Boundary Conditions - Thunderhead Engineering
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1. Lawrence Berkeley National Laboratory for their gracious responses to our many questions We also thank Ron Falta at Clemson University and Alfredo Battistelli at Aquater S p A Italy for their help with T2VOC and TMVOC Without TOUGH2 T2VOC TOUGHREACT and TOUGH Fx HYDRATE PetraSim would not exist In preparing this manual we have liberally used descriptions from the user manuals for the TOUGH family of codes Links to download the TOUGH manuals are given at http www petrasim com More information about the TOUGH family of codes can be found at http www esd Ibl gov TOUGH2 Printed copies of the user manuals may be obtained from Karsten Pruess at lt K Pruess Qlbl gov gt The original development of PetraSim was funded by a Small Business Innovative Research grant from the U S Department of Energy Additional funding was provided by a private consortium for the TOUGHREACT version and by the U S Department of Energy NETL for the TOUGH Fx HYDRATE version We most sincerely thank our users for their feedback and support Time Dependent Essential Direchlet Boundary Conditions In this example we demonstrate how to apply time dependent boundary conditions The user should refer to the PetraSim manual for further discussion In this example we will first illustrate the basic concepts using a single cell model We will add boundary condition cells to define boundary conditions on the model cell We will then demonstrate how to apply time2. dependent boundary conditions to a more complex model Create a One Cell Model Following the instructions already presented in previous example problems make a new model using EOS1 and dimensions of 10x10x10 meters Edit the default layer to have only one cell in the Z direction Create a 1x 1 regular mesh Use the default material properties for the model The initial conditions for the model should be a temperature of 100 C and a pressure of 1 0E6 Pa single phase liquid 5 Print time history data for the model cell Penn The single cell model is shown below In the following description model cell means this 10x10x10 cell We add cells to define the boundary conditions These will be called boundary condition cells EI Petrasim CAPetraSim 2010 Examples Time Dependent BCs2011 04 DAVTime dependent temperature besim I EE lets Eile Edit Model Properties Analysis Results View Help gt RBeEX NESAS GHG GHBOG L a BOB gt Be Aa amp ONE amp Eero ye EG B Layers v Find B S Default RR Internal Boundaries lt gt 48 Active Cell Count 1 1 Figure 1 Single cell model Material for Temperature Boundary Condition For the temperature boundary condition cell we do not want flow into or out of the cell This can be accomplished by making a special material that has zero permeability and small porosity To make a new material to use in applying t
3. expand the ExtraCells list and double click the TempBC cell Click the Sources Sinks tab Click Heat In In the options list select Table Click the Edit button and type or paste the values shown Table 1 ON POY Pa JO LNL ES Click OK to save changes and exit the Heat Rates dialog Click OK to save changes and exit the Edit Cell Data dialog Edit Solution Controls Parameters relating to the solver and time stepping can be found in the Solution Controls dialog To specify the simulation end time On the Analysis menu click Solution Controls In the End Time list click User Defined and type 30 days In the Max Time Step list click User Defined and type 1 days Click the Weighting tab For Permeability at Interface list click Harmonic Weighted see the PetraSim user manual and the TOUGH2 user manual for a supporting discussion Click the Options tab 7 For Boundary condition Interpolation click Rigorous Step 8 Click OK ge eS Edit Output Controls By default the simulation will print output every 100 time steps For this simulation we will specify output every time step To specify the output frequency 1 Onthe Analysis menu click Output Controls 2 Inthe Print and Plot Every Steps box type 1 3 Click OK Save and Run The input is complete and you can run the simulation View Time History Plots To view time history plots On the PetraSim Results menu click Cell History Plots In the Variable list click T
4. Click OK We now repeat this for all top cells 1 Spin the model click the Select Mesh Layer tool and click on the top cell in the lower left corner This will select the entire top layer 2 Right click and select Edit Cells 3 Inthe Vol Factor box type 237 137E20 4 Inthe Material list select TEMP we want to use the special boundary condition material 5 Click the Sources Sinks tab 6 Click Heat In 7 8 In the options list select Table Flux and input the values shown in Table 2 Click OK File Edit Model Properties Analysis Results View Help BeE xX NSSABR O BT GHBOG L Bee gt h BS a amp MERE e amp er syte v Find lt S XN lt BB Active Cell Count 198 198 Figure 6 Selection of lower left cell in thin top layer Table 2 Specification of heat flow using flux Time Flux O 7 41830900E 22 518400 1 55084888E 22 604800 0 00000000E 0 691200 1 55084888E 2 777600 3 03391822E 2 864000 4 38439078E 2 950400 5 54324442F 2 1036800 6 45983168E 2 1123200 7 09409330E 2 1209600 7 41830900E 2 1296000 7 41830900E 2 1382400 7 09409330E 2 1468800 6 45983168E 2 1555200 5 54324442E 2 1641600 4 38439078E 22 1728000 3 03391822E 22 1814400 1 55084888E 2 1987200 1 55084888E 22 Select the at least two model cells name them and select the print options Run the analysis and essentially the same results will be obtained in the mod
5. deg C In the Cell Name list click TempBC In the Cell Time History window on the File menu click Export Data and save the data You can then import the data and compare the calculated boundary condition temperatures to SRG PR the desired values as shown in Figure 3 6 Inthe Cell Name list click Model to view the time history of the temperature in the model cell This response shows a temperature change from 100 C to a maximum of 100 5983 C Figure 4 A hand calculation gives an analytic value of 100 597 C Specified PetraSim e po Qu ov v 3 e oO le Qu Qa E v r 500000 1000000 1500000 2000000 2500000 3000000 Time sec Figure 3 Comparison of calculated and desired boundary condition cell temperatures BJ cell Time History CAPetraSim 2010 Examples Time BCs 2011 04 04 Time dependent temperature besim Eh File View Primary Data T deg C Variable T dego Cell Name Id TempBC 2 5 0E05 1 0608 1 5606 2 0E06 2 5606 3 0606 Time Figure 4 Time history response of model cell When finished you can close the Cell History dialog Boundary Condition using Thin Cell We now repeat the specifying a temperature boundary condition but using a thin cell instead of adding an extra cell 1 Open the previous model 2 Delete the extra cell 3 Save the model under a different name To define th
6. e thin cell In the Tree View expand the Layers node and click Default On the Edit menu click Properties In Dz click Custom In the first row Fraction box type 0 999 and in the Cells box type 1 Figure 5 In the second row Fraction box type 0 001 and in the Cells box type 1 Figure 5 Click OK to save changes to the default layer Au PWN P Figure 5 Input of cell sizes If you close and reopen the Edit Layers dialog you will notice that Dz has been changed to a Regular mesh with a Factor of 1 001E 03 This is an alternate way to describe the same sizes for two elements We now need to regenerate the mesh On the Model menu click Create Mesh For Mesh Type select Regular In the X Cells box type 1 In the Y Cells box type 1 PWN bP 5 Click OK to create the mesh To set the boundary conditions in the thin top cell 1 Spin the model and click on the top cell 2 Onthe Edit menu click Properties 3 Inthe Cell Name box type TempBC 4 Inthe Vol Factor box type 1 0E20 this factor multiplies the geometric cell volume of 1m 5 Inthe Material list select TEMP we want to use the special boundary condition material 6 Click the Sources Sinks tab Click Heat In and input the same values as described in the previous Heat Flow into Boundary Condition Cell section 7 Click the Print Options tab and select both print options 8 Click OK Select the mode
7. el cells Summary This has illustrated how to apply temperature only boundary conditions in a PetraSim TOUGH2 model Other combinations of boundary conditions are discussed in the PetraSim User Manual The principles are the same 10 References 1 Pruess Karsten Oldenburg Curt and Moridis George TOUGH2 User s Guide Version 2 0 Berkeley CA USA Earth Sciences Division Lawrence Berkeley National Laboratory November 1999 LBNL 43134 2 Falta Ronald et al et al T2VOC User s Guide Berkeley CA USA Earth Sciences Division Lawrence Berkeley National Laboratory March 1995 LBNL 36400 3 Pruess Karsten Personal communication 2003 email 11
8. gg HUNDESHEAD 403 Poyntz Avenue Suite B Manhattan KS 66502 USA 1 785 770 8511 www thunderheadeng com TOUGH2 Example Time Dependent Essential Direchlet Boundary Conditions PetraSim 5 Table of Contents ACKNOWIEdSEMENTS visiisscci ccs cssciscsiscsissssseccecesseadscsssasieessesedscssssiiesseseadsosssdadeatsasedseassassestessedssssssaiessaaseds iv Time Dependent Essential Direchlet Boundary Conditions scssscccsssssssssesseceeeccscansssseeceeeeessanenes 1 Create a One Cell Model rennen sehen anal nennen area denne bad avden ehren vane 1 Material for Temperature Boundary Condition su4022222222000000nnnnnnnnnnennennnnnnnennnnnnnennnnnnnnnnennnnnnnnnnen 1 Define Temperature Boundary Condition in Thin Cell 20s0000002222200snsnenonnnnnennnnnnnennnnnnnnnnnnn nennen 2 Heat Flow into Boundary Condition Cell s rrrrrrnnnnnnnnrnrvrnnnnnnnnnnnrnnnrnssnnnnnnnnrvnnssnsnnnnnnrnnsnnssnsnsnnnnrnnsenssnsnnnn 3 Edit Solution Controls rnnere ee ee ER E ea ne Eau ek 5 Edit Output Controls nenne een 5 Save nd Run nee tele E OA A anebe teens nee leerer 5 View Time History Plots cccccssssecececessesessnaecececesecsesaeaeceeecssscsesaeaeeeeecuseeseaaeaeceeecusseeuaaaeeeeecssseseaeseeeeeess 5 Boundary Condition using Thin Cell rrrnnrorrrnnrnnnnnnnnrnrvrnssrannnnnnrnnnrnssnannnnnnrsnnssnsnnnnnnrnrsnnssnsnsnnnnrnnsenssnnnnn 7 Boundary Condition using Thin Cell and Polygonal Mesh r
9. he temperature boundary conditions Penn On the Properties menu click Edit Materials In the Material Data dialog click New In the Name box type TEMP Click OK to create the new material by default the new material data will be based on theROCK1 data For the TEMP material change the value in the Porosity box to 0 001 The cell will be essentially all solid so we can use the solid properties for our heat capacity calculations and neglect the heat capacity ofthe small amount of fluid in the cell For the TEMP material in all three Permeability boxes X Y and Z type 0 0 There will be no flow into the cell Click OK to save changes and exit the Edit Materials dialog Define Temperature Boundary Condition in Thin Cell To modify the thin cell so that it defines a temperature boundary condition PWN bP 5 Spin the model and click on the top This should select only the thin cell Right click and select Edit Cells In the Cell Name box type TempBC In the Vol Factor box type 1 0E20 the volume of the cell will be the actual volume 1 time the factor for a volume of 1 0E20 m In the Material list select TEMP we want to use the special boundary condition material We will return to define sources sinks in the extra cell We use the default initial conditions in the boundary condition cell To turn on detailed printing of time history data 1 2 Click the Print Options tab Click to select both print op
10. l cell name it and select the print options Run the analysis and essentially the same results will be obtained Boundary Condition using Thin Cell and Polygonal Mesh We now repeat the specifying a temperature boundary condition but using a polygonal mesh 1 Open the previous model 2 Save the model under a different name We have already defined the spacing for the thin cell so that does not need to be modified To regenerate the mesh 1 On the Model menu click Create Mesh 2 For Mesh Type select Polygonal 3 Click OK to create the mesh To calculate and set the boundary conditions in the top lower left polygonal cell 1 Spin the model and click on the top cell in the lower left corner top layer cell Figure 6 Note that the projected area is 0 4217 m and that the volume is 4 2169E 3 m 2 On the Edit menu click Properties 3 Inthe Cell Name box type TempBC In the Vol Factor box type 237 137E20 this factor was chosen to give the cell a volume of 1 0E20 m the same value as in the previous examples gt In the Material list select TEMP we want to use the special boundary condition material Click the Sources Sinks tab Click Heat In In the options list select Table Flux and input the values shown in Table 2 These values were 0 N o calculated to give the same heat flow as in the previous examples but use an area of 0 4217 m 9 Click the Print Options tab and select both print options 10
11. rnnnarorvrnnsnannnnrnrvnnsrnsnnnnnnvnvvnnssnsnrnnnnvsnsenssnsnnnn 8 Re ferencesusujklaiknnske delene tee raserte 11 Disclaimer Thunderhead Engineering makes no warranty expressed or implied to users of PetraSim and accepts no responsibility for its use Users of PetraSim assume sole responsibility under Federal law for determining the appropriateness of its use in any particular application for any conclusions drawn from the results of its use and for any actions taken or not taken as a result of analyses performed using these tools Users are warned that PetraSim is intended for use only by those competent in the field of multi phase multi component fluid flow in porous and fractured media PetraSim is intended only to supplement the informed judgment of the qualified user The software package is a computer model that may or may not have predictive capability when applied to a specific set of factual circumstances Lack of accurate predictions by the model could lead to erroneous conclusions All results should be evaluated by an informed user Throughout this document the mention of computer hardware or commercial software does not constitute endorsement by Thunderhead Engineering nor does it indicate that the products are necessarily those best suited for the intended purpose Acknowledgements We thank Karsten Pruess Tianfu Xu George Moridis Michael Kowalsky Curt Oldenburg and Stefan Finsterle in the Earth Sciences Division of
12. t flow V is the cell volume p is the rock density cp is the rock heat capacity AT is the change in temperature and At is the change in time Note that since the porosity is very small we only use the rock properties and apply this to the entire cell volume The calculated heat flows to obtain the desired temperature time history are shown in Table 1 Table 1 Calculated heat flow to change boundary cell to desired temperature Heat Flow 3 12830090E 22 110 3956 172800 120 3368 259200 129 3893 137 1572 1 84889759E 22 432000 143 3013 1 27940331E 22 6 518400 147 5528 6 53992972E 21 604800 149 7261 0 00000000E 00 8 691200 149 7261 6 53992972E 21 91 777600 147 5528 1 27940331E 22 864000 143 3013 1 84889759E 22 950400 137 1572 2 33758617E 22 1036800 129 3893 1123200 120 3368 1209600 110 3956 1296000 a 1382400 89 60442 2 99157914E 22 17 1468800 79 66317 2 72411102E 22 1555200 70 61074 2 33758617E 22 1641600 62 84276 1 84889759E 22 1728000 56 69873 1 27940331E 22 1814400 52 44717 6 53992972E 21 1900800 50 27391 0 00000000E 00 1987200 50 27391 6 53992972E 21 2073600 52 44717 2160000 56 69873 2246400 62 84276 2332800 70 61074 2419200 79 66317 2 99157914E 22 BR 2505600 89 604421 3 12830090E 22 30 2592000 1 00308642E 22 To specify this heat flow into the boundary cell In the tree display
13. tions To define the connection between the boundary condition cell and the model cell gt oN aM Click the Connected Cells tab In the To Cell box type 1 this boundary condition cell will be connected to the model cell with ID 1 In the Orientati box type 1 use the TEMP material X permeability value for this connection In the Dist This box type 0 001 the flow distance in this boundary cell is small so that the temperature boundary condition is applied to the surface of the model cell In the Dist To box type 5 0 the true distance of flow in the model cell In the Area box type 100 the true area between the cells In the Gravitati box type 1 the boundary cell is directly above the model cell In the Rad He box type 0 0 no radiation heat transfer Click OK to save changes and exit the Edit Cell Data dialog Heat Flow into Boundary Condition Cell We have now created a boundary condition cell that has a volume of 1 0E20 m a density of 2600 kg m a porosity of 0 001 and a specific heat of 1000 J kg C For this example we will specify a sinusoidal temperature history with an average of 100 C a amplitude of 50 C and a period of 30 days Figure 2 BE B 85 8 Temperature deg C 0 5 10 15 20 25 30 Time days Figure 2 Desired boundary condition temperature history We calculate the heat flux as follows AT Q Vpc Evi where Q is the hea
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