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Chapter 5_FlowSimulation

1. 12 HH1 HH1 ado HH1 12 SC1 SC1 ado Storage Coeff Aqf 1 12 RP1 RP1 ado RP1 TIME 0 00 13 end 15a 100 100 00001000 15b 0 16 10 0000 1 0000 0 2500 17 1 4 4 4 4 4 4 1 1 1 1 7 end of sources input 9 end of boundary input 11 end of river input 12 RP1 RP1 ado RP1 TIME 10 00 13 end 16 20 0000 1 0000 0 2500 POS 7 end of sources input 9 end of boundary input 11 end of river input 12 RP1 RP1 ado RP1 TIME 152 00 13 end 16 162 0000 1 0000 0 2500 17 1 1 1 17 1 1 1 1 1 4 1 7 end of sources input 9 end of boundary input 11 end of river input 12 RP1 RP1 ado RP1 TIME 345 00 AES end 16 345 0000 1 0000 0 2500 17 1 4 4 4 4 4 1 1 1 7 end of sources input 9 end of boundary input 11 end of river input 15 16 0 0000 1 0000 0 2500 File ends with an empty line END OF FILE 5 2 7 Output data description The simulation program produces different types of output files Some of these files contain information on the calculation process flairs flg others contain the calculation results using various formats flairs flp flairs flo and the time series output file graphnode out Print output file flairs flp Selecting View Print from the Calibration pull down menu displays the print output file flairs flp This file co
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3. The program is capable of handling a variety of problems such as steady state and transient flow anisotropy and inhomogeneities Kxx Kxy Kyx Kyy Kzz Dirichlet Neuman and mixed boundary conditions phreatic conditions possible for parts of the model area multi layered systems containing many aquifers and aquitards flow in a vertical cross section transient recharge imported from Fluzo the Triwaco program for the calculation of flow in the unsaturated zone non linear recharge relations for sources and sinks rivers boundaries and top systems e groundwater flow under variable density conditions e clustering of rivers line sinks or sources to simulate drains or multi screen wells with given abstraction rate The mathematical background of the simulation package is given in paragraph 5 3 The program requires a number of readable standard scii input files and generates various output files When used in combination with the TriShell default file names are assumed for all input and output files 5 2 3 Simulation options After allocation of the values for all model parameters one may start the groundwater flow calculations First selecting Calibration Options from the menu bar the Calculation options dialog box is opened In this dialog box the user specifies parameters related to the iteration process Description Function Inner iteration Sets the maximum number of inner iterations
4. Selecting View Ado file from the parameter pull down or pop up menu starts the graphical presentation program TriPlot loads the grid information and a spatially visualisation of the selected parameter In this GIS like environment the parameters can easily be checked compared with other parameters on a spatial scale but also for individual cells nodes 5 1 5 Definition of initial head parameters The initial head for each aquifer is defined by HHi The initial head for the topsystem is defined by HT Defining the initial head may be required for some cases It is however more often used to speed up the simulation run of Flairs in the calibration process or as initial heads for scenario calculations The initial head is then defined by the output of the former simulation result Triwaco computes groundwater heads flow by iteration starting from groundwater heads equal to 0 0 A quicker calculation process may be obtained if initial headvalues are used which are closer to the heads to be calculated The initial head is often defined by the output of the former simulation result The initial head for each aquifer is defined by The initial head for the topsystem is defined by HT These parameters can be defined under the Modified tab by choosing Parameter Add Internal The groundwaterhead from a former simulation result is defined by using an expression PHI where 715 the aquifer number HT is defined as PHIT 5 1 6 Definition
5. ICsrc sequential number of the source ICriv 1 NCsrc laq sequential number of the aquifer the river or source is active in Isrc identification number of the source involved Set 4c will be repeated NCsrc times Set 4 should be repeated for each collection unit and omitted if no collection units are defined The maximum number of collection units equals 50 Set 5 End of sum input literal text string This string should always be present it indicates the end of the section 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 9 Royal Haskoning Triwaco User s Manual Set 6 Isrc laq Ist Qsrc Hsrc source ID Format active aquifer number 3 15 2 E10 4 type of source discharge or recharge rate groundwater head Isrc the source ID as defined in the grid teo file laq the number of the aquifer the source is active in Ist a flag for identifying the type of sources If Ist 20 the source is defined by a given rate Qsrc If Ist 21 the source is defined by a given head Hsrc Qsrc abstraction or infiltration rate lt 0 abstraction Hsrc fixed groundwater head Set 6 should be repeated as many times as required In stead of using Set 6 sources are generally defined using the source parameter sets IS SHi and SQi 1 Moreover using the source parameters the user may also specify clustered sources ISi 2 The use of source parameter sets overrides the values defined by Set 6 If no
6. Outer iteration Sets the maximum number of outer iterations Convergence Sets the criterion for convergence 5 Relaxation Sets the relaxation factor 5 1 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 6 Royal Haskoning Triwaco User s Manual Calculation options Iteratian Inner iteration 5t Outer iteration 1 00 Convergence 0 00001 Relaxation 1 0000 During calculations Flairs will pause and display a warning if the maximum number of linear or inner iterations is exceeded If the user decides to continue calculations Flairs automatically doubles the number of inner iterations For each outer iteration the number of inner iterations will be checked Calculations will proceed until the number of inner iterations during a single outer iteration equals 2 or less or until the maximum number of outer iterations is reached Apart from the maximum number of iterations the user has to specify a criterion for convergence The program checks whether or not differences are less than the criterion specified The initial conditions for each outer iteration depend on the head change between outer iterations In case of badly converging systems a relaxation factor may be defined In that case the head change between outer iterations is multiplied with the relaxation factor This causes a more stable iteration process but also results in smaller head changes thus requiring more iterations to reach a solut
7. Set 11 End of river input literal text string This string should always be present it indicates the end of the section In stead of using Sets 6 8 and 10 the user is advised to define the parameters in question by the appropriate parameter sets Adore files The text strings defined in Sets 7 9 and 11 however should never be omitted In the next section all model parameters are being defined The boundary river and source parameters mentioned above should be defined here too unless the user has specified Sets 6 8 and 10 Set 12 consists of three records Pname riwaco parameter name Format A4 Fname parameter file name Format A60 FPname user defined parameter name Format A20 Pname is the pre defined Triwaco parameter name Fname the name of the file containing the parameter including the full path FPname a user defined name describing the parameter this name may be different from the predefined parameter name Set 12 should be repeated as many times as required If Pname is not one of the pre defined Triwaco parameter names Set 12 will be ignored Parameters that are not defined by Set 12 will obtain a default value equal to 0 except for the anisotropy parameters PYi and TYi which will be assigned the value of the corresponding PX and TX i Set 13 End literal text string This string should always be present it indicates the end of the section 5 Execution of Groundwater Flow Simulations FLAIRS and
8. either for one single river or drain or for a number of connected clustered rivers or drains In that case the amount of water to be abstracted or infiltrated is given and the program computes the head The program assumes that the head over the whole river is constant and the same for all rivers belonging to the cluster At each river point the abstraction or infiltration rate is computed by di 21 r C with O abstraction or infiltration rate F 4 the area of the river or drain in the given point This area is computed from the length of the A river assigned to the point and the hydraulic radius Rw of the river or drain at that point h the groundwater head in the aquifer he the water level in the river or the piezometric head in the drain the resistance to flow towards a line sink or from a line source This river resistance usually F has different values for infiltration h gt h and for drainage h lt h The program offers the possibility to define a different resistance for drainage and for infiltration For fully penetrating rivers the hydraulic resistance will have a value of zero In that case the infiltration rate can not be calculated from the given relation Still the rate will be treated as the unknown but the groundwater head is given the same value as the river level For clustered rivers with a given infiltration or abstraction rate the head will de treated as the unknown while
9. top aquifer Note that the program Flairs should not be used for transient calculations with a salt fresh interface because the salt water body is assumed to be stagnant In that case or if the interface passes the top of the lower most aquifer one should use the variable density module FLAIRSVD 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 30 Royal Haskoning Triwaco User s Manual 5 4 Executing model simulations with MODFLOW 5 4 1 Introduction Groundwater flow calculations can be carried out in a way similar to the calculations with the standard Triwaco programs In stead of running the program Flairs the program runMFfli will be called This program reads the standard input file flairs fli translates the input into ModFlow input files runs ModFlow with these files and writes and converts the standard ModFlow output back into standard Triwaco output format default file name flairs flo All ModFlow files remain present so the user can not only check the regular log print and output files but also the ModFlow output flairs out The ModFlow input files all have standard file names which differ only by their extension e g FLAIRS BAS BCF DRN RIV GHB RCH PCG et cetera There are however some restrictions in using ModFlow The program runMFfli does not support at this time all top systems boundary conditions and river or source types which can be defined for Flairs The program however does support the f
10. with boundary type Ibt 0 Set 9 End of boundary input literal text string This string should always be present it indicates the end of the section 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 10 Royal Haskoning Triwaco User s Manual Set 10 Iriv laq Irt Hriv river ID Format active aquifer number 3 15 E10 4 type of river river water level lriv the river ID as defined in the grid teo file laq the number of the aquifer the river is active in Irt a flag for identifying the type of boundary condition If Irt O the river is defined by a given water level Hriv If Irt 21 the river is defined by a given flux Qriv Hriv the river water level for Irt 20 or Iriv laq Irt Qriv Nclus river ID Format active aquifer number 3 15 type of river E10 4 I5 river discharge or recharge river cluster number Qriv the recharge or discharge rate for Irt 21 Nclus the river cluster number for Irt 21 clustered rivers will have the same head Set 10 should be repeated as many times as required In stead of using Set 10 the rivers are generally defined using the river parameter sets RA HR and 1 N The value for RAi equals Irt 1 For clustered rivers the parameter should be defined also The use of river parameter sets overrides the values defined by Set 10 If no river parameter sets are defined rivers that are not defined by Set 10 will not be active equivalent to 0
11. 7 MODLFOW parameter handling by emnes 5 34 540 COMANO INe Call ORTU 5 38 Royal Haskoning Triwaco User s Manual 5 1 Creating a Calibration data set 5 1 1 Introduction So far the model parameters are defined in the Initial data set by their map and par files only and no link to grid exists Therefore this link will be established by creating a so called Calibration data set 5 1 2 Opening a Calibration data set Selecting data set Add from the pull down menu and Calibration from the create new data set dialog window displays the calibration data info window Demonstration model Description Directory Mame Calib1 C Projdirs Demo Calib X Cancel B azed DF of Initial Dataset Initial Grid Name of Grid Dataset Grid The user has to provide the following information A A descriptive name of the data set and the data set s directory name where the files needed for the groundwater model calculations are located B The name of the data sets the calibration set is based on e g an Initial data sef and a Grid data set Confirming the selection with the laf button causes the program to open the Calibration data set window displaying all model parameters defined The Calibration data set window consists of three tab sheets Inherited parameters This sheet displays all model parameters defi
12. MODFLOW 11 Royal Haskoning Triwaco User s Manual In the next section the calculation parameters are being defined One can discriminate between parameters needed for steady state calculations and those needed for the transient calculations only Of course the latter only need to be present if transient calculations are required and lfss 1 see Set 2 Set 14 EPS maximum number Inner Iterations Format 2 15 E10 4 maximum number Outer Iterations convergence criterion the maximum number of iterations allowed for the linearized equations the maximum number of iterations allowed for the non linear equations EPS the criterion for convergence for the linearized equations For steady state calculations continue with Set 17 Set 15a Norf number of nodes for time series Format 15 Norf the number of nodes for which time series output will be generated Set 15b 11 12 INgrf node number for time series Format 16 15 li 1 Ngrf the numbers of the FE nodes for which time series output is required The node numbers correspond with the numbers from the FE grid file grid teo Set 15b should be repeated Ngrf 16 times and omitted if Ngrf 0 The time series output for the Ngrf nodes defined by the node numbers of Set 15b are written to the output file graphnode out Set 16 Tend DHmx DT stress input time Format 3 E10 4 maximum allowable head change per time step initial time step
13. and tertiary drainage infiltration system 5 Pipe drainage and irrigation or precipitation Top system number 5 drainage only and Top system number 6 both drainage and infiltration defined by 8 parameters groundwater discharge depends on the precipitation or irrigation excess the head in the top aquifer and the drainage resistance 6 Polder with a fixed water level and precipitation Top system number 7 defined by 4 parameters groundwater recharge or discharge depends on a fixed water level the total resistance of the drainage system and the precipitation excess 7 Phreatic drainage with precipitation Top system number 10 defined by 4 parameters groundwater discharge depends on the head in the top aquifer the resistance and the base of the drainage system and on the precipitation excess 8 Polder with a fixed water level and single drainage system Top system number 11 defined by 5 parameters groundwater recharge or discharge depends on the precipitation excess and the resistance and level of a single drainage system 9 Predefined recharge or discharge characteristic Top system number 12 defined by 5 parameters groundwater recharge or discharge depends on meteorological quantities and soil parameters The soil parameters are obtained by curve fitting of the Van Genuchten relations IR RP1 RP2 RP4 RP5 RP6 RP7 RP8 RP9 RP10 RP11 RP412 RP13 1 P 2 H OC wW 3 W BD 4 C
14. due to rivers canals and drains be approximated by a series of point sources sinks situated in a series of nodal points the river nodes e he transmissivities and storage coefficients are constant within an element and are equal to the average of the values at the nodal points This so called lumped parameter approach has the advantage that these terms are easily incorporated and the system of equations will be symmetric We will now define an a priori solution for the given differential equation 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 19 Royal Haskoning Triwaco User s Manual P YAG e B With the unknown coefficient a known shape function The shape functions are defined piecewise linear such that 51 in nodal point 7 a 0 in all other nodal points Hence will have the value of amp in nodal point 7 Substitution of i in the partial differential equation results in the following equation i 6 44 0 0 The coefficients have to be determined such that R is minimized over the model area The value of R is minimized by making it orthogonal with the shape functions i 1N 7 and integrating over the model area The integration can be performed by using Greens theorem f 7v o r v Ev e aa 8 I with the boundary of the model area n the normal on the
15. source parameter sets are defined sources that are not defined by Set 6 will have a default abstraction rate of Qsrc 0 with source type Ist 0 Set 7 End of sources input literal text string This string should always be present it indicates the end of the section Set 8 Ibnd laq Ibt Hbnd boundary point number Format active aquifer number 3 15 E10 4 type of boundary groundwater head lond the boundary point number as defined in the_grid teo file laq the number of the aquifer the boundary condition is given for Ibt a flag for identifying the type of boundary condition If Ibt 20 the boundary is defined by a given head Hsrc If Ibt 21 the boundary is defined by a head dependent flux Hbnd fixed groundwater head for Ist 20 Or Ibnd laq Ibt BA boundary point number Format active aquifer number 3 15 2 E10 4 type of boundary head dependent flux parameter head dependent flux parameter BA BB head dependent flux parameters for Ist 21 Set 8 should be repeated as many times as required In stead of using Set 8 boundary conditions are generally defined using the boundary parameter sets IB BHi BA and i 1 N Parameters BAI and BBi define the head dependent boundary flux IB 1 The use of boundary parameter sets overrides the values defined by Set 8 If no boundary parameter sets are defined boundaries that not defined by Set 8 will have a default boundary head of Hbnd 0
16. the calculations Selecting Run Simulation from the Calibration pull down menu starts model simulations A window showing the calculation process RunMFli and a dosbox with ModFlow will be displayed and the program will be added to the tasks window Once the calculation has stopped the Result parameters Tab sheet will be updated After the first run this Tab sheet will be added to the Calibration data set f a calibration file has been defined the program automatically compares the calculation results with the observed heads fluxes runM Ffi version 1 2 2001 File Help FLI file processed without errors run D Im c Xnragra Mriwaco AMe odFlow MODEL Wb EAE 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 33 Royal Haskoning Triwaco User s Manual The simulation program produces different types of output files writes and converts the standard ModFlow output back into standard Triwaco output format default file name flairs flo All ModFlow files remain present Some of these files contain information on the calculation process errors encountered flairs flg others contain the calculation results using various formats flairs flp flairs flo 5 4 5 Viewing output results maps Selecting View Results from the Calibration pull down menu starts the graphical presentation program TriPlot loads the grid information and displays the layout of the m
17. the rate of the cluster of rivers is given The type of river or drain that will be used is determined by a river type parameter defined by the user By default the program assumes that the river is defined by a given water level 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 24 Royal Haskoning Triwaco User s Manual Top systems The discharge or recharge of groundwater at the top of the first aquifer can be characterized by the so called top systems A top system describes the interaction between the groundwater system and a drainage infiltration system consisting of generally small surface waters and drains A short description of the topsystems is listed below A more detailed description is given in Appendix A 1 Precipitation Top system number 1 defined by 1 parameter groundwater recharge is equal to the precipitation excess 2 Polder with fixed water level Top system number 2 defined by 3 parameters groundwater recharge and discharge depend on a fixed water level and the total resistance of the drainage infiltration system 3 Phreatic drainage Top system number defined by parameters groundwater discharge depends on the head in the top aquifer the resistance and the base of the drainage system 4 Three level drainage system Top system number 4 defined by 13 parameters groundwater recharge or discharge depends on the precipitation excess and the resistance and levels of a primary secondary
18. zero Setting the value for B also to zero a natural or no flow boundary is created Both types of boundary conditions can be used simultaneously for parts of the boundary The type of boundary condition that will be used is determined by the boundary type parameter to be defined by the user By default the program assumes the boundary condition to be defined by a given head Leakage The leakage term 3 in the equations defines the flow of groundwater between two adjacent aquifers The leakage is defined assuming the following simplifications flow in the aquitards is vertical e he storage in aquitards can be neglected Taking these two assumptions into account the leakage term is given by the next equation g 120 c with the groundwater head the aquifer under consideration the groundwater head the adjacent aquifer c the hydraulic resistance of the aquitard 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 23 Royal Haskoning Triwaco User s Manual Sources In the program Flairs the terms sources and sinks are reserved for groundwater abstractions or infiltrations defined in nodal points These nodal points have to be defined as such in the Finite Element Grid The abstraction or infiltration rate of a point source or sink can be defined in two ways in the program e An abstraction or infiltration can be defined by a given rate The amount of water to be abstracte
19. Description and source PCG2 parameter MXITER Maximum number of outer iterations per time step Taken from FLI file Il usually less than 100 will be enough ITER1 Maximum number of inner iterations per time step Taken from FLI file IO usually lt 30 for linear problems and 10 for non linear problems NPCOND Type of preconditioning to be used Fixed at 1 Modified Incomplete Cholesky method HCLOSE Head change criterion for convergence Taken from FLI file EPS Usually 0 01 or 0 001 RCLOSE J Residual criterion for convergence Computed from HCLOSE RCLOSE 86400 HCLOSE RELAX Relaxation parameter Taken from FLI file R Usually set to 1 however a value of 0 97 to 0 99 may prevent zero divide and non diagonally dominant matrix errors in case rewetting is active NBPOL Not used for NPCOND 2 a Fixed dummy value IPRPCG Printout interval Fixed to 1 MUTPCG Print type Fixed to 1 number of iterations head changes and residuals are printed IPCGCD Recalculation Cholesky decomposition Fixed at 0 recalculated each outer iteration 5 4 4 Executing the model simulation For starting the model calculations one first selects Generate input from the Calibration pull down menu bar This will generate the input file needed flairs fli This input file may be viewed or edited selecting View from the pull down menu The input file contains all parameters needed for
20. ERATIONS USED 114 143 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 7 Royal Haskoning Triwaco User s Manual Triwaco computes groundwater heads flow by iteration starting from groundwater heads equal to 0 0 A quicker calculation process may be obtained if initial headvalues are used which are closer to the heads to be calculated The initial head is often defined by the output of the former simulation result Definition of the initial head is described in par 5 1 5 5 2 5 Viewing output results maps Selecting View Results from the Calibration pull down menu starts the graphical presentation program TriPlot loads the grid information and displays the layout of the model area Now the user can contour or classify the result parameters and view the results in plane view or can select a cross section of the model area Alternatively the user can select one of the parameters from the result parameters sheet and viewing the parameter separately selecting View Adore from the Parameter pull down menu or View Adore file from the pop up menu right hand mouse button Adding other parameters selecting Param Load from the TriPlot menu bar gives the user the opportunity to compare result parameters with model input parameters 5 2 6 Input data description The input file flairs fli for the groundwater simulation program contains the definition of the hydrogeological system including references to all input pa
21. GHB and DRN Hydraulic resistance RP2 RP3 RP4 Drainage resistance RPS Infiltration resistance Controlled water level River River water level HRx GHB and DRN or RIV and DRN River width Drainage resistance RWx Infiltration resistance CDx Cix 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 36 Royal Haskoning Triwaco User s Manual Drainage DRN GHB H lt Horn Infiltration GHB or RIV H H 4 4 Maximum infiltration flux RIV DRN package active GHB package active Sas RIV package active 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 37 Royal Haskoning Triwaco User s Manual 5 4 8 Command line calls RUNMFII Program for the generation of ModFlow model input files and for carrying out groundwater flow calculations with ModFlow Calculation results are converted to a Triwaco output file flairs flo The command call is similar to that for the standard Triwaco groundwater flow module FLAIRS A standard input file flairs fli must be generated from the TriShell Also a standard grid file grid teo is required Output will be written to files flairs flo flairs flp and flairs log If no arguments are given the program opens in Windows mode The appropriate input files grid teo flairs fli and calib chi can be selected and the program may be run using the pull down menus Command line call RunMFfli exe set dir grid dir flairs fli calib chi No options are availab
22. MESTEP nnn Where the result of e OP1 is governed by the topsystem parameters RP4 drainage resistance infiltration resistance and RP10 base elevation of system e OP2 is governed by the topsystem parameters RP5 drainage resistance RP8 infiltration resistance and RP11 base elevation of system e OP3 is governed by the topsystem parameters RP6 drainage resistance infiltration resistance and RP12 base elevation of system e TOP4 is governed by the topsystem parameters RP13 surface level Graphnode graphnode out The output file graphnode out contains time series output for transient calculations For a number of nodes defined by the user in the input file for transient calculations groundwater heads and the interface can be written as a function of time The time and parameter values are exported to the time series output file graphnode out The time series data is listed in columns The first of these columns contains the time value the other columns contain values for the various parameters successively for each of the grid nodes specified The heading of the file specifies for which nodes parameters have been exported to the time series output file The information from the time series output file can easily be imported in a spreadsheet 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 16 Royal Haskoning Triwaco User s Manual 5 2 8 Command line calls Program for the
23. NB the number of boundary points defining the sub area for water balance calculations NB 20 Set 3b XB YB coordinates of boundary points for water balance sub Format 2 F10 4 areas XB YB the X and Y coordinates of the boundary points The coordinates of the last boundary point are not necessarily equal to the coordinates of the first boundary point Set 3b will be repeated NBP 1 times Sets 3a and 3b should be repeated Nsar times for each of the water balance sub areas and omitted if Nsar 0 Set 4a HCU NCriv NCsrc name of collection unit Format number of rivers in collection unit A20 2 15 number of sources in collection unit HCU identification string for the collection unit A collection unit is a combination of rivers and sources for which the total recharge is computed and written tot the print output file flairs flp NCriv number of rivers belonging to the collection unit NCsrc number of sources belonging to the collection unit Set 4b ICriv laq lriv sequential number of collection unit s river Format 3 15 aquifer number of river river number river ID ICriv sequential number of the river ICriv 1 NCriv laq sequential number of the aquifer the river or source is active in lriv identification number of the river involved Set 4b will be repeated NCriv times Set 4c ICsrc laq Isrc sequential number of collection unit s source Format 3 15 aquifer number of source source number source ID
24. a phreatic surface in the top aquifer and e computation of a sharp salt fresh water interface in the lowermost aquifer Anisotropy Although Triwaco assumes that transmissivities and permeabilities of all aquifers are by default isotropic the user can define an anisotropic transmissivity or permeability The transmissivity or permeability tensor may vary through the model area which implies that the principal axes of the tensor can have different orientations in different points of the model s domain The values in the direction of the principal axes of the transmissivity tensor are given by T4 and The angle between the direction of T and the positive X axis is given by lt 2 Now the values of the transmissivity components the Cartesian coordinate system T Tyx and T y are given by Mohr s circle and may be written as a ee ee To TTi cos ari sin i Ty F F Ty cosa sin x 21 rm T sin t T cos a For each element of the Finite Element Grid the values of T4 T2 and are calculated from the values the nodes that constitute the corner points of the element The transformation equations 21 is carried out using the average values of T4 and Phreatic conditions Whenever the groundwater table falls below the top of the upper aquifer the aquifer is phreatic This implies that aquifer transmissivity becomes a function of the piezometric head h The phreatic
25. alues may be defined If a parameter is not redefined the values from the previous calculation period are assumed to remain valid At least the Sets 7 9 11 and 13 should be repeated Set 26 and 27 are similar to Set 16 and 17 and redefine the transient calculation parameters and the print output options A new stress input time Tenp will be defined and new values for the initial time step or maximum allowable head change may be given Sets 18 to 27 should be repeated for every new stress input time thus producing Sets 28 n 10 to 37 n 10 The transient calculation stops if the value of Teno defined in one of the Sets 26 or 36 n 410 is smaller than the previous value of the parameter Tend Example Flairs input file Flairs fli Set Example text 1 MATRIX Transient calculation 2 3 1 1 0 0 2 1 0000 3a 5 3b 142811 471333 3b 142654 471117 3b 142890 11 470345 87 3b 143169 470972 3b 142884 471332 3a 4 3b 142338 13 470137 27 3b 142968 77 470229 18 3b 142578 13 470333 86 3b 142324 09 470356 84 9 end of sum input 7 end of sources input 9 end of boundary input 11 end of river input 12 IR Calib lR ado IR 12 RP2 Calib RP2 ado RP2 12 RP3 Calib RP3 ado RP3 12 HT HT ado HT 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 13 Royal Haskoning Triwaco User s Manual
26. ameter selected or to Modify the parameter Choosing the Parameter pull down menu from the menu bar displays a slightly different selection of possibilities Info Delete Add Allocate View Adore and Adore as text Copy and Paste Shell ersion 3 0 1 6 t Parameter Calibration Tools Window Help Info JE J amp lete Add c pull down suy Allocate Calibration dataset Modify parameter Par C Ctrl C Map TA Seb Ado Baste 27 Ado az text IH NUDE Lonst Hecharge parameter number RPI NODE Const mur Precipitation exc gPa HP NODE Jh Hydraulic resistar E dit Man file lat 2 APS NODE Const 300 premade resistan pan P Edit Par file NODE Const Parameter pop up menu pr tae Ri ight hand Mouse Button Selecting Modify parameter moves the selected parameters from the Inherited parameters Tab sheet to the Modified parameters Tab sheet The parameter s original and map files in the Initial data set s directory remain unaffected and a new set of par and map files may be created These files will be located in the Calibration data set s directory To add or delete a parameter the Modified parameters Tab sheet should be active visible Only here a parameter other than the Inherited parameters can be added Adding a parameter displays the parameter i
27. ation is carried out with ModFlow Monet produces a Tesnet compatible output file with a number of additional sets that facilitate the generation of Modflow datafiles 1 Mesh refinement around sources in the input file is ignored 2 Density polygons may be digitised clockwise or counter clockwise and do not have to appear in a particular order in the input file 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 31 Royal Haskoning Triwaco User s Manual 3 The density of the polygon with the largest area is used as the default area constraint for the entire model 4 Rivers that cross the boundary more than once will be split into separate rivers with the same river id Monet first reads the boundary river and source input and snaps all input points that are closer to each other than EPFIX Set EPFIX to 0 if you don t want nodes to be snapped The intersection points with the rivers and the boundary are calculated and the rivers and sources are clipped to the boundary polygon Next the density polygons are read and sorted on de creasing area After reading all input the smallest rectangle enclosing the boundary polygon is calculated and rectangular grid cells are created within the enclosing rectangle The distance between the gridlines is determined by the node distance of the density polygons Finally the centers of the grid cells are calculated and used to generate a triangular mesh 5 4 3 Simulation options After allocatio
28. boundary directed outward Using Darcy s law one obtains TVo Aad ar m T with P the flux across the boundary into the model area 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 20 Royal Haskoning Triwaco User s Manual Through substitution of the approximate solution and approximation of the boundary flux by a series of point sources or sinks we obtain the following Finite Element equation vo 9 g tg R tO a 4 jal 10 N g D 0 The time derivative has been given by a completely implicit finite difference equation The integrations in the equations can be easily performed due to the simple form of the shape function Note that due to the definition of the different recharge terms the Finite Element equations can be nonlinear This implies that both nonlinear and linear iterations have to be carried out to solve the equations The linear iterations used to determine the solution of a linearized system of equations are referred to as inner iterations The nonlinear iterations are referred to as outer iterations These are used to update the linearization of the equations in order to obtain an accurate solution to the nonlinear problem 5 3 4 Solution technique The resulting Finite Element equations will generally form a system of nonlinear equations mainly due to the nonlinear character of the recharge term 4 Mor
29. calculation of groundwater flow program name Flawin95 FlawinVD FlawinVDEXT Normally if a calibration file calib chi exists a comparison between calculated and observed heads will be carried out A standard input file flairs fli must be generated from the TriShell Also a standard grid file grid teo is required Output will be written to files flairs flo flairs flp and flairs log If no arguments are given the program opens in Windows mode The appropriate input files grid teo flairs fli and calib chi can be selected and the program may be run using the pull down menus Command line call Flawin95 exe set dir grid dir flairs fli calib chi options One may choose from the following options calibration file checking f no Flairs computation Example Flawin95 C model cal C model grid flairs fli calib chi Flawin95 C model cal C model grid flairs fli calib chi f 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 17 Royal Haskoning Triwaco User s Manual 5 3 Mathematical background of FLAIRS 5 3 1 Introduction In this documentation a description will be given of the governing differential equations and the Finite Element formulation of these equations Furthermore a description will be given of the way recharges and fluxes are treated in the program Special options such as anisotropy and phreatic transmissivity are discussed and the way the Finite Element equations are solved will be descr
30. d infiltrated is given by the user and the program computes the hydraulic head at the sources location For multi screen wells the sources may be clustered over successive aquifers the separate abstraction rates are totaled and the hydraulic heads is assumed to be equal for all aquifers considered Similarly wells in the same aquifer that are connected by a suction pipe are treated in the same way he head at the abstraction or infiltration well is given and the program will calculate the rate Both cases are easily treated in the Finite Element equations The type of source or sink that will be used is determined by a source type parameter to be defined by the user By default the program assumes the source to be defined by a given rate Note that due to the definition in the partial differential equations an infiltration rate must be given by positive values whereas abstraction rates have negative values Rivers Rivers and drains are line sources or line sinks usually defined in the top aquifer In the program Flairs these line sources are approximated by a series of point sources situated in the so called river points nodes that together define the river s course Similarly to the point sources the discharge from or recharge towards these rivers may be defined in two ways e The head at the river or the piezometric head in the drain is given The program will calculate the discharge rate e Adischarge or recharge rate is given
31. e conjugate gradient method the user is referred to the handbooks on numerical methods When transient calculations are carried out the user also has to provide the maximum change in groundwater head that is allowed during each time step The program will now compute the size of the time step to be used This time step depends on the maximum change in groundwater head during the previous time step and the maximum allowable change defined by the user If the calculated change dh is smaller than the allowable change 2 the new time step will become OA 4 oq 16 IM nu Gs If the change in groundwater head dh during a time step is greater than the maximum change Afw the calculation will be repeated once with a time step ae 0 cate nia 1 IM Ji IM for Ji 17 d A 05 Ae For fnm lt 05 Hence the multiplication factor between two successive time steps varies between a minimum value of 0 5 and a maximum of 2 0 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 22 Royal Haskoning Triwaco User s Manual 5 3 5 Recharge terms and Boundary fluxes As discussed in the previous section vertical recharge into an aquifer can be divided into four parts depending on the origin of the water see equation 2 recharge from or discharge towards a so called top system recharge or discharge due to leakage through a separating layer recharge from or discharge towards rive
32. ent calculations are carried out aquifer conditions at a given location may also vary in time The aquifer conditions will also influence the value of the storage coefficient to be used For a confined aquifer the storage coefficient is defined by the elastic storativity 5 whereas for phreatic conditions the storage coefficient is given by the effective porosity n Interface conditions The groundwater in the lowermost aquifer can be flowing over a body of a heavier but supposedly stagnant fluid For example in coastal areas the fresh water is separated by a relatively sharp interface from relatively stagnant salt water The elevation of the interface Hj is given according to the Badon Ghyben Herzberg equation il 1 Hy can Br s H LH E Hy 23 The variables h and h represent the salt water head in the stagnant salt water body and the piezometric head in the fresh water respectively The parameter is a measure for the density differences between the 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 28 Royal Haskoning Triwaco User s Manual fresh and the salt water and is defined by fa 24 we the fluid density for the fresh water body pu the fluid density for the salt water body For each element of the Finite Element Grid the values of h and are calculated from the values in the nodes belonging to the element Definition scheme Interface conditions H Re
33. eover the fact that both the transmissivity and the storativity of the top or bottom aquifer may change with the groundwater head also results in non linearity of the equations This is the case whenever phreatic conditions or a salt fresh water interface are present The Finite Element equations are given in an implicit way So they contain parameters related to the unknown groundwater head at the new time level for instance the recharge q Hence the recharge q will be unknown too The recharge q is approximated in the following way e one In case of phreatic conditions both the transmissivity and the storativity are calculated for the known values of the groundwater head The resulting linear equations are solved by the conjugate gradient method When a solution is found the process may be repeated using the new values of the groundwater head Thus two types of iterations are performed e inner iterations or linear iterations e outer iterations or nonlinear iterations For both types of iterations the user defines the maximum number of iterations allowed A maximum for the number of linear or inner iterations is as a rule of thumb equal to the total number of unknowns which will be sufficient in most cases The number of outer iterations required is strongly dependent on the non linearity of the different terms For a completely linear system one single outer iteration is sufficient The number of iterations f
34. er Drain level of system of pipe drains Hp Polder water level or controlled water level Hs Surface level with respect to the ordnance level H Level of base of semi pervious top layer Kn Horizontal permeability of semi pervious top layer Ky Vertical permeability of semi pervious top layer L Horizontal distance between drains R Wetted perimeter of pipe drains BD Drainage base or bottom level of the open drains BD Drainage base or bottom level of the primary drainage system BD Drainage base or bottom level of the secondary drainage system BD Drainage base or bottom level of the tertiary drainage system W Drainage or infiltration resistance between ditches or drains Wa Drainage resistance between ditches or drains Wa Drainage resistance of the primary drainage system Wa Drainage resistance of the secondary drainage system Wa Drainage resistance of the tertiary drainage system Wi Infiltration resistance between ditches or drains Wi Infiltration resistance of the primary drainage system Wi Infiltration resistance of the secondary drainage system Wis Infiltration resistance of the tertiary drainage system 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 26 Royal Haskoning Triwaco User s Manual 5 3 6 Special options Regarding the transmissivity or permeability of the aquifers Triwaco offers a number of special options The options available are e aquifer anisotropy e computation of
35. es V10nn STEADY STATE V10nn STEADY STATE V20nn STEADY STATE V20nn STEADY STATE V30nn STEADY STATE V30nn STEADY STATE Top system fluxes and leakage QSxx STEADY STATE QSxx TIME nnnnnnnnnn QRCH STEADY STATE QRCH TIME nnnnnnnnnn QDR1 STEADY STATE QDR1 TIME nnnnnnnnnn QKWx STEADY STATE QKWx TIME nnnnnnnnnn _ x indicates leakage from aquifer x 1 to aquifer x Recharge and discharge to rivers QRIx STEADY STATE QRIx TIME nnnnnnnnnn Recharge and discharge to sources QSCx STEADY STATE QSCx TIME nnnnnnnnnn Boundary fluxes QBOx STEADY STATE QSOx TIME nnnnnnnnnn x number of aquifer The string nnnnnnnnnn stands for one of the output times defined by the user the format used for the output times is F10 4 The length of the output parameter name is in all cases twenty characters including spaces or blanks Drainage result file top4q out If applicable for topsystem 4 see input description then the drainage infiltration fluxes are written to top4q out Is same as in the flairs flo file steady state calculations transient calculations Drainage infiltration fluxes TOP1 AT TIMESTEP 1 TOP1 AT TIMESTEP nnn TOP2 AT TIMESTEP 1 TOP2 AT TIMESTEP nnn TOP3 AT TIMESTEP 1 TOP3 AT TIMESTEP nnn TOP4 AT TIMESTEP 1 TOP4 AT TI
36. ference level Bottom Aquifer fresh water salt water Similarly to a phreatic aquifer one can distinguish the following situations e The aquifer is completely fresh the interface is below the base of the aquifer hence Hg for lS Hay 25a e The aquifer is partly fresh the interface is between the top and the base of the aquifer hence for Hay lt lt Any 25b e The aquifer is completely salt the interface is above the top of the aquifer hence r for Lhe Ayal 25c It is assumed that the interface will not pass the top of the aquifer and reach the overlying aquifer Thus aquifer conditions may vary depending on the value of the piezometric head The value of the piezometric head differs for each node of the Finite Element Grid Consequently the lowermost aquifer can be completely fresh partly fresh and partly salt or completely salt at the same time The aquifer conditions will also influence the value of the storage coefficient to be used For a completely fresh aquifer the storage coefficient is defined by the elastic storativity S For interface conditions with a partly fresh aquifer the storage coefficient is defined by with n representing the effective porosity 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 29 Royal Haskoning Triwaco User s Manual In case of a single aquifer model both a phreatic surface and a salt fresh water interface may appear in the same
37. ge Input parameter dimension RCH Recharge package RECH L T GHB General Head Boundary Cond L T L Q Cond Hono Ho L T DRN Drain package Horan L Cond L2 T Q Cond B Hoe Hoen 7 L T Q 0 Heer 5 TS RIV River Package I L Hay L Cond L T Q Cond Hay Hoen Dea L T Cond Hay Reor Hce 5 Where in Triwaco a distinction be made between an infiltration and a drainage situation the GHB DRN and RIV package do not differentiate between these two situations The conductance is supposed to be a constant regardless of the prevailing condition Therefore the upper boundary condition in Triwaco be it a top system or a river is translated into a combination of the ModFlow boundary packages mentioned The precipitation excess or groundwater recharge is simulated using the RCH package The conductance of the GHB or RIV package is based on the infiltration resistance of top system or river whereas the conductance of the DRN package is based on the drainage resistance Thus the program runMFfli will interpret the top system and river information and generate the corresponding ModFlow packages Triwaco Top system ModFlow packages 1 Precipitation excess RP1 RCH IR 2 Controlled water level RP1 GHB Hydraulic resistance Drainage resistance RP2 RP3 IR 4 Not yet fully functional RP1 RP13 IR 711 Precipitation excess RP1
38. hat become dry the value of 1 0 E 32 is assumed signifying the cell is inactive and does not participate in the groundwater flow However whenever the water table rises above the aquifer s base elevation the cell should participate in the groundwater flow again This process is called rewetting and is supposed to be active Values for the rewetting threshold and the frequency of updating are fixed Rivers Streams and rivers are usually defined by line elements and will be converted to a combination of ModFlow s DRAIN and GHB package thus accounting for differences in drainage and infiltration resistances Generally this approach will be permitted as long as the groundwater head does not fall below the bottom level of the river However in cases very low groundwater heads may be expected the linear relation between the head difference and the infiltration flux is not valid any more In that case the RIV package should be used in stead of the GHB package The user can specify which line elements are to be defined by the RIV package by adding the parameter BRx and modifying Rax HoLa BR General BR Description Bottomlevel of rivers aquifer Parameter file BH2 par Mame Map file BR2 ung Result file BR2 ado E FSettings lt amp lt Parameter type Default value Status i RIVER 0 Allocator Expression Expression IF HR1 1 5 gt TH1TH1 Cancel For those rivers that s
39. hould be converted to the RIV package the river activity parameter RAx should be set to 3 In addition the parameter BRx is added representing the river s bottom elevation This parameter can be added selecting User Defined from the Parameter pull down menu and filling in the parameter definition window After having allocated all parameters the input file can be generated as usual 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 35 Royal Haskoning Triwaco User s Manual Translation of model parameters For the definition of the upper boundary condition Triwaco uses the so called top systems together with line elements or rivers The top system parameters are distributed parameters defined in each node of the grid and represent the node s influence area The river parameters representing line elements are defined in each river node and are valid for an area equal to the length of the river stretch multiplied by the river width which is generally considerably smaller than the river node s influence area In ModFlow the upper boundary condition is defined for cells belonging to the uppermost layer regardless of the fact whether the boundary condition represent a distributed parameter or a line element The area represented is accounted for in the conductance parameter Cond The following ModFlow packages are used to define the upper boundary condition Code Packa
40. ibed 5 3 2 Partial differential equation The partial differential equation that is solved by approximation in the program Flairs follows from Darcy s law and the equation of continuity In the derivation of the equations the Dupuit Forchheimer assumption is used so that the partial differential equation can be written in terms of the potential h or groundwater head as SL T i ZJ s There are no restrictions on the transmissivity tensor T Therefore the transmissivity can be anisotropic while the principal directions do not coincide with the coordinate axes E S nd bi L E 1 For a multi aquifer system the equation 1 holds for each aquifer The aquifers are coupled through the recharge term g The top aquifer may be phreatic In that case transmissivity is a function of the groundwater head and the permeability of the aquifer while storativity changes if the aquifer changes from confined to phreatic conditions In the lower most aquifer a salt fresh water interface may be present The salt water is assumed to be at rest and the interface can be obtained from the Badon Ghijben Herzberg equation In that case transmissivity is again a function of the groundwater head and the aquifer permeability Also storativity changes when the aquifer changes from completely fresh to partly fresh Note that Flairs should not be used for transient calculatio
41. ibilities and or limitations of the simulation package The default grid has finite elements with the corresponding simulation package Flairs Flairs is a three dimensional saturated groundwater flow simulation program The program uses triangular elements with linear shape functions The numerical calculations are based on Galerkin s method For Finite Difference Grid Triwaco uses ModFlow 96 provided by the USGS ModFlow also is a three dimensional saturated groundwater flow simulation program Executing model calculations with ModFlow is explained in chapter 5 4 5 2 2 Simulation Package FLAIRS Flairs uses a Finite Element grid created by the program Tesnet and parameter files in Adore format generated by various allocators and with the extension ado With the aid of the program TriPlot or other Windows programs the results can be visualized as contour maps or hydrographs The results can directly be used for post processing and auxiliary programs Flairs calculates the groundwater heads and fluxes in a groundwater domain that is divided into aquifers and aquitards Important features in Flairs are the rivers line source sinks and point sources which are active within aquifers and the large selection of different top systems that control the flux from the surface or confining layer to the first aquifer Hydrogeological parameters are given at the nodes of a Finite Element Grid These input parameters have to be available in Adore format
42. ion 5 2 4 Executing the model simulation For starting the model calculations one first selects Generate input from the Calibration pull down menu bar This will generate the input file needed flairs fli This input file may be viewed or edited selecting View Input from the pull down menu The input file contains all parameters needed for the calculations description of the input file flairs fli is given in paragraph 5 2 6 Selecting Run Simulation from the Calibration pull down menu starts model simulations A window showing the calculation process will be displayed and the program will be added to the tasks window Once the calculation has stopped the Result parameters Tab sheet will be updated After the first run this Tab sheet will be added to the Calibration data set If a calibration file has been defined the program automatically compares the calculation results with the observed heads fluxes The simulation program produces different types of output files Some of these files contain information on the calculation process errors encountered flairs flg others contain the calculation results using various formats flairs flp flairs flo Flars version 3 0 jun2002 File Run Help Calibl OUTER ITERATION 3 MAXIMUM 100 INNER ITERATION 10 MAXIMUM 500 INACCURACY REQUIRED CURRENT PHEVIOUS PHEV 1 PHEY 2 0 000010 0 000559 0 000631 0 000743 0 000905 OUTER ITERATION NUMBER 2 1 INNER IT
43. le Example RunMFfli C Projdirs Modflow C Projdirs Monet flairs fli MFU2FLO Program for the conversion of ModFlow output to a standard Triwaco output file flairs flo The existence of a MODFLOW compatible grid file is required The program searches the working directory set dir for a MODFLOW output file with the same name as the input file mentioned on the command line Command line call MFu2Flo exe set dir grid dir flairs fli calib chi No options are available Example MFu2Flo C Projdirs Modflow C Projdirs Monet flairs fli 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 38
44. lt of the calculation For steady state calculations the output file contains the following variables average groundwater heads for the top system groundwater heads for each aquifer piezometric head at the salt fresh water interface recharge to the top system sum of drainage infiltration in topsystem leakage through the separating layers discharge or recharge of rivers for each aquifer discharge or recharge of sources for each aquifer boundary fluxes for each aquifer similarly for transient calculations the output file contains the following variables average groundwater heads for the top system at the end of each period groundwater heads for each aquifer at the end of each period recharge to the top system at the end of each period leakage through the separating layers at the end of each period discharge of rivers for each aquifer at the end of each period discharge of sources for each aquifer at the end of each period boundary fluxes for each aquifer at the end of each period 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 15 Royal Haskoning The parameter sets in the file flairs flo have the following names Triwaco User s Manual steady state calculations transient calculations Phreatic and piezometric heads PHIT STEADY STATE PHIT TIME nnnnnnnnnn PHIx STEADY STATE PHIx TIME nnnnnnnnnn x number of aquifer Variable density correction flux
45. lver are partly fixed and partly read from the flairs fli input file The parameters read from the input file are the maximum number of inner and outer iterations 1 and set 14 of the input file the relaxation factor set 2 of the input file and the max max criterion of convergence EPS set 14 of the input file rlax Note that the parameter EPS specified in the calculation options window has a quite different meaning within Triwaco than the criterion for convergence within ModFlow The parameter EPS is now used to define the physical closure limits which depend on the system units The head change criterion HCLOSE has the dimension of Length and the residual criterion of convergence RCLOSE the dimension of Length 3 Time Where ModFlow generally uses the system units meters and seconds most Triwaco users employ the system units meters for length and days for time Therefore the recommended value of 0 01 or 0 001 for the head change criterion HCLOSE can be adopted However because the residual criterion for convergence RCLOSE depends on the time unit the recommended value equal to HCLOSE should be multiplied by 86400 the number of seconds per day 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 32 Royal Haskoning Triwaco User s Manual The program runMFfli reads the value for HCLOSE from the input file and computes the value for RCLOSE afterwards ModFlow
46. n of the values for all model parameters one may start the groundwater flow calculations First selecting Calibration Options from the menu bar the Calculation options dialog box is opened In this dialog box the user specifies parameters related to the iteration process Description Function Inner iteration Sets the maximum number of inner iterations Outer iteration Sets the maximum number of outer iterations Convergence Sets the criterion for confergence Relaxation Sets the relaxation factor 1 Calculation options r teratian Inner iteratian 5t Outer iteration 100 Convergence 0 00001 Relaxation 1 0000 Apart from the maximum number of iterations the user has to specify a criterion for convergence The program checks whether or not differences are less than the criterion specified The initial conditions for each outer iteration depend on the head change between outer iterations In case of badly converging systems a relaxation factor may be defined In that case the head change between outer iterations is multiplied with the relaxation factor This causes a more stable iteration process but also results in smaller head changes thus requiring more iterations to reach a solution ModFlow calulation settings The program runMFfli assumes that Version 2 of the Preconditioned Conjugate Gradient solver is used PCG2 in the ModFlow calculations The parameters for this so
47. ned in the initial data set the calibration set is based on Modified parameters This sheet displays all parameters created or modified in the actual calibration data set Result parameters This sheet displays all parameters that result from the model calculations It is displayed only after model calculations have been carried out inherited parameterstab sheet Modiied parameters tab sheet Resut parameters tab shest Demonstration model ni Modified parameters Result parameters Type Allocator Default Description 2 IH HODE Const 11 Recharge parameter number APT NODE arpadi O01 Precipitation excess 1 amp DD 1 0 5 Execution of Groundwater Flow Simulations FLAIRS MODFLOW 3 Royal Haskoning Triwaco User s Manual Double clicking on one of the parameters starts the graphical editor DigEdit For each of the parameters the user can create a new map and par file or modify the existing map and par file These changes take place in the directory of the Initial data set the Calibration set is based on Pressing the right hand mouse button displays the parameter pop up menu This menu allows the user to retrieve Info to View or edit the map or par file to View the Ado file the file containing the parameter values assigned to the nodes of the grid to Allocate the par
48. nfo window This window can also be accessed from the Info command in the pull down and pop up windows Deleting a modified parameter from the Modified parameters Tab sheet restores the original settings for this parameter The parameter reappears in the Inherited parameters Tab sheet 5 1 3 Allocating model parameters Selecting Allocate from the parameter pull down or pop up menu starts the selected allocator and an Ado or Adore file will be generated After allocation the status of the parameter will change from X to 9 The Ado file contains an array with parameter values interpolated at the locations of the nodes of the grid This array is preceded by the name of the parameter a code indicating whether the array contains one constant value or as many values as there are nodes and the number and format of values that follow The array is concluded with the text ENDSET Such an array with parameter values is called an Adore set The number of values in the array depends on the type of parameter and equals the total number of nodes the number of river nodes the number of source nodes or the number of boundary nodes see appendix B for a complete overview and the lay out of the map parameter and corresponding ado files appendix C gives an overview of currently available allocator types 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 4 Royal Haskoning Triwaco User s Manual 5 1 4 Viewing the allocated parameters
49. ns with a salt fresh water interface due to the assumption of a stagnant salt water body Phreatic conditions and a salt fresh water interface may be defined in one and the same aquifer in case of single aquifer systems In case of transient calculations or if salt water is present in more than one aquifer the variable density module of FLAIRS FLAIRSVD should be used The use of this module requires additional input and some minor changes in the standard Flairs input file which is carried out in the TriShell automatically when the corresponding Program Group is choosen in the Grid data set Water course ARStr actions Groundwater recharge n Phreatic a NN grondwater level ENS Aquifer 1 Vertical flow E 22220200222 Aquitard H 1 Basis of 5 Execution of Groundwater Flow Simulations FLAIRS MODFLOW 18 Royal Haskoning Triwaco User s Manual The recharge term q comprises a number of different effects In the program Flairs is divided into four distinctive components depending on the origin of the water recharge from a top system at the top of the uppermost aquifer due to e g precipitation infiltration etc leakage through the separating aquitards between aquifers discharge to point sources or recharge from point sinks discharge to rivers and drains and recharge from line sinks A multi aquifer system with several recharge terms is sho
50. ntains information on the water balances of the various aquifers including the error in the water balance for each aquifer These errors should be within reasonable limits e g less than a few percent at a maximum Furthermore the discharges towards the rivers sources and boundaries are summarized The print output file flairs flp is always generated and contains e A water balance for every aquifer For transient calculations this water balance is given for every time step together with a cumulative water balance A water balance for the sub areas defined in the input file usage described together with flairs fli The total recharge or discharge for each collection unit defined in the input The recharge from or the discharge towards all river nodes The recharge from or the discharge towards all point sources and sinks 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 14 Royal Haskoning Triwaco User s Manual e The boundary heads and boundary fluxes for all boundary nodes Optionally the following output may be added to the print file provided the corresponding print flags are enabled in the flairs fli input file e The groundwater heads for each aquifer and for every node e The location of the salt fresh water interface for every node The recharge from the top system and the leakage through the aquitards for every node In case of transient calculations this output is given at the end of every calculation pe
51. o Hp Wat Wa Was Wi Wi Wis BD BD BD Hs 5 P Hs He H K K L R 6 P Hs He H K K L R 7 Co W Hp 8 not in use 9 not in use 10 P BD Hs 11 P Co Wa Wi Hp 12 P a b Hs As can be noticed from this table the top system parameters RPxx for different top systems do not necessarily represent the same physical parameter For example parameter RP1 may represent precipitation P the surface level elevation Hs or the controlled water level Hp Moreover different top systems require a different number of parameters ranging from only one for top system type 1 to as much as thirteen top system type 4 The physical parameters associated with the top system parameters are listed in the following table One can distinguish parameters related to the meteorological condition precipitation and evapotranspiration soil parameters surface and surface water levels and parameters with respect to the geometry and resistances of the drainage system 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 25 Royal Haskoning Triwaco User s Manual Name Definition of parameter P Precipitation excess or irrigation excess ET mx Maximum Evapotranspiration A soil parameter obtained by curve fitting B soil parameter obtained by curve fitting b gt 1 Co Hydraulic resistance of semi pervious top lay
52. o account other than by their hydrogeological properties Fully 3D For combined groundwater flow and transport modeling however it is usually preferred to create a fully 3 dimensional model taking all layer boundaries into consideration The program runMFfli will translate the input file to a fully 3 D ModFlow model if the following Triwaco parameters are used in stead of the transmissivity TXx e the aquifer s permeability PXx e the aquifer s top elevation RLx and e the aquifer s base elevation THx 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 34 Royal Haskoning Triwaco User s Manual The parameters representing the aquitards don t need any modification The input file can be generated as usual selecting Generate input from the Calibration pull down menu It is recommended to check the input file and to remove the lines defining the parameter TXx which may appear in the input file if both TXx and PXx are defined in the same data set Recharge and rewetting The recharge is computed for each cell from the corresponding Triwaco parameter generally top system parameter RP1 By default recharge is supposed to take place in the uppermost active cell NRCHOP 3 in the RCH1 package Unlike Triwaco ModFlow allows cells to go dry if the water table falls below the base of the aquifer in Triwaco only the uppermost layer may become dry resulting in a zero value for this aquifer s transmissivity For cells t
53. odel area Now the user can contour or classify the result parameters and view the results in plane view or can select a cross section of the model area Alternatively the user can select one of the parameters from the result parameters sheet and viewing the parameter separately selecting View Adore from the Parameter pull down menu or View Adore file from the pop up menu right hand mouse button Adding other parameters selecting Param Load from the TriPlot menu bar gives the user the opportunity to compare result parameters with model input parameters 5 4 6 Output data description The output description of Triwaco files is described in section 5 2 7 The simualtion results are saved in bot Triwaco standard output files flairs flo flairs flg and flairs flp but also in the standard ModFlow output file format flairs out The output of ModFlow files is described in the standard ModFlow manual provided by the USGS 5 4 7 MODFLOW parameter handling by TRIWACO The standard input file with the default model parameters may be used without any modifications In that case the program will generate ModFlow input files that are compatible with the Triwaco stratification of aquifers with horizontal groundwater flow and aquitards with vertical flow The prevailing parameters are the aquifer transmissivity and the hydraulic resistance of the intermediate confining layers The depths and thickness of the various layers are not taken int
54. of a calibration file calib chi If a calibration file calib chi is present Triwaco automatically compares calculated hydraulic heads fluxes with the data from observation wells After comparison Triwaco will calculate the average deviation the average absolute deviation the squared average deviation the minimum deviation and the maximum deviation To view or edit the calibration file select Calibration Calibration View Create Input from the pull down menu The input file has a fixed format described in chapter 10 The output of the calibration can be viewed as table Calibration Calibration View Output or as a background map in Triplot Calibration l Calibration View A comprehensive description on the usage of the calibration calib chi file is given in chapter 10 Version 3 0 2 3 rameter Calibration Tools Window Help Options Generate Input Run Simulatian View b Calibration Create Input View Output View Log View Map 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 5 Royal Haskoning Triwaco User s Manual 5 2 Executing model simulations with FLAIRS 5 2 1 Introduction Triwaco can handle two types of grids Finite Element Grids and Finite Difference Grids Once one of these is selected in the Grid definition window Triwaco will use the corresponding simulation package The choice between the two is depending on the type of problem poss
55. ollowing Steady state calculations for multi layered aquifer systems both semi and fully 3D Top system type 1 2 4 and 11 defined by the RCH GHB and DRN packages Rivers of type 1 RAx 1 defined by the GHB and DRN packages Rivers to be defined by the RIV and DRN packages special type RAx 3 Constant head boundaries IBx 0 defined by constant head cells Given rate abstraction wells ISx 0 defined by the WEL package For transient calculations and implementation of other boundary conditions the user should modify the ModFlow input files or contact the Triwaco Help Desk assistant 5 4 2 Using the Simulation Package MODFLOW Groundwater flow calculations can be carried out in a way similar to the calculations with the standard Triwaco programs One only has to define ModFlow as the simulation package in the Grid data set info window by selecting ModFlow in the Progam Group pull down menu Triwaco will then use Monet for generating the finite difference grid and ModFlow 96 to calculate grondwaterflow HE TestMF FDBrid Description FDGrid Directory Mame FO Grd x Cancel Path EAM y Models TestMF FO Grid Program Group Default arid Default MModFlow Minimum Distance wp AMD Sat Between boundary ri 10 0 Between points in density polygons as fraction of the density of the polygon 0 50 Monet is used as two dimensional mesh generator for Triwaco when the simul
56. or more complex situations may increase strongly with complexity Default the program sets the maximum number of outer iterations to 100 a number that is hardly ever reached and the maximum number of inner iterations to 500 If the number of inner iterations appears not to be sufficient the program asks the user whether or not to continue the calculations If the user agrees to continue the program doubles the number of inner iterations allowed 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 21 Royal Haskoning Triwaco User s Manual The program will stop if the maximum number of outer iterations is exceeded For each outer iteration the number of inner iterations will be checked For transient calculations the program will proceed with a new time step if the maximum number of outer iterations has been reached or if the number of inner iterations during an outer iteration equals 2 or less Apart from the maximum number of inner iterations the user has to specify a criterion for convergence The program checks whether or not the norm of the right hand side vector and the residual vector differ less than the criterion given Hence if the system of equations to be solved is given in matrix notation 12 the residual vector becomes for an approximate solution A l us ll 13 1 and we accept as the correct solution if kl 14 4 where Joi r eer 2 15 For a description of th
57. rameter files boundary conditions output options and so on The input file may be generated automatically from the TriShell or edited manually The input required in the flairs fli consists of the following sets Set 1 HEAD identification of project or grid Format A40 HEAD is an alphanumerical string for identification of the project s grid Set 2 Naq Iffr Ifss Ifsf Iftr Nsar Rrlax number of aquifers Format flag for confined phreatic calculations 6 15 F10 4 flag for steady state transient calculations flag for variable density or salt fresh water interface dummy flag used only in previous versions of Flairs number of sub areas for water balance calculation relaxation factor for non linear iterations Naq the number of aquifers flag for semi confined 0 or phreatic 71 calculations Ifss a flag for steady state 0 or transient 71 computations also used for the definition of the Surface water option FLAIRSSF 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 8 Royal Haskoning Triwaco User s Manual Ifsf a flag for absence 70 presence 71 of a salt fresh water interface variable density FLAIRSVD 2 Iftr a dummy flag in former versions for preparing Trace output Nsar the number of sub areas a water balance will be calculated for Rrlax the relaxation factor for the non linear iterations Set 3a NB number of boundary points for water balance sub Format 15 areas
58. riod for which the user enabled print output by setting the appropriate flag If all print flags are enabled the print file may become very large Therefore by default these print flags are disabled and the print file only contains the water balances and an overview of the river source and boundary fluxes Simulation log file flairs flg Selecting View Log displays the execution log file flairs flg This file contains information on the progress of the calculation process Any error during the simulation are written to this file The following information is written to this file e General information regarding the used grid the number of aquifers the type of the top aquifer and the computation of a salt fresh water interface e Information concerning the input parameters and the parameter files used Warnings and Error messages are included e Information concerning the iteration process The convergence criterion the maximum number of iterations and the number of iterations used are reported Consultation of the execution log file is advised whenever an error message is generated Even if the calculation seems to have finished without problems a quick check of the log file may confirm whether or not the program has terminated correctly Simulation result file flairs flo Finally all calculation results are stored in the result file flairs flo which contains the output parameters in Adore format These parameters provide the resu
59. rs canals and drains recharge from sinks or discharge towards sources Horizontal recharge is given by the boundary fluxes In this section all recharge terms are treated in more detail In all cases a relation between the recharging or discharging flux and the piezometric head in the aquifer can be defined These relations vary from simple to very complicated as can be seen from the description of the various recharge terms in the following sections First the boundary fluxes are treated and next the vertical recharge terms in order of increasing complexity Boundary fluxes Boundary fluxes can be considered to result from a line source or line sink in the two dimensional model area In the Finite Element program these line sources are approximated by a series of point sources located at the boundary nodes The boundary flux is defined positive flowing into the model area There are two ways in which the boundary fluxes can be calculated e he groundwater head at the boundary may be given and the flux will be calculated as function of the gradient of the groundwater head at the model s boundary Qo TV 18 e he groundwater flux across the boundary is given as function of the groundwater head at the boundary ga Bh B 19 Here m d per and B m d per m m d are the boundary flux parameters A given constant flux independent of the groundwater head may be obtained by setting the value for B to
60. size Tend the stress input time or time at which a new time step starts and new input data may be defined end time of calculation period DHmx the maximum allowable change in groundwater head per time step for the time period considered DT the size of the initial time step for the time period considered Set 17 Iprn Irst Iphit Iqrch print and output flags Format 4 4n I5 Iphin Iqkwn n 1 Naq Iqrin Iqscn n 1 Naq Iprn code for printing 71 not printing calculation results to the print output file flairs flp default value O no print output If IprnzO calculation results not to the print output file If Iprnz1 calculation results to the print output file default If Iprnz2 calculation results to the print output file and top system fluxes will be written to file Top4Q out only if top system 4 is selected and flairs flo Irst code for generating restart record If Irst 0 no restart record default If Irst 1 a restart record will be written at time Tenp transient calculations only Iphit code for writing 71 or not writing calculation results for the parameter PHIT to the output files flairs flo default value 1 Iqrch code for writing 71 or not writing calculation results for the parameter QRCH to the output files flairs flo default value 1 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 12 Royal Haskoning Triwaco User s Manual Iphin code for writing 71 or not
61. transmissivity is calculated by the program Flairs using the following parameters which have to be specified by the user e permeability tensor which may be anisotropic K K4 Kz and 2 e elevation of the base of the upper aquifer Hs1 e elevation of the top of upper aquifer The elevation of the top and the base of the upper aquifer are measured with respect to the same reference level that is used for the piezometric heads 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW 27 Royal Haskoning Triwaco User s Manual Definition scheme Phreatic conditions Top Aquifer 4 The aquifer s transmissivity is computed with the following assumptions e When the piezometric head is below the base of the aquifer the aquifer is dry hence 0 for x Hg 22a e When the piezometric head is between the base and the top of the aquifer the aquifer is phreatic hence T Kdh Hg for h Hy 22b e When the piezometric head is above the top of the aquifer the aquifer is confined hence It is assumed that the phreatic surface will not fall below the base of the aquifer and reach the underlying aquifer Thus aquifer conditions may vary depending on the value of the piezometric head The value of the piezometric head differs for each node of the Finite Element Grid Hence the upper aquifer can be partly dry partly phreatic and partly confined at the same time Moreover when transi
62. triwaco groundwater modelling software 5 Execution of Groundwater Flow Simulations FLAIRS and MODFLOW ROYAL HASKONING Chapter 5 Execution of groundwater flow simulations 5 1 Creating a Calibration data 5 3 5 3 5 1 2 Opening a Calibration data 5 3 95 4 9 Allocalng mod l Daratmelers 2552 e se tee orta oo rb ve a o pube TAM DR EE RENE 5 4 5 1 4 Viewing the allocated parameters cccccssscccsesecccssserccsesereceueetenssserseauersesauetenssserenseeesanneerenses 5 5 5 1 5 Definition of initial head ParaMetelS cece ceccccseceeceeeeceececeeeeeceececseeeeseeceseeecseeeeseeeessaeessaees 5 5 5 1 6 Definition of a calibration file Calib CHI cccccescecceeseecceseeecceseecseuseecseuseessageeecsuseesssasesssneees 5 5 5 2 Executing modelsimullations With niet aaa exeo ten ette taces REOR OE tue 5 6 SN M MTOdtUCiON essa e a 5 6 5 2 2 olimulation Package FLAIRS siib pontes a 5 6 9 2 3 OlMUIAUOMPODMONS sana a a deett ences a a a E 5 6 5 24 Executing the model SIMULATION E a a dead 5 7 5 2 5 Viewing output results Eu EM 5 8 5 2 0 0
63. wn below Note that the numbering of aquifers and aquitards in Triwaco is always top down and the number of aquifers is one greater than the number of aquitards The layer covering the uppermost aquifer is also referred to as aquifer number 0 and is part of the top system 5 3 3 Finite element equations The Finite Element equations are derived from the partial differential equation given in equation 1 Subdividing the recharge term q in four distinctive components this equation is written as al Lo RR al 2 Pep oe XV ty wy BP ocv 2 or ct The components of the recharge term are Fa Recharge from the top system the shallow drainage system cf Recharge due to leakage Fy Recharge from rivers canals and drains t Recharge from sources or sinks For the sake of simplicity the first four terms of the equation 2 will be combined 3 Vc z Vay J 3 with T representing the transmissivity tensor The Finite Element equations are derived using Galerkin s method The following simplifying assumptions are made The spatially distributed recharge terms 7 recharge and leakage can be approximated by an infiltration or abstraction in the nodal points of the grid If the value in point is given the strength at that point is given by du A M where 4 represents the area of influence of nodal point 7 e The recharge
64. writing calculation results for the parameter PHIn n ranges from 1 to Naq see Set 2 to the output files flairs flo default value 1 Iqkwn code for writing 71 not writing calculation results for the parameter QKWn n ranges from 1 to Naq see Set 2 to the output files flairs flo default value 1 Iqrin code for writing 71 or not writing calculation results for the parameter QRIn n ranges from 1 to Naq see Set 2 to the output files flairs flo default value 1 Iqscn code for writing 71 or not writing calculation results for the parameter QSCn and QBOn n ranges from 1 to Naq see Set 2 to the output files flairs flo default value 1 The flags Iphit Iqrch and following are only required in case of transient calculations Selecting a value 0 not writing to output diminishes the size of the output file considerably However calculation results for those parameters will be lost Note that the last flag for QKWn n Naq is a dummy because the parameter does not exist Set 17 is the last input set for steady state calculations For transient calculations a number of input sets have to be repeated to define new input at successive stress input times or to redefine the calculation parameters and print output options if desired Set 18 to 25 redefine the input parameters by repeating Sets 6 to 13 Starting at stress input time Teno the end of the previous calculation period see Set 16 new parameter v

Chapter 5_FlowSimulation

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