Master thesis Thermal dispersion in porous media: Numerical model and physical insights

1. Master thesis Thermal dispersion in porous media: Numerical model and physical insights 22. August 2017 Tuong Vi Tran (B.Sc.)

2. Table of content • Introduction • Mathematical model • Software application (OpenGeoSys) • Set up vertical flow oriented problem • Numerical studies • Convergence study • Result & Discussion • Comparison to analytical reference solution • Rayleigh [102, 103,104] • Nusselt number • Thermal grid Peclet number • Comparison three existing thermal dispersion tensor (Bear-Scheidegger, no dispersion, equivalent dispersion using analytical model • Summary and outlook

3. Problem definition • Water Simple problem: Widely used as benchmark and to understand physics • porous media in a closed box • Isotropic permeability • Homogenous

4. Mathematical model

5. Mathematical Model • Governing equations • 2D steady state flow • Fluid mass conservation (continuity) • Linear momentum conservation (Darcy’s law) • Boussinesq Approximation in PCS_TYPE LIQUID FLOW Q1: isgravityeffectalreadysetasdefault in OGS?? @Aaron in MFP Introduction

6. Mathematical Model • Governing equations • Energy conservation • Thermal diffusivity • Thermal dispersion tensor in PCS_TYPE HEAT_TRANSPORT • ks, e, rho C considered alpha_L & alpha_Tconsidered Introduction

7. Non dimensional numbers • Rayleigh number • Nusseltnumber • Thermal gridPecletnumber Q2: Ra considerationthroughalpha – e?!? tried : e = 0.3092 & 1,xx due tobackwardscalculation @Marwan & Prof. Graf-> e = const = 0.3092 & k variabel

8. Non dimensional numbers • Rayleigh number Q3: Change of solid properties? Whichpropertieswereused in benchmarkproblem? @Marwan

9. Parameter Introduction

10. Software application - OpenGeoSys

11. Set up vertical flow oriented problem

12. Schedule : Goal • Working skript (iteration, nofailure in writing) • Nodispersion • Withdispersion • Changingparameterstogetreasonableresults

13. Problem definition Boundarycondition = = • Initial condition • T = 273.15 [K] • p = 0 [Pa] • u = 0 [m s-1] • v = 0 [m s-1]

14. General Structure Input Files Processfile (*.pcs) # MAIN_KEYWORD1 $SUB_KEYWORD1 valuevaluevalue $SUB_KEYWORD2 valuevalue # MAIN_KEYWORD2 $SUB_KEYWORD1 valuevalue [..] # STOP • 2D thermal Dispersion in PM #PROCESS $PCS_TYPE LIQUID_FLOW $NUM_TYPE NEW $BOUNDARY_CONDITION_OUTPUT #PROCESS $PCS_TYPE HEAT_TRANSPORT $NUM_TYPE NEW $BOUNDARY_CONDITION_OUTPUT #STOP

15. Geometry file (*.gli) #POINTS 0 0 0 0 $NAME POINT0 1 1 0 0 $NAME POINT1 2 1 1 0 $NAME POINT2 3 0 1 0 $NAME POINT3 #POLYLINE $NAME PLY_0 $POINTS 0 1 2 3 0 #POLYLINE $NAME LEFT $POINTS 0 3 #POLYLINE $NAME RIGHT $POINTS 1 2 #SURFACE $NAME SURF_0 $POLYLINES PLY_0 $TYPE 0 #STOP

16. Meshfile (*.msh) #FEM_MSH $PCS_TYPE NO_PCS $NODES 1089 0 0 0 0 1 1 0 0 2 1 0 1 3 0 0 1 4 .031249999999942 0 0 5 6.24999999998734E-02 0 0 6 9.37499999998264E-02 0 0 7 .124999999999779 0 0 8 .156249999999689 0 0 9 .187499999999599 0 0 10 .218749999999509 0 0 [...] 1087 9.37500000069132E-02 0 .468750000008495 1088 3.12500000023044E-02 0 .468750000004119 $ELEMENTS 1024 0 0 quad 3 97 355 96 1 0 quad 97 98 353 355 2 0 quad 355 353 179 354 3 0 quad 96 355 354 95 4 0 quad 98 99 358 353 5 0 quad 99 100 356 358 6 0 quad 358 356 177 357 7 0 quad 353 358 357 179 8 0 quad 179 357 362 361 […] Gridsize: 32 x 32 elements Δ

17. Boundaryconditions (*.bc) #BOUNDARY_CONDITION $PCS_TYPE LIQUID_FLOW $PRIMARY_VARIABLE PRESSURE1 $GEO_TYPE POINT POINT3 $DIS_TYPE CONSTANT 0.0 #BOUNDARY_CONDITION $PCS_TYPE HEAT_TRANSPORT $PRIMARY_VARIABLE TEMPERATURE1 $GEO_TYPE POLYLINE LEFT $DIS_TYPE CONSTANT 274.15 #BOUNDARY_CONDITION $PCS_TYPE HEAT_TRANSPORT $PRIMARY_VARIABLE TEMPERATURE1 $GEO_TYPE POLYLINE RIGHT $DIS_TYPE CONSTANT 273.15 #STOP

18. Initial conditions (*.ic) #INITIAL_CONDITION $PCS_TYPE LIQUID_FLOW $PRIMARY_VARIABLE PRESSURE1 $GEO_TYPE DOMAIN $DIS_TYPE GRADIENT 1 0 10000 #INITIAL_CONDITION $PCS_TYPE HEAT_TRANSPORT $PRIMARY_VARIABLE TEMPERATURE1 $GEO_TYPE DOMAIN $DIS_TYPE CONSTANT 273.15 #STOP

19. Fluid Property file (*.mfp) #FLUID_PROPERTIES $FLUID_TYPE LIQUID $PCS_TYPE PRESSURE1 TEMPERATURE1 $DENSITY 4 1000 273.15 0.01 $VISCOSITY 1 0.001 $SPECIFIC_HEAT_CAPACITY 1 4200.0 $HEAT_CONDUCTIVITY 1 0.65 $TEMPERATURE 273.15 $GRAVITY 9.81 #STOP #FLUID_PROPERTIES $FLUID_TYPE LIQUID $DENSITY 4 1000 273.15 1e-5 $VISCOSITY 1 0.001 $SPECIFIC_HEAT_CAPACITY 1 4200.0 $HEAT_CONDUCTIVITY 1 0.65 #STOP 4 due to density temperature dependency

20. Material Property file (*.mmp) (1) #MEDIUM_PROPERTIES $GEOMETRY_DIMENSION 2 $POROSITY 1 0.1 $TORTUOSITY 1 1.0e+000 $PERMERABILITY_TENSOR ISOTROPIC 4.84404e-13 $STORAGE 1 0.0 $HEAT_DISPERSION 1 0 0 #STOP #MEDIUM_PROPERTIES $GEOMETRY_DIMENSION 2 $POROSITY 1 0.30925 $TORTUOSITY 1 1.0e+000 $PERMERABILITY_TENSOR ISOTROPIC 1e-9 $STORAGE 1 0.0 $HEAT_DISPERSION 1 0.1 0.01 #STOP ; Isotropic

21. Solid Property file (*.msp) #SOLID_PROPERTIES $DENSITY 4 2.5 $THERMAL EXPANSION 0.01 CAPACITY 1 850.0 CONDUCTIVITY 1 1.591444 #STOP #SOLID_PROPERTIES $DENSITY 4 2.5 $THERMAL EXPANSION 1.0e-005 CAPACITY 1 850.0 CONDUCTIVITY 1 1.591444 #STOP CONDUCTIVITY 1 3 Q3: Change of solid properties? Whichpropertieswereused in benchmarkproblem? @Marwan

22. Numericfile (*.num) $OVERALL_COUPLING 2 1000 #NUMERICS $PCS_TYPE LIQUID_FLOW $LINEAR_SOLVER ; method error_tolerancemax_iterations theta precond storage 2 2 1.e-016 10000 1.0 100 4 $COUPLING_CONTROL ERNORM 1e-3 $ELE_UPWINDING .5 #NUMERICS $PCS_TYPE HEAT_TRANSPORT $LINEAR_SOLVER ; method error_tolerancemax_iterations theta precond storage 2 5 1.e-012 1000 1.0 100 4 $ELE_GAUSS_POINTS 2 $COUPLING_CONTROL ERNORM 1e-3 $ELE_UPWINDING .5 #STOP $OVERALL_COUPLING 2 1000 #NUMERICS $PCS_TYPE LIQUID_FLOW $LINEAR_SOLVER ; method error_tolerancemax_iterations theta precond storage 3 2 1.e-016 10000 1.0 100 4 $COUPLING_CONTROL ERNORM 1e-3 $ELE_UPWINDING .5 #NUMERICS $PCS_TYPE HEAT_TRANSPORT $LINEAR_SOLVER ; method error_tolerancemax_iterations theta precond storage 3 5 1.e-012 1000 1.0 100 4 $NON_LINEAR_ITERATIONS ;type---error_method--- max_iterations--relacation -- tolerance(s) PICARD LMAX 25 0.0 1.e-3 $ELE_GAUSS_POINTS 2 $COUPLING_CONTROL ERNORM 1e-3 $ELE_UPWINDING .5 #STOP

23. Time step control file (*.tim) #TIME_STEPPING $PCS_PROCESS LIQUID_FLOW $TIME_START 0.0 $TIME_END 138474340 $TIME_STEPS 1 1e-9 1 1e-5 1 1e-2 10 1 11 30 60 60 600 600 600 1800 #TIME_STEPPING $PCS_TYPE HEAT_TRANSPORT $TIME_START 0.0 $TIME_END 138474340 $TIME_STEPS 1 1e-9 1 1e-5 1 1e-2 10 1 11 30 60 60 600 600 600 1800 #STOP after 1s, 10s, 30s, 1min, 10 min, 30min total simulation ~ 16.6 d #TIME_STEPPING $PCS_PROCESS LIQUID_FLOW $TIME_START 0.0 $TIME_END 138474340 $TIME_STEPS 1 1e-9 1 1e-5 1 1e-2 10 1 11 30 60 60 600 600 600 1800 504 3600 365 86400 30 864000 30 2592000 #TIME_STEPPING $PCS_TYPE HEAT_TRANSPORT $TIME_START 0.0 $TIME_END 138474340 $TIME_STEPS 1 1e-9 1 1e-5 1 1e-2 10 1 11 30 60 60 600 600 600 1800 504 3600 365 86400 30 864000 30 2592000 #STOP after 1s, 10s, 30s, 1min, 10 min, 30min, 1h, 24h, 10d, 30d total simulation 4.39 a

24. Output file (*.out) #OUTPUT $NOD_VALUES PRESSURE1 TEMPERATURE1 $ELE_VALUES VELOCITY1_X VELOCITY1_Z $GEO_TYPE DOMAIN $DAT_TYPE PVD $TIM_TYPE STEPS 1 #OUTPUT $NOD_VALUES PRESSURE1 TEMPERATURE1 $ELE_VALUES VELOCITY1_X VELOCITY1_Z $GEO_TYPE DOMAIN $DAT_TYPE TECPLOT $TIM_TYPE STEPS 1 #STOP #OUTPUT $NOD_VALUES PRESSURE1 TEMPERATURE1 $ELE_VALUES VELOCITY1_X VELOCITY1_Y $GEO_TYPE DOMAIN $DAT_TYPE PVD $TIM_TYPE STEPS 1 #STOP

25. Numericalstudies

26. Temperature distribution Studies

27. Temperature distribution Studies

28. Temperature distribution Studies

29. Velocity x directiondistribution Denstiyeffect -> againstclockwise flow… Central region -> slowmotion Studies

30. Velocity z directiondistribution Studies

31. Velocity [magnitude] distribution Studies

32. Summary andoutlook

33. Next step Summary