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1 2 3 4 5 6 7 8 9 10

CHAPTER B: BENCHMARK PROBLEMS IN THE PORFLOW MANUAL

Shortcuts:


CASE B.01 - Two-Dimensional Transient Infiltration

CASE B.02 - Two-Dimensional Steady-State Infiltration

CASE B.03 - Jornada Test Trench Simulation

CASE B.04 - Saltwater Intrusion into a Confined Aquifer

CASE B.05 - Saturated Flow in a Fractured Porous Medium

CASE B.06A - Flow to a Geothermal Well

CASE B.06B - Flow to a Geothermal Well


************************************************************************
TITLe CASE B.01 - Two-Dimensional Transient Infiltration
************************************************************************
//// Ross, B., J.W. Mercer, S.D. Thomas, and B.H. Lester, 1982.
//// Benchmark Problems for Repository Siting Models, NRC-report
//// NUREG/CR-3097, December, 1982.
************************************************************************
/
USER ACRi - August 29, 1993
/
GRID NODEs 16 by 12
COORDINATE X NODEs with MINImum = 0 and MAXImum = 0.15
COORDINATE Y NODEs RANGE 0.10
GRAVITY constants 0, -1 relative value
/
ROCK density = 2385 kg_per_m_cubed, Porosity = 0.45
PROPERTY averages by UPWIND
HYDRaulic properties for P: ss=0., kx=1.157e-7, ky=1.157e-7
/
MULTiphase CONDuctivity TABLe of 2 sets
/* sl krl */
0.333333 0.
1.000000 1.
/
MULTiphase TABLe of 2 sets
/* sl Pcap */
0.333333 1 m
1.000000 0.
/
SET initial P = -.90 m
/
BOUNDary P at Y-: FLUX = 0
BOUNDary P at Y+: FLUX = 0
LOCAte from (1, 1) to (1, 7)
BOUNDary P at X-: FLUX = 0 in SELEcted region
LOCAte from (1, 8) to (1,12)
BOUNdary P at X-: LINEar function 0.06 -1. Y in SELEcted region
/
CONVergence of P GLOBAL criterian=1.E-5, iterations=30
/
DIAGNOSTIC P, U, S at (3,11) every 100 steps
DEBUG GEOMETRY OFF
/
SAVE H, P, S on 'B1.ARC'
SELEct (1,1) to (999,999) interval (2,1)
OUTPut U, V, P H, and S in SELEcted region in NARRow mode
/
SOLVE for P to 43891 sec in steps of .1 sec in AUTO mode
/
END
/

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************************************************************************
TITLe CASE B.02 - Two-Dimensional Steady-State Infiltration
************************************************************************
//// Magnuson S.W., R.G. Baca & A.J. Sondrup, August 1990. Independent
//// Verification and Benchmark Testing of The PORFLO-3 Computer Code,
//// Version 1.0, EGG-BG-9175; INEL, Idaho Falls, ID 83415.
************************************************************************
/
GRID NODEs 32 by 33
COORdinate X range 150
COORdinate Y RANGE 35
/
GRAVity 0., -1 (normalized; absolute value not required for single-phase)
/
ROCK density 1.0, porosity = 0.1875, 0.25, 0.1852
HYDRaulic properties: ss = 1.E-7, (kx,ky,kz) --> 3*750
PROPerty averages by GEOMetric mean option
/
SET initial P -10. everywhere
/
SELEct subdomain (1,1) to (1,17)
BOUNdary P: index X- LINEar function: 21 -1 Y for SELEcted segment
SELEct subdomain (1,18) to (1,99)
BOUNdary P: index X- FLUX = 0. for SELEcted segment
/
SELEct subdomain from (32,1) to (32,13)
BOUNdary P: index X+ LINEar function: 19 -1 Y for SELEcted segment
SELEct subdomain from (32,14) to (32,99)
BOUNdary P: index X+ FLUX = 0. for SELEcted segment
/
BOUNdary P: index Y+ FLUX = 1. m/yr EVERywhere in
BOUNdary P: index Y- FLUX = 0. EVERywhere
/
MULTifluid VAN Genuchten GENEral form: 2, 0.2, 0.25, 0, 1
MULTifluid CONDuctivity POWEr law: 4, 1, 0, 0, 0.25
/
CONVergence epsilon=1.0E-3 iter_max 500
DIAGnostic NODE (9, 25) EVERY 1 STEPS
DEBUG GEOMETRY OFF
/
SAVE on 'B2.ARC' P S H
SOLVE for 100 minimum 5 in STEAdy state
/
SELEct (1,1) to (999,999) interval (2,2)
OUTPut U, V, P H, S, and MOIS in SELEcted region in NARRow mode
/
END
/

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************************************************************************
TITLe CASE B.03 - Jornada Test Trench Simulation
************************************************************************
//// Magnuson S.W., R.G. Baca & A.J. Sondrup, August 1990. Independent
//// Verification and Benchmark Testing of The PORFLO-3 Computer Code,
//// Version 1.0, EGG-BG-9175; INEL, Idaho Falls, ID 83415.
************************************************************************
/
GRID NODEs 56 by 47
/
COORdinate X values at NODEs are:
0. 5. 15. 25. 35. 45. 55. 65. 75. 85. 95. 105.
115. 125. 135. 145. 155. 165. 175. 185. 195. 205. 215. 222.
228. 235. 245. 255. 265. 275. 285. 295. 305. 315. 325. 335.
345. 355. 380. 405. 430. 455. 480. 505. 530. 555. 580. 605.
630. 655. 680. 705. 730. 755. 780. 800.
/
COORdinate Y values at NODEs are:
-650. -645. -630. -605. -580. -555. -530. -505. -480. -455. -430. -405.
-380. -355. -330. -305. -295. -285. -275. -265. -255. -245. -235. -225.
-215. -205. -195. -185. -175. -165. -155. -145. -135. -125. -115. -105.
-95. -85. -75. -65. -55. -45. -35. -25. -15. -5. 0.
/
ZONE 1 from ( 1,44) to (56,47)
ZONE 2 from ( 1,38) to (56,43)
ZONE 3 from ( 1, 1) to (56,37)
ZONE 4 from (12,22) to (32,30)
/
GRAVity vector: 0., -1. (only relative value required)
/
FOR zone 1
HYDRaulic props S=0.0, kx=790.9, ky=790.9, kz=790.9 cm/day
ROCK POROsity eff = 0.368, total = 0.368, diffusive = 0.266
MULTiphase: VAN genuchten+MUALem n=1.982 alpha=0.0334, sr=0.2772
/
FOR zone 2
HYDRaulic props S=0.0, kx=469.9, ky=469.9, kz=469.9 cm/day
ROCK POROsity eff = 0.351, total = 0.351, diffusive = 0.2525
MULTiphase: VAN genuchten+MUALem n=1.632 alpha=0.0363, sr=0.2806
/
FOR zone 3
HYDRaulic props S=0.0, kx=415.0, ky=415.0, kz=415.0 cm/day
ROCK POROsity eff = 0.325, total = 0.325, diffusive = 0.2391
MULTiphase: VAN genuchten+MUALem n=1.573 alpha=0.0345, sr=0.2643
/
FOR zone 4
HYDRaulic props S=0.0, kx=4150., ky=4150., kz=4150. cm/day
ROCK POROsity eff = 0.325, total = 0.325, diffusive = 0.2391
MULTiphase: VAN genuchten+MUALem n=1.573 alpha=0.0345, sr=0.2643
/
PROPerty averages using GEOMetric mean option
/
SET initial P = -724. cm everywhere
/
BOUNdary cond P: index X-, FLUX = 0. everywhere
BOUNdary cond P: index X+, FLUX = 0. everywhere
SELEct (1,47) to (24,47)
BOUNdary cond P: index Y+, FLUX = 2. cm/day SELEct
SELEct (25,47) to (56,47)
BOUNdary cond P: index Y+, FLUX = 0. SELEct
/
CONVergence for FLOW = 1.0E-3 iter 1
CONVergence for P 1.E-3 iter 1
DIAGnostic node at (4,46) every 100 steps
DEBUG GEOMETRY OFF
SAVE on 'B3.ARC' S
/
*********** Time for full simulation is 30 days
SOLVe for 30 days in steps of 0.0005 days factor = 1.02 max 0.02
***********
SELEct (1,1) to (999,999) interval (2,2)
OUTPut in SELEcted region in NARRow mode
/
END
/

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************************************************************************
TITLe CASE B.04 - Saltwater Intrusion into a Confined Aquifer
************************************************************************
//// Henry, H.R., 1964. Effects of Dispersion on Salt Encroachment in
//// Coastal Aquifers, Sea Water in Coastal Aquifers, U.S. Geological
//// Survey Water Supply Paper 1613-C, p. C71-C84.
************************************************************************
/
GRID NODEs 41 by 21
COORdinate x: NODEs with min=0.0, max=2.0
COORdinate y: NODEs with min=0.0, max=1.0
/
GRAVity 0, -1. nomalized value
/
SET initial H to 0. everywhere
/
/top and bottom no flow boundary
BOUNdary for P IB=Y+, flux=0.0
BOUNdary for P IB=Y-, flux=0.0
BOUNdary for P IB=X-, flux=6.60E-5
BOUNdary for P IB=X+, LINEar function 0. -1.025 * Y
/
BOUNdary for C IB=Y+, flux = 0.
BOUNdary for C IB=Y-, flux = 0.
BOUNdary for C IB=X-, value= 0.
/BOUNdary for C IB=X+, value= 1.
BOUNdary for C IB=X+, value= 1. FLOW ! fixed inflow; zero grad outflow
/
DENSity LINEar rho=1, a1=0., c*=0., a2=-0.025
/
ROCK POROsity = 0.35
HYDRaulic ss = 0.0, kx=0.01, ky=0.01
TRANsport C kd=0, Dm = 1.88571E-5
/
DIAGnostic node at 11,2 every 100 steps
DEBUG GEOMETRY OFF
/
SELEct (1,1) to (999,999) interval (2,2)
OUTPut U,V,P,C in SELEcted region in NARRow mode
SOLVe STEAdy state mode for P,C max = 5000, min= 3000
SAVE U,V,H,C 'B4.ARC'
/
END
/

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************************************************************************
TITLe CASE B.05 - Saturated Flow in a Fractured Porous Medium
************************************************************************
//// Magnuson S.W., R.G. Baca & A.J. Sondrup, August 1990. Independent
//// Verification and Benchmark Testing of The PORFLO-3 Computer Code,
//// Version 1.0, EGG-BG-9175; INEL, Idaho Falls, ID 83415.
************************************************************************
/
GRID NODEs 49 by 93
/
COORdinate X values at NODEs are:
0.000 1.250 2.500 3.750 5.000 6.250 7.500 8.125 8.750 9.062
9.375 9.562 9.750 9.875 10.000 10.125 10.250 10.438 10.625 10.937
11.250 11.875 12.500 13.750 15.000 16.250 17.500 18.125 18.750 19.062
19.375 19.562 19.750 19.875 20.000 20.125 20.250 20.438 20.625 20.937
21.250 21.875 22.500 23.750 25.000 26.250 27.500 28.750 30.000
/
COORdinate y values at NODEs are:
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
9.0 9.5 9.9 10.1 10.5 11.0 12.0 13.0 14.0 15.0
16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0
26.0 27.0 28.0 29.0 29.5 29.9 30.1 30.5 31.0 32.0
33.0 34.0 35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0
43.0 44.0 45.0 46.0 47.0 48.0 49.0 49.5 49.9 50.1
50.5 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0
60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0
69.5 69.9 70.1 70.5 71.0 72.0 73.0 74.0 75.0 76.0
77.0 78.0 79.0 80.0
/
ZONE 1 from (1, 1) to (49,93)
ZONE 2 from (15,59) to (15,81) FRACture width=0.030 cm
ZONE 3 from (35,13) to (35,35) FRACture width=0.030 cm
/
FOR zone 1 $the basalt matrix
HYDRaulic props S=0.0, kx=4.e-3, ky=4.e-3, kz=4.e-3 cm/sec
ROCK DENSity = 1
ROCK POROsity effective = 0.24, total = 0.24, diffusive = 0.24
PROP for P using GEOMetric mean option
/
FOR zone 2 and 3 $fractures
HYDRaulic porps S=0.0 K=(3*6.E2) cm/sec
/HYDRaulic porps S=0.0 K=(3*6.E3) cm/sec
ROCK DENSity 1
ROCK POROsity = (3*1.0)
/
SET LINEar function P = 0. + 0.0025 Y
/
BOUNdary cond for P: index X-, grad = 0.
BOUNdary cond for P: index X+, grad = 0.
BOUNdary cond for P: index Y-, value = 0.
BOUNdary cond for P: index Y+, value = .2
/
DIAGnostic node at (13,69) every 100 steps
DEBUG GEOMETRY OFF
SELEct window from (13,1) to (13,93)
SAVE on 'B5.ARC' P and H only
/
MATRix for P X and Y directions
CONVERGENCE CRITERION 1.E-7
/
SOLVe for STEAdy state max 1000 min 500
SELEct (1,1) to (999,999) interval (2,5)
OUTPut P in SELEcted region in NARRow mode
/
END
/

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************************************************************************
TITLe CASE B.06A - Flow to a Geothermal Well
************************************************************************
//// Pruess, K., 1987. TOUGH Users Guide. NUREG/CR-4645. U.S. Nuclear
//// Regulatory Commission (NRC), Washington, D.C. (Problem 4)
************************************************************************
/
PROBLEM with EVAPoration in EQUIlibrium mode
/
GRID NODEs is 1 by 44
/
COORDINATE r [m] values at NODEs are:
0. 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5
10 12 15 20 25 30 37.5 45 55 65
75 90 105 120 140 165 195 230 270 320
380 450 550 650 750 850 975 1100 1200 1350
1500 1700 1900 2100
/
GRAVITY constant 0, 0, 0, 9.81
/
REFErence T = 300 !deg_centigrade
DENSity primary fluid: uniform rho* = 712.22 !kg_per_m^3
DENSity SECOnd fluid: GAS law rho* = 46.19 !kg_per_m^3
VISCosity for primary fluid: 8.60E-5 !kg_per_s_m
VISCosity for SECOnd fluid: 1.60E-5 !kg_per_s_m
/
FLUId SPECific heat = 5741 !J/kg_K
FLUId SPECific heat for SECOnd phase = 5538 !J/kg_K
FLUId second phase ENTHalphy: h0 = 1.51E6; a = 5538 !J/kg
FLUId thermal CONDuctivity = 5.45E-1 !W/m_K
FLUId thermal CONDuctivity SECOnd phase = 7.18E-2 !W/m_K
FLUId COMPressibility = 3.00E-9 !pascal^-1
/
GAS molecular weight: H2O = 18
GAS PRESsure = 9.00E6 !pascal
/
ROCK DENSity = 2650 !kg/m^3
ROCK POROsity = 0.20
HYDRaulic ss= 0.; k_x = 8.02E-7, k_y = 8.02E-7 !m^-1; m/s
THERmal property cp_s = 1000; Kt_s = 5.25 !J/kg_K; W/m_K
/
MULTiphase POLYnomial: a=0, b=0, c=0, d=0, e=0, sr=0.3
MULTiphase CONDuctivity POWEr law: n=4., a=1., b=0., c=0., sr=0.3, sg=0.05
MULTiphase CONDuctivity SECOnd phase POLYnomial COMPlimentary
a=0., b=2., c=0., d=-2., e=1., sr=0.3, sg=0.05
/
METHOD P P2 DEFAULT
PROPerty P, P2, T MAXimum option
/
SET T initially to 300 !deg_centigrade
BOUNdary for P ib = Y- FLUX = 0
BOUNdary for P2 ib = Y- FLUX = 0
BOUNdary for T ib = Y- FLUX = 0
/
LOCAte source at (2,2)
SOURce FLOW: strength = -3.13E-5 in SELEcted region !m^3/m^3_s
/
CONVergence for FLOW criterian=1.E-4, max iter = 999
/
SAVE OFF
HISTory at (2,2)
HISTory every 2 steps on 'B6A.HIS'
DIAGnostic TIME, P, T, S at (2,2) every 100 steps
DEBUG GEOMETRY OFF
/
SELEct (2,1) to (2,999) interval (1,2)
OUTPut for SELEcted region in NARRow mode
/
SOLVe for 1E5 sec in steps of 1 1.02 100
/
END
/

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************************************************************************
TITLe CASE B.06B - Flow to a Geothermal Well
************************************************************************
//// Pruess, K., 1987. TOUGH Users Guide. NUREG/CR-4645. U.S. Nuclear
//// Regulatory Commission (NRC), Washington, D.C. (Problem 4)
************************************************************************
/
PROBLEM with EVAPoration in EQUIlibrium mode
/
GRID NODEs is 1 by 44
/
COORDINATE r [m] values at NODEs are:
0.0 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5
10 12 15 20 25 30 37.5 45 55 65
75 90 105 120 140 165 195 230 270 320
380 450 550 650 750 850 975 1100 1200 1350
1500 1700 1900 2100
/
GRAVITY constant 0, 0, 0, 9.81
/
REFErence T = 300 !deg_centigrade
DENSity primary fluid: uniform rho* = 1000 !kg_per_m^3
DENSity SECOnd fluid: GAS law rho* = 46.19 !kg_per_m^3
VISCosity for primary fluid: 8.60E-5 !kg_per_s_m
VISCosity for SECOnd fluid: 1.00E-5 !kg_per_s_m
/
FLUId SPECific heat = 5741 !J/kg_K
FLUId SPECific heat for SECOnd phase = 5538 !J/kg_K
FLUId second phase ENTHalphy: h0 = 1.51E6; a = 5538 !J/kg
FLUId thermal CONDuctivity = 5.45E-1 !W/m_K
FLUId thermal CONDuctivity SECOnd phase = 7.18E-2 !W/m_K
FLUId COMPressibility = 3.00E-9 !pascal^-1
/
GAS molecular weight: H2O = 18
GAS PRESsure = 9.00E6 !pascal
/
ROCK DENSity = 2650 !kg/m^3
ROCK POROsity = 0.20
HYDRaulic ss= 0.; k_x = 8.02E-7, k_y = 8.02E-7 !m^-1; m/s
THERmal property cp_s = 1000; Kt_s = 5.25 !J/kg_K; W/m_K
/
MULTiphase POLYnomial: a=0, b=0, c=0, d=0, e=0, sr=0.3
MULTiphase CONDuctivity POWEr law: n=4., a=1., b=0., c=0., sr=0.3, sg=0.05
MULTiphase CONDuctivity SECOnd phase POLYnomial COMPlimentary
a=0., b=2., c=0., d=-2., e=1., sr=0.3, sg=0.05
/
METHOD P P2 DEFAULT
PROPerty P, P2, T MAXimum option
/
SET T initially to 300 !deg_centigrade
BOUNdary for P ib = Y- FLUX = 0
BOUNdary for P2 ib = Y- FLUX = 0
BOUNdary for T ib = Y- FLUX = 0
/
LOCAte source at (2,2)
SOURce FLOW: strength = -3.13E-5 in SELEcted region !m^3/m^3_s
/
CONVergence for FLOW criterian=1.E-4, max iter = 999
/
SAVE OFF
HISTory at (2,2)
HISTory every 2 steps on 'B6B.HIS'
DIAGnostic TIME, P, T, S at (2,2) every 100 steps
DEBUG GEOMETRY OFF
/
SELEct (2,1) to (2,999) interval (1,2)
OUTPut for SELEcted region in NARRow mode
/
SOLVe for 1E5 sec in steps of 1 1.02 100
/
END
/

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