration See also Freezer acceleration factor q Il 218 See also Melter Broyden II 219 See also Rotary drum filter recommendations II 219 Il 220 Splitter Wegstein 11 218 See Equilibrium unit operations Rigorous heat exchangers II 112 II 121 STCALC Bell Delaware method II 114 II 116 See Stream calculator fouling layer thickness Il 120 Stream blending fouling resistance 11 120 See Stream calculator shellside heat transfer correlations 11 114 Stream calculator 1 183 shellside pressure drop correlations 11 116 blending 11 183 Sieder Tate equation II 115 splitting 11 184 stream analysis method 11 118 synthesis 11 185 TEMA exchanger types Il 113 Stream splitting tubeside heat transfer correlations II 115 See Stream calculator tubeside pressure drop correlations Il 119 Stream synthesis Rotary drum filter 11 153 See Stream calculator calculation methods 11 153 Structured packed column hydraulics Il 80 applications Il 81
73. Solid melting and freezing units are important operations in many industries in cluding food glass and edible oil manufacture Solid components in a mixture may be melted and transformed into a liquid component and liquid components may be frozen and transformed into solids in the PRO II melter freezer unit operation The operating temperature and pressure of the melter freezer is specified by the user The unit may operate in one of two modes m The temperature is specified and PRO II determines which components are to undergo phase transformation based on the normal melting tem perature of each component m The component and fraction to be frozen or melted is specified This is the only criteria used for determining which components undergo phase transformation The melting temperature is ignored for the calculations and components not specifically given by the user do not undergo a solid liquid phase change PRO II Note For more information on specifying components undergoing phase transformation using the MELFRAC FREFRAC keyword on the OPERATION statement see Section 107 Melter Freezer of the PRO II Key word Input Manual The resulting product streams are then flashed isothermally at the given temperature and pressure conditions to determine their thermodynamic prop erties Only the distribution between vapor and liquid and or water phases is considered in the flash calculations True solid liquid equilibrium is not consider
74. Temperature T 3 a Thereactants are brought to the reference temperature and phase The en thalpy difference H2 H is calculated by the prevailing enthalpy calcula tion methods for that reactor b The total heat of reaction A Hr is then calculated by summing all the indi vidual heats of reaction occurring in the reactor c Thereactor effluents are brought to the outlet thermal conditions resulting in Ha Il 128 Reactor Heat Balances May 1994 Section 2 6 Reactors Heat of Reaction Duty H H AH H H4 1 The total reactor duty is the sum of the individual path duties This process is completely independent of enthalpy datum hence users can supply enthalpy values at any arbitrary datum with good results For vapor phase reactions the reference pressure is taken as 1 atm Should the reference phase condition checked by the flash operation be found to be liquid for either the reactants or products the pressure is lowered further un til only vapor is present Similarly for the liquid phase reactions the refer ence pressure of reactants or products is increased until only liquid is present When the ADIABATIC option is active duty may be supplied on the OP ERATION statement Unlike the FLASH unit operation the reactor also has reference state enthalpies H2 and H3 and heat of reaction AH which can be changed and which will change the outlet enthalpy An adiabatic reactor will actually be a fix
75. Ut liquid viscosity rate of dry solids in the feed ke cake resistance ez angle of filtration D diameter of filter drum W width of filter drum O drum rotational speed in rad s 27 d RPM rotational speed of drum in revolutions min Atot total filter area 21 DW The actual pressure drop across the drum filter is then given by AP Ap 1 0 7 where Cr filter cake compressibility factor The value of the filter cake compressibility factor can vary from 0 for an in compressible cake to 1 0 for a highly compressible cake Industrially the value of Cr is typically 0 1 to 0 8 The filter bed thickness is given by CE MED 8 oD Wp 1 8 Il 154 Rotary Drum Filter May 1994 Section 2 7 Solids Handling Unit Operations The filter bed will never become completely dry but will always contain a certain amount of liquid which cannot be removed by filtration This liquid remains in the spaces between particles and is held in place by the surface tension of the liquid This residual cake saturation is a function of a dimen sionless group known as the capillary number Nc The capillary number is given by AP 9 where PL liquid density The residual cake saturation so is calculated based on the value of the capil lary number For 0 002 Nc 0 03 1 718 0299 log ig N 10 For Nc 0 03 s 1 02759 0957 log N 11 For Nc 0 002 5 7 0 072 12 The average level of saturation
76. able during and in no way whatsoever affect flowsheet conver gence Exergy results appear after the Stream Summary reports in the PRO II output report The availability function B is defined as B H TS 1 where Hz enthalpy T temperature S entropy Interpreting Exer gy In the exergy report enthalpy and entropy are reported on a total stream Reports basis and reflect the actual state of the stream i e at whatever phase condi tions prevail at the actual stream temperature and pressure The availability functions shown in Table 2 9 5 1 are provided in the exergy report 1 206 Exergy May 1994 Section 2 9 Utilities Table 2 9 5 1 Availability Functions Availability Function Description B EXS The exergy availability at the EXisting State i e actual state of the stream B TES The exergy availability at reference temperature Tzero and actual stream pressure B EVS The exergy availability at the EnVironmental State i e the reference or zero state at Tzero and Pzero B EVS TOTAL is calculated rigorously assuming the stream is actually at Tzero Pzero conditions and no assumptions are made about the phase state B EVS VAPOR also is calculated at Tzero and Pzero but an a priori assumption is made that the stream is exclusively in a vapor state This is provided as a convenience to users who make this simplifying assumption when performing manual calculations B MES This re
77. ains calculations for single stage constant entropy isentropic opera tions such as compressors and expanders The entropy data needed for these calcu lations are obtained from a number of entropy calculation methods available in PRO II These include the Soave Redlich K wong cubic equation of state and the Curl Pitzer correlation method Table 2 2 1 1 shows the thermodynamic systems which may be used to generate entropy data User added subroutines may also be used to generate entropy data Table 2 2 1 1 Thermodynamic Generators for Entropy Generator Phase Curl Pitzer VL Lee Kesler LK VL Lee Kesler Pl cker LKP VL LIBRARY L Soave Redlich Kwong SRK VL Peng Robinson PR VL SRK Kabadi Danner SRKKD VL SRK and PR Huron Vidal SRKH PRH VL SRK and PR Panagiotopoulos Reid SRKP PRP VL SRK and PR Modified SRKM PRM VL SRK SimSci SRKS VL UNIWAALS VL Benedict Webb Rubin Starling BWRS VL Hexamer VL Hayden O Connell HOCV V Truncated Virial TVIRIAL V Ideal gas Dimer IDIMER V abatic or polytropic efficiency The Curl Pitzer method is used to calculate entropies for a number of thermodynamic systems For example by choosing the keyword SYSTEM CS Curl Pitzer entropies are selected Once the entropy data are generated see Section 1 2 1 of this manual Basic Principles the condition of the outlet stream from the compressor and the compressor power requirements are computed using either a user input adi
78. algorithm the reader should be familar with this material before proceeding In general the extensions of the Chemdist and LLEX algorithms for reactive distillation are suited to the same size systems i e distillation systems which have a smaller number 10 vs 100 of chemi cal species Larger systems can be simulated but a large number of calcula tions can be expected Basic Algorithm Figure 2 4 1 4 shows a schematic of an equilibrium stage for the case of two phase distillation with chemical reaction The equations which describe the inte rior trays of the column on which reactions occur are essentially the basic equations which have terms added for generation and consumption of chemical species The equilibrium equations will be affected only indirectly through the formation or disappearance of chemical species Similarly the energy balance equation is affected through the enthalpies of the species enthalpies If two chemicals react to form a third and produce heat in doing so then the enthalpy of the reaction product must be low enough to account for the disappearance of the moles of the reacting species and the heat of reaction Il 60 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Figure 2 4 1 4 Reactive Distillation V In y L In Equilibrium Stage Bulk Liquid Phase L1DRAW Total Draw Only LODRAW V Yin Ta ING Bulk Liquid Phase The mass bal
79. all column model is used to obtain a straight line relationship between the loga rithm of the pressure drop and the logarithm of the F factor At the end of region II and the beginning of region III where the capacity limit is reached the pres sure drop is obtained from the capacity correlation Finally the correlation in re gion II is modeled by using a quadratic polynomial to join regions I and III At the juncture of regions I and II the polynomial approximation has the same slope as the wetted wall correlation in region I It should be noted that the pres sure drop correlations for all Sulzer packing types were developed without con sidering the liquid viscosity Efficiency The column efficiency or separation performance for Sulzer packing is meas ured by the number of theoretical stages per meter NTSM The NTSM is therefore the inverse of the height equivalent of a theoretical plate HETP The NTSM is defined as NTSM Shg Dg a 4 V 19 where Shg Sherwood number of the vapor phase kgdn DG DaG diffusion coefficient of the vapor phase aj interfacial area per unit volume of packing m m dp hydraulic diameter of packing m kG vapor phase mass transfer coefficient PRO II Unit Operations Reference Manual Column Hydraulics 11 83 Distillation and Liquid Liquid Extraction Columns Section 2 4 The mass transfer in Sulzer packings has been modeled by neglecting the liq uid phase mass transfer coefficien
80. alue model and the sidestream withdrawal factors the material balance 4 can be rewritten as fij olia tl Gp ta SRy lija Cija Siw 13 The set of equations defined by 13 still form a tridiagonal matrix so that equation 7 still applies Bij and Cij from 8 and 9 now become B Rjj t 0 SRy Cj O j S 14 Outer Loop The outer loop in the Inside Out algorithm updates the simple thermody namic model parameters and checks for convergence In the inner loop the distillation equations are solved for the current simple thermodynamic mod els The convergence check in the outer loop therefore compares the rigor ously computed enthalpies and VLE K values from the new compositions resulting from the inner loop calculations The simple model used for VLE K values is given by equations 11 and 12 The initial value of Kp on each stage j is computed by In K _ w In K In K 15 t 1 The simple K values can be calculated very quickly for a given temperature Also once new molar flows are computed in the inner loop a new bubble point temperature can be easily computed Once the molar flows are com puted the mole fractions are obtained from T 16 Xij M and substituting equation 11 into the bubble point equation 17 Lu Liga Hd 1 18 Y OX i K PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms 11 53 Distillation and Liquid Liquid Extraction Colu
81. alues Me tur n He Jam Noe 2100 37 He 700 He lam ur Fiam Ng 2100 38 700 Flam Fouling In most exchanger applications the resistance to heat transfer increases with Factors use as a result of scaling caused by crystallization or deposition of fine mate rial These factors may or may not increase the pressure drop in the ex changer For both the tubeside and shellside the user may input separate factors to account for thermal and pressure drop resistances due to exchanger fouling Thermal fouling resistances cannot be calculated analytically Tables for thermal heat transfer coefficients the inverse of thermal resistances for a number of common industrial applications may be obtained from standard references on heat exchangers such as Perry s handbook or the book by Kern PRO II also allows the user to account for the effect of fouling on pressure drop by inputting a thickness of fouling layer Il 120 Rigorous Heat Exchanger May 1994 Section 2 5 Heat Exchangers References aa Perry R H and Chilton C H 1984 Chemical Engineers Handbook ae 6th Ed 2 Kern 1950 Process Heat Transfer McGraw Hill N Y 3 Gnielinski V 1979 Int Chem Eng 19 3 380 400 4 Willis M J N and Johnston D 1984 A New and Accurate Hand Calculation Method for Shellside Pressure Drop and Flow Distribution pa per presented at the 22nd Heat Transfer Conference Niagara Falls N Y PRO II Unit Ope
82. ams of a flowsheet and generate a unit calculation sequence For loop convergence direct substitution as well as Wegstein and Broyden acceleration are available PRO II Unit Operations Reference Manual II 211 Flowsheet Solution Algorithms Section 2 10 ERC Sequential Modular Solution Technique General PRO II solves process flowsheets using a Sequential Modular Solution Information Technique This technique solves each individual process unit applying the best solution algorithms available Additionally PRO II applies several ad vanced techniques known as Simultaneous Modular Techniques to enhance simulation efficiency Methodology Any given simulation is equivalent to a large system of nonlinear simultane ous equations This system of equations includes the evaluation of all neces sary thermodynamic properties for all streams in the flowsheet as well as all rates and compositions using the selected thermodynamic and unit models In principle it is possible to solve all these equations simultaneously but PRO II utilizes a different approach Every unit in the flowsheet is solved us ing the most efficient algorithms developed for each case For example one can choose different methods for multiple distillation columns ranging from shortcut to a variety of rigorous models and for each case PRO II will use the corresponding specialized column algorithms Should an error occur in any unit due
83. ance equations are the only equations which must have con sumption and production terms added The new equation is 29 NF Mij exp Xi j Lj exp Vij Vj expXij 1 Lj 1 exp Vij Vi Y FiZi k 1 NRxkj NrxEq Nrxcnv V i k z Y Vikrk Vik Y Visi e expOtarj DLj exp Yi Rosj Vj ef k 1 k 1 k 1 The kinetic rates of reaction are given by nA 30 r ko exp RP VJ iar ter K 20 where V the reaction volume A B denote chemical species A and B a b the stoichiometric coefficients of chemical species A and B in the stoichiometric equation respectively exp A RT the Arrhenius rate expression for temperature dependence II denotes the product of the concentrations of the chemicals raised to their stoichiometric coefficients PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms I 61 Distillation and Liquid Liquid Extraction Columns Section 2 4 The only place the reaction volume is used in the distillation calculations is in the kinetic rate expression equation 30 It is extremely important that the tray reaction volumes are consistent with the volume basis used in deter mining the kinetic rate expression If the reaction is a homogeneous liquid phase reaction and the rate expression is based on liquid phase reactions done in a CSTR then the liquid volume should be used This volume corre sponds to the liquid volume on the tray and in the downcomer Do not use the entire mechanical volume
84. and S3 all of which contain the three gaseous components C1 C2 and C3 as well as inert gas C4 The flowrates and com positions of the three streams are known They are mixed to form stream S4 and the MVC is used to specify the total flowrate of S4 as well as the final ra tio of C1 to C2 and of C2 to C3 The MVC specifications are to be met by varying the flowrates of the 3 input streams Figure 2 10 4 2 1 Multivariable Controller Example Spec 1 S4 rate S3 rate iVary Vary S2 rate 4 Spec 3 composition I 226 Multivariable Feedback Controller May 1994 Section 2 10 Flowsheet Solution Algorithms Figure 2 10 4 2 2 MVC Solution Technique The MVC is essentially an expanded form of the feedback controller Its main advantage is that it accounts for the interdependence of control vari ables that are inherently coupled several control variables affect the same specification In the above application for example each MVC specifica tion is directly affected by all the MVC variables to a greater or lesser extent Trying to solve the problem using a series of simple feedback controllers will be inefficient and may even result in failure if the changes in the individ ual controller variables have opposing effects on the specifications Note though that if the variables are not coupled it is generally more efficient to use separate feedback controllers for each variable and specification pair PRO II
85. are fixed in the basecase can be optimization variables Thus for an isothermal flash where both temperature and pressure are fixed both the temperature and pressure may be optimization variables For an adiabatic flash on the other hand the pressure is fixed and the temperature is calculated Here it is incor rect to make the temperature an optimization variable Only the pressure is available for this purpose In addition care must be taken that optimization variables are not varied by any other unit This mistake is especially com mon when the parameter defined as an optimization variable is already fixed by the remainder of the flowsheet Consider for example the flowsheet in Figure 2 10 5 2 If the rate of stream 3 is declared as an optimization variable and the splitter S1 is specified with a fixed rate going to stream 2 then however much the op timizer changes the rate of stream 3 the flowsheet solution does not change The solution stops in the OPTIMIZER with an error message that another unit is also varying the rate of stream 3 One way to model this particular case would be to specify a splitter fraction on S1 and vary the rate of stream 3 Alternatively depending on the problem to be solved the splitter specifi cation can also be varied directly PRO II requires upper and lower bounds to be provided for all variables For best OPTIMIZER performance
86. ases may be mod eled only using free water thermodynamic method sets with the DE CANT ON option of the WATER statement activated either explicitly or by default In the HCURVE module only a single liquid phase appears in the results produced by all rigorous VLLE K value methods and VLE K value methods that do no decant free water HCURVE tables report several properties on a DRY BASIS Dry basis is meaningful only when using a free water decanting K value method with the decant option activated see VLE VLLE and Decant Considerations above In this situation dry basis means free water has been ignored during the cal culation of the dry properties This strategy applies only to liquid phase calculations properties of vapor even vapor containing water are not af fected In the typical case solubility and miscibility of water in the non aqueous liquid phase are not considered when performing water decanting This means in almost all cases that dry properties are calculated on a com pletely water free basis that ignores all dissolved or entrained water as well as any free water In a completely analogous manner properties reported for the WATER liquid phase are only meaningful when a free water de canting K value method is used When using a non decanting VLE K value method at most a single liquid phase is reported When using a non decanting rigorous VLLE K value method the HCURVE module ignores the liquid liquid
87. ation variable is solved within the specified tolerance PRO II Note For more information on using the free water decant option see Section 20 6 Free Water Decant Considerations of the PRO II Keyword Input Manual References Perry R H and Green D W 1984 Chemical Engineering Handbook 6th Ed McGraw Hill N Y 2 Rachford H H Jr and Rice J D 1952 J Petrol Technol 4 sec 1 19 sec 2 3 3 Prausnitz J M Anderson T A Grens E A Eckert C A Hsieh R and O Connell J P 1980 Computer Calculations for Multicomponent Vapor Liquid and Liquid Liquid Equilibria Prentice Hall Englewood Cliffs N J May 1994 Section 2 1 Flash Calculations Three phase For three phase flash calculations with a basis of 1 moles unit time of feed Flash F the MESH equations are simplified to yield the following two nonlinear Calculations equations LAG D l Ya 2 d lt tolerance 23 i If Ly 1 1 b z d S tolerance 24 i where a 1 K 25 b 1 K Kj Kj 26 d K 4 L b L 27 Equations 23 through 27 are solved iteratively using a Newton Raphson technique to obtain L1 and L2 The solution algorithm developed by SimSci is able to rigorously predict two liquid phases This algorithm works well even near the plait point i e the point on the ternary phase diagram where a single phase forms Table 2 1 1 1 shows the thermodynamic methods in PRO II which are able to handle VL
88. ations The stripping factor here is defined as 8r E M j where Sj the Stripping Factor for stage j V the net vapor leaving the stage L the net liquid leaving the stage Kp the base component K value from the simple K value model see equation 11 The inner loop solves the system of equations LSS Hi uU 5 re Si ul k LSS H Ji 5 iis Siw vl k 0 0 H Jb Soul v3 r 0 k LSS 2 SP f f 5 ID S a r 0 k In equation 2 Hj is the heat balance for stage j May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns E LSS vy SS a sense L la a V J He ba Ha Va j NF NQ H E 9 0 i l i l 3 and SPx is a design specification equation This system of equations is solved using the Newton Raphson method The first Jacobian matrix is obtained by finite difference approximation This Ja cobian is then inverted and at subsequent iterations the inverse Jacobian is updated using Broyden s method To evaluate the errors in the enthalpy and specification equations for a given set of stripping factors the component flows and stage temperatures must be computed for the given stripping factors and simple model parameters Fig ure 2 4 1 2 shows a schematic diagram of a simple stage Figure 2 4 1 2 Schematic of a Simple Stage for I O Writing the material balance for this stage in terms of net liquid and vapor flowrates results in LSS VSS 4 dte E es C s
89. atives PRO II calculates the derivatives of the objective function specification and constraints with respect to the OPTIMIZER variables using finite differ ences A small perturbation is made to each variable separately and the flow sheet is resolved Each derivative is then calculated by af f h fe 3 Ox B h To obtain the best derivative information the step size h for each variable x should be small enough so that the higher order terms which are neglected in the above formula are minimized However if h is too small the derivatives will be dominated by flowsheet noise The accuracy of the derivatives can be improved by tightening the flowsheet tolerances and by using the appro priate perturbation steps By default the perturbation steps are calculated as 246 of the range of each of the variables this is increased to 5 if NOSCALE is entered on the OPTPARAMETER statement The user can override this default by enter ing values for APERT or RPERT If the functions and derivatives are well behaved the ideal perturbation size is given by i R i typical where r the relative accuracy with which the functions are evalu ated For simple functions this is on the order of machine precision 10 for complex flowsheets with sufficiently tight tolerances the relative accuracy is on the order of 10 to 10 PRO II Unit Operations Reference Manual Flowsheet Optimization 11 235 Flowsheet Soluti
90. automatically creates a loop for the MVC which incorporates all the units that are affected by changes in the MVC variables The units inside this loop will be solved repeatedly until all the MVC specifications are met within tolerance If the MVC affects units in a recycle loop either the MVC loop or the recycle loop may be the outermost one If the units affected by MVC variables and specs are all inside the recycle loop the MVC will be solved repeatedly every time changes are made to converge the recycle loop If on the other hand MVC specifications or variables affect any unit outside the recycle loop the latter is converged each time the MVC varies a control variable This choice of sequencing usually results in the lowest solution times To override the default the desired sequence must be specified explic itly using a SEQUENCE statement The Algorithm The MVC uses a first order unconstrained optimization method to simultane ously converge all the specifications The objective function to be mini mized consists of the sum of the squared errors in the specifications If bounds on the control variables are defined these are included in the objec tive function as penalty terms Figure 2 10 4 2 2 illustrates the solution pro cedure for an MVC with 2 variables and specifications Contours of Objective Function Control sum of squared errors Variable V2 Basecase Control Variable V1 PRO II Unit Operations Reference
91. ay be defined using one of four types of heat input models User defined Model This heat model is given by V 19 Q C Cytt C C T C v where Q heat duty in millions of heat units time C1 C2 C3 C4 C5 constants in units of millions of heat units time T vessel temperature at time t Vi volume of depressuring vessel at time t Vi volume of depressuring vessel at initial conditions If values for the constants are not provided the general heat model defaults to Q 0 0 i e to adiabatic operation PRO II Unit Operations Reference Manual 11 245 Depressuring Unit Section 2 11 API 2000 Model This heat model is recommended for low pressure vessels and is given by Q C A 20 where C1 C2 constants whose values are given in Table 2 11 2 At current vessel wetted area Aj Ai initial wetted area ft For At Ci C2 20 200 20000 1 000 201 1000 199300 0 566 1001 2800 963400 0 338 gt 2800 21000 0 820 A dimensionless area scaling factor may also be used with the API 2000 heat model If a scaling factor Afac is specified the current vessel wetted area is not equal to the initial wetted area but is instead calculated using v 21 A A Aac v APISCALE Model This heat model is similar to the API 2000 heat model except the heat duty is scaled and is given by V 22 G t Q Ci A V Again an area scaling factor may or may not be specified If Arac is used At is given
92. be done at calculation time i e while PRO II is solving the design equations This option is however neither nec essary nor recommended in these cases For minimum internal temperature approach specifications however zones analy sis is required at calculation time in order to accurately identify pinch points Un der these conditions the weighted LMTD is used in equation 1 Example An example of a zones analysis of a countercurrent heat exchanger is given next and shown in Figure 2 5 2 1 Figure 2 5 2 1 Zones Analysis for Heat Exchangers Il 110 Zones Analysis Temperature T T ww May 1994 Section 2 5 Heat Exchangers Consider a countercurrent heat exchanger with a hot side containing a super heated hydrocarbon water vapor mixture which enters at temperature Thin point 1 The hot fluid changes phase when it cools down to Th dewhc the dew point of the hydrocarbon A zone boundary is created at this phase change As the stream continues to cool it changes phase yet again when it reaches the aque ous dew point Th dewaq Again a zone boundary is created here After further cooling another phase change occurs at Th bub the bubble point of the stream and continues to cool until it reaches Th out point 2 The cold side containing a subcooled liquid enters at temperature T in point 3 and is heated to the bubble point Tc bub A zone boundary is cre ated at this point The cool stream is further h
93. by equation 17 If Afac isn t specified At is set equal to the initial wetted area API RP520 Model This heat model applies to uninsulated vessels above ground level and is the recommended model for pressure vessels The heat model is given by Q 21000 A 23 Again an area scaling factor may or may not be specified If Arac is used At is given by equation 17 If Afac isn t specified At is set equal to the initial wetted area Il 246 Depressuring May 1994 Section 2 11 Depressuring Unit API RPSCALE Model This heat model is similar to the API RP520 model but with scaling applied Itis given by 0 82 V 24 V 1 Q 21000 A Again an area scaling factor may or may not be specified If Afac is used At is given by equation 21 If Afac isn t specified At is set equal to the initial wetted area Fire Relief Model The fire relief model is given by 9 C C 4 25 where C1 C2 C3 user supplied constants Gas Blowdown Model The gas blowdown model assumes an external heat input to the vessel metal followed by transfer of heat from the vessel metal to the gas Initially the vessel temperature is taken to be the same as the gas temperature The exter nal heat input is then calculated from v 26 Qext C t Cyt C C i Toan Cs V t The heat transfer to the fluid inside the vessel is computed using Qi h Ayap AT hj Aj AT 27 AT Tai T uid 28 where hy heat transfer coefficie
94. ce Time t V Q 22 where C residence time in the dissolver sec V operating volume of the dissolver m volumetric rate of bottoms product m sec PRO II Unit Operations Reference Manual Dissolver 1l 169 Solids Handling Unit Operations Section 2 7 Concentration C 2C 0 Q 23 Solution Procedure The solution procedure or algorithm using the above equations performs se quential calculations of the solid liquid problem through mass transfer kinet ics and vapor liquid equilibrium calculations along with heat and material balances This iteration loop is repeated until product stream compositions do not change and convergence is obtained I References Parikh R Yadav T and Pang K H 1991 Computer Simulation and Design of a Stirred Tank Dissolver Proceedings of the European Symposium on Computer Applications in Chemical Engineering Elsevier 2 Treybal R E 1980 Mass Transfer Operations 3rd Ed McGraw Hill N Y l 170 Dissolver May 1994 Section 2 7 Solids Handling Unit Operations ED Crystallizer General Information 26 1 26 2 The crystallizer is used for separation through the transfer of the solute component from a liquid solution to the solid phase The crystallization process depends on both phase equilibria as well as kinetic or nonequili brium considerations Solid liquid equilibrium is defined in terms of solubility which is the equilib rium comp
95. component J then that component will likely not distribute between both products Therefore to test if the correct key components are se lected equation 5 should be applied to those components lighter than the light key and heavier than the heavy key If they fail the test described above then new key components should be selected May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 It should be noted that an exact value of Rmin is not needed This value is nec essary only to provide an estimate of the product composition and to deter mine if the specified reflux ratio is reasonable The Underwood equations assume a constant relative volatility as well as a constant liquid vapor rate ra tio throughout the column The first equation to be solved is T r2 teur 6 Hg Hy 7 q A where q thermal condition of feed heat to convert to saturated vapor heat of vaporization HgG molar enthalpy of feed as a saturated vapor Hp molar enthalpy of feed Hy molar latent heat of vaporization Xzp mole fraction of component J in feed a value between the relative volatilities of the light and heavy keys i e Onk 21 lt 6 lt ouk The second equation to be solved is WS y Sus xs 8 a where Rmin minimum reflux ratio L D min Xjp mole fraction of component J in distillate The algorithm used to solve for Rmin is given in Figure 2 4 4 1 PRO II Unit Operations Reference Manual Shortcut Di
96. corre sponding to a conventional distillation situation Furthermore use of the esti mate generator is not meant to provide the most optimum starting point although this may often be the case but rather to provide a starting point with a high probability of reaching solution The Simple estimate generator computes tray flows from constant molar over flow and the temperatures and mole fractions from L F flashes The Conventional estimate generator uses the Fenske method to determine product mole fractions as follows m Perform shortcut Fenske calculations to determine the product splits and compositions The flows from the product information are used to initi ate the shortcut calculations and when possible the performance specifi cations desired for the rigorous solution will be used for specifications Note that only specifications pertaining to the product rates or composi tions have any meaning for the shortcut model i e rigorous specifica tions such as tray temperatures and tray flows including reflux have no meaning When rigorous specifications cannot be used the initial esti mate generator will use alternate specifications selected in this order the rate from the product information and a fractionation index Fenske trays equal to approximately 1 2 of the column theoretical trays m Basedon the shortcut results the product temperatures are calculated Any user provided temperatures are used directly m The column l
97. ctly what is required Carefully select the bounds and constraints to ensure that the flowsheet is physically well defined over the entire solution space The flowsheet will not solve if for example flowrates or absolute temperatures are al lowed to go negative Flowsheet tolerances should be tightened for improved accuracy This is necessary in order to obtain good first order derivatives and is particu larly important when the flowsheet contains columns or recycle loops Solution Algorithm Introduction PRO II uses Successive Quadratic Programming SQP to solve the non linear optimization problem The algorithm consists of the following steps To simplify the notation define x Gt eX jp Xn j as the vector of the opti mization variables which define the state of the system L e 7 Set the cycle counter k 1 and solve the flowsheet at x Perturb each optimizer variable by some amount hi and resolve the flow sheet Use the base case flowsheet solution and the n additional flowsheet solutions to approximate the first derivatives of the objective function specifications and constraints via finite differences If k 2 2 use the first order derivatives at the previous and current cycles to approximate the second order derivatives Solve a quadratic approximation to the nonlinear optimization problem QP subproblem This yields a search direction dy Set the search step al Solve the flowsheet at x 2 x Od
98. d for a given column diameter the column vapor load is used The vapor load may be determined by using Vload ACFS pg p p where Il 74 Column Hydraulics Vload vapor load capacity ACFS actual vapor volumetric flow rate pa vapor density PL liquid density 1 May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Pressure Drop For valve sieve or bubble cap trays the total tray pressure drop is a sum of the dry tray pressure drop and the pressure drop due to the liquid holdup on the trays AP AP AP 2 where AP total pressure drop inches liquid APary dry tray pressure drop inches liquid APj pressure drop through the liquid on the trays inches liquid The dry tray pressure drop is obtained from nomographs relating the pres sure drop to the weight of the valves at low vapor flow rates and to the square of the vapor velocity at high vapor flow rates For sieve trays the method of Fair is used to calculate the dry tray pressure drop which is given by AP 1 0 186 C P P 3 where Cy discharge coefficient vg 7 superficial vapor velocity For bubble cap trays the dry tray pressure drop is calculated by the method of Bolles 02 4 2 AP ary 7120 pg pj pg hy vo Ky PG PLYG 4 where hs bubble cap slot height The dry cap coefficient K2 in equation 4 is a function of the ratio of the annular to riser areas For valve trays
99. d automat ically by the optimization algorithm are reported in the output report if OPRINT ALL is selected on the OPTPARAMETER statement The signs of the multipliers follow the following convention m If the multiplier of a specification or constraint is positive then increas ing the corresponding MINI MAXI or VALUE will increase the value of the objective function m If the multiplier of a specification or constraint is negative then increas ing the corresponding MINI MAXI or VALUE will decrease the value of the objective function In addition the magnitude of the shadow prices indicates which specifica tions and constraints have the greatest effect on the optimal solution References 1 Fletcher R 1987 Practical Methods of Optimization Wiley 2 Gill P E Murray W and Wright M H 1981 Practical Optization Academic Press Il 238 Flowsheet Optimization May 1994 Section 2 11 Depressuring Unit ESI Depressuring General Information Theory All unit operation calculation methods described in previous chapters of this manual relate to process units operating under steady state conditions PRO II also provides a model for one unsteady state process unit the depressuring unit This unit operation may be used to determine the time pressure temperature relationship when a vessel containing liquid vapor or a vapor liquid mixture is depressured through a relief or control valve The
100. d or calculated to satisfy a process requirement If a heater cooler is used with the pumparound it must be located on the pumparound return tray The pumparound return tempera ture pressure liquid fraction and temperature drop will be computed if it is not specified Heater coolers may be located on any tray in the column A heater cooler is treated only as a heat source or sink Rigorous models of external heat ex changers are available via the attached heat exchanger option 81 deum PRO II Note For more information on using attached heat exchangers see Sec tion 81 Simple Heat Exchanger of the PRO II Keyword Input Manual Feed rates side draw rates and heater cooler duties may be either fixed or computed For each varied rate or duty a corresponding design specification must be made Mathematical There are many different approaches to solving the distillation equations This Models is evident from the large number of articles on the subject in the chemical engi neering literature There are many classes of distillation problems wide and nar row boiling azeotropic homogeneous and heterogeneous liquid phases electrolytic and reactive Unfortunately no one algorithm is yet available which can reliably solve all of these problems PRO II provides different algorithms which excel in solving certain classes of problems and often provide solution ca pability over a very wide range of problems Eldist is designed to solve a spe ci
101. del two assumes to reflux between the sections The second model type is very useful for simulation of petroleum refinery heavy ends columns For these columns it is impossible to select key components to define the fractionation within the various sections Therefore the separations must be indirectly defined using product stream properties As the number of prod ucts increase it becomes increasingly difficult to define non conflicting prod uct specifications There are also usually upper and lower limits for each specification based on material balance considerations and feed repre sentation Care must be exercised to define specifications which result in unique rates for all products either directly or indirectly Calculation failures are always related to specifications Some possible prob lems include m Conflict of fractionation indices with intensive stream property specifica tions In general this combination of specifications should be avoided and fractionation index used only in conjunction with stream bulk prop erties such as rates and gravities m Specifications which do not result in a unique rate for each product stream m Component definition which does not allow the desired separations to be accomplished either too few components or incorrect component boil ing point ranges m Distortion of ASTM TBP initial and endpoints by the Fenske model be cause of the infinite reflux assumption 5 and 95 specificatio
102. ds the method from the GPSA Engineering Data Book and the method from the ASME Power Test Code 10 PRO II Note For more information on using the COMPRESSOR unit operation see Section 56 Compressor of the PRO II Keyword Input Manual This method is more rigorous than the default GPSA method and yields better answers over a wider rage of compression ratios and feed compositions For a real gas as previously noted the isentropic volume exponent also known as the isentropic coefficient ns is not the same as the compressibil ity ratio k The ASME method distinguishes between k and n for a real gas It rigorously calculates ns and never back calculates it from k Adiabatic Efficiency Given In this method the isentropic coefficient ns is calculated as n ln P P4 In V V3 10 where Vi volume at the inlet conditions V2 volume at the outlet pressure and inlet entropy conditions The compressor work for a real gas is calculated from equation 8 and the factor f from the following relationship W 144 75 7 Lf V Ie rp 14 i 11 The ASME factor f is usually close to 1 For a perfect gas f is exactly equal to 1 and the isentropic coefficient n is equal to the compressibility factor k PRO II Unit Operations Reference Manual Compressor Il 21 Isentropic Calculations Section 2 2 The polytropic coefficient n is defined by n In P P ln V V3 12 where V3 volume at the outlet press
103. e d 1 G d E deus pcs psu Energy balance GT EIR Cass T Eu PD 9 2 where G mass flow per unit area through the reactor b extent of reaction per unit mass Ri rate or reaction for the ith reaction R total reaction rate of whole system z axial distance from the inlet of the reactor T temperature at a distance z from the inlet PRO II Unit Operations Reference Manual Plug Flow Reactor PFR 145 Reactors Section 2 6 o 3 Q heat transferred to or from the reactor per unit area P pressure J heat transfer ratio E d 4 p mean heat capacity of the species in the reactor AHR total heat of reaction Equations 1 and 2 may be combined to eliminate the reaction rate term to give dr d amp Q 5 dz dz G or z 6 T T J amp Qaz o where T Ty 0 at z 0 7 are the initial conditions There are now various cases that may arise I Temperature programmed reactor a Isothermal If T z T then equation 1 can be integrated by standard numerical methods b If T z is specified i e a profile for T is given then equation 1 can be solved by numerical quadratures IL Heat control programmed a Adiabatic If Q z 0 we have the constancy of T J and equation 1 can be written as a function of only b If Q z 0 lt z lt L is specified profile of heat transfer given equations 1 and 2 have to be solved simultaneously
104. e f n friction factor obtained from the Moody diagram for a smooth pipe L nocslip liquid holdup vsi vs Vsg Vs superficial liquid velocity Vsg superficial gas velocity The liquid holdup term HL is computed using the following correlations Hi Npy d H H wheno 0 H H Y whenod 0 W 14 1 A inf ani Nf Jisinc 80 0 333sin 1 80 14 where Np Froude number Niy liquid velocity number ab c d e f g constants May 1994 Section 2 3 Pressure Calculations The BBM method calculates the elevation and acceleration pressure drop terms using the relationships given in equations 3 and 4 or equations 7 and 8 for two phase flow Beggs Brill Moody Palmer BBP This method uses the same elevation and acceleration correlations described above for the Beggs Brill Moody BBM method The equation for the fric tion pressure drop term is the same as that given for the BBM method in equations 9 through 12 For this method however the Palmer corection factors given below are used to calculate the liquid holdup H 0 541 H pay lt 0 H 0918 H ggm gt 0 15 where HLBBM liquid holdup calculated using the BBM method Dukler Eaton Flanigan DEF This method uses the Dukler correlation to calculate the friction term The friction factor is given by f f My 128 0 478y 0 444 0 094 0 0084 16 y In 17 f 0 0056 0 5Np 18 where NRe R
105. e criterion Flash solved Ore E Xi men TOL 14 x 4 If the compositions are still changing from one iteration to the next a damping factor is applied to the compositions in order to produce a stable convergence path 5 Finally the VLE convergence criterion is checked i e the following con dition must be met 15 TER TER 1 X J p Y J ror If the VLE convergence criterion is not met the vapor and liquid mole fractions are damped and the component K values are re calculated Rigor ous K values are calculated using equation of state methods generalized correlations or liquid activity coefficient methods 6 Acheck is made to see if the current iteration step ITER is greater than the maximum number of iteration steps ITER max If ITER ITERmax the flash has failed to reach a solution and the calculations stop If ITER ITERmax the calculations continue 7 Steps 2 through 6 are repeated until the composition convergence criteria and the VLE criterion are met The flash is then considered solved 8 Finally the heat balance equation 8 is solved for the flash duty Q once V and L are known PRO II Unit Operations Reference Manual Basic Principles Il 7 Flash Calculations Section 2 1 Flash Tolerances Bubble Point Flash Calculations Il 8 Basic Principles The flash equations are solved within strict tolerances All these tolerances are built into the PRO II flas
106. e for bypass flow and the Reynolds number Js is a function of the baffle spac ing Jr is a function of the number of baffles The Bell method is used to com pute these correction factors The heat transfer coefficient for an ideal tube bank hideal is obtained from the following relationships 8 2 0 037NP Np 2 Nu tur 0 1 2 3 142 443N a er 1 0 5 1 3 3 Nyu lam 0 664 ReG Np 0 5 4 Nyu bund OBH N uiam Nyaa Nnu bunayk 5 Nideal zl L Rigorous Heat Exchanger May 1994 Section 2 5 Heat Exchangers where NReG Reynolds number as defined by Gnielinski rDslpp Npr i Prandlt number a W total mass flow rate in shellside c specific heat of fluid E F shell void fraction Ds shell inside diameter b baffle spacing Ub fluid viscosity at bulk temperature Nyu Nusselt number k thermal conductivity of shellside fluid L effective length of shell subscripts tur and am refer to the turbulent and laminar flow regimes and bund refers to the tube bundle Alternatively the user may supply the shellside heat transfer coefficient directly Tubeside For turbulent flow in circular tubes the tubeside heat transfer coefficient is obtained from the Sieder Tate equation 0 14 6 1 0 023Np NE e k e r u Uw fluid viscosity at the wall temperature Ny u where The above relationship holds for the following flow regimes Npe gt 10000 matri DT l
107. e I O algorithm will usually converge the fastest The I O algorithm can be used to solve most re finery problems and is very fast for solving crude columns and main frac tionators The I O algorithm also solves many chemical systems and when possible should be the first choice for systems with a single liquid phase The Sure algorithm in PRO II is the same time proven algorithm as in PROC ESS This algorithm is particularly useful for hydrocarbon systems where water is present It is the best algorithm to solve ethylene quench towers which have large water decants in the upper portion of the tower The Sure algorithm is also appropriate for many other refining and chemical systems Il 46 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns General Column Model Figure 2 4 1 1 Schematic of Complex Distillation Column PRO II Unit Operations Reference Manual Chemdist is a new algorithm developed at SimSci for the simulation of highly non ideal chemical systems Chemdist is a full Newton Raphson method with complete analytic derivatives This includes composition de rivatives for activity and fugacity coefficients Chemdist allows two liquid phases to form on any stage in the column and also supports a wide range of two liquid phase condenser configurations Chemdist with chemical reac tions allows In Line Procedures for non power law kinetic reactions PRO II Note For mor
108. e allows that variable to move through its full range at every optimization cycle If the OPTIMIZER contains more than one VARY statement the changes in the variables determined in step 3 of the above algorithm will all be reduced by the same factor until all the variables are within the limits imposed by the individual STEPSIZEs Hence the relative change in the variables is not af fected by the STEPSIZE on each variable Termination Criteria The following conditions are tested at every optimizer cycle 1 Is the relative change in the objective function at consecutive cycles less than 0 005 or the user defined value RTOL for the objective function 2 Isthe relative change in each variable at consecutive cycles less than 0 0001 or the user defined values RTOL for each variable 3 Has the maximum number of cycles been reached 4 Does the scaled accuracy of the solution fall below 107 or the user de fined value SVERROR The scaled accuracy which is also known as the Kuhn Tucker error is calculated from KTE V f d s E usi 5 where Vf a vector which contains the first derivatives of the objec tive function d the search direction from the QP subproblem hand g specifications and constraints respectively The weights on the specifications and constraints A and u are determined automatically when the QP subproblem is solved step 3 in the algorithm pre viously described These weights are referred to as multi
109. e calcula ble from the heat of formation data available in the component library dat abank Temperature constraints can be specified For isothermal reactors the heat of reaction data is optional If supplied the required heat duty will be calculated A single reaction is considered for the stoichiometric and simultaneous equilibria of two reactions are computed for the methanator model For chemical equilibrium calculations in PRO II ideal behavior is assumed for reaction in either the liquid or vapor phase PRO II Note Select the required phase using the PHASE entry of the OPERA TION statement For a reaction aA bB cC dD 1 The equilibrium constant is for vapor phase d _PcPp 2 eq a b i Pa Pg for liquid phase Xx 3 eq a b X4 XB where p the partial pressure of component x the mole fraction of component in the liquid May 1994 Section 2 6 Reactors v Note Keg is dimensionless for liquid phase reactions and has the dimension of pressure unit with a c d a b for vapor phase reactions The temperature dependency of the equilibrium constant is expressed as In K A z C In T D T E T 4 FT G T HeT where Keq reaction equilibrium constant A H Arrhenius coefficients T absolute temperature When no approach data are given all reactions go to equilibrium by default The approach to equilibrium can be given either on a fractional conversion basis or b
110. e changes in the individual iteration vari ables Both of these modifications can result in a fractional step in the New ton direction The fractional step size is reported in the iteration summary of the LLEX output Note An a of 1 indicates that the solution procedure is progressing well and that as the solution is approached should become one For highly non linear systems which may oscillate the user can restrict the step size by specifying a damping factor which reduces the changes in the composition variables A cutoff value is used by the algorithm so that when the value of the sum of the errors drops below the given level the full New ton correction is used This serves to speed the final convergence The iteration history also reports the largest errors in the mass balance the energy balance and the liquid liquid equilibrium equations Given a good in itial estimate these should decrease from iteration to iteration However for some systems the errors will temporarily increase before decreasing on the way to finding a solution The keyword ERRINC limits the size of the in crease in the sum of the errors All derivatives for the Jacobian matrix are calculated analytically User added thermodynamic options that are used by LLEX must provide partial derivatives with respect to component mole fractions and temperature LLEX uses the chain rule to convert these to the needed form References 1 Bondy R W
111. e configured to operate in both modes simultaneously When configured to operate in both modes a single set of feed streams and feed blending factors is utilized by both the splitting and synthesis calculations However each mode uses the feed streams and blending factors independently In no way do the splitting calculations af fect the synthesis calculations In a completely complementary manner the synthesis calculations never in any way affect the splitting calculations PRO II Note Only selected topics are discussed here to clarify ambiguities and enhance user understanding of the purpose and use of the Stream Calculator module Refer to Section 122 Stream Calculator in the PRO II Keyword In put Manual for information about all features and options available for this module As stated in the PRO II Keyword Input Manual feed blending may be con sidered a third mode of operation but this viewpoint is slightly misleading In fact feed blending is merely a preliminary setup operation that prepares available feed stream data for use in subsequent stream splitting and or stream synthesis calculations Without the subsequent splitting or synthesis calculations which are required feed blending performs no useful function Feed blending occurs whenever feed streams are present in the definition of a Stream Calculator module The result of this blending is a single combined stream that is a composite of all the individually declared feed st
112. e file that in cludes selected data for each heating cooling curve generated by every HCURVE unit in the problem flowsheet A typical example of the HCURVE data included in the ASC file is shown in Table 2 9 2 2 Table 2 9 2 1 Sample HCURVE ASC File 13 F100 0 0 228 00 000 00 281 89 108 45 0 00000E 00 390 34 21 325 4 7685 0 00000E 00 0 81725 0 18275 0 00000E 00 232 00 000 00 220 65 227 53 0 00000E 00 448 18 16 231 9 8631 0 00000E 00 0 62201 0 37799 0 00000E 00 236 00 000 00 162 69 339 24 0 00000E 00 501 93 11 598 14 496 0 00000E 00 0 44446 0 55554 0 00000E 00 240 00 000 00 115 57 430 33 0 00000E 00 545 90 7 9673 18 126 0 00000E 00 0 30533 0 69467 0 00000E 00 244 00 000 00 79 685 500 58 0 00000E 00 580 26 5 3071 20 787 0 00000E 00 0 20339 0 79661 0 00000E 00 248 00 000 00 52 146 555 42 0 00000E 00 607 57 3 3549 22 739 0 00000E 00 0 12857 0 87143 0 00000E 00 252 00 000 00 30 150 600 03 0 00000E 00 630 18 1 8744 24 219 0 00000E 00 0 71833E 01 0 92817 0 00000E 00 256 00 000 00 11 608 638 20 0 00000E 00 649 81 0 69776 25 396 0 00000E 00 0 26741E 01 0 97326 0 00000E 00 258 77 000 00 0 00000E 00 662 26 0 00000E 00 662 26 0 00000E 00 26 094 0 00000E 00 0 00000E 00 1 0000 0 00000E 00 260 00 000 00 0 00000E 00 664 14 0 00000E 00 664 14 0 00000E 00 26 094 0 00000E 00 0 00000E 00 1 0000 0 00000E 00 This data in the table above should be interpreted as follows DBHCRV HC00 ISO 13F100 0 0 12 The statement above identifies the data as an
113. e information on inputting reaction kinetics using In Line Procedures see Section 47 Procedure Data of the PRO II Keyword Input Manual Eldist is an extension of Chemdist for modeling distillation of aqueous elec trolyte mixtures The aqueous chemistry is solved using third party software from OLI Systems The electrolyte calculation computes true vapor liquid equi librium K values which are converted to apparent vapor liquid equilibrium K Values Eldist then uses these in the vapor liquid equilibrium calculations A schematic diagram of a complex distillation column is shown in Figure 2 4 1 1 A typical distillation column may have multiple feeds and side draws a reboiler a condenser pumparounds and heater coolers The col umn configuration is completely defined the number of trays and the loca tions of all feeds draws pumparounds and heater coolers Note that the optimizer can change feed draw and heater cooler locations Partial Condenser Overhead Vapor gt Liquid Side Draw NE rsen Water Pumparounds Feed Vapor Side Draw I Feed Liquid Side Draw Bottoms Rigorous Distillation Algorithms 11 47 Distillation and Liquid Liquid Extraction Columns Section 2 4 Trays are numbered from the top down The condenser and reboiler are treated as theoretical stages and when present the condenser is stage one There are no hard limits on the number of fe
114. eated until it reaches the aque ous dew point Tc aewag It is heated even further until it reaches the hydrocarbon dew point Tc aewhc Finally it is heated until the final tempera ture of Tc out point 4 is reached Based on phase change points alone the maximum number of zones which may be created is seven as shown in Fig ure 2 5 2 1 Additionally PRO II will further subdivide these zones into smaller zones of equal DT The calculation procedure is then as follows m The ends of the exchanger constitute the overall zone boundaries and the total exchanger heat duty is calculated If the overall U and A values are specified the overall duty is estimated m The duty for each zone is calculated and then the corrected LMTD val ues for each zone are obtained Equation 2 is then used to determined the weighted average LMTD value for the exchanger m The heat transfer coefficients are calculated for each zone m The areas for each zone are determined using the zone values for U Q LTMD and equation 1 and then are summed to give the heat transfer area for the entire exchanger 81 G PRO II Note For more information on using a simple heat exchanger model in PRO II see Section 81 Simple Heat Exchanger of the PRO II Keyword Input Manual Reference LT Bowman R A Mueller and Nagle 1940 Trans ASME 62 283 PRO II Unit Operations Reference Manual Zones Analysis I 111 Heat Exchangers Section 2 5 BEX
115. ed The calculation scheme for this unit operation is shown in Figure 2 7 7 1 May 1994 Section 2 7 Solids Handling Unit Operations Figure 2 7 7 1 Calculation Scheme for Melter Freezer Use component melting temperature to determine phase transformation Freeze all of component liquid or melt all of com ponent solid based on MP and operating temperature PRO II Unit Operations Reference Manual Are components specified using the MELFRAC FREERAC keywords Ignore component melting temperature For specified comps freeze specified fraction of liquid or melt specified fraction of solid equal to user input value For all other comps no solid liquid phase transformation is considered Do isothermal flash on resulting products to determine thermodynamic conditions Melter Freezer 179 Solids Handling Unit Operations Section 2 7 This page intentionally left blank Il 180 Melter Freezer May 1994 Section 2 8 Stream Calculator jae EX Stream Calculator General Information 22 Feed Blending Considerations The Stream Calculator is a multi purpose module intended to facilitate the manipulation of process streams in a PRO II simulation flowsheet There are two distinctly different modes of operation available stream splitting and stream synthesis A single Stream Calculator module may operate in either of these two modes exclusively or may b
116. ed as Cg7 Vo Po p Po e i where VG superficial vapor velocity m s PG vapor density kg m prL liquid density kg m Capacity correlations are obtained by plotting the experimental capacity data on a so called Souder diagram On this diagram the capacity factor is plotted versus the flow parameter which is defined as Q L G pg 7p Hah where L liquid flow kg s G vapor flow kg s The liquid phase capacity factor cL is defined by 16 Cp V p p P where VLt superficial liquid velocity m s cr is related to the vapor capacity factor by 17 cif mij n where m and n are constants The straight line correlations given in 17 were obtained for two separate hy draulic regimes Low liquid loads cr 1 2 lt 0 07 m s High liquid loads cL 1 2 gt 0 07 m s The capacity correlations have been shown to predict the column capacity within an accuracy of 6 May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Pressure Drop The pressure drop model used in PRO II for structured packings is a sum of three separate correlations as shown in Figure 2 4 3 1 Figure 2 4 3 1 Pressure Drop Model 10 mbar m log Ap Az ami iad limit i a 50 of capacity limit 1 i The F factor in Figure 2 4 3 1 is defined as F factor Veo re 18 Region I is for columns operating below 50 capacity In this region the wetted w
117. ed duty reactor The outlet temperature is determined by trial and error to satisfy the duty The reactor duty can be calculated from equation 1 The heat balance will be printed in the reactor summary if the PRINT PATH statement is input The heat of reaction may be furnished by the user as a function of the moles of base component reacted Alternatively the heat of reaction will be com puted by PRO II if not supplied through the following relationship 2 A H A Ay products Ay reactants where AH heat of formation of each component at 25 C Heat of formation data are available in the component databank for library components and can be estimated for petroleum components using internal correlations For NONLIBRARY components this data must be furnished PRO II Note If it is desired not to calculate the heat of reaction the NOHBAL option should be selected on the RXCALCULATION statement PRO II Unit Operations Reference Manual Reactor Heat Balances 129 Reactors Section 2 6 EH Conversion Reactor The CONREACTOR unit operation is a simple conversion reactor No kinetic information is needed nor are any reactor sizing calculations per formed The desired conversion of the base component is specified and changes in the other components will be determined by the corresponding stoichiometric ratios Conversions may be specified as a function of tempera ture as follows Fractional
118. eds draws pumparounds etc This results from the PRO II memory management system Table 2 4 1 1 shows the features available with each algorithm Pumparounds can be used for liquid and or vapor The return tray can be above or below the draw tray Note that when the pumparound return is mixed phase liquid and va por that both the vapor and the liquid are returned to the same tray PRO II provides hydrodynamic calculations for packings supplied by Norton Co and Sulzer Brothers Both rating and design calculations are available In rating mode the diameter and height of packing are specified and the pres sure drop across the packed section is determined In design mode the height of packing and the pressure drop are specified and the packing diame ter is calculated Tray rating and sizing is also available and may be performed for new and ex isting columns with valve sieve and bubble cap trays Valve tray calcula tions are done using the methods from Glitsch Tray hydraulics for sieve trays are calculated using the methods of Fair and for bubble cap trays with the methods of Bolles Rating and design calculations are available The I O and Sure algorithms provide a free water decant option This is used in refinery applications to model water being decanted at the condenser or at other stages in the distillation column Table 2 4 1 1 Features Overview for Each Algorithm 1 0 Sure j Chemdist LLEX Eldist Pumparounds Y Y N N N
119. eed streams are al lowed for this unit operation The mixer unit is like the valve unit operation solved in a similar manner to that of an adiabatic flash unit In this unit the temperature of the single out let stream is computed for a specified outlet pressure and a duty specification of zero The number of feed streams permitted is unlimited The outlet prod uct stream will not be split into separate phases PRO II Unit Operations Reference Manual Equilibrium Unit Operations 1 13 Flash Calculations Section 2 1 Splitter Figure 2 1 2 3 Splitter Unit The temperature and phase of the one or more outlet streams of the splitter unit are determined by performing an adiabatic flash calculation at the speci fied pressure and with duty specification of zero The composition and phase distribution of each product stream will be identical One feed stream or a mixture of feed streams are allowed Il 14 Equilibrium Unit Operations May 1994 Section 2 2 Isentropic Calculations read i EEJ Isentropic Calculations PRO II contains calculation methods for the following single stage constant entropy unit operations m Compressors adiabatic or polytropic efficiency given m Expanders adiabatic efficiency specified PRO II Unit Operations Reference Manual Il 17 Isentropic Calculations Section 2 2 ET E259 Compressor General Information Il 18 Compressor PROIII cont
120. ensity kg m S solubility kg solute kg liquid C liquid phase concentration of solute kg m t time sec As At 0 equation 1 becomes p AK p S O 2 V np A An 3 where r radius of solid particle m and dr 4 Pop k 0 5 O PRO II Unit Operations Reference Manual Dissolver 1l 165 Solids Handling Unit Operations Section 2 7 Figure 2 7 5 1 Continuous Stirred Tank Dissolver 105 ll 166 Dissolver Equation 4 describes the mass transfer rate per unit area as dependent on two factors the mass transfer coefficient and concentration difference The mass transfer coefficient is the liquid phase coefficient since diffusion of the solute from the particle surface through the liquid film to the bulk of the liquid solution is the dominant or rate controlling step The concentration difference is the dif ference between the equilibrium concentration at the solid liquid interface and the solute concentration in the dissolver liquid Integrating equation 4 for constant kL ky 5 Ar gj Ot P represents the change in particle size due to the dissolution process The following simplifying assumptions are used in the development of the dissolver model m The solid particles are spherical in shape m There is no settling breakage or agglomeration of solid particles m The liquid in the dissolver follows a continuous stirred tank type flow whereas the solid particles are in plug flow As a result
121. ent equilibrium equations where Y em ey em K HION HION OHION OHION H20AQ p H20AQ Y em ey em K HION HION HCO3ION HCO3ION H20AQ Y on e COAQ CO2AQ H20AQ em e em K mon Hron Ycosiox cosiox HCO3ION Y i HCOS3ION HCO3ION y activity coefficients K equilibrium constants 1 2 3 Activity coefficients and equilibrium constants are functions of temperature pressure and molarities of components or ions In addition there are four independent atom balance equations and one elec troneutrality equation Sodium Balance NaCl In m NAION Chlorine Balance NaCl In Moron Moles MW 5 1000 0 Carbon Balance e Moles o MWr9 1000 0 4 5 6 CO n cosson MyCco310N Meong sno MW 5 1000 0 H Balance H O In Molesy 6 Maleno BW 707 1000 m m m 0 CO3ION OHION HCO3ION Electroneutrality Equation Il 70 ELDIST Algorithm m m M 2m m m 0 HION NAION Mucosion CO3ION OHION OLION 7 8 May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns The inside loop solves these eight equations for eight unknowns using New ton s method Once these unknowns are computed and true aqueous mole fractions of aqueous components are determined all ions are combined to translate them in terms of aqueous mole fractions of the original compo nents These componen
122. erms of only the overhead product The rate and composi tion of the bottoms stream then is calculated as the difference between the combined feed and the overhead product Alternatively use only FBTMS RBTMS and XBTMS splitting specifications to define all component split ting in terms of only the bottoms product In the latter case the rate and composition of the overhead product is calculated as the difference between the combined feed and the bottoms product Splitting factors of zero exclude the component or group of components from the specified product stream Negative splitting factor values are invalid Note The XOVHD and XBTMS splitting factors specify only the relative composition of components in the overhead and bottoms products respectively This means they do not and cannot be used as a basis for calculating the rate of either product Since mass balance between the combined feed and the products is always enforced some splitting factor that establishes a basis for calculating product flowrates is required For this reason the distribution of at least one component must be specified using an FOVHD FBTMS ROVHD or RBTMS separation factor Stream synthesis is useful for dynamically creating a stream or modifying the composition and rate of a stream during flowsheet convergence calculations Stream synthesis does not require the presence of any feeds to the Stream Calcu lator but always creates something from nothing a virtua
123. ers of the PRO II Keyword Input Manual Certain restrictions apply for example if the location of COLUMN feeds draws heaters or coolers are used as variables within the OPTIMIZER the rate and or heat duty cannot also be used If the variables to be manipulated by the optimizer are specifications made on the flowsheet basecase the simplest specifications should be chosen if possible since this speeds up the solution time For example suppose a split ter specification is an optimization variable The basecase specification on the splitter should be a molar rate or ratio this being the simplest specifica tion possible The optimizer varies the value of this specification and re solves the flowsheet Making a more complex specification on the splitter such as the weight rate of a given component in a given product from the splitter and varying this in no way alters the solution to the optimization problem but may increase the computational effort PRO II Unit Operations Reference Manual Flowsheet Optimization 1 231 Flowsheet Solution Algorithms Section 2 10 Figure 2 10 5 2 Choice of Optimization Variables The problem may be more acute when column specifications are optimiza tion variables Here the simplest specifications i e rate of recovery or re flux should always be chosen since these specifications will make the column easier and faster to solve It is important to note that only those flowsheet parameters which
124. es not affect flowsheet convergence It is al ways executed during the output calculations phase of simulator execution after the flowsheet has fully converged and therefore does not affect the con vergence calculations Also like the HCURVE this unit is not accessible via the CONTROLLER MVC or CASESTUDY One feature worth discussing further is the XVALUE option of the EVALU ATE statement Quite often tables of generated data bracket but do not ex actly match points of great interest such as experimental compositions The XVALUE option allows the user to specify exact component mole fraction values so these points can be very closely investigated 198 Binary VLE VLLE Data May 1994 Section 2 9 Utilities Output Considerations The XVALUE entry accepts liquid vapor mole fractions for component i one of the two components declared on the COMP entry on the same EVAL state ment If only one value is given it is assumed to be the starting value with the number of points determined by the DELX and POINTS entries If two values are given they are assumed to be the starting and terminal values with the num ber of points to generate specified by the POINTS entries The default starting and ending mole fraction values are 0 0 and 1 0 When three or more points are supplied only those specific points are generated Results of each EVALUATE statement are printed as tables or optional plots The format of the report tables c
125. exchanger in the simula tion When using any of these options the end point states of the desired stream are obtained from the converged solution of the unit operation and in general cannot be modified by supplying additional input data for the curve AII calculations use the standard thermodynamic flash and transport tech niques discussed in earlier sections of this manual and in the PRO II Key word Input Manual and PROVISION User s Guide A single thermodynamic method set is used in each HCURVE module When more than one thermo dynamic method set is present in the simulation a unit specific method may be used to choose the one set that will be used for all curves in the HCURVE module When the unit specific method is not specified the default thermo dynamic data set will be used Il 192 Heating Cooling Curves May 1994 Section 2 9 Utilities The GAMMA option available for most heating cooling curves is valid only when the thermodynamic method set being used employs a liquid activity K value method Critical Point and The extreme phase discontinuities inherent at the critical point pose particu Retrograde Region larly severe calculation situations for dew and bubble curve generation al Calculations though all curve calculations experience some difficulties in this region Generally it is not uncommon for flash calculations to fail as the curve crosses the critical point When possible it is suggested that the Phase Enve l
126. expander which is re ported as work in PRO II is then given by GHP HEAD F 33000 14 PRO II Unit Operations Reference Manual Expander Il 27 Isentropic Calculations Section 2 2 This page intentionally left blank Il 28 Expander May 1994 Section 2 3 Pressure Calculations FS EX Pressure Calculations PRO II contains pressure calculation methods for the following units m Pipes single and two phase flows m Pumps incompressible fluids PRO II Unit Operations Reference Manual Il 31 Pressure Calculations Section 2 3 PERT Pipes General Information Basic Calculations Il 32 Pipes PRO II contains calculations for single liquid or gas phase or mixed phase pressure drops in pipes The PIPE unit operation uses transport properties such as vapor and or liquid densities for single phase flow and surface tension for vapor liquid flow The transport property data needed for these calculations are obtained from a number of transport calculation methods available in PRO II These include the PURE and PETRO methods for vis cosities Table 2 3 1 1 shows the thermodynamic methods which may be used to generate viscosity and surface tension data Table 2 3 1 1 Thermodynamic Generators for Viscosity and Surface Tension Viscosity Surface Tension PURE V amp L PURE PETRO V amp L PETRO TRAPP V amp L API L SIMSCI L KVIS L PRO II contains numer
127. eynolds number The liquid holdup Hr used in calculating the mixture density p in the fric tion term is computed using the Eaton correlation In this correlation the holdup is defined as a function of several dimensionless numbers The elevation term is calculated using equation 3 The mixed density p however is calculated not by using the Eaton holdup but by using the liquid holdup calculated by the Flanigan correlation H 1 ZU 0 326 ie 19 PRO II Unit Operations Reference Manual Pipes Il 35 Pressure Calculations Section 2 3 Figure 2 3 1 1 Various Two phase Flow Regimes Il 36 Pipes The acceleration term is calculated using the Eaton correlation dP dL Wh n e 8e Im AL 20 where W mass flow rate v fluid velocity Vsg superficial gas velocity qm mixture flow rate subscripts g and refer to the gas and liquid phases Mukherjee Brill MB The Mukherjee Brill method is recommended for gas condensate systems In the MBN method a separate friction pressure drop term is given for each re gion of flow Figure 2 3 1 1 shows the various flow patterns which the MB method is able to handle SEGREGATED Bubble Bubble Slug Annular mist Vertical Pipes Horizontal Pipes For stratified flows in horizontal pipes dp dL 7 fp v 2g d e1 For bubble or slug flows AP dD 7 fp Vn 28ed 22 For mist flows dP dD 7 ff p v 28
128. fect the flowsheet convergence PRO II Unit Operations Reference Manual 11 189 Utilities Section 2 9 LEXI Phase Envelope General The PHASE ENVELOPE module generates a phase envelope or constant liq Information uid fraction curve in tablular or plot form for streams using the Soave Redlich K wong or Peng Robinson equation of state methods Ww Note The phase envelope module is currently limited to the Soave Redlich Kwong and Peng Robinson thermodynamic methods only Up to five separate curves or tables may be specified for each phase envelope module Figure 2 9 1 1 shows a typical phase envelope Figure 2 9 1 1 Phase Envelope Phase Envelope PH1 100 I Critical Point 0 d D a c 2 2 eo n e 9 a 50 0 Temperature F Calculation Flash computations often fail at the critical conditions However for the Methods Phase Envelope module the true critical point cricondentherm criconden bar and points of the phase envelope are determined with the method of Michelsen This method provides a direct solution for the mixture critical point and encounters no difficulties in the critical region Regions of retro grade condensation are also accurately predicted ll 190 Phase Envelope May 1994 Section 2 9 Utilities 2 9 2 E PRO II Note See the HCURVE section of this manual for more information on retrograde condensation Michelsen developed his technique with
129. fic class of problems namely electrolytic systems The LLEX liquid liquid extractor is for liquid liquid extraction systems PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms I 49 Distillation and Liquid Liquid Extraction Columns Section 2 4 Inside Out Algorithm Il 50 Rigorous Distillation Algorithms The Inside Out I O column algorithm in PRO II is based on an article by Russell in 1983 The I O column algorithm contains a number of novel fea tures which contribute to its excellent convergence characteristics The algo rithm is partitioned into an inner and outer loop In the inner loop the heat material and design specifications are solved Simple thermodynamic mod els for enthalpy and vapor liquid equilibrium VLE K values are used in the inner loop This along with the form of the simple model and the choice of primitive variables allows the inner loop to be solved quickly and reliably In the outer loop the simple thermodynamic model parameters are updated based on the new compositions and the results of rigorous thermodynamic calculations When the rigorously computed enthalpies and K values match those of the simple thermodynamic models and the design specifications are met the algorithm is solved Inner Loop The primitive variables in the inner loop are the stripping factors and sidestream withdrawal factors The inner loop equations are the stage enthalpy balances and the design specific
130. g a reaction volume These are the most difficult systems to solve The actual function used to increase the reaction volume is a combination of functions Initially there may not be any products present in the tower and the reaction may proceed very quickly Therefore the volume is initially in creased on a log fraction basis which very gradually introduces the reaction After the products begin to accumulate on the trays the reaction volume is in creased linearly The transition between the two modes is at 25 PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms 11 63 Distillation and Liquid Liquid Extraction Columns Section 2 4 Summarizing if the reaction homotopy is used the initial problem is solved with no chemical reaction on the trays After the solution is reached the reac tion volume is increased by a small amount and the problem is resolved us ing the no reaction solution as a starting point After the solution is reached the reaction volume is again increased and the problem is resolved This con tinues until the reaction volume has been fully introduced The number of in crements and the initial volume may be specified by the user If the steps are small or the problem is not particularly difficult the problems at each volume are solved in a small number of iterations Even with this the distillation equations are being solved at each volume step and it may take quite a few iterations to solve O
131. gh conversion are possible The plug flow reactor model in PRO II is not equipped to find the hot spot or ignition temperature The user can manipu late the exit cooling temperature for countercurrent reactors or stream prod uct temperature for autothermal reactors to get either the low conversion or the high conversion solution Reference i Smith J M 1970 2nd Ed Chemical Engineering Kinetics McGraw Hill NY PRO II Unit Operations Reference Manual Plug Flow Reactor PFR 147 Reactors Section 2 6 This page intentionally left balnk ll 148 Plug Flow Reactor PFR May 1994 Section 2 7 Solids Handling Unit Operations U Solids Handling Unit Operations The following types of solids handling equipment may be simulated in PRO II Dryer Rotary drum filter Filtering centrifuge Countercurrent decanter Melter Freezer Dissolver Crystallizer PRO II Unit Operations Reference Manual 11 151 Solids Handling Unit Operations Section 2 7 EM Dryer General Information Calculation Methods Il 152 Dryer PRO I has the capability of simulating a simple continuous solids dryer in which the drying gas and solid streams flow countercurrent to each other The liquid typically water content of the solid stream is reduced by contact with the hot gas stream The dryer unit is simulated in much the same way as the flash drum unit is If the stream composition and rate are fixed the
132. gy energy mol gas constant temperature a temperature exponent Cj concentration of jth species total number of reacting components y exponents of concentration Ri reaction rate for reaction i For multiple simultaneous reactions the overall reaction rate for each react ing component is s E 2 4 R PajAjexp x 1 T c i l j l where Rj net rate of production of species j Solution of a CSTR involves the simultaneous solution of equation 1 and equation 2 Il 142 Continuous Stirred Tank Reactor CSTR May 1994 Section 2 6 Reactors Multiple Steady Adiabatic exothermic reactions in CSTRs may have two valid steady state States solutions as illustrated in Figure 2 6 5 2 Figure 2 6 5 2 Thermal Behavior of CSTR The qr line represents heat removal and is linear with increase in tempera ture The qg curve represents heat generation At low temperatures the curve increases exponentially with temperature due to increased reaction rate As the reactants are exhausted the extent of reaction levels off Thus there are three places where the two curves intersect The top and bottom intersections represent stable solutions The middle one represents the ignition tempera ture Reactors above that temperature tend to stabilize at the high reaction rate and reactors below that temperature tend to stabilize at the low reaction rate In the PRO II CSTR unit operation either solution is possible and there
133. h 2V a Vis 9 where r radius of vessel h tangent to tangent vessel height The end cap volume Vena is again given by equation 4 above Spherical Vessel 4 3 6 Vy 3 or Vic 6 All the valve equations are based on vapor flow only through the valve The valve upstream pressure is assumed to be the same as the vessel pressure For supersonic flow the pressure drop across the discharge valve AP should satisfy the relationship AP gt 0 5C7 P4 7 where Cr critical flow factor dimensionless actual pressure drop P P2 psia P upstream pressure psia P2 downstream pressure psia The valve rate for supersonic flow is given by W 2 8 C CP VG 8 where W vapor flow rate through valve Ibs hr Cy valve flow coefficient dimensionless Gf specific gravity at temperature T R The gas specific gravity can be written as 520 MW 9 MW T atr G where MW molecular weight of discharge stream MWair molecular weight of air T temperature of stream R PRO II Unit Operations Reference Manual 11 243 Depressuring Unit Section 2 11 Il 244 Depressuring The stream molecular weight is given by ww anro i P where z gas compressibility factor R gas constant 1 98719 BTU lb mol R pv 7 vapor density lb ft Substituting equations 9 and 10 in equation 8 gives the following expres sion for the vapor rate through a valve under supersonic flow conditions
134. h algorithm and may not be input by the user Table 2 1 1 1 shows the values of the tolerances used in the algorithm for the Rachford Rice equation 12 the composition convergence equations 13 and 14 and the VLE convergence equation 15 Table 2 1 1 1 Flash Tolerances Equation Tolerance Rachford Rice 12 1 0e 05 Composition Convergence 1 0e 03 13 14 VLE Convergence 15 1 0e 05 For bubble point flashes the liquid phase component mole fractions xi still equal the component feed mole fraction zi Moreover the amount of vapor V is equal to zero Therefore the relationship to be solved is Y Ku Y 10 16 i i The bubble point temperature or pressure is to be found by trial and error Newton Raphson calculations provided one of them is specified The K values between the liquid and vapor phase are calculated by the ther modynamic method selected by the user Equation 16 can however be highly non linear as a function of temperature as K values typically vary as exp 1 T For bubble point temperature calculations where the pressure and feed compositions has been given and only the temperature is to be deter mined equation 16 can be rewritten as i ia 0 17 Equation 17 is more linear in behavior than equation 16 as a function of temperature and so a solution can be achieved more readily Equation 16 behaves in a more linear fashion as a function of pressure as the K values vary as 1
135. halpy Hj are obtained and the point P1 T1 S1 H1 is obtained The constant entropy line through S1 is followed until the user specified outlet pressure is reached This point represents the temperature T2 and enthalpy conditions H2 for an adiabatic efficiency of 100 The adi abatic enthalpy change AHad is given by AH ad H H 3 If the adiabatic efficiency Yad is given as a value less than 100 the actual enthalpy change is calculated from AH AH Yaa 4 The actual outlet stream enthalpy is then calculated using H H AH 5 Point 3 on the Mollier chart representing the outlet conditions is then obtained The phase split of the outlet stream is obtained by performing an equilibrium flash at the outlet conditions The isentropic work Ws performed by the compressor is computed from W H Hj J2 AH J 6 where J mechanical equivalent of energy May 1994 Section 2 2 Isentropic Calculations 56 ASME Method In units of horsepower the isentropic power required is GHP AH 778 F 33000 7 GHP AH 778 F 33000 GHP 4 Yad 8 HEAD A aq 778 9 where GHP work hP AH enthalpy change BTU Ib F mass flow rate Ib min HEADsaa Adiabatic Head ft The factor 33000 is used to convert from units of ft Ib min to units of hP The isentropic and polytropic coefficients polytropic efficiency and polytropic work are calculated using one of two metho
136. hanges depending upon whether the thermodynamic methods set that is being used is able to predict two liquid phases VLLE or only a single liquid phase VLE The tables of results are clearly labeled and only two additional notes are presented here 1 Inthe mole fraction results tables X 1 in the header represents the molar liquid fraction and Y 1 represents the molar vapor fraction of component one X 2 and Y 2 identify the same quantities for the second component of the binary In VLLE results listings only the first and second liquid phase columns are distinguished by asterisks For example X 1 repre sents mole fractions of component 1 in the first liquid phase while X 1 is used for fractions of component in the second liquid phase Since at most only a single vapor phase exists asterisks never appear with vapor data headings such as Y 1 or Y 2 2 In VLLE results listings of activity coefficients and vapor fugacity coeffi cients an additional column appears labeled Distribution Coefficient The distribution coefficients are liquid liquid equilibrium analogs of vapor liq uid equilibrium K values Therefore the distribution coefficient of compo nent i would be defined as Ky x x 1 where Kp liquid liquid distribution coefficient of component i xj liquid mole fraction of component i I II represent the first and second liquid phases respectively PRO II Unit Operations Reference Manual Binary VLE VLLE
137. his is the integration of sidestrip pers and pumparounds with column units Consider the crude column shown in Figure 2 10 1 2 PRO II Unit Operations Reference Manual Sequential Modular Solution Technique 1 213 Flowsheet Solution Algorithms Section 2 10 Figure 2 10 1 2 Column with Sidestrippers gt OVERHEAD VAPOR WATER NAPHTHA 175 F 50 MM Btu hr x D Zx 310 F 4000 lb hr STEAM 5 MM Btu hr Q 9 10 i KEROSENE 4 4500 Ib hr STEAM 450 F Pe eee 25 MM Blu hr p Q pM c y DIESEL 3 1500 Ib hr STEAM T 12 2 10000 Ib h e STEAM 60 psig 600 F TOPPED CRUDE There are three pumparounds and three sidestrippers in the flowsheet A strict application of the Sequential Modular Solution Technique requires six tear streams Instead by grouping the column and sidestrippers and solving them simultaneously the number of tear streams is reduced to only three pumparound recycles Moreover if the attached heat exchangers correspond ing to the pumparounds are also grouped a unique model is obtained that does not contain recycles further improving the simulation efficiency Il 214 Sequential Modular Solution Technique May 1994 Section 2 10 Flowsheet Solution Algorithms PATE Calculation Sequence and Convergence General Information Tearing Algorithms PRO II performs an analysis of the flowsheet and determines
138. homotopy equations are what enable us to move smoothly from the easy problem to the difficult problem The most general conditions for the homotopy equation are H x t some function of f x and g x 0 31 such that Hix 0j FU 0 Hix 1 fx 0 The simplest transformation is a linear homotopy In this case the homotopy equation becomes x t tf x 1 1 glx 0 32 In equation 32 tis varied from zero to 1 The first challenge is choosing the proper homotopy the second is determining the sequence of t that allows you to move from the simple equations to the difficult equations The methods for tracking the homotopy path from 0 to 1 are classified as either simplicial discrete methods or continuation differential methods based on the integration of an initial value method Currently the reactive distillation algorithm in PRO II uses a classical homotopy with a set of predefined steps In most cases involving reaction this approach is sufficient The reactive distillation algorithm uses a physical homotopy with the reac tion volume being linked directly to the homotopy parameter That is in itially the reaction volume is zero and the simple set of equations corresponds to the basic distillation problem At the final point the reactive volume is equal to the specified volume and the equations are the full set de scribing reactive distillation This homotopy is only used for those systems usin
139. ible operational modes of the CSTR CSTR Operation The possible operational modes for the CSTR are Modes m adiabatic fixed or zero heat duty m isothermal fixed temperature In addition for the boiling pot model there is another optional mode of operation W isometric fixed volume of reacting liquid phase The reactor volume is required for the vapor and liquid models The pressure specification is fixed for all three models when input explicitly as the operat ing pressure or pressure drop or when calculated as the pressure of the com bined feed to the reactor Il 144 Continuous Stirred Tank Reactor CSTR May 1994 Section 2 6 Reactors aa Se EH Plug Flow Reactor PFR Figure 2 6 6 1 Plug Flow Reactor Design Principles The plug flow reactor is an idealized model of a tubular reactor Whereas the feed mixture to a CSTR reactor gets instantaneously mixed the fluid ele ments entering the plug flow reactor are assumed to be unmixed in the direc tion of the flow Since each element of feed spends the same time in the reactor the plug flow reactor is also a convenient method of modeling a batch reactor on a spatial basis instead of on a time variable basis A schematic diagram of a plug flow reactor is shown in Figure 2 6 6 1 The steady state mass and energy balance for the one dimensional PFR for M simultaneous reactions can be derived as follows Mass balanc
140. icted based on a given feed composition b Operating data are to be checked by comparison of the predicted product prop erties with the actual product properties The operating product rates are used for this case The selection of components cannot be over emphasized for such studies While minimization of component numbers is desirable for simulation cost reduction sufficient components must be included to enable accurate simulation In particu lar for case a the yields predicted can be greatly influenced by the components chosen For case b it is a relatively simple matter to adjust the components used as required to more accurately predict product properties For case a this a more complex task with judgment necessarily applied in light of the simulation requirements The standard cuts used by PRO II have been developed for crude unit simulation and will give good results It is generally recommended that com promises to the standard cuts be made in the heavier components above 800 F where possible For series of columns the shortcut model itself can be important For the crude vacuum unit combination shown in Figure 2 4 4 5 the system may be simulated as one column or two It is usually better to use two shortcuts since the crude unit products will be well defined while the vacuum prod ucts may be somewhat nebulous In this way the crude unit yields will not be affected by errors in definition of the vacuum unit yields and b
141. id Liquid Extraction Columns Troubleshooting Il 96 Shortcut Distillation Values of fractionation indices differing greatly from the above values sug gest impossibilities or conflicts in the product specifications used for the model When it is desired to use the shortcut model to verify yields and properties it is suggested that the product yields and or gravities be used in conjunction with the typical fractionation induces shown above It is interesting to note that values se lected anywhere within the ranges given will produce nearly identical products This also illustrates rather graphically the controlling effect of product draw rate versus trays for such columns When using the shortcut model for rate prediction it is recommended that fractionation indices not be used in conjunction with intensive properties Definition of the fractionation with FINDEX may very well result ina case that is impossible to converge For yield prediction a combination of product ASTM 95 temperatures and gaps works very well for crude units For the topped crude a gap of 100 to 150 F with the gas oil usually gives a reasonable operation or the gravity of the topped crude may also be used for a specification Simple Columns Simple columns are defined as consisting of one feed and two products with reboilers and condensers Systems with two overhead products partial con densers are simulated with one combined overhead product with the
142. illation 1 99 Section 2 4 Distillation and Liquid Liquid Extraction Columns PERF Liquid Liquid Extractor General Information Basic Algorithm Figure 2 4 5 1 Schematic of a Simple Stage for LLEX Liquid liquid extractions are modeled in PRO II using the general trayed column model in conjunction with the LLEX algorithm The LLEX algo rithm in PRO II is a Newton based method which is suited to solving non ideal distillation problems involving a smaller number 10 vs 100 of chemical species LLEX is designed to solve liquid liquid equilibrium problems with more than one equlibrium stage Figure 2 4 5 1 shows a schematic of an equilibrium stage with a lighter liq uid denoted as liquid 1 and a heavier liquid liquid 2 in equilibrium The equations which describe the interior trays of the column are as follows with all rates compositions and enthalpies expressed on a molar basis Component Mass Balance Equations M s exi Xi n exe X is ex Xs i Gs LA 1 exei Eis Fij i 1 NT Energy Balance Equation ge Bei at s iat Ba i a 2 Q FH i 1 NT ll 100 Liquid Liquid Extractor May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 Liquid Liquid Equilibrium Equations LLE Xj Xj IK i LNTandj LNC 3 Summation of Mole Fractions S 1 Lerx i LNT 4 epe Yew x i2LNT 5 where Fiz total feed flow to tray i
143. int of the process stream being investigated The physi cal state of the stream must be fully defined at these two limiting points The information presented here is intended to extend user understanding and pro vide insight into the capabilities and limitations of the HCURVE mod ule Several different types of curves may be requested and each type of curve offers a number of options for defining the end point states of the stream Examples of data that sufficiently define a stream state include m Specifying both temperature and pressure or m Specifying enthalpy content and either temperature or pressure The stream itself always supplies all composition information 123 PRO II Note See Chapter 123 Heating Cooling Curves of the PRO II Key word Input Manual for input requirements and calculation options available for heating cooling curves Calculation Any number of heating cooling curves may be requested in each HCURVE Options unit but you must identify the process stream for each curve Alternatively instead of explicitly identifying a process stream the HCURVE module al lows you to specify a stream by describing a configuration of a unit opera tion such as a heat exchanger flash drum or distillation column For example you may elect to instruct the HCURVE module to generate a curve with points spaced at equal temperature and pressure increments between the inlet and outlet conditions on the hot side of a heat
144. ion w Note In general convergence is enhanced when the reflux quantity is esti mated generously Liquid and Vapor Mole Fractions PRO II generates reasonable profiles for liquid and vapor mole fractions us ing one of the initial estimate models selected by the user The user could provide the mole fraction profile to aid the convergence Estimate Generator The temperature rate and composition profiles not provided by the user are generated by PRO II using one of the built in estimate generator models When using the estimate generator product rates are still provided with the product information Il 66 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Various models used for the estimate generation are shown below in Table 2 4 1 2 with the column algorithm Table 2 4 1 2 Default and Available IEG Models Algorithm IEG Method 1 0 Chemdist SURE LLEX ELDIST Simple Default Default Default Default Yes Conventional Yes Yes Yes Refining Yes Yes Yes Electrolyte Default For electrolytic systems simple IEG is same as electrolyte IEG The estimate generator will work for most columns regardless of complexity or configuration Of course for simulations in which a column model is be ing used to simulate a combination of unit operations columns flash drums etc the estimate generator should not be used since it sets up profiles
145. iquid loading is calculated by using the reflux estimate pro vided by the user Note that an L D ratio of 3 0 is assumed if no reflux quantity is provided m A column heat balance is performed If side coolers are present and du ties have been provided the flow profiles are appropriately adjusted PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms 11 67 Distillation and Liquid Liquid Extraction Columns Section 2 4 The Refining estimate generator uses the Fenske method just like the conven tional estimate generator The four steps described above for the conven tional method are repeated here In addition the bottom tray temperature is adjusted for the effect of stripping stream if present Adjustment is also made for inter linked columns if present In light of the above procedure it is good practice to Recommendations m Provide reasonable estimates with the product information m Provide a reasonable reflux estimate m Provide temperature guesses for subcooled products the estimate gener ator would use the saturated values m Provide the side cooler heater estimates if possible 68 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns EXE ELDIST Algorithm The ELDIST algorithm in PRO II is a combination of a Newton based method which is used in Chemdist for solving MESH equations and the solution of liquid phase speciation equations de
146. is constant for each stage This assumption along with the fixing of the ratio of the overflow solids concentration to the underflow solids concentration decouples the solution of equations 1 4 and enables the equations to be solved simultaneously Equa tions 1 4 may be re written as b 6 de Fi for stage 1 5 Qy ANa By io y m Fiy for stages 2 to N 1 6 Oy XNA By is Fw for stage N 7 where R D 0 0 8 U OR s Y Pi D Countercurrent Decanter May 1994 Section 2 7 Solids Handling Unit Operations O R 9 D C _ Fi fa ay il D Dj 20 R 1 11 Qu l 12 13 Ry Ov U Uy OyRy N 1 NHUN By Dy Yy Uy 14 s e Oy Ry 15 NU DO C C _ Fy iN 16 iN Dy Dy Uy Ry DO 17 1 18 R N Ey The underflow and overflow stream temperatures from each stage are the same and are assumed equal to the stage temperature i e the stage is in ther mal equilibrium Calculation For the rating calculations the total mass balances are solved easily once the Scheme total solids and percent solids underflow at each stage are specified The cal culation procedure is given below m First the underflow rates are calculated from equation 1 The wash water rate to the last stage is known and the last stage overflow rate is then calculated using Oy F Uy 4 7 Uy 19 m The remaining overflow rates are then calculated from the last
147. is no built in logic to ascertain that the correct solution is found The final solution can be influenced by the addition of an initial estimate on the OPERATIONS statement Generally the CSTR will find the high temperature solution if the in itial estimate is above the ignition temperature and the low temperature solution for initial estimates below the ignition temperature For some exothermic reactions and for all endothermic reactions there may be only one intersection between the heat generation and heat removal curves indicating only one steady state PRO II readily finds this solution PRO II Unit Operations Reference Manual Continuous Stirred Tank Reactor CSTR 143 Reactors Section 2 6 Boiling Pot Model When the CSTR is operated as a boiling pot reactor the reactions take place in the liquid phase and the vapor product in equilibrium with the reacting liquid is drawn off From a degree of freedom analysis for the boiling pot reactor Variables T P Q F Xj Yj V Total 2N 5 Equations Material Balance equation 1 SN Total 2N 3 35 15 71 Reaction rate equation 3 Energy balance equation 2 The degrees of freedom or the number of variables to be fixed is 2 The rest of the variables or unknowns are then calculated by solving the model equa tions Since the pressure P is fixed by the CSTR input the user can choose to fix one of the other variables T Q or V This leads us to the discussion on the poss
148. is present with the hydrate the chemical potential differ ence between water in the liquid phase and the empty hydrate is given by und ar E 8 1 k t where A u chemical potential difference between water in the liquid phase and the empty hydrate Xw mole fraction of water in the liquid phase For gas mixtures a binary interaction parameter aj representing the interac tion between the most volatile hydrate forming gas molecule and all other molecules is introduced into equation 8 9 Aw RT bec 3 a D yk 2 OK Dil b vih ry n dus i k PRO II Unit Operations Reference Manual Hydrates 203 Section 2 9 Utilities where Qk Yk binary interaction parameter between the most volatile com ponent and component k mole fraction of component k in the vapor phase The method used for determining the temperature and pressure conditions un der which hydrates form is given in Figure 2 9 4 2 Figure 2 9 4 2 Method Used to Determine Hydrate forming Conditions Il 204 Hydrates Assume Tf calculate the bubble point pressure Pbp Calculate the vapor bubble point composition yi For the first iteration assume hydrate formation pressure Pbp Calculate the Langmuir constants fugacities alphas are in the PRO II Is an inhibitor present Apply a correction factor to the liquid phase water mole fraction Update the hydrate formation temperature Tf Ca
149. ium Flash MESH Equations Il 4 Basic Principles Figure 2 1 1 1 shows a three phase equilibrium flash The Mass balance Equilibrium Summation and Heat balance or MESH equations which may be written for a three phase flash are given by Total Mass Balance F V L L Component Mass Balance Fz Vy L L Equilibrium Y Ky Xy Vj Ky Xy Ky Xi a X24 HU K 2i li Summations gt 170 i i b x7 X 0 i i 1 2 3 4 5 6 7 May 1994 Section 2 1 Flash Calculations Heat Balance FH Q7 VH LHy LH 8 Two phase For a two phase flash the second liquid phase does not exist i e L2 0 Isothermal Flash and L L in equations 1 through 8 above Substituting in equation 2 Calculations for L from equation 1 we obtain the following expression for the liquid mole fraction xi Zi 9 V K Dpt X The corresponding vapor mole fraction is then given by yj7 Kx 10 The mole fractions xi and yi sum to 1 0 i e Y E 210 11 i However the solution of equation 11 often gives rise to convergence difficul ties for problems where the solution is reached iteratively Rachford and Rice in 1952 suggested that the following form of equation 11 be used instead 12 Ls yocp o TOL n i i K E41 Equation 12 is easily solved iteratively by a Newton Raphson technique with V F as the iteration variable Figu
150. ive of the VLE equations with respect to the bulk liquid phase A new Jacobian matrix is calculated and the Newton Raphson algorithm calculates new values for the iteration variables The cycle repeats until convergence is achieved This approach is not as direct as using the individual component composi tions for each liquid phase However it results in more stable performance of the Newton Raphson algorithm because a second liquid phase is not continu ally appearing and disappearing Liquid draws are dealt with in terms of bulk liquid properties i e other than for a condenser it is not possible to directly specify the selective withdrawal of any one liquid phase PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms 11 59 Distillation and Liquid Liquid Extraction Columns Section 2 4 Reactive Distillation Algorithm References 1 Bondy R W 1991 Physical Continuation Approaches to Solving Reactive Distillation Problems paper presented at 1991 AIChE Annual meeting 2 Bondy R W 1990 A New Distillation Algorithm for Non Ideal System paper presented at AIChE 1990 Annual Meeting 3 Shah V B and Bondy R W 1991 A New Approach to Solving Electrolyte Distillation Problems paper presented at 1991 AIChE Annual meeting The Chemdist and LLEX algorithms in PRO II support both liquid and vapor phase chemical reactions Since reactiive distillation is an extension of the basic chemicals distillation
151. l Heat Balance Equation Heat Duty Product Enthalpy Feed Enthalpy 20 Phase Equilibrium Equations Solid liquid Equilibrium T f temperature 21 where XS lute equilibrium mole fraction of solute in crystallizer liquid at crystallizer temperature Vapor liquid Equilibrium Y f X 13 where Yi vapor phase mole fraction of component i Xi liquid phase mole fraction of component i Solution Procedure The solution procedure for the crystallizer model uses the above equations to perform solid liquid calculations through crystallization kinetics in a super saturated liquid solution and VLE calculations along with material bal ances The algorithm used is shown in Figure 2 7 6 3 ll 176 Crystallizer May 1994 Section 2 7 Solids Handling Unit Operations Figure 2 7 6 3 MSMPR Crystallizer Algorithm PRO II Unit Operations Reference Manual Initialize merged product stream as feed stream Solve VLE and solid liquid problems Compare old and new product stream compositions Are stream Problem compositions solution same reached Merge liquid and vapor product streams Flash merged product stream Treybal R E 1980 Mass Transfer Operations 3rd Ed McGraw Hill N Y Crystallizer 1 177 Solids Handling Unit Operations Section 2 7 Y E Melter Freezer General Information Calculation Methods vS l 178 Melter Freezer
152. l k and x the calculated rate after trial k Broyden uses an approxi mation Hx to the inverse of the Jacobian which is being updated at every iteration Broyden s procedure provides x as follows z 4 ua a d Ax 4 where dy a damping factor In equation 4 Ax is given by Ax H x 7X 5 The update of Hk is performed using the following formula PRO II Unit Operations Reference Manual Acceleration Techniques II 219 Flowsheet Solution Algorithms Section 2 10 T 6 E Hii yy dy AM 4 AG Hi 6 A Hy 4 T AX Hay where lOO ur 7 Y 06 4 7x 70 73 7 The algorithm starts with Ho J avoiding thus expensive numerical calcula tions and inversion of the Jacobian The damping factor has a default value dy 1 at every iteration and it is reset to a smaller value automatically to pre vent the new estimates x from becoming negative Recommended Uses for Broyden It is recommended that the Broyden acceleration be applied only after suffi cient direct substitution trials have been made If the initial estimate of the re cycle stream composition is far different from the expected solution e g zero total rate a number of trials should first be made with direct substitu tion Once started Broyden acceleration will be applied every trial without exception The Broyden method works best for cases involving multiple recycle steams which are interdependent PRO II will apply Broyden acceleratio
153. l mass flow that in troduces a discontinuity in the material balance of the flowsheet Typically the synthesized stream is intended to serve as an source stream that feeds the flowsheet When used in this manner the synthesized stream does not compro mise the mass balance of the overall flowsheet since it is considered to originate in an infinite source that is external to the flowsheet Note The XPROD splitting factors specify only the relative composition of components in the synthesized product This means they do not and cannot be used as a basis for calculating the rate of the synthesized product some splitting factor that establishes an absolute basis for calculating product flow rate is required For this reason the rate of at least one component must be specified using an FPROD or RPROD separation factor PRO II Unit Operations Reference Manual 1 185 Stream Calculator Section 2 8 This page intentionally left blank Il 186 Stream Calculator May 1994 Section 2 9 Utilities EX Utilities This section describes a number of supplemental calculation methods available in PRO II These include the following calculations Phase envelope Heating or cooling curve Binary vapor liquid and vapor liquid liquid equilibria verification Hydrate prediction Exergy These calculation modules are performed after the process flowsheet has solved and therefore do not af
154. l solid components Kj exp AG RT j5 L2 NR 3 where NR number of reactions AGj change of Gibbs free energy of formation at modified temperature T T T AT AT temperature approach The second part of the objective function is the conservation of element groups and mass balance equations created from the constraints on chemical equilibrium For each element group the output flowrate has to be equal to the feed flowrate i e NS NP NC 4 b my YY my Amp k 1 NE fl p j l where bk feed quantity of element group k NE number of element groups mjk number of element group k contained in component j If the product rate of a component is fixed either by the constraint of fixed product rate or by the fixed percentage of feed amount reacted the additional mass balance constraint can be written as d ni j 1 NSFIX 5a or NP 5b d n j 2L NCFIX j1 where dj specified or derived fixed product rate NSFIX number of solid components with fixed product rate NCFIX number of fluid components with fixed product rate PRO II Unit Operations Reference Manual Gibbs Reactor 137 Reactors Section 2 6 l 138 Gibbs Reactor If a reaction has a specified reaction extent the additional mass balance con straint is NR NS NP 6 ver a j n n PY ya Lap j r 1 NR j l p i where E fixed reaction extent aj matrix element derived from the inverse of stoichiometric coefficient matrix
155. lations Il 8 Dew Point Flash Calculations Il 9 Two phase Adiabatic Flash Calculations Il 9 Water Decant Il 9 Three phase Flash Calculations Il 11 Equilibrium Unit Operations Il 12 Flash Drum Il 12 Valve Il 13 Mixer Il 13 Splitter Il 14 Compressor Il 18 General Information Il 18 Basic Calculations Il 19 ASME Method Il 21 GPSA Method Il 23 General Information Basic Calculations TOT M pw ao General Information Il 32 Basic Calculations I 32 Pressure Drop Correlations Il 34 PRO II Unit Operations Reference Manual Table of Contents TOC 1 General Information Il 41 Basic Calculations Il 41 Rigorous Distillation Algorithms 11 46 General Information 11 46 General Column Model Il 47 Mathematical Models Il 49 Inside Out Algorithm Il 50 Chemdist Algorithm Il 56 Reactive Distillation Algorithm Il 60 Initial Estimates Il 65 ELDIST Algorithm Il 69 Basic Algorithm Il 69 Column Hydraulics Il 73 General Information Il 73 Tray Rating and Sizing Il 73 Random Packed Columns Il 76 Structured Packed Columns 11 80 Shortcut Distillation 11 85 General Information 11 85 Fenske Method 11 85 Underwood Method Il 86 Kirkbride Method 11 89 Gilliland Correlation 11 89 Distillation Models 11 90 Troubleshooting 11 96 General Information Il 100 Basic Algorithm Il 100 kw e c Heat Exchangers Simple Heat Exchangers Il 106 General Information Il 106 Calculation Methods 11 106 Zones Analysis Il 109 General Information Il 109
156. lculate the chemical potential Determine the hydrate formation pressure Pf that satisfies 1 Based on gas components present determine type of hydrate formed Is Pf Pop Correct hydrate formation conditians determined May 1994 Section 2 9 Utilities References Munck J Skjold Jorgensen S and Rasmussen P 1988 Computations of the Formation of Gas Hydrates Chem Eng Sci 43 10 pp 2661 2672 Ng H J and Robinson D B 1976 The Measurement and Prediction of Hydrate Formation in Liquid Hydrocarbon Water Systems Ind Eng Chem Fundam 15 4 pp 293 298 Parrish W R and Prausnitz J M 1972 Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures Ind Eng Chem Proc Des De velop 11 1 pp 26 35 Peng D Y and Robinson D B 1979 Calculation of Three Phase Solid Liquid Vapor Equilibrium Using an Equation of State Equations of State in Engineering and Research Advances in Chemistry Series No 182 ACS pp 185 195 PRO II Unit Operations Reference Manual Hydrates 1 205 Utilities Section 2 9 B H TS EH Exergy General Exergy or availability calculations may be requested by the user by supply Information ing the EXERGY statement in the General Data Category of input All en tries are optional When requested exergy calculations are performed in the final stages of writing the PRO II output report As such exergy calculations are not avail
157. ld side m Hotside outlet to cold side inlet temperature approach m Hotside inlet to cold side outlet temperature approach m Hot side outlet to cold side outlet temperature approach m Minimum internal temperature approach m Overall heat transfer coefficient U and area A given ll 108 Simple Heat Exchangers May 1994 Section 2 5 Heat Exchangers Zones Analysis General Information Calculation Methods Conventionally for a simple heat exchanger the logarithmic mean temperature difference is calculated using the stream temperatures at the inlet and outlet of the unit equations 3 and 4 in the previous section 2 5 1 Simple Heat Ex changers Optionally PRO II can compute a duty averaged LMTD This op tion becomes increasingly useful when phase changes occur along the length of the exchanger Under these conditions the LMTD calculated as described for the simple heat exchanger may often be inadequate because of the non linearity of the enthalpy temperature characteristics of the stream changing phase Zone analysis may therefore be extremely useful for locating internal temperature pinches In this method the heat exchanger is divided into a number of zones and the heat exchanger design equation is then applied to each zone separately The number of zones may be specified by the user or be automatically selected by PRO II Automatic selection by PRO II ensures that all the phase changes are located
158. lied only after one or more trials with direct replacement have been made If the initial estimate of the recycle stream composition is far different from the expected solution e g zero total rate a number of trials should first be made with direct replacement Once started Wegstein acceleration may be applied every trial or at frequen cies specified by the user Recommended Uses for Wegstein The Wegstein method works best for situations in which convergence is unidirectional that is when a key component or components either builds up or decreases in a recycle stream Because the Wegstein method does not consider the interaction effects of components it may not be suitable for cases involving multiple recycle steams which are interdependent Under these conditions the method may cause oscillation and hinder convergence If oscillation occurs with direct replacement upper and lower q values at 0 5 may be used in the Wegstein equation forcing averaging to take place Reference Wegstein J H 1958 Comm ACM 1 No 6 9 Broyden s method is a Quasi Newton method It consists of updating the inverse of the Jacobian at each iteration instead of calculating it or approximating it nu merically This method takes specifically into account all interactions between component rates and temperature of all streams included in the recycle loop Let x represent the estimated rate of all components in a recycle stream at the begin ning of tria
159. mation to the Jacobian matrix a very poor starting estimate or infeasible design specifications The E K error is the average error between the K values predicted using the simple thermodynamic model and the rigorously computed K values using the compostions and termperatures resulting from the inner loop calcula tions A large E K indicates highly compostion sensititve K values The error sum E SUM is the sum of the enthalpy specification and the bub ble point errors This value is not used in the convergence check E SUM is a good indicator of how convergence is progressing and is similiar to the ERROR SUM for the Sure Algorithm With Estimate and All iteration printout levels the following intermediate printout results PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms Il 55 Distillation and Liquid Liquid Extraction Columns Section 2 4 ITER 1 E K 1 017E 01 E ENTH SPEC 1 392E 03 E SUM 3 159E 01 COMPONENT ERROR AVG 4 491E 02 MAX T 1 1 814E 01 ENTHALPY ERROR AVG 0 000E 00 MAX T 4 LIQ 0 000E 00 K VALUE ERROR AVG 1 017E 01 MAX T 1 C 1 3 310E 01 INNER 0 E ENTH SPEC 1 104E 02 SPEC ERROR AVG 134E 02 MAX SPEC 1 2 267E 02 HBAL ERROR AVG 5 368E 03 MAX TRAY 2 1 230E 02 TEMP CHANGE AVG 8 500E 01 MAX TRAY 1 2 461e 00 INNER 1 E ENTH SPEC 1 854E 04 ALPHA 1 0000 SPEC ERROR AVG 886E 04 MAX SPEC 1 3 756E 04 HBAL ERROR AVG 9 114E 0
160. mns Section 2 4 Il 54 Once K has been determined equation 12 can be arranged so that the bubble point temperature can be solved for directly The bubble point expression is 1 19 bubble In K A We i B pe The simple enthalpy models are of the form H T H E AH H Hh AH 20 where H the vapor enthalpy Hry the liquid enthalpy H the vapor ideal gas enthalpy H the liquid ideal gas enthalpy AH the vapor enthalpy departure from the ideal gas enthalpy AHL the liquid enthalpy departure from the ideal gas enthalpy The simple model for the enthalpy departure is given by AH A B T T AH C D T T 21 where the departures are modeled in terms of energy per unit mass The I O algorithm has four different levels of intermediate iteration printout These are None Part Estimate and All None results in no iteration print out Part results in partial intermediate printout and is useful to monitor the progress of the algorithm toward solution Estimate should be used to debug a non converged column Estimate prints the initial column estimate and more information on actual equation errors to help determine what the con vergence difficulty is A prints out the column temperature liquid and va por profiles at each iteration and the same comprehensive intermediate printout as Estimate Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns
161. mp to the fluid pressure increase HP q AP 17143 e 1 where HP required pump power hp q volumetric flow rate gal min AP pressure increase psi e percent efficiency The factor 1714 3 converts the pump work to units of horsepower The work done on the fluid calculated from 1 above is added to the inlet enthalpy The temperature of the outlet fluid is then obtained by performing an adi abatic flash Note The PUMP unit should only be used for incompressible fluids Com pressible fluids may be handled using the COMPRESSOR unit operation LI Reference GPSA Engineering Data Book 9th Ed 5 9 PRO II Unit Operations Reference Manual Pumps II 41 Section 2 4 Distillation and Liquid Liquid Extraction Columns EX Distillation and Liquid Liquid Extraction Columns The PRO I simulation program is able to model rigorous and shortcut distilla tion columns trayed and packed distillation columns random and structured packings as well as liquid liquid extraction columns PRO II Unit Operations Reference Manual Distillation and Liquid Liquid Extraction Columns 1I 45 Distillation and Liquid Liquid Extraction Columns Section 2 4 EEJ Rigorous Distillation Algorithms General Information This chapter presents the equations and methodology used in the solution of the distillation models found in PRO II It is recommended reading for those who want a better understanding
162. n the General Data category of input Values of these tolerances may also be provided on the LOOP statements Care should be exercised that inside loop tolerances are set always as tight or tighter than those for outside loops Temperature convergence test Error in 7 2 temperature Temperature T T Ee n mi T tolerance Pressure convergence test lt e P tolerance Errorin _ Pa Pi pressure pa 3 n Default component flow temperature and pressure tolerances of ec 0 01 eT 1 0 F 0 55 C and ep 0 01 will be assigned by PRO II These toler ances may also be redefined in the General Data category of input or on the LOOP statement These convergence tests are applied to all streams but the user has the option to apply them to the tear streams only PRO II Unit Operations Reference Manual Calculation Sequence and Convergence II 217 Flowsheet Solution Algorithms Section 2 10 EU Acceleration Techniques General Information Wegstein Acceleration Unless acceleration techniques are requested by the user PRO II will use di rect substitution for closure of all recycle streams This method usually works well however for loops in which closure is asymptotic an accelera tion technique becomes desirable to reduce the number of trials required The Wegstein acceleration technique takes advantage of the result of the pre vious trials b
163. n R ol pS mS uP 26 op wye 27 sout Ry out Vout Rein function R l S p 28 AP AP in Nj 1 AP AP RE AP out 29 SS g where APs in mean shellside end space pressure drop at exchanger inlet APs out mean shellside end space pressure drop at exchanger outlet Rs in end space resistance at exchanger inlet Rs out end space resistance at exchanger outlet denotes an average Tubeside The tubeside pressure drop APts is calculated as the sum of the pressure drops in the tubes plus the pressure drops in the return bends FG Ln 30 435x10 DS 2nG 31 AP AP AP 32 where AP pressure drop in tubes AP pressure drop in return tubes APs total pressure drop in the tubeside Hc fluid viscosity factor friction factor Gt mass flux L tube length n number of tube passes Di tube inner diameter Sp specific gravity of fluid PRO II Unit Operations Reference Manual Rigorous Heat Exchanger II 119 Heat Exchangers Section 2 5 The friction factor F and viscosity factor Uc are computed using different correlations for each flow regime For turbulent flows Nre gt 2800 0 14 33 us 1 33 am log F 0 2643log 9 Ng 2 5103 34 For laminar flows NRe lt 2100 0 25 35 s 1 35 am log o F 0 9952log 19 Nge 0 31537 36 For transition flow regimes 2100 lt NRe lt 2800 F and uc are obtained by in terpolation between the laminar and turbulent v
164. n be solved PRO II Unit Operations Reference Manual Flowsheet Optimization 11 229 Flowsheet Solution Algorithms Section 2 10 Figure 2 10 5 1 Optimization of Feed Tray Location Typical Application Figure 2 10 5 1 depicts a typical optimization application Overhead CALCULATOR i Feed Tray Location Profit Function OPTIMIZER In this example the OPTIMIZER determines the feed tray location which maximizes a profit function computed by the CALCULATOR This profit function includes the value of the overhead product less the operating costs of the column Hence 2 maximize Total profit computed by CALCULATOR objective function such that Lower limit lt Feed tray location lt Upper limit bounds The feed tray location is the optimization variable The flowsheet has two ad ditional degrees of freedom the heat duties of the reboiler and the condenser These are used as flowsheet variables inside the column in order to meet the COLUMN specifications on the purity of the overhead and bottoms products Il 230 Flowsheet Optimization May 1994 Section 2 10 Flowsheet Solution Algorithms Objective Function Exactly one objective function is required in the OPTIMIZER it must be de fined so that it is the result of a calculation within PRO II and not a value which is fixed by the user The OPTIMIZER objective may be either a design or performance objective It ma
165. n there are 2 de grees of freedom that may be fixed Any one of the following combination of specifications may be used when defining the dryer unit operation DRYER SPECIFICATION 1 SPECIFICATION 2 OPERATION ISOTHERMAL TEMPERATURE PRESSURE ISOTHERMAL TEMPERATURE DP ADIABATIC TEMPERATURE FIXED DUTY PRESSURE FIXED DUTY DESIGN TEMPERATURE GENERAL DESIGN SPECIFICATION DESIGN PRESSURE GENERAL DESIGN SPECIFICATION DESIGN DP GENERAL DESIGN SPECIFICATION A design specification may be the amount of feed vaporized or the moisture content of the solids product or a rate or fraction or PPM specification on either product stream The design specification is used along with mass balance equations to calcu late the operating dryer temperature or pressure the other is specified A two phase VL flash is performed to determine the vapor and liquid phase distributions The details of the calculation flash algorithm may be found in Section 2 1 Flash Calculations May 1994 Section 2 7 Solids Handling Unit Operations cy Rotary Drum Filter General In solid liquid separations horizontal rotary drum filters are often used to Information decrease the liquid content of a stream containing solids For a given filter diameter and width rating calculations PRO II will compute the pressure drop cake thickness average cake saturation as well as determine the rates of the solid cake and filtrate product streams For design calculati
166. n to all recy cle streams corresponding to each loop Caution must be taken when using Broyden acceleration with a user supplied set of streams to accelerate if this set does not contain all the tear streams of the loop or loops it belongs to the inter dependence may not be well represented by Hx and therefore the algo rithm may behave poorly Reference Broyden C G 1965 Math Comp 19 pp 577 593 Il 220 Acceleration Techniques May 1994 Section 2 10 Flowsheet Solution Algorithms PAD Flowsheet Control General Information PRO II allows both feedback controllers and multivariable controllers to be included within a flowsheet These units which are described in more detail below allow specifications on process units or streams to be met by adjust ing upstream flowsheet parameters If there is a one to one relation between a control variable and a specification it is best to use a feedback controller If on the other hand several specifications and constraints are to be handled simultaneously the multivariable controller should be used Both the feedback and multivariable controllers terminate when the error in the specifications is within tolerance By default the general flowsheet toler ances are used as shown in Table 2 10 4 1 Table 2 10 4 1 General Flowsheet Tolerances Temperature Absolute tolerance of 0 1F or equivalent Pressure Relative tolerance of 0 005 Du
167. ndom packed column hydraulics See also Structured packed column hydraulics See also Tray column hydraulics Compressor Il 18 ASME method Il 21 efficiency adiabatic Il 21 I 23 efficiency polytropic Il 22 11 24 GPSA method Il 23 Mollier chart Il 20 polytropic compression curve Il 19 Continuous Stirred Tank Crystallizer CSTC See Crystallizer Continuous stirred tank reactor II 141 boiling pot model 11 144 design principles 1 141 multiple steady states 1 143 operation modes 11 144 Conversion reactors See Reactors Countercurrent decanter 11 161 algorithm 11 163 calculation methods 11 161 Crystallizer 11 171 11 177 crystal growth rate Il 172 crystal nucleation rate Il 172 crystal nucleii number density Il 173 heat balance Il 176 magma density Il 174 PRO II Unit Operations Reference Manual mass balance Il 175 population balance equations II 173 solid liquid equilibrium Il 176 solution algorithm Il 176 vapor liquid equilibrium Il 176 CSTR See Continuous stirred tank reactor D Depressuring 11 241 heat input models 11 245 theory 1 244 valve rate equations 11 243 vessel volume 11 242 Dew point flash calculations Il 9 Dissolver Il 165 Il 170 heat balance Il 169 mass balance 11 168 mass transfer coefficient correlations 11 166 mass transfer rate 11 166 model assumptions 11 166 particle size distribution Il 168 residence time 11 169 solid liquid equilibrium 11 169 solution algorithm 1 170 vapor liquid equilib
168. ngineer s Handbook 6th Ed Chapt 18 McGraw Hill N Y Vital T J Grossell S S and Olsen P L Estimating Separation Efficiency 1984 Hydrocarbon Processing Dec 75 78 Bolles W L and Fair J R Improved Mass transfer Model Enhances Packed column Design 1982 Chem Eng July 12 109 116 Intalox High performance Separation Systems 1987 Norton Bulletin IHP 1 Frank O 1977 Chem Eng 84 6 Mar 14 111 128 May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 E229 Shortcut Distillation General Information Fenske Method PRO II contains shortcut distillation calculation methods for determining column conditions such as separations minimum trays and minimum reflux ratios The shortcut method assumes that an average relative volatility may be defined for the column The Fenske method is used to compute the separa tions and minimum number of trays required The minimum reflux ratio is determined by the Underwood method The Gilliland method is used to cal culate the number of theoretical trays required and the actual reflux rates and condenser and reboiler duties for a given set of actual to minimum reflux ra tios Finally the Kirkbride method is used to determine the optimum feed location The shortcut distillation model is a useful tool for preliminary design when properly applied Shortcut methods will not however work for all systems For highly non ideal sy
169. ns are much better than initial and endpoint specifications Since the solution of the entire system of two product sections is iterative and si multaneous it is possible that a poor specification in one section may result in a seeming problem for another section Usually there is a single specification which binds the system and prevents solution Inspection of the trial calculated results will often reveal the interactions of the specifications and hence the incompatibility For petroleum refinery heavy ends calculations the predicted fractionation indices may be evaluated in the light of typical values for such columns See Table 2 4 4 1 PRO II Unit Operations Reference Manual Shortcut Distillation 11 97 Section 2 4 Distillation and Liquid Liquid Extraction Columns Il 98 Shortcut Distillation Examination of the component distribution to the various product streams in the stream printout is useful for checking the component definition for rea sonableness For the most accurate simulation of crude units the standard cut ranges should be used Cut ranges may be broadened to reduce the simu lation cost however Table 2 4 4 2 illustrates the effect of changing the cut ranges on the product yields for a typical crude unit Table 2 4 4 2 Effect of Cut Ranges on Crude Unit Yields Incremental Yields from Base Base Case 1 Case2 Case3 Case4 o Case 5 Product Case Increase Increase Increase
170. nsfer coefficient Ao total exchanger area ATm mean temperature difference The simple heat exchanger model in PRO II may be used to simulate heat ex change between two process streams heat exchange between a process stream and a utility stream or to heat or cool a single process stream The simple model does not rigorously rate the exchanger i e pressure drops shell and tubeside heat transfer coefficients fouling factors are not calculated ll 106 Simple Heat Exchangers May 1994 Section 2 5 Heat Exchangers Figure 2 5 1 1 Heat Exchanger Temperature Profiles 1 Tin 1 Tin 2 Tout ee Temperature Temperature T T 2 Tin Distance Along Exchanger z Distance Along Exchanger z COUNTERCURRENT COCURRENT For countercurrent or cocurrent flows as shown in Figure 2 5 1 1 the appropriate expression for the mean temperature difference is the logarithmic mean i e For countercurrent flows l 1 3 AT epis T za os 3 Im For cocurrent flows l il 4 AT NNUS an To A lm T n T where ATim LMTD logarithmic mean temperature difference superscript 7 denotes one side of the heat exchanger superscript 2 denotes the other side of the heat exchanger In actual fact the flows are not generally ideally countercurrent or cocurrent The flow patterns are usually mixed as a result of flow reversals e g in ex changers with more than one tube or shell pass
171. nt between the vessel and the vapor phase of the fluid Avap area of vapor phase in vessel Tfluid temperature of fluid in the vessel at time t h heat transfer coefficient between the vessel and the liquid phase of the fluid Alig area of liquid phase in vessel PRO II Unit Operations Reference Manual II 247 Depressuring Unit Section 2 11 Il 248 Depressuring The gas is depressured isentropically using either a user defined isentropic ef ficiency value or the default value of 1 0 For each time interval the heat transfer from the vessel is calculated by using the Nusselt heat transfer corre lations The heat transfer coefficient between the vessel and the vapor phase of the fluid hy is determined using p 03K er Ny Phy 29 y r where ky thermal conductivity of vapor phase NGr dimensionless Grashof number Npr dimensionless Prandtl number hfac heat transfer coefficient factor 21 0 by default The Grashof and Prandtl numbers are given by the following relationships P p Be AT a Gr 2 Hu CP by 31 PRO A where B volumetric coefficient of thermal expansion 1 F 8c acceleration due to gravity y viscosity of vapor AT Twall Tfluid cpv heat capacity of vapor The heat transfer coefficient between the vessel and the liquid phase of the fluid hi is determined in a similar manner using the following relationships 1 3 32 _ 013k Ng Np hg 32 r h where kj thermal
172. ntropic constant entropy conditions The dew point may also be determined for the hy drocarbon phase or for the water phase In addition any general stream specifica tion such as a component rate or a special stream property such as sulfur content can be made at either a fixed temperature or pressure For the flash drum unit there are two other degrees of freedom which may be set by imposing external specifications Table 2 1 2 1 shows the 2 specification combinations which may be made for the flash unit operation Table 2 1 2 1 Constraints in Flash Unit Operation Flash Operation Specification 1 Specification 2 ISOTHERMAL TEMPERATURE PRESSURE DEW POINT TEMPERATURE V 1 0 PRESSURE V 1 0 BUBBLE POINT TEMPERATURE V 0 0 PRESSURE V 0 0 ADIABATIC TEMPERATURE FIXED DUTY PRESSURE FIXED DUTY ISENTROPIC TEMPERATURE FIXED ENTROPY PRESSURE FIXED ENTROPY TPSPEC TEMPERATURE GENERAL STREAM SPECIFICATION PRESSURE GENERAL STREAM SPECIFICATION May 1994 Section 2 1 Flash Calculations Valve Figure 2 1 2 1 Valve Unit Mixer Figure 2 1 2 2 Mixer Unit The valve unit operates in a similar manner to an adiabatic flash The outlet pressure or the pressure drop across the valve is specified and the tempera ture of the outlet streams is computed for a total duty specification of 0 The outlet product stream may be split into separate phases Both VLE and VLLE calculations are allowed for the valve unit One or more f
173. nual providing a reference source for the background behind the various PRO II calculation methods Whatis in This manual contains the correlations and methods used for the various unit This Manual operations such as the Inside Out and Chemdist column solution algorithms For each method described the basic equations are presented and appropri ate references provided for details on their derivation General application guidelines are provided and for many of the methods hints to aid solution are supplied Who Should Use For novice average and expert users of PRO II this manual provides a good This Manual overview of the calculation modules used to simulate a single unit operation or a complete chemical process or plant Expert users can find additional details on the theory presented in the numerous references cited for each topic For the novice to average user general references are also provided on the topics discussed e g to standard textbooks Specific details concerning the coding of the keywords required for the PRO II input file can be found in the PRO II Keyword Input Manual Detailed sample problems are provided in the PRO II Application Briefs Manual and in the PRO II Casebooks Finding What A Table of Contents and an Index are provided for this manual Cross you Need references are provided to the appropriate section s of the PRO II Keyword Input Manual for help in writing the input files PRO II Unit Operati
174. obability Yxi may be described by a Langmuir type adsorption expression Gif 2 ki 1 Gis j j 1 2 m Necomp k 1 2 a N oomp where fk fugacity of hydrate forming component k Cki adsorption constant Using equation 2 equation 1 then becomes ARER wea 3 i k The adsorption constant Cx is related to the spherical core cell potential by 1e Wir 2 4 Cy KT ee iT Je dr where k Boltmann s constant 1 38 x 10 erg K T temperature K W r spherical cell potential erg r radial coordinate A The spherical cell potential W is a function of the radius of the unit cell the coordination number of the cavity containing the gas molecule and sum of the interactions between the enclosed gas molecule and the water molecules in the lattice wall The Kihara potential between a single gas molecule and one water molecule in the lattice wall is given by I 202 Hydrates May 1994 Section 2 9 Utilities r 12 6 J 5a T r 4e 2 forr gt 20 r 20 r 20 D n forrs 20 5b where T Kihara potential ergs characteristic energy ergs g core radius A 0 20 collision diameter A Summing the gas water interactions over the entire lattice yields o 6 6 W r 2ez au ed n Z a4 s gt Re r R R r Re and r N N q 7 l iota pa NN 45 10 11 R R R R where z coordination number of cavity R cell radius When liquid water
175. of how the distillation models are solved This chapter also explains how the intermediate printout relates to the equa tions being solved All of the distillation algorithms in PRO II are rigorous equilibrium stage models Each model solves the heat and material balances and vapor liquid equilibrium equations The features available include pumparounds five con denser types generalized specifications and interactions with flowsheeting unit operations such as the Controller and Optimizer Reactive distillation is available for distillation and liquid extraction Automatic water decant is available for water hydrocarbon systems Modelling a distillation column requires solving the heat and material bal ance equations and the phase equilibrium equations PRO II offers four dif ferent algorithms for modeling of distillation columns m the Inside Out I O algorithm m the Sure algorithm m the Chemdist algorithm and m the ELDIST algorithm For electrolyte systems the Eldist algorithm is available and for liquid liquid ex tractors the LLEX algorithm should be used Eldist Chemdist and the LLEX also allow chemical reaction Eldist is used when equilibrium electrolytic reac tions are present Chemdist and LLEX allow kinetic equilibrium non electro lyte and conversion reactions to occur on one or more stages For most systems SimSci recommends using the I O algorithm When more than one algorithm can be used to solve a problem th
176. olumns For the CONVENTIONAL model Fenske relationships defining the column sections each section having two products are solved simultaneously thus the inter action of reflux between the sections is considered For the REFINE model each section is solved independently starting from the bottom This model closely approximates typical oil refinery columns in which total liquid draws are sent to side strippers and little if any liquid is returned to the next lower tray As the number of products increases the difficulty in definition of noncon flicting specifications also increases There are often upper and lower limits for each specification For example the total product rate cannot exceed the feed rate Furthermore for specifications such as ASTM TBP temperatures the selection of the components to represent the feed streams can be very im portant For example it would not be reasonable to attempt to separate ten components into six products etc Care should be exercised that the specifi cations define rates for all products either directly or indirectly For illustra tion consider the following example shown in Figure 2 4 4 4 Feed For this column four specifications are required Selection of two specifica tions each for products A and C would satisfy this requirement however it might not be sufficient to define stream B Therefore a better set of specifica tions would include values for all the products A B and C A
177. on Algorithms Section 2 10 To aid the user in selecting appropriate stepsizes a full diagnosis is printed when the maximum number of OPTIMIZER cycles is set equal to 2 In addi tion to the forward difference formula given above the derivatives are also calculated using backward differences and central differences The information shown in Table 2 10 5 1 is then displayed for each variable for the objective function and each specification and constraint Table 2 10 5 1 Diagnostic Printout Sign backward central forward orOor Effect none or low or high Maximum deviation percentage Current perturbation size value Suggested perturbation size value Unless a variable has no effect the first line displays the sign of the back ward central and forward derivatives If the maximum difference between the central derivative and forward or backward derivatives is greater than 196 it is reported on line 3 The perturbation size should be chosen so as to minimize this difference The current value of the absolute perturbation is reported on line 4 and a suggested perturbation calculated assuming that the accuracy of the flowsheet solution is 10 is printed on the last line Note that this value is only intended as a guideline the change in the maximum deviation should be monitored when the perturbation size is modified Note also that if the magnitude of a variable changes by several orders of magni tude the perturbation size de
178. on is met 104 PRO II Note For more information on specifying limits on the number of stages when running in design mode see Section 104 Countercurrent De canter of the PRO II Keyword Input Manual I Reference Scandrett H E Equations for Calculating Recovery of Soluble Values in a Countercurrent Decantation Washing System 1962 Extractive Metal lurgy of Aluminum 1 83 ll 164 Countercurrent Decanter May 1994 Section 2 7 Solids Handling Unit Operations Y E Dissolver General Information Development of the Dissolver Model Dissolution of solids into liquid solutions is a mass transfer operation which is widely used in the chemical industry in both organic as well as inorganic processes A unit operation that utilizes mass transfer controlled dissolution is the stirred tank dissolver The contents of the stirred tank dissolver are well mixed using an agitator and when it is operated in a continuous man ner the unit can be called a continuous stirred tank dissolver or CSTD The PRO II dissolver is of the CSTD type The dissolution of a solute from the solid particle into the surrounding liquid can be modeled as the rate of decrease in volume of the solid particle Pp vel Vl e Ah p aol 1 where Pp density of solid particle kg m Vp X volume of particle m Ap surface area of particle m liquid phase mass transfer coefficient kg m sec Py liquid d
179. on is not satisfied m The maximum number of iterations have been performed m Three consecutive controller iterations fail to reduce the specification error May 1994 Section 2 10 Flowsheet Solution Algorithms For controllers that are not inside other loops the above conditions cause an error message and all calculations are terminated For controllers inside recy cle or other loops the calculations are continued until the maximum number of iterations allowed for these outer loops has been performed If the control ler specification is still not met flowsheet solution then terminates PRO II Unit Operations Reference Manual Feedback Controller 1 225 Flowsheet Solution Algorithms Section 2 10 Multivariable Feedback Controller General The multivariable feedback controller MVC in PRO II allows control vari Information ables to be varied to satisfy an unlimited number of flowsheet specifications The specifications can include stream and unit operating conditions as well as CALCULATOR results The control variables can be defined as stream or unit operating conditions thermodynamic properties and CALCULATOR results The number of variables must equal the number of specifications If desired upper and lower bounds as well as maximum step sizes can also be included for each control variable Figure 2 10 4 2 1 shows an example of a simple MVC application There are three input streams S1 S2
180. on problems made up of process modules introducing some aspects of equation oriented strategies This new concept covers several techniques to improve the performance of strictly sequential modular solvers including Optimal tear streams selection Controlled simulations Unit grouping Stream referencing Flowsheet specifications All stream tear stream convergence Linear and nonlinear derived models Inside out strategies Simple rigorous iterative procedures two tier algorithms PRO II applies several simultaneous modular techniques when solving proc ess flowsheets Overviews of optimal tear stream techniques can be found in section 2 10 2 Calculation Sequence and Convergence and the use of Con trollers in simulations is reviewed in section 2 10 4 Flowsheet Control Sev eral other strategies inside out all stream convergence Simple rigorous are used to solve individual models 33 44 ES PRO II Note Stream referencing which is very useful in enhancing conver gence properties of recycles involving only heat exchangers thermal recycles is described in Chapter 33 Reference Streams of the PRO II Keyword Input Manual See Chapter 44 Specs Constraints and Objectives for information on flowsheet specifications Process Unit PRO II uses Unit Grouping to allow improved simulation efficiency Unit Grouping grouping is a special technique that simultaneously solves groups of units that are closely associated One example of t
181. on the zone boundaries No zone should account for more than 20 of the total heat exchanger duty therefore a minimum of 5 zones is re quired PRO II may use up to a maximum of 25 zones The design equation for the heat exchanger is given by Q U ALMTD H H 1 om o tones tout in For a total of n zones LMTDzones is calculated from the individual zones val ues as a weighted LMTD LMTD ones E E 2 Q LMTD i l where Q total exchanger duty Qi heat duty in zone i LMTD Aogarithmic mean temperature difference for zone i The LMTD values for the individual zones are computed using the tempera tures of the streams entering and leaving each zone PRO II Unit Operations Reference Manual Zones Analysis l 109 Heat Exchangers Section 2 5 For countercurrent flows in zone i 1 1 3 fat J r i T 3 inj out i out i inj LMTD i 1 Tini out i T outi inj For cocurrent flows in zone i 1 1 4 T a m inj ini out i out i LMTD Tj i ind De touti For all the heat exchanger specifications described above except for the mini mum internal temperature approach the zones analysis is independent of the calculation of the overall heat duty In these cases by default the LTMD zones value is calculated and reported after the equations for the exchanger have been solved but is not used in heat transfer calculations The user may how ever specify that the zones analysis
182. ond liquid phases respectively The new equations which are identical in form to those listed in the basic al gorithm section above equations 22 26 will not be repeated here The K values which are used in the VLE equations are calculated by performing a LLE flash That is the K value is evaluated at the composition of one of the liquid phases produced by the LLE flash Chemdist uses the K value de rivatives with respect to the two liquid phases the chain rule and the defini tion of a total derivative to calculate the derivatives of the VLE equation with respect to the bulk liquid flow and composition That is the bulk liquid flows are subject to the all of the constraints imposed by the LLE equations The equations are solved in a two step approach After initialization and cal culation of the Jacobian matrix the Newton Raphson algorithm calculates new values for the iteration variables X Y L V T i The resulting tray temperatures and composition of the bulk liquid phases are used in perform ing liquid liquid equilibrium flash calculations If a single liquid phase ex ists the calculations proceed as in the basic algorithm If a second liquid phase is detected the liquid compositions of the two liquid phases are used to calculate the K values and the derivatives with respect to each liquid phase Using the chain rule and the definition of a total derivative these com position derivatives are used to calculate the derivat
183. ondensate loading 50 bbI MMSCF The friction pressure drop term is computed from equations 2 or 6 where the friction factor used is obtained from the Moody charts The elevation term is calculated using equations 3 or 7 while the acceleration term is given by equation 24 The liquid holdup term HL is given by H 1 H 31 A 32 H l e R l i 33 A 2 314 IN A N C B 0 0814 i 0 05554 i Rar p R 1 E Vo 35 Ve 2 2 Pin Vom 36 g o Pz Po 2 amp pj p D 37 D o 9 do 0 617 9 Vw 38 Be qo 0 617 q where o surface tension qo in situ oil volumetric flowrate qw in situ water volumetric flowrate qm mixture volumetric flowrate Np diameter number l or L and g or G refer to the liquid and gaseous phases May 1994 Section 2 3 Pressure Calculations Oliemens This method uses the Eaton correlation previously described above to calculate the liquid holdup The friction factor is obtained from the Moody diagrams and the friction pressure term is computed using dP dL fG ie 8 d gPor um 39 G qp t qp 1 Bj A 40 Porr7 Pp d Bj 41 By Hy Hy 42 where G mass flux Hins no slip liquid holdup Poti Oliemens density deg effective diameter A pipe cross sectional area Py fluid density p1Hr pgHe I or L and g or G refer to the liquid and gas phases respectively The acceleration term is set equal to
184. ons PRO II will determine the drum diameter and width required for a given pressure drop Calculation As a solid liquid mixture is filtered a layer of solid material known as the Methods filter cake builds up on the filter surface Vacuum filtration is used to drain liquid through the filter cake An important characteristic of the filter cake is its permeability The permeability is defined as the proportionality constant in the flow equation for laminar flow due to gravity through the bed The per meability is a function of the characteristics of the cake such as the spheric ity and size of the cake particles and the average porosity of the cake and is given by K g d e4 1 where K permeability of filter cake 8c acceleration due to gravity dp diameter of cake particle average porosity of filter cake A B are constants Q The values of the constants A and B in equation 1 are a function of 0 the ratio of the particle sphericity to the cake porosity A and B are given by For gt 1 5 A exp 2 49160 0 2099 B exp 1 74456 0 20850 2 3 PRO II Unit Operations Reference Manual Rotary Drum Filter 1 153 Solids Handling Unit Operations Section 2 7 For 1 5 A exp em es B exp 1 1069 SUE 4 5 gt The pressure drop across the filter cake is then given by 2Lu Sk 6 AP ms oD WA where L liquid volumetric flowrate through the cake
185. ons Reference Manual Introduction Int 1 Symbols Used in This Manual Symbol Meaning em Indicates a PRO II input coding note The number beside the symbol indicates the section in the PRO II Keyword Input Manual to refer to for more information on coding the input file w Indicates an important note RR Indicates a list of references Int 2 Introduction May 1994 This page intentionally left blank May 1994 Section 2 1 Flash Calculations n EX Flash Calculations PRO II contains calculations for equilibrium flash operations such as flash drums mixers splitters and valves Flash calculations are also used to determine the thermodynamic state of each feed stream for any unit operation For a flash calcu lation on any stream there are a total of NC 3 degrees of freedom where NC is the number of components in the stream If the stream composition and rate are fixed then there are 2 degrees of freedom that may be fixed These may for example be the temperature and pressure an isothermal flash In addition for all unit opera tions PRO II also performs a flash calculation on the product streams at the outlet conditions The difference in the enthalpy of the feed and product streams constitutes the net duty of that unit operation PRO II Unit Operations Reference Manual Il 3 Flash Calculations Section 2 1 i PAKI Basic Principles Figure 2 1 1 1 Three phase Equilibr
186. ope see Section 2 9 1 Phase Envelope of this manual module be used to generate a phase diagram since that model can compute a complete phase diagram including the critical point and correctly finds both solutions when retrograde phenomena are present Many systems commonly encountered in natural gas applications exhibit a phase behavior known as retrograde condensation That is above the criti cal pressure in the two phase region it is possible for the condensate to va porize as the temperature is decreased For such systems it often is possible to obtain two different valid solutions for the dew point temperature at a fixed pressure depending on how the curves are initialized and the size of the temperature increments Experience has shown that the Peng Robinson PR K value generator is somewhat more stable when predicting dew points in the retrograde region than is the Soave Redlich K wong equation of state Figure 2 9 2 1 Phenomenon of Retro grade Condensation Cricondenbar Region of Retrograde Condensation Constant Cricondentherm Liquid Fractions l l i i i PRO II Unit Operations Reference Manual Heating Cooling Curves 11 193 Utilities Section 2 9 VLE VLLE and Decant Considerations Water and Dry Basis Properties GAMMA and KPRINT Options The HCURVE module currently does not perform rigorous liquid liquid equilibrium calculations Systems exhibiting two liquid ph
187. or A positive blending factor indicates additive blending of the stream while a negative factor causes subtracting a stream to create the com bined feed In this way the careful user can create a combined feed of al most any desired composition Note that true mass balance between the Stream Calculator and the rest of the flowsheet is achieved only when all feed streams have a blending factor of unity Blending factors greater than unity cause a virtual creation of mass flow while factors less than unity cause a virtual removal of mass Note this adjustment represents a discontinuity between the mass contained in the individual feed streams and the single combined feed that is created There is no accounting for this gain or loss and any products of such a Stream Cal culator that feed back into the flowsheet cause the flowsheet to be out of mass balance However whenever feed streams are present mass balance is preserved across the Stream Calculator i e the products and the combined feed are kept in mass balance The stream splitting capability of the Stream Calculator allows dividing the combined feed into two product streams of virtually any desired composi tion This is a brute force black box operation since equilibrium and ther modynamic constraints such as azeotrope formation are not applied This capability is useful when fast non rigorous modeling is desired or expedient For example assume a flowsheet under cons
188. or a simple column Selection of the separation key components is a primary importance for the Un derwood method It is extremely important that the light and heavy keys be dis tributed in both products with their distribution defining a sharp separation This may mean that the keys must be split with middle component s which dis tribute loosely in both products allowed to float as required to meet the sharp separation of the keys Incorrect selection of keys can give poor and meaningless results moreover this can result in failure of the Underwood calculations As a general rule of thumb the more nonideal a column the more the Underwood method will under predict the reflux requirements The column heat requirements will be predicted based on the condenser type selected For subcooled condensers it is necessary to define the temperature to insure that the subcooling effect is considered For type 2 condensers mixed phase the separation into vapor and liquid products should not be attempted in the shortcut model since this would re quire two specifications for a flash drum Separation into liquid and vapor products is accomplished by sending the shortcut overhead product mixed phased to an equilibrium flash drum calculation When the column overhead is known to contain water it is important that the estimated overhead product rate include both water and hydrocarbon product While any type of product specification may be used
189. or a LNG cell Outlet temperature Tout Cell duty Sqcell Phase of outlet stream Hot cold stream temeprature approaches Minimum internal temeprature approach MITA Note The last three specifications listed above outlet phase temperature ap proach and MITA can only be accomplished using a feedback controller unit May 1994 Section 2 5 Heat Exchangers Figure 2 5 4 2 LNG Exchanger Solution Algorithm Figure 2 5 4 2 shows the algorithm used to solve an LNG exchanger Use equation 1 for all cells with specified outlet T or P Set T of unspecified cell s based on overall energy balance Satisfy MITA phase Any celis approach T specs with MITA prase Tcuc E Tspec lt TOL Calculate T of or approach specs unspecified cells Calculate exchanger duty PRO II Unit Operations Reference Manual LNG Heat Exchanger I 123 Heat Exchangers Section 2 5 Zones Analysis 2 I 124 LNG Heat Exchanger When phase changes occur within the LNG heat exchanger PRO II can per form a Zones Analysis to locate and report any internal temperature pinches or crossovers For the LNG exchanger the UA and LMTD for the ex changer are calculated using the composite hot and cold streams Note See Section 2 5 2 Zones Analysis for more details May 1994 Section 2 6 Reactors VERUS ES Reactors PRO II offers the following chemical reactors Conversion
190. or unequal baffle spacing effects PRO II Unit Operations Reference Manual Rigorous Heat Exchanger I 117 Heat Exchangers Section 2 5 The stream analysis method proposed in 1984 by Willis and Johnson is an iterative analytical method At each iteration the crossflow resistance Re the window flow resistance Rw the tube to baffle resistance Rt b the shell to baffle resistance Rs p the leakage resistance Rj the flowrate through the windowed area Ww the crossflow pressure drop APc the window pressure drop APw and the crossflow fraction Fe are calculated as follows R function D tube bank layout p S 15 0 68565 16 1 9exp 2 _ Sin Ry 2 20S 17 R y func tube to baffleclearance tube to baffle leakage area p 18 R y 7 func shell to baffleclearance shell to baffle leakage area p p R func Reo Ro 19 Ww 20 W 05 T R k Ri AP R W 21 AP RW 22 0 5 2 AP R 23 gT W where Sc crossflow area Dc crossflow equivalent diameter Iterations are stopped once the value of Fc meets the following criterion er Foie 24 F lt 0 01 c iter ll 118 Rigorous Heat Exchanger May 1994 Section 2 5 Heat Exchangers The shellside end space pressure drops at the inlet and outlet of the ex changer APs in and APs out and the actual shellside pressure drop APss are then calculated using the equations Z 25 AP in Ry in Win Ry in functio
191. osition of the solute in a liquid solution containing the solvent compo nent Solubility is a function of temperature and is calculated from either the van t Hoff equation or user supplied solubility data The solubility is rigorously calculated if electrolyte thermodynamic methods are used Crystallization can occur only in a supersaturated liquid solution A supersaturated liquid is one in which the solute concentration exceeds the equilibrium solubility at the crystal lizer temperature Supersaturation is generally created by cooling the liquid and or evaporation of the solvent Additionally for crystallization systems where evaporation of solvent occurs the vapor phase and liquid solution satisfy vapor liquid equilibrium PRO II Note For more information on using the van t Hoff and user supplied solubility methods see Section 26 1 van t Hoff Solubility and 26 2 User sup plied Solubility in the PRO II Keyword Input Manual The quantity of crystals formed depends on the residence time in the crystallizer and is determined by the kinetics of the crystallization process Crystals are gen erated from supersaturated solutions by formation of nuclei and by their growth The primary driving force for both nucleation and crystal growth is the degree of supersaturation In addition nucleation is also influenced by mechanical distur bances such as agitation and the concentrations and growth of solids in the slurry These rate relationship
192. ous pressure drop correlation methods and also allows for the input of user defined correlations by means of a user added subroutine An energy balance taken around a steady state single phase fluid flow system results in a pressure drop equation of the form 1 acc dP dL dP dD dP dD dP dL total friction elevation acceleration The pressure drop consists of a sum of three terms m the reversible conversion of pressure energy into a change in elevation of the fluid m the reversible conversion of pressure energy into a change in fluid acceleration and m the irreversible conversion of pressure energy into friction loss May 1994 Section 2 3 Pressure Calculations The individual pressure terms are given by dP dD 7 fov 2g d 2 dL dL gpsinQ g 3 dP dD pv g dv dL 4 where land g refer to the liquid and gas phases the pressure in the pipe the total length of the pipe d the diameter of the pipe friction factor p fluid density v fluid velocity 8c acceleration due to standard earth gravity g acceleration due to gravity d angle of inclination dP dL total pressure gradient dP dL r friction pressure gradient dP dL e elevation pressure gradient dP dL acc acceleration pressure gradient For two phase flow the density velocity and friction factor are often different in each phase If the gas and liquid phases move at the same velocity then the
193. pacity is computed by using 95 and 85 of the valve capacities respectively The tray pressure drop is cal culated by the Fair method for sieve trays and by the method of Bolles for bubble cap trays Capacity The capacity of a trayed column is defined in terms of a vapor flood capacity factor at zero liquid load CAFo Nomographs are used to obtain the capacity factors based on tray spacing and vapor density PRO II Unit Operations Reference Manual Column Hydraulics I 73 Distillation and Liquid Liquid Extraction Columns Section 2 4 Foaming on trays is taken into account by using a so called system factor Table 2 4 3 2 shows the system factors to be used to correct the vapor capac ity factors Table 2 4 3 2 System Factors for Foaming Applications System Absorbers over 0 F Absorbers below 0 F Amine Contactor Vacuum Towers Amine Stills Amine Regenerator H2S Stripper Furfural Fractionator Top Section of Absorbing Type Demethanizer Deethanizer Glycol Contactors Glycol Stills and Glycol Contactors in Glycol Synthesis Gas CO Absorber CO Regenerator Caustic Wash Caustic Regenerator Foul Water Sour Water Stripper Alcohol Synthesis Absorber Hot Carbonate Contactor Hot Carbonate Regenerator Oil Reclaimer Factor 85 80 80 85 85 85 85 85 50 65 80 85 65 60 35 85 90 10 For sizing an existing trayed column or for calculating the percent of floo
194. pliers or shadow prices see the following section PRO II Unit Operations Reference Manual Flowsheet Optimization 11 237 Flowsheet Solution Algorithms Section 2 10 L If none of the above conditions are satisfied the optimizer continues to the next cycle If at least one of conditions 1 to 4 is satisfied the following con ditions are also tested 5 Is the relative error for each specification less than 0 001 or the user de fined value RTOL or ATOL for each specification 6 Isthe relative error for each constraint less than 0 001 or the user defined value RTOL or ATOL for each constraint If both 5 and 6 are satisfied the OPTIMIZER terminates with the message SOLUTION REACHED If the relative error for any specification or con straint is greater than the required tolerance the OPTIMIZER will terminate with SOLUTION NOT REACHED The optimization problem may also fail for one of the following reasons m Another unit in the flowsheet may fail to converge m The number of column controller or recycle loops which is allowed is insufficient m The optimization problem is infeasible Postoptimality Analysis Shadow Prices Once the flowsheet optimization has converged and the appropriate operating conditions have been determined the shadow prices or Lagrange multipliers can be used to assess the sensitivity of the objective function to the specifica tions constraints and bounds These values which are calculate
195. presents stream exergy availability at Modified Environmental State computed as follows B MES H Tzero X Si xi log Xi where H total stream enthalpy Si entropy of component i xi mole fraction of component i in the stream These calculations are carried out at the same conditions used to compute B EVS VAPOR E T This function is equal to B EXS B TES E P This function is equal to B EXS B EVS VAPOR E M This function is equal to B EXS B MES For unit operations the availability is calculated as follows DELTA B Y B EXS feeds X B EXS products W EXT 2 The external work done by the unit operation and the heat duty of the unit op eration are also given in the exergy report References ea 1 Venkatesh C K Colbert R W and Wang Y L Exergy Analysis Using a Process Simulation Program presented at National Converence of the Mexican institute of Chemical Engineers October 17 1980 2 de Nevers Noel and Seader J D Mechanical Lost Work Thermodynamic Lost Work and Thermodynamic Efficiencies of Processes presented at 86th AIChE National Meeting Houston Texas April 1979 PRO II Unit Operations Reference Manual Exergy 207 Utilities Section 2 9 This page intentionally left blank 1 208 Exergy May 1994 Section 2 10 Flowsheet Solution Algorithms EAD Flowsheet Solution Algorithms PRO II is able to find all recycle stre
196. r fraction of minimum trays is selected as the mid point for a table of trays and reflux Based on the corresponding reflux ratio the column top con ditions are calculated and the associated condenser duty determined The reboiler load is computed from a heat balance Note that the selection of the proper condenser type is vital to accurate calculation of heat duties Also the condenser type selected will have no effect whatsoever on the separations predicted Figure 2 4 4 2 shows the condenser types available in PRO II for the shortcut distillation model Water may be decanted at the condenser OVHD LDRAW a Partial b Mixed c Bubble Point d Specified Temperature e Subcooled PRO II Unit Operations Reference Manual Shortcut Distillation 11 89 Section 2 4 Distillation and Liquid Liquid Extraction Columns Distillation Models Figure 2 4 4 3 Shortcut Distillation Column Models Il 90 Shortcut Distillation There are two shortcut distillation models available in PRO II as shown in Fig ure 2 4 4 3 In the first method CONVENTIONAL which is the default total reflux conditions exists in the column In the second method REFINE the shortcut col umn consists of a series of one feed two product columns starting with the bottom section In this model there is no reflux between the sections Conventional Simple Columns Simple columns are defined a columns in which a single feed location may be defined
197. r the flowsheet in Figure 2 10 5 1 for example the COLUMN is solved repeatedly until the OPTIMIZER has determined the optimal feed tray loca tion These iterative loops are referred to as cycles Frequently flow sheets to be optimized also contain recycle streams Therefore each optimization cycle may involve a number of recycle trials Likewise any column must be converged in a number of iterations at every flowsheet pass This terminology is maintained throughout the PRO II program and all supporting documentation Cycles Number of optimizer steps see section on Solution Algorithm below Trials Number of recycle trials in each flowsheet solution Reset to zero after each flowsheet solution Iterations Number of column iterations per column solution For both columns and recycle loops the maximum number of trials and itera tions allowed should be increased to prevent flowsheet failure While the de faults may be adequate when solving the basecase the OPTIMIZER may cause the flowsheet to move to a new state where the columns and recycle loops are more difficult to converge PRO II Unit Operations Reference Manual Flowsheet Optimization 1 233 Flowsheet Solution Algorithms Section 2 10 Recommendations When solving an optimization problem the following points should be noted Always solve the base case separately Check the results carefully to ensure that the problem setup and solution are exa
198. r the side draw products are also pro vided by the user PRO II Unit Operations Reference Manual Rigorous Distillation Algorithms I 65 Distillation and Liquid Liquid Extraction Columns Section 2 4 For columns with condensers it is important to provide an estimate of the re flux either as the liquid from tray one or the vapor leaving tray two the top product plus reflux For simple columns with liquid or moderately vapor ized feeds constant molar overflow may be assumed and the vapor from the reboiler tray 6 assumed to be the same as the tray 2 vapor The reboiler va por may also be provided by giving an estimate of the liquid leaving the tray above the reboiler For columns in which the feed has high vapor rate there will be a sharp break in the vapor profile at the feed tray For such columns at least four va por rates should be provided top tray feed tray tray below feed and bottom tray For columns in which the reflux is to be used as a performance specification the reflux should be set at the specification value in the estimate enhancing convergence The effect of side draws must be considered for complex fractionators It is usually safe practice for such columns to add the side product rates and multi ply by two to estimate a top reflux rate For columns having steam feeds the steam flow must be included in the va por estimates An estimate of the decanted water should also be included with the product informat
199. rations Reference Manual Rigorous Heat Exchanger I 121 Heat Exchangers Section 2 5 EEFI LNG Heat Exchanger General Information Calculation Methods I 122 LNG Heat Exchanger PRO II contains a model for a LNG Liquified Natural Gas heat exchanger This type of exchanger is also called a Cold Box and simulates the ex change of heat between any number of hot and cold streams An advantage of this type of exchanger is that it can produce close temperature approaches which is important when cooling close boiling point components Typically LNG exchangers are used for cryogenic cooling in the natural gas and air separation industries The LNG exchanger is divided into hot or cold cells representing the indi vidual cross flow elements Cold cells represent areas where streams are cooled while hot cells represent areas where streams are heated The follow ing assumptions apply to the LNG heat exchanger m Each LNG exchanger must have at least one hot and one cold cell m The exchanger configuration is ignored m At least one cell does not have a product specification and all unspeci fied cells leave at the same temperature Equation 1 applies to every cell in the LNG exchanger q i H out Hi mc Tout E Tin 1 where d4cell heat transferred in exchanger cell Hou enthalpy of stream leaving the cell Hin enthalpy of stream entering the cell The following specifications may be set f
200. re 2 1 1 2 shows the solution algorithm for a two phase isothermal flash i e where both the system temperature and pressure are given The follow ing steps outline the solution algorithm 1 The initial guesses for component K values are obtained from ideal K value methods An initial value of V F is assumed 2 Equations 9 and 10 are then solved to obtain xi s and yi s 3 After equation 12 is solved within the specified tolerance the composi tion convergence criteria are checked 1 e the changes in the vapor and liquid mole fraction for each component from iteration to iteration are calculated Oirer 7 Vire 13 Yi lt TOL PRO II Unit Operations Reference Manual Basic Principles Il 5 Flash Calculations Section 2 1 Figure 2 1 1 2 Flowchart for Two phase T P Flash Algorithm Given zi feed mole frac T P temp pres F total feed rate Set initial value of V F Calculate ideal Ki s ITER 2 ITER 1 Calculate zi Ki 1 Y 1 yi Ki xi xi Calculate Ki s Calculate Lyi Xxi Calculate composition changes from one iteration step to the next Ay YurER VurER 1 AX 2 XirER ITER Check if maximum number of flash iterations have been exceeded Il 6 Basic Principles May 1994 Section 2 1 Flash Calculations Figure 2 1 1 2 continued Flowchart for Two phase T P Flash Algorithm Are Ayil yi and Apply damping l xil xi s toX s y s TOL Check VLE convergenc
201. ream 2 is to be varied by a CONTROLLER in order to achieve a certain concentration of A in the feed to the reactor Reactor Unit 3 Heat Exchanger Unit 2 me I Flash Drum Unit 4 A In this example the controller would normally be placed inside the recycle loop after unit 1 Here the CONTROLLER adjusts the flowrate of stream 2 to achieve the desired concentration in stream 3 The recycle loop is then solved to obtain a new value for the recycle flowrate This configuration is effective when a good initial estimate for stream 4 is available If the initial estimate of the flowrate of stream 4 is unavailable positioning the controller inside the recycle loop may cause the flowrates of stream 2 calculated by the controller to change significantly from one controller solution to the next This in turn causes the recycle loop to experience difficulties In this situ ation it would be more appropriate for the controller to be the outermost loop allowing the recycle loop to solve and generate an estimate for the flowrate of stream 4 prior to any controller action By default PRO II prints convergence information at each controller itera tion The controller may fail to converge under the following conditions m The specification is not affected by the control variable m The control variable is at the user specified maximum or minimum value and the specificati
202. reams The resultant combined feed then serves as the sole reference of feed stream data for all splitting and synthesis factors that refer to feed data For splitting cal culations the FOVHD and FBTMS factors refer to the component composi tions stored in the combined feed For synthesis calculations the FPROD factors refer to the component compositions stored in the combined feed The FEED statement allows the user to supply a single feed blending factor for each feed stream Each such factor is a relative scaling factor that 1s used to multiply the total flowrate of its respective feed stream All the feed streams then are blended together to yield the combined feed stream that has total rate dictated by the feed blending factors The proportion of each com ponent in the combined feed is the result of proportional blending based on the fraction of each component in the original individual feed streams PRO II Unit Operations Reference Manual 11 183 Stream Calculator Section 2 8 Stream Splitting Considerations ll 184 Stream Calculator It is important to remember that feed blending always occurs whenever two or more streams feed the Stream Calculator All streams that do not have a feed blending factor supplied by the user assume a blending factor of unity This means each such stream is blended at exactly 100 of its rate in the flowsheet The Stream Calculator allows the user to assign any value to each feed blend ing fact
203. reviously for compressors The calculations however pro ceed in the reverse direction to the compressor calculations The Mollier chart Figure 2 2 2 1 plots the pressure versus the enthalpy as a function of entropy and temperature This chart is used to show the methods used to calculate the outlet conditions for the expander as follows P Pressure H Enthalpy m A flash is performed on the inlet feed at the higher pressure P1 and tem perature T1 using a suitable K value and enthalpy method and a suit able entropy calculation methods The entropy S1 and enthalpy H1 are obtained and the point P1 T1 S1 H1 is obtained m The constant entropy line through S is followed until the lower user specified outlet pressure is reached This point represents the tempera ture T2 and enthalpy conditions H2 for an adiabatic expander efficiency of 10096 The adiabatic enthalpy change AHaa is given by AH H H 1 m Ifthe adiabatic efficiency Yaa is given as a value less than 100 the actual enthalpy change is calculated from AH AH Yad 2 PRO II Unit Operations Reference Manual Expander Il 25 Isentropic Calculations Section 2 2 Il 26 Expander m The actual outlet stream enthalpy is then calculated using H H AH 3 m Point 3 on the Mollier chart representing the outlet conditions is then obtained The phase split of the outlet stream is obtained by performing an equilibrium flash at
204. rium 11 169 Distillation rigorous Il 46 Chemdist algorithm Il 56 ELDIST algorithm Il 69 general column model Il 47 1 0 algorithm Il 50 initial estimate generators IEGs Il 65 reactive distillation Il 60 Distillation shortcut See Shortcut distillation Dryer Il 152 E ELDIST See Distillation rigorous Entropy thermodynamic generators Il 18 Equilibrium unit operations Il 12 flash drum Il 12 mixer Il 13 splitter Il 14 Index Idx 1 valve Exergy Expander efficiency adiabatic Mollier chart F Feedback controller recommendations for use typical application Filtering centrifuge calculation methods Flash calculations See also Equilibrium unit operations MESH equations Flash drum See Equilibrium unit operations Flowsheet control Flowsheet optimization See Optimizer Flowsheet solution algorithms tear streams Free energy minimization reactor See Reactors Gibbs Freezer G General reactor conversion reactor Gibbs reactor H HCURVE DBASE option GAMMA option output Retrograde condensation Using PDTS with Heat exchangers See also LNG heat exchangers See also Rigorous heat exchangers See Simple heat exchangers See also Zones analysis I Initial estimate generators IEGs See Distillation rigorous Isentropic calculations See Compressor See also Expander Isothermal flash calculations Newton Raphson technique solution algorithm flowsheet Idx 2 Index Il 13 11 206 Il 25 Il 26 Il 25 Il 222
205. rther minimize Gibbs free energy A Fibonacci search procedure is applied when A is close to zero When a Fibonacci search is performed the thermophysical properties of the reactor mixture can be either based on the same properties from the final result of the previous iteration or updated at each searching step of a new The convergence criterion is based on the relative or absolute change of Gibbs free energy and the relative change of component product rate be tween two consecutive iterations c gt s if c g 10 Or eue ri lt if g lt 3 ge and 0 of j h D lt if n n gt 0 01 a and nO nf jp jr pO 1 e lt if nip nj 0 016 ip The variable 6 is the convergence tolerance which is defaulted to 1 0E 4 and can be specified by the user The precision limit for a component product flowrate in any phase is 0 016 For any change in the product rate less than this value the solution will be considered to be converged PRO II Unit Operations Reference Manual Gibbs Reactor 1 139 Reactors Section 2 6 LI l 140 Gibbs Reactor Phase Split When a fluid phase condition of either vapor liquid vapor liquid liquid liq uid or vapor liquid liquid is specified for the reactor the Gibbs free energy of fluid components is calculated based on the specified fluid phases On the other hand if the fluid phase is unknown or not specified for the reactor pha
206. s a general rule it is best that specifications omissions be limited to the top stream May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 Specifications may be grouped into two general categories m Bulk properties Gravities Rates mole volume weight m Intensive properties ASTM TMP Distillations Component rates purities Special properties As a general rule fractionation indices may be defined in conjunction with bulk properties but will not work well when used with intensive properties For intensive properties the additional flexibility of allowing PRO II to cal culate the Fenske trays is highly desirable The nature of the Fenske calculations necessitates judgment when using specifications such as ASTM TBP distillation points End points and initial points may be distorted by the Fenske model because of the infinite reflux assumption resulting in trimming of the stream tails initial points too high end points too low Moreover the component selection may also greatly affect the initial and end points For these reasons it is recommended the 596 and 9596 points be chosen in lieu of initial and end points Refinery Heavy Ends Columns The second model is extremely useful for prediction of yields and analyzing data for crude units vacuum units cat fractionators bubble towers etc There are generally two possible situations when dealing with such columns a Yields are to be pred
207. s are normally expressed as power law expres sions which are similar to equations for power law kinetics used for chemical re actions The constants in the two rate equations are the nucleation rate constant and growth rate constant The heat effect associated with the crystallization process is obtained from the in put value of the heat of fusion of the solute component This along with the en thalpies of the feed and product streams will determine the heating cooling duty required for the crystallizer This duty is generally provided by an external heat exchanger across which a AT is maintained The feed consisting of the fresh feed and recycled product slurry is circulated through the heat exchanger to the crystallizer If the external heat exchanger option is not turned on in the input file the duty is assumed to be provided by an internal heater cooler PRO II Unit Operations Reference Manual Crystallizer 1 171 Solids Handling Unit Operations Section 2 7 Figure 2 7 6 1 Crystallizer Crystallization Kinet ics and Population Balance Equations Il 172 Crystallizer Heat Duty Q r OVHD Product E Crystallizer BTMS Product B Recirculation Slurry All crystallizers have some degree of mixing supplied by an agitator and or pum paround The limiting case is ideal mixing where conditions in the crystallizer are uniform throughout and the effluent conditions are
208. s given in Figure 2 6 5 1 FEED PRODUCTS mm FLOWRATE FLOWRATE q TP V Figure 2 6 5 1 Continuous Stirred Tank Reactor t l COOLANT COOLANT IN OUT Design Principles The steady state conservation equations for an ideal CSTR with M inde pendent chemical reactions and N components species can be derived as Mass balance M 1 i l Energy balance N N M 2 Fs AT Fy HT CAH R V Q 0 jel jel i l where Cj exit concentration of T component Fizz mole rate of component j in product Fy mole rate of component j in feed P reactor pressure PRO II Unit Operations Reference Manual Continuous Stirred Tank Reactor CSTR II 141 Reactors Section 2 6 Qij Sstoichiometric coefficient of jth species for ith reaction volume of the reacting phase Ri rate of ith reaction H T molar enthalpy of product H Tt molar enthalpy of feed Tf feed temperature T reactor temperature AHi molar heat of reaction for the ith reaction Q heat removed from the reactor In PRO II only power law models for kinetics are provided However any kinetic model can be introduced through the user added subroutines feature in PRO II For further details refer to Chapter 7 of the PRO II User added Subroutines User s Manual The resulting general expression for the rate of the ith reaction is El a 3 R A exp a II cH jel where Ai Arrhenius frequency factor Ei activation ener
209. scribed in Section 1 2 9 Electrolyte Mathematical Model Basic Algorithm Column mesh equations are solved by a Newton Raphson algorithm in the outer loop while liquid phase speciation along with K value computations are handled by the inner loop as shown in Figure 2 4 2 1 Figure 2 4 2 1 ELDIST Algorithm Schematic Main ELDIST Initial Estimate Routine TPLVXY Generator IEG T P L V X Y Outer Newton Raphson Loop Same as CHEMDIST T P L V X Y X Xro K s and Derivatives Inner Speciation Loop OLI Method Inner Speciation Loop Input to the inner loop model are temperature pressure and component mole fractions for liquid and vapor phase Temperature pressure and liquid phase mole fractions are needed for speciation calculations and for computation of liquid phase fugacities Vapor phase mole fractions along with the above in formation are needed for K value and K value derivatives computations To better describe the liquid phase speciation concept consider the aqueous system of components H20 CO and NaCl If NaCl precipitation is not al lowed then there are eight unknowns for a given system These are Molesuoo Mion MouioN MHcosION MNAION McLion and M coeAQ M is molality moles per kg solvent of a component or an ion PRO II Unit Operations Reference Manual ELDIST Algorithm I 69 Distillation and Liquid Liquid Extraction Columns Section 2 4 There are three independ
210. se split trials can be performed to evaluate the number of fluid phases in the reactor The starting iteration number and the frequency of phase split trial can be adjusted by the user In each phase split trial a new fluid phase is added to the current fluid phases If the Gibbs free energy is reduced as a result of adding this new phase the new fluid phase is accepted The reactor modeling generally follows the algorithm described in the papers of Gautam et al 1979 and White et al 1981 Additional information can be found in the book by Smith 1991 References 1 Gautam R and Seider W D 1979 Computation of Phase and Chemical Equilibrium Part I AIChE J 25 991 999 2 Gautam R and Seider W D 1979 Computation of Phase and Chemical Equilibrium Part II AIChE J 25 999 1006 3 White C W and Seider W D 1981 Computation of Phase and Chemical Equilibrium Part IV AIChE J 27 466 471 4 Smith W R and Missen R W 1991 Chemical Reaction Equilibrium Analysis Theory and Algorithm Krieger Publication Company Malabar Florida May 1994 Section 2 6 Reactors PECTUS NN Continuous Stirred Tank Reactor CSTR The Continuous flow Stirred Tank Reactor CSTR is a commonly used model for many industrial reactors The CSTR assumes that the feed is in stantaneously mixed as it enters the reactor vessel Heating and cooling duty may be supplied at user s discretion A schematic of a CSTR i
211. separa tion to vapor and liquid products being accomplished in an ensuing flash drum Troubleshooting is usually simple for such columns Fenske calculation failures are usually caused by m Impossible or conflicting specifications which result in impossible mate rial balances In particular look for this situation when component mole fractions are specified m User specified fractionation index minimum Fenske trays for which it is impossible to meet other specifications m Poor product rate estimates in particular caused by not accounting for water in the top product Underwood calculation failures are caused by incorrect separation key selec tion Possible causes are m Heavy and light key components which both distribute to the same product m Heavy and light key components which do not define a sharp separation For this case split keys must be defined May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 U Note The trial calculations for the shortcut fractionator will be printed when a PRINT statement with the keyword TRIAL is included in the SHORTCUT unit operation This may be used to help diagnose Fenske failures Complex Columns For complex columns more than two products a series of two product col umns are used to represent the separations with the feed introduced into the bottom section The default model type one considers the effect of reflux be tween the sections mo
212. stage backwards to the first stage using equation 2 m Once UN and Ow are calculated for all stages the component balance equa tions are then solved using the Thomas algorithm a version of the Gaussian elimination procedure This method of solving the triagonal equations 5 7 avoids matrix inversion buildup of truncation errors and avoids negative values of xi N being produced The triagonal equations can be reduced to PRO II Unit Operations Reference Manual Countercurrent Decanter 1 163 Solids Handling Unit Operations Section 2 7 igy0 O s 0 xa di4 id Ol pO 0 fxs di 000 0 Pya kiwal dint 0000 1 Xin diN where 3 21 P 1 Bi Ji 22 il p a 23 us N y By OPN m Fin Oy dy iN RB By CuPy 1 24 The solution of this matrix results in the immediate solution of the last stage composition xj N using the last row of the matrix i e Xin div 25 The compositions on other stages are then obtained by backward substitution Xin 1 7 4in 1 PN 1 iN 26 For the design mode calculations the number of stages is not given but a re covery specification is made on either the overhead or underflow product In this case PRO II will begin the calculations described above by assuming a minimum number of stages present If the design specification is not met the number of stages will be increased and the design equations re solved until the specificati
213. stems shortcut methods may give very poor results or no results at all In particular for columns in which the relative volatili ties vary greatly shortcut methods will give poor results since both the Fen ske and Underwood methods assume that one average relative volatility may be used for calculations for each component The relative volatility between components i and j at each tray in the col umn is equal to the ratio of their K values at that tray i e IE e t a yy N N Jj Xj Ky where y mole fraction in the vapor phase x mole fraction in the liquid phase subscripts i j refer to components i and j respectively superscript N refers to tray N For small variations in volatility throughout the column an average volatil ity may be defined This is taken as the geometric average of the values for the overhead and bottoms products o 2 N aT od 2 y y uy PRO II Unit Operations Reference Manual Shortcut Distillation 11 85 Section 2 4 Distillation and Liquid Liquid Extraction Columns The minimum number of theoretical stages is then given by PEE iB min av log Oi where subscripts B D refer to the bottoms and distillate respectively Underwood The values of the relative volatilities of the feed components determine Method Il 86 Shortcut Distillation which components are the light and heavy key components The light key component for a feed of equivalent component concentrations is usually
214. stillation 11 87 Section 2 4 Distillation and Liquid Liquid Extraction Columns Figure 2 4 4 1 Algorithm to Determine Rmin Il 88 Shortcut Distillation Determine q for feed using Equation 7 Assume an average column temperature Select light heavy key components Calculate a J s Are the selected keys correct Is the criterion of Equation 6 met Determine the distribution of components that lie between the keys Use Equation 6 to determine values of For all values of write Equation 8 for each component Solve equations simultaneously to determine D Rmin 1 Assume the temperatures of the product streams Determine D B average column temperature Is the average temperature close to the initial guess Determine Rmin May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 Kirkbride Method Gilliland Correlation Figure 2 4 4 2 Shortcut Distillation Column Condenser Types The optimum feed tray location is obtained from the Kirkbride equation 9 LH 0 206 wa 8 hie ES P D Xy p Up where m number of theoretical stages above the feed tray p number of theoretical stages below the feed tray The Gilliland correlation is used by PRO II to predict the relationship of minimum trays and minimum reflux to actual reflux and corresponding theo retical trays The operating point selected by the user expressed as either fraction of mini mum reflux o
215. t Np 700 L D gt 60 where Nyu Nusselt number NRe Reynolds number Ad tub Npr Prandlt number tube length effective tube diameter W total mass flow rate in tubeside At cross sectional tube area PRO II Unit Operations Reference Manual Rigorous Heat Exchanger II 115 Heat Exchangers Section 2 5 For laminar flow regimes NRe lt 2000 a different relationship is used for the heat transfer coefficient depending on the value of the Graetz number The Graetz number NGz is defined as D 7 Ne NRe Np Iz For Naz lt 100 a relationship first developed by Hausen is used 008N ul 8 Ny 73 66 140 047 NC Bw For NGz gt 100 the Sieder Tate relationship is used 0 14 9 u Ny 1 86 NL 2 Ha For transition flow regimes where 2000 lt NRe lt 10000 the tubeside film co efficient is obtained by interpolation between those values calculated for the laminar and turbulent flow regimes Um Bs lian Ni Re 2000 0 h th trans 8000 am where htans heat transfer film coefficient for the transition regime hturb heat transfer film coefficient for the turbulent flow regime hiam heat transfer film coefficient for the laminar flow regime The user may also supply the film coefficients directly Pressure Drop _Shellside Correlations The shellside pressure drop may be determined by one of two methods the Bell Delaware method or the stream analysis method The Bell Delaware
216. t kr This was done because the value of the vapor phase mass transfer coefficient kc is most often much less numeri cally than kL Experimental data were used to obtain the following relation ship for the Sherwood number Shg Ret Scd 2o The relationship for the interfacial area is given by a P Vp 21 For metal packing types such as the MELLAPAK series the factor m in equa tion 20 usually has a value of 0 8 For gauze packings such as BX or CY the factor m has a value closer to 1 i e independent of the liquid load This is because gauze packings are more completely wetted regardless of the liq uid load while for metal packings the wetted area increases with increasing liquid load The NTSM correlations are obtained by substituting equations 20 and 21 into equation 19 BA References 1 Il 84 Column Hydraulics Spiegel L and Meier W Correlations of Performance Characteristics of the Various Mellapak Types Capacity Pressure Drop and Efficiency 1987 Paper presented at the 4th Int Symp on Distillation and Absorption Brighton Eng Sulzer Chemtech Document No 22 54 06 40 Separation Columns for Distillation and Absorption 1991 Sulzer Chemtech Document No 22 13 06 40 Ballast Tray Design Manual 1974 Glitsch Bulletin No 4900 5th Ed Tsai T C Packed Tower Program has Special Features 1985 Oil amp Gas J 83 35 Sept 77 Perry R H and Chilton C H 1984 Chemical E
217. t compositions from Keg for the reaction Calculate the conversion and adjust by the fractional approach to equilibrium Calculate the enthalpy of products and perform an adiabatic flash to determine the outlet temperature If the calculated and assumed temperatures do not agree repeat the calculations with the new temperature Only one approach to equilibrium i e either a temperature approach or a fractional conversion approach is allowed PRO II Unit Operations Reference Manual Equilibrium Reactor 135 Reactors Section 2 6 a a Il 1 General Information Mathematics of 36 Free Energy Minimization Gibbs Reactor Gibbs Reactor The Gibbs Reactor in PRO II computes the distribution of products and reac tants that is expected to be at phase equilibrium and or chemical equilibrium Components declared as VL or VLS phase type can be in both chemical and phase equilibrium Components declared as LS or S type are treated as pure solids and can only be in chemical but not phase equilibrium The reactor can be at either isothermal or adiabatic conditions Reaction and product specifications can be applied to impose constraints on chemical equilibrium Available constraints include fixed product rates fixed percentage of feed amount reacted global temperature approach and reaction extent or tempera ture approach for each individual reaction The mathematical model does not require the kno
218. termined at the initial point will no longer be appropriate To ensure consistent flowsheet solutions it may also be necessary to invoke the COPY option an OPTPARAMETER keyword Here the entire PRO II database is stored which allows the flowsheet variables to be initialized iden tically for each perturbation evaluation rather than at the final value from the previous perturbation Bounds on the Variables For best optimizer performance it is very important to supply appropriate up per and lower bounds for each variable The bounds are used for the auto matic scaling of the variables As discussed previously they are also used to determine the default perturbation size and finally they may also affect the magnitude of the optimizer steps during the first three cycles see the section following Il 236 Flowsheet Optimization May 1994 Section 2 10 Flowsheet Solution Algorithms STEP Sizes By default the OPTIMIZER variables are not allowed to move more than 30 60 and 90 percent to their upper or lower bound during optimization cycles 1 2 and 3 respectively This is intended as a safety feature it prevents the optimizer from moving too far particularly when the derivatives are inac curate The STEP keyword is used to override this default by providing an absolute limit for the maximum change in a variable during one optimization cycle Providing a value for STEP which is larger than MAXI MINI for a particular variabl
219. the Soave Redlich Kwong method However the method may be applied to any equation of state provided that an algorithm for evaluation of component fugacities and their first partial de rivatives with respect to temperature pressure and composition for specified temperatures pressures compositions and fluid states may be developed We have extended his technique to include the Peng Robinson equation of state Ww Note Water will always be treated as a regular component in PRO II for phase envelope calculations regardless of whether water is declared as a decanted phase or not Reference Michelsen M L 1980 Calculations of Phase Envelopes and Critical Points for Multicomponent Mixutres Fluid Phase Equil 4 pp 1 10 The Phase Envelope calculations are always performed after the flowsheet has fully converged and therefore does not affect the convergence calcula tions Also like the HCURVE this unit is not accessible via the CONTROL LER MVC or CASESTUDY PRO II Unit Operations Reference Manual Phase Envelope 1 191 Utilities Section 2 9 H EXE Heating Cooling Curves General The HCURVE module provides a variety of options to calculate and report Information properties of process streams in a PRO II simulation In general a heat ing cooling curve is generated for a process stream between two defined points or states the user must provide information that defines both the in itial point and end po
220. the pressure drop through the liquid is given by AP 04 Q A yea 9 where L total liquid flow rate gpm lw weir length inches hw weir height inches The pressure drop through the liquid on the sieve or bubble cap tray is given by AP B hj 6 PRO II Unit Operations Reference Manual Column Hydraulics Il 75 Distillation and Liquid Liquid Extraction Columns Section 2 4 For sieve trays hy 7h h My 2 7a OW For bubble cap trays hy mh how hpg 2 7b where has calculated height of clear liquid over trays dynamic seal hy weir height hs static slot seal weir height minus height of top slot above plate floor how height of crest over weir hng hydraulic gradient across plate The dimensionless aeration factor B in equation 6 is a function of the superficial gas velocity Random Packed Columns containing conventional randomly oriented or dumped packings such Columns as Raschig rings Berl saddles and Pall rings may be modeled by PRO II Table 2 4 3 3 shows the random packing types supported by PRO II Il 76 Column Hydraulics May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Table 2 4 3 3 Random Packing Types Sizes and Built in Packing Factors te TYPE Random mm 6 3 9 5 12 7 15 9 19 25 4 131 7 138 1 50 8 76 2 88 9 Packing Type in 0 25 0 375 0 5 0 625 10 75 1 0 1 25 1 5 2 0 3 0 13 5 size 15 25 840 1450 5470
221. the same as those of the crystal lizer contents Such a unit is commonly known by the name of Mixed Suspension Mixed Product Removal MSMPR crystallizer or Continuous Stirred Tank Crystal lizer CSTC A further assumption made in the development of the crystallizer model is that breakage or agglomeration of solid particles is negligible Growth Rate Gk gGEXP where G growth rate of crystals m sec ka growth rate constant m sec S supersaturation ratio 1 e Xsolute XS lute Xs lute Xsolute actual mole fraction of solute in liquid Xs lute equilibrium mole fraction of solute in liquid at the crystal lizer temperature Nucleation Rate Biss s yen jJ um a r P m 2 where Bo crystal nucleation rate number sec m kg nucleation rate constant Mr magma density i e concentration of crystals in slurry kg crystals m slurry RPM impeller speed revolutions min BEXPI BEXP2 BEXP3 BEXP4 exponents May 1994 Section 2 7 Solids Handling Unit Operations Nucleii Number Density 3 G where no nucleii number density number m m slurry liquid volume fraction in slurry m liquid m slurry Population Balance Equations For discrete particle size distribution for crystals number density n r can be expressed as a histogram with m divisions and ry as the average particle size of the k division Figure 2 7 6 2 Crystal Particle Size Distribution z E E
222. the stream that has been initialized by the user In the case of the Process Method an algorithm that preserves as much as possible the order in which the user placed the units is used Single variable controllers which affect units within loops will be included in the loops In turn multivariable controllers and optimizers which affect units within loops will not be included in the loops If any of these options is not desired a user defined calculation sequence should be used Recycle loops concern two primary effects Composition and Thermal changes for streams The reference stream concept in PRO II may often be used to redefine the tearing process and eliminate thermal recycles To illustrate how both algorithms find tear sets and calculation sequences consider the following simplified flowsheet shown in Figure 2 10 2 1 PRO II Unit Operations Reference Manual Calculation Sequence and Convergence 1I 215 Flowsheet Solution Algorithms Section 2 10 Figure 2 10 2 1 Flow sheet with Recycle Given the way this flowsheet is drawn it has two recycle streams R1 R2 The SimSci method will find the calculation sequence U3 U1 U2 U4 as only one tear stream S3 and is the minimum tear set The sequence U3 U1 U2 will be solved until convergence is reached and only then unit U4 will be solved Depending of the sequence entered by the user the Process Method will identify the calculation sequences shown in Table 2 10 2 1 Table 2 10
223. ther authors report increases in solution times from 30 to 300 depending on the difficulty of the problem In fair ness if the problem takes 3 times as long using the homotopy the engineer devoted a great deal of time generating the initial estimates in order to get any solution In many cases there is no choice References 1 Bondy R W Physical Continuation Approaches to Solving Reactive Distillation Problems paper presented at 1991 AIChE Annual meeting 2 Ficken F A 1951 The Continuation Method for Functional Equations Communications on Pure and Applied Mathematics 4 Il 64 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns Initial As previously mentioned initial column profiles are needed for solution of Estimates the column heat mass equilibrium and performance specification balances These may either be provided by the user or generated internally by PRO II using an initial estimate generator User provided Estimates Ideally the only estimates the user has to provide is either the overhead rate or the bottoms rate with the product information On the other extreme the user can provide the complete estimates for the temperature flowrates and composition profiles PRO II s initial estimate generation IEG algorithms generate these numbers relatively well and the user need not provide any in itial estimates except for difficult simulations PRO
224. thod more rigorous calculations are made based on the size of the packing and the total vapor and total liquid leaving a packed stage The height of a vapor phase transfer unit is given by H lo D 0 3048 z 3 048 Sco 737 34G f f i 11 where Hg height of vapor phase transfer unit m Q packing parameter Dy lesser of column diameter or 0 6096 m 2 ft Zp height of packed bed m ScG gas phase Schmidt number uc pGDG DcG gas phase diffusion coefficient m s GL liquid mass velocity based on column cross section kg m s f quas fo pups fo ouo 9 a 1 24 for ring packings 1 11 for saddle packings b 0 6 for ring packings 0 5 for saddle packings PRO II Unit Operations Reference Manual Column Hydraulics Il 79 Distillation and Liquid Liquid Extraction Columns Structured Packed Columns Il 80 Column Hydraulics Section 2 4 The height of a liquid phase transfer unit is given by H 0 Cy z 3 048 Se 12 where d packing parameter Cfl function of Fr Fi vo vat at constant L V VG superficial vapor velocity m s vGf superficial vapor velocity at flood m s ScL liquid phase Schmidt number uu pr DL Dyj liquid diffusion coefficient m s The HETP is then computed from HETP Hot x In 4 1 13 where N ratio of slope of equilibrium line to operating line mV L Packing factors for the various random packing types are given in Table 2 4 3 3
225. tional constant uL liquid viscosity L liquid mass flux G vapor mass flux Alternately the flood point may be supplied by the user PRO II Note For more information on supplying a user input approach to flood using the FLOOD keyword see Section 77 Column Hydraulics of the PRO II Keyword Input Manual Pressure Drop The column pressure drop may be calculated by one of two methods The Norton method uses a generalized pressure drop correlation 0 5 9 01 2 Pc L Pc AP function F v V L Ps Lab s where v UL pL liquid kinematic viscosity May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns The Tsai method uses the following correlation for computing pressure drop 0 5 10 AP function C C Fai L Pc amp G Pz j where PL PG However there are no published packing factors for the Tsai method Therefore the Norton packing factors are utilized by PRO II when equation 10 is used 0 5 C operating capacity factor vG PS Efficiency The column efficiency may be measured by the Height Equivalent to a Theo retical Plate HETP The HETPs for most chemical systems are generally close in value for a fixed packing size regardless of the application By de fault therefore the HETP values are determined by a Rules of thumb method suggested by Frank If Norton IMTP packing is used an alternate method may be used to com pute the HETP values In this me
226. tionary head d E fae Outside packed floating head Pull through floating head U tube bundle Externally sealed floating tubesheet Rigorous Heat Exchanger Il 113 Heat Exchangers Section 2 5 Il 114 a amp Heat Transfer Correlations PRO II Note For more information on using a rigorous heat exchanger model in PRO II see Section 82 Rigorous Heat Exchanger of the PRO II Keyword Input Manual Shellside The Bell Delaware method is used to compute the heat transfer coefficient on the shellside The method accounts for the effect of leakage streams in the shellside The shellside heat transfer coefficient is given by h Nigeat Te Ji Ip Js 4 1 where h average shellside heat transfer coefficient hideal shellside heat transfer coefficient for an ideal tube bank Jc correction factor for baffle cut and spacing J correction factor for baffle leakage effects Jp correction factor for bundle bypass flow effects Js correction factor for inlet and outlet baffle spacing J correction factor for adverse temperature gradient build up The correction factor Jc is a function of the fraction of the total tubes in the crossflow Jj is a function of the tube to baffle leakage area and the shell to baffle leakage area Jp is a function of the fraction of crossflow area availabl
227. to define the split the Underwood calculations will only be useful when the specifications describe a sharp split between a light and heavy key If the number of Fenske trays fractionation index is given in lieu of a specification this may also invali date the Underwood calculations If desired the user may supply estimates of the Fenske trays required for the separation For columns in which there are a large number of trays this will speed convergence PRO II Note For more information on supplying estimates of the number of Fenske trays using the FINDEX keyword see Section 78 Shortcut Distillation of the PRO II Keyword Input Manual Complex Columns For complex columns in which there are more than two products it be comes impossible to select key components to define the fractionation within the various sections For such columns the separation is defined indirectly in terms of stream properties The PRO II program allows a wide variety of such properties PRO II Unit Operations Reference Manual Shortcut Distillation 11 91 Section 2 4 Distillation and Liquid Liquid Extraction Columns se Figure 2 4 4 4 Shortcut Column Specification Il 92 Shortcut Distillation PRO II Note For a list of stream properties which may be defined in the short cut distillation column see Table 43 2A in Section 43 Flowsheet Parameters of the PRO II Keyword Input Manual As mentioned above two models are available for complex c
228. truction includes a rather com plicated reactor Further assuming the feed and desired product conditions are known a Stream Calculator could be used as a quick simple preliminary reactor model that would produce the desired reaction products without re quiring the developer to worry about kinetics reaction rates and other reac tion complexities Development of the remainder of the flowsheet could proceed immediately while the time consuming development of a rigorous reactor model could be deferred Stream splitting always requires the presence of at least one feed as well as both the OVHD overhead and BTMS bottoms product streams All of the combined feed is distributed between these two products If all feed streams have blending factor values of unity i e 1 0 overall flowsheet ma terial balance is preserved May 1994 Section 2 8 Stream Calculator Stream Synthesis Considerations The stream splitting operation also requires the user to supply a splitting fac tor for every component in the flowsheet even if that component does not appear in any of the feeds to the Stream Calculator The disposition of each component must be defined in one and only one splitting factor specification The most straightforward way to accomplish this is to define splitting factors for all components in terms of only one product For example use only FOVHD ROVHD and XOVHD splitting specifications to define all compo nent splitting in t
229. ts are referred to as Reconstituted Components Over all mole fractions for these components would be the aqueous mole fractions true mole fraction plus reconstitution of ions Hence for a given set of in put liquid mole fractions x the inside loop returns two sets of liquid mole fractions namely the true mole fractions x and the reconstituted mole frac tions Xs Once the speciation equations are solved vapor liquid equilibrium constants K values and its derivatives are computed as a function of T P Xt and y Outer Newton Raphson Loop Outer loop model is solved by the Newton Raphson algorithm There are 2NC 3 equations and 2NC 3 unknowns on each theoretical tray Independent variables on each tray are a Natural log of liquid mole fractions In x NC b Natural log of vapor mole fractions In y NC c Tray liquid rate L 1 d Tray vapor rate V 1 e Tray temperature T 1 2NC 3 The equations to be solved on each tray are Component Balance NC mb n j x n 1 j L n 1 y n Lj V1 fiy uj Vin Sun 9 x nj L n SL n 0 Vapor Liquid Equilibrium NC vlen j In y n j In k njj x n 0 10 Energy Balance 1 Eb n F n Hf n V n 1 H n 1 L n 1 h n 1 11 Vin SUin A n L n SL n h n Q n 0 PRO II Unit Operations Reference Manual ELDIST Algorithm ll 71 Distillation and Liquid Liquid Extraction Columns Section 2 4 Summation x 1 SX n i
230. ttoms product rate may be set to zero so that a boiling pot reactor can be modeled As part of this functionality a single non volatile component may be specified The non volatile component is typically a catalyst which may used in the kinetic reaction rate expressions Kinetic Reaction Homotopy Volume Based The solution of the Mass Equilibrium Summation and Enthalpy balance equations can be a difficult task for non ideal chemical systems The addition of reaction terms further complicates the challenge Chemdist and LLEX both have a homotopy procedure to simplify obtaining a solution to reactive distillation columns The basic procedure is straightforward m Start with a set of equations to which you know the answer m Then modifiy the equations a little and solve them m Modify them again and re solve using the last solution Eventually the equations will be deformed into the equations to which you want the answer Il 62 Rigorous Distillation Algorithms May 1994 Section 2 4 Distillation and Liquid Liquid Extraction Columns This procedure has a formalized mathematical basis with the theoretical un derpinings beginning as early as 1869 Ficken 1951 Mathematically a ho motopy is a deformation or bending of one set of equations that are difficult to solve f x 0 into a set whose solution is known or easily found g x 0 A new set of equations referred to as the homotopy equations is constructed from f x and g x The
231. ty Relative tolerance of 0 005 Miscellaneous Relative tolerance of 0 01 If the specification does not set a temperature pressure or duty the miscella neous relative tolerance is used The tolerances on the controller specifica tions can be modified either by changing the tolerances at the flowsheet level or directly within the controller unit as part of each SPEC definition PRO II Unit Operations Reference Manual Flowsheet Control 221 Flowsheet Solution Algorithms Section 2 10 AYS Feedback Controller General Information Figure 2 10 4 1 1 Feedback Controller Example 222 Feedback Controller The PRO II CONTROLLER is analogous to a feedback process controller it varies a particular parameter control variable in order to meet a downstream specification on a process unit or stream property or rate Each CONTROLLER involves exactly one specification and control variable The specification may be made on a stream property or rate a unit operating condition or a CALCULA TOR result The control variable can be a stream or unit operating condition a thermodynamic property or a CALCULATOR result Figure 2 10 4 1 1 illustrates a typical controller application Here the controller varies the cooler duty in order to achieve a desired flowrate of stream 6 CONTROLLER controlling stream 6 flowrate The CONTROLLER uses an iterative search
232. ual 11 241 Depressuring Unit Section 2 11 OL L V Wo 1 Fin i0 Vo Po X o Vo Po 1 where Fio moles of component i at time t 0 xLo mole fraction of component i in liquid xo mole fraction of component i in vapor Vo initial liquid volume in vessel V initial vapor volume in vessel If no liquid holdup is specified m The composition of the vessel contents is set equal to the composition of the feed and the temperature and pressure of the vessel are set equal to that of the feed stream The total number of moles of each component in the vessel at time t 0 Fi o is calculated using _ feed 2 Fig ni Vo Pr mix where Fio moles of component i at time t 0 xfeed mole fraction of component i in feed Vo volume of vessel Pf mix mixture density of feed stream Calculati ng the The volume of the vessel holdup liquid is calculated for spherical vertical cylin Vessel Volume drical or horizontal cylindrical vessels using the following relationships Il 242 Depressuring Horizontal Cylinder Vessel V Ga bab a Vac 3 where r radius of vessel L tangent to tangent vessel length Vjac volume factor which corrects for pipes and fittings Vena end cap volume which is given by 3 5 4 Vond 8 Tr The optional user supplied volume correction factor Vfac defaults to a value of 1 0 if not supplied May 1994 Section 2 11 Depressuring Unit Valve Rate Equations Vertical Cylinder Vessel V Ga
233. ugh the basket is given by Ro Freed Wiig B Wop Pos de 20 filtr P where Ffir rate of filtrate Ffeed total mass rate of feed to centrifuge Wliq weight fraction of liquid in feed Wsol weight fraction of solid in feed Finert total mass rate of inert components in feed For design calculations an iterative method solution method is used in com bination with the equations given above to calculate the filter diameter re quired to produce a specified filtrate flow References Treybal R E 1980 Mass Transfer Operations 3rd Ed McGraw Hill N Y 2 Grace H P 1953 Chem Eng Prog 49 8 427 3 Dombrowski H S and Brownell L E 1954 Ind Eng Chem 46 6 1207 May 1994 Section 2 7 Solids Handling Unit Operations Ta Countercurrent Decanter General Information Calculation Methods Figure 2 7 4 1 Countercurrent Decanter Stage Mixtures of solids and liquids may be separated by countercurrent decanta tion CCD This unit operation consists of several settling tanks in series If the purpose of the CCD unit is to obtain a thickened underflow then the tank is referred to as a thickener The solid liquid mixture is flowed countercur rently to a dilute liquid wash stream In each tank the solids from the slurry feed settles under gravity to the bottom of the tank The clarified overflow is transferred to the previous tank to be used as the wash liquid while
234. ulk proper ties may then be described for the vacuum unit to aid solution On the other hand if definitive vacuum product specifications are available the single unit model can insure more accurate vacuum unit yields PRO II Unit Operations Reference Manual Shortcut Distillation 11 93 Section 2 4 Distillation and Liquid Liquid Extraction Columns Figure 2 4 4 5 Heavy Ends Column Naphtha Crude Feed Distillate Gas Oil Light gas oil Heavy gas oil Resid The crude preflash system shown in Figure 2 4 4 6 presents a different case Figure 2 4 4 6 Crude Preflash System Naphtha Crude Feed LSR I Naphtha Distillate Topped crude Il 94 Shortcut Distillation May 1994 Distillation and Liquid Liquid Extraction Columns Section 2 4 For this case common products will be produced on both units and a single col umn model attempting to represent all the products is difficult 1f not impossi ble For systems such as this it is much better to always use a two column model The sections in actual distillation columns are interlinked through both feeds and liquid refluxes Refluxes at each section are governed by heat balances around that section and the entire system Although some adjustment in reflux is possi ble there is an upper limit to the number of trays which can be present in any section For a crude column this is usually around 6 to 8 theoretical trays This is beca
235. ure and actual outlet enthalpy con LH Il 22 Compressor ditions The polytropic work i e the reversible work required to compress the gas in a polytropic compression process from the inlet conditions to the discharge conditions is computed using W 144 n n 1 f P V fep PSU D s where Wp polytropic work For ideal or perfect gases the factor f is equal to 1 The polytropic efficiency is then calculated by y 7 W W 14 Note This polytropic efficiency will not agree with the value calculated using the GPSA method which is computed using Yp n 1 n k D k Polytropic Efficiency Given A trial and error method is used to compute the adiabatic efficiency once the polytropic efficiency is given The following calculation path is used 1 The isentropic coefficient isentropic work and factor f are computed using equations 10 11 and 12 2 The polytropic coefficient is calculated from equation 12 3 Aninitial value of the isentropic efficiency is assumed 4 Using the values of f and n calculated from steps 1 and 2 the polytropic work is calculated from equation 13 5 The polytropic efficiency is calculated using equation 14 6 If this calculated efficiency is not equal to the specified polytropic efficiency within a certain tolerance the isentropic efficiency value is updated 7 Steps 5 and 6 and repeated until the polytropic efficiency is equal to the specified value Reference
236. use the heavy end mixtures have wide boiling ranges Once the product rates are fixed each mixture can only have limited bubble point ranges In other words the fractionation within each section is restricted and depends to a large extent on the overall heat balance The Fenske model is useful in defining the fractionation requirements within each section While the fractionation index Fenske trays is only qualitatively definitive it is useful in evaluating the feasibility of desired separation The fractionation index is approximately equivalent to the number of theo retical trays times the reflux ratio thus the theoretical stages required for a given separation may be estimated These trays must then be adjusted ac cordingly to correspond to actual trays Experience has shown that the fractionation indices fall into certain ranges for refinery columns Table 2 4 4 1 below illustrates typical values Table 2 4 4 1 Typical Values of FINDEX Crude Typical FINDEX LSR Naphtha 5 7 Naphtha Kero 4 5 Kero Diesel 2 5 3 5 Diesel Gas Oil 2 25 Gas Oil Topped Crude 1 25 1 75 Cat Fractionators Gasoline Light Cycle 5 7 Light Cycle Heavy Cycle 1 5 2 5 Heavy Cycle Clarified Oil 1 1 1 5 Vacuum Units Overhead Light Gas Oil 2 2 5 Light Gas Oil Heavy Gas Oil 1 25 1 75 Heavy Gas Oil Resid 1 1 5 PRO II Unit Operations Reference Manual Shortcut Distillation 11 95 Section 2 4 Distillation and Liqu
237. ut ignores the interaction between different components To use this technique at least one trial must be made with direct replacement Let xy represent the estimated rate of a component or a temperature of a recy cle stream at the beginning of trial k and xy41 the calculated rate or tempera ture after trial k The estimated rate for trial k 7 xx41 will be computed using these values as follows X17 45 0799 1 In equation 1 q is the so called acceleration factor and is determined by the following formula w 2 m 2 w 1 where Ww E 3 fc Table 2 10 3 1 shows how values of q affect convergence Table 2 10 3 1 Significance of Values of the Acceleration Factor q q Convergence Region q lt 0 Acceleration q 0 Direct Substitution 0 lt q lt 1 Damping q 1 Total damping no convergence The more negative the value of q the faster the acceleration However if the value of q thus determined is used without restraint oscillation or divergence often results Itis therefore always necessary to set upper and lower limits on the value of q These limits should be set based on the stability of the recycle stream Normally the upper limit should be at 0 0 A conservative value for the lower limit may be set at 20 0 or 50 0 to speed up the convergence l 218 Acceleration Techniques May 1994 Section 2 10 Flowsheet Solution Algorithms LI Broyden Acceleration The Wegstein acceleration can be app
238. wledge of reaction stoichiometry from the user except when the reaction extent or a temperature approach is to be specified for the individual reaction Objective Function of Gibbs Free Energy Minimization The objective function which is to be minimized is composed of two parts The first is the total Gibbs free energy of the mixture in all phases P NS oc NP NC c 1 RPL RF tL RT jel p l j l where NS number of solid components NP number of fluid phases NC number of fluid components Gyre Gibbs free energy of solid component at standard state Gjp Gibbs free energy of fluid component at reactor tempera ture and pressure T reactor temperature nye number of moles of solid component Njp number of moles of fluid component In the design equation 1 the Gibbs free energy is represented by a quadratic function G N G n AG n N n i N n A G N n 2 May 1994 Section 2 6 Reactors When a temperature approach is applied for all reactions global approach or for individual reactions individual approach the standard state free ener gies of formation are modified in a way that the relation between the reaction equilibrium constant and change of Gibbs free energy of formation is satis fied see equation 3 The standard state Gibbs free energy is defined as at reactor temperature 1 atm and ideal gas state for all fluid components and at reactor temperature 1 atm and solid state for al
239. y a temperature approach The conversion itself can be specified as a function of temperature When the temperature approach is given Keq is computed at T where T Treaction AT endothermic reactions T Treaction AT exothermic reactions Based on the value of Keq conversion of base component and product com positions can be calculated If the approach to equilibrium is specified on a fractional conversion basis the conversion of the base component B is given by Cs 7 B Pe Br 5 where Bg moles of component B in the product Br moles of component B in the feed Bg moles of component B at equilibrium A specified approach to equilibrium x Co CiT CT The coefficients Co C1 and C2 may appear in any combination and missing values default to zero For a fixed approach C1 and C2 are zero When no ap proach data are given reactions attain equilibrium and Co 1 0 C120 0 and C2 0 0 The equilibrium reactor can also be used with specialized reactor models for shift and methanation reactions PRO II Unit Operations Reference Manual Equilibrium Reactor I 133 Reactors Section 2 6 Shift Reactor Model Methanation Reactor Model ll 134 Equilibrium Reactor The purpose of the shift reactor model is to simulate the shift conversion of carbon monoxide into carbon dioxide and hydrogen with steam CO H 0 CO H 6 Just as in the Stoichiometric Reactor the desired conversion is determined
240. y be expressed as an operational criterion e g maximum recovery or minimum loss or an economic criterion e g minimum cost or maximum profit The CALCULATOR can be used to develop more complex objective functions which account for a variety of design and economic factors PRO II Note For a complete list of the stream and unit operation variables which may be used to define the objective function see Section 43 Flowsheet Parameters of the PRO II Keyword Input Manual Finally the objective function may also be defined via a user written subroutine Note that the objective function should be continuous in the region of inter est The OPTIMIZER will perform best if the objective function shows a good response surface to the variable it should neither be too flat nor too highly curved Unfortunately in practice many objective functions tend to be quite flat which may cause the optimizer to terminate at different solu tions when different starting points are used These solutions which are all valid within tolerance will have similar objective function values but the val ues of the variables may be quite different Optimizer Variables Any flowsheet value which is defined as a fixed input parameter can be used as a variable for the PRO II optimizer This includes stream rates or proper ties unit operating conditions thermodynamic properties and CALCULA TOR results PRO II Note For a full list see Section 43 Flowsheet Paramet
241. ystal ky crystal shape factor 1 for cubic crystals 7 6 for spherical crystals l 174 Crystallizer May 1994 Section 2 7 Solids Handling Unit Operations For the case of no solids in feed the magma density is M 6p k n Gt 12 C vo Material and Heat These equations are given in simplified form below Balances and Phase Equilibria Material and Heat Balance Equations Overall F E B 13 where F feed rate kg sec E overhead product rate kg sec B bottom product rate kg sec Component Solute F solute E solute B solute 14 Solvent F solvent E solvent B solvent 15 Inerts F E B i 1 2 N 16 where subscripts solute solvent and i refer to the solute solvent and inert components respectively Solid liquid Solute Balance _ pLiq C 17 F solute Pu P F pliq 18 B solute B solute P where ro component rate of solute in feed liquid kg sec Pr component rate of solute in crystallizer feed kg sec Bois component rate of solute in bottoms product liquid kg sec P rate of solute component crystals in bottoms product kg sec PRO II Unit Operations Reference Manual Crystallizer 1 175 Solids Handling Unit Operations Section 2 7 Solute Vapor Balance E 19 E ole F solute M tues where Ysolute vapor phase mole fraction of solute MWvapor molecular weight of overhead product kg kgmol MWsolute molecular weight of solute kg kgmo

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