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CHAPTER 5: VARIABLY SATURATED MULTI-PHASE PROBLEMS

Shortcuts:

CASE 5.01 - Three Phase Flow: Transmission Oil-Water-Air/Simulation of PNL Data

CASE 5.02 - Two Phase Flow: Oil-Water Reservoir in a Fracture Simulation of Oil Recovery with Water Injection

CASE 5.03 - Two Phase Flow: Oil-Water Reservoir in a Fracture Simulation of Oil Recovery with Water Injection

*************************************************************************
TITLe CASE 5.01 - Three Phase Flow: Transmission Oil-Water-Air
///// Simulation of PNL Experimental Data
///// Piepho, M.G. and A.K. Runchal, 1991. "A Comparison of Three
///// Methods for Solving Flow Equations of Two Immiscible Fluids in
///// Variably Saturated Media" , WHC-SA-1289-FP, WHC, Richland, WA.
************************************************************************
USER akrunchal: acri: 950331
***************** GRID NODEs & GEOMETRY SELECTION
GRID NODEs IS 14 BY 14 BY 26
COOR X RANGE = 12
COOR Y RANGE = 12
COOR Z RANGE = 24
GRAVity 0.,0.,-981.
/
***************** INITIAL AND BOUNDARY CONDITIONS
SET P = -111.9143 $ cm of water
SET P2= -75.0000 $ cm of water
/
BOUNdary for P: at X-, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P: at X+, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P: at Y-, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P: at Y+, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P: at Z-, VALUe = -111.9143 $ cm of water
BOUNdary for P: at Z+, FLUX = 0 $ Horizontal no-flow boundary
BOUNdary for P2: at X-, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P2: at X+, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P2: at Y-, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P2: at Y+, FLUX = 0 $ Vertical no-flow boundary
BOUNdary for P2: at Z-, FLUX = 0 $ Horizontal no-flow boundary
BOUNdary for P2: at Z+, FLUX = 0 $ Horizontal no-flow boundary
/
***************** SOIL PROPERTIES
////////////////////////////////////////////////////////////////////
SOIL bulk DENSity: 2.5, POROsity 3*0.36
HYDR SS = 0., KX = 1440.00, KY = 1440.0, KZ = 1440.0 $ CM/DAY
MULTIPHASE: VAN Genuchten: n=3.743; Aow=0.1742, SM=0.028
MULTIPHASE: VAN Genuchten: n=3.743; Aao=0.0895131, SM=0.028, SECOnd phase
/
***************** PHYSICAL PROPERTIES
////////////////////////////////////////////////////////////////////
DENS PRIMary = 0.998 GM PER CM CUBED, CONSTANT $ (WATER)
DENS SECOndary = 0.84 GM PER CM CUBED, CONSTANT $ (TRANS OIL)
VISC PRIMary = 1.002 CP, CONSTANT $ (WATER)
VISC SECOndary = 71.0 CP, CONSTANT $ (TRANS OIL)
PROPERTIES for P & P2 ARITH !!!GEOMetric Mean
/
***************** SOURCE
////////////////////////////////////////////////////////////////////
LOCATE node (13,13,23)
/Source units are: Mass divided by density of 1st phase
SOURCE P2 TABLe of TIME 4 sets: (0,0) (.02,266.) (0.47,266.) (0.49,0) SELEct
/
***************** SOLUTION OPTIONS
////////////////////////////////////////////////////////////////////
/
RELAX S=0.2, S2= 0.5
MATRIX sweeps IN Z direction
CONVergence for P, 1.E-3, 10
CONVergence for P2, 1.E-3, 10
CONVergence tolerance for flow: 5.E-3, niter 20
CONVergence tolerance for flow second phase: 1.E-2, niter 20
/
***************** OUTPUT OPTIONS
////////////////////////////////////////////////////////////////////
DIAGNOSTIC node: (13,13,23) every 5 steps
DEBUG GEOMETRY OFF
SELEct window (8,11,11) to (99,99,99) in (1,1,1)
OUTPut P,P2, S, S2 by XZ planes for SELEcted window
/
!!!!!SOLVe for 0.5416 day in step of AUTO 0.001 day $ full simulation
SOLVe for 0.02 day in step of AUTO 0.001 day
/
!!!!!SAVE S, S2 on 'C51.ARC'
save off
/
END
/
/

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************************************************************************
TITLe CASE 5.02 - Two Phase Flow: Oil-Water Reservoir in a Fracture
///// Simulation of Oil Recovery with Water Injection
///// Linear Saturation vs. Capillary Pressure Characteristics
///// Bill Dershowitz (Golder Inc.) Test Problem 10/01/2000
************************************************************************
PROBlem type: MULTiphase with TWO Phase Oil & Water
GRID 22 x 3 x 22
COORdinates X MINIMUM -100 to +100
COORdinates Z MINIMUM 0 to +200
/
LOCATE ID=WATER_IN (11,2, 4) to (11,2, 4)
LOCATE ID=OIL_OUT (12,2,18) to (12,2,18)
/
LOCATE ID=MORE_WATER (1,1, 1) to (999,999,6)
LOCATE ID=MORE_OIL (1,1, 7) to (999,999,999)
/
BOUN FLUX = 0 !All other faces set to no flow
SET P LINEar 9.0, -1.0, Z
SET S 0.9 in ID=MORE_WATER
SET S 0.1 in ID=MORE_OIL
/
/::::::::: Water is injected at a constant rate
/::::::::: Oil & Water are withdrawan based on local saturation
SOURce P ID=WATER_IN 0.01 ! Injection Well
SOURce P ID=OIL_OUT LINEar 0. -0.01 * S ! Recovery Well
SOURce P2 ID=OIL_OUT LINEar 0. -0.01 * S2 ! Recovery Well
/
DENSity of FIRSt phase = 1000 ! water
DENSity of SECOnd phase = 600 ! oil
VISCosity of FIRSt phase = 2.32E-04 ! water
VISCosity of SECOnd phase = 3.22E-04 ! oil
FLUId COMPressibility = 5.40E-6 FIRSt ! water 5.51e-10 1/pascal
FLUId COMPressibility = 1.87E-5 SECOnd ! oil 3.18e-9 1/pascal
/
FOR type(s) 1 thru 1 skipping 1
MATErial DENSity 2500
MATErial POROsity 1
HYDRaulic 1.0E-10 1.00E-03 1.00E-03 1.00E-03
/
MULTiphase TABLe of 2 sets:
0.1 10.
0.9 0.1
/
MULTiphase COND TABLe of 4 sets:
0.0 0.0
0.1 0.0
0.9 1.0
1.0 1.0
MULTiphase COND TABLe of 4 sets for SECOnd phase:
0.0 0.0
0.1 0.0
0.9 1.0
1.0 1.0
/
PROPerty P P2 MAXIMUM
/
DIAG TIME P S BP BP2 at (12,2,18) every 100 steps
/
SELECT (8,2,1) TO (13,2,999)
OUTPut XZ PLANES U W P P2 S S2 SELEct NARROW
/HISTORY on file '502.HIS' EVERY 100 STEPS PLOTS
/HISTORY at (11,2,4) (11,2,7) (11,2,10) (11,2,13), (11,2,16) (12,2,18)
/
CONVergence FIRSt 1.E-4 1
CONVergence SECOnd 1.E-5 10 REFE
/
SAVE OFF EVERY TIME = 10000 UNITS '502.SAV'
/
SOLVe for 1.E6 dt=100 dt_increase_factor 1.01; dt_max = 1000
/
END
/
/

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************************************************************************
TITLe CASE 5.03 - Two Phase Flow: Oil-Water Reservoir in a Fracture
///// Simulation of Oil Recovery with Water Injection
///// Van Genuchten Saturation vs. Capillary Pressure Characteristics
///// Bill Dershowitz (Golder Inc.) Test Problem 10/01/2000
************************************************************************
PROBlem type: MULTiphase with TWO Phase Oil & Water
GRID 22 x 3 x 22
COORdinates X MINIMUM -100 to +100
COORdinates Z MINIMUM 0 to +200
/
LOCATE ID=WATER_IN (11,2, 4) to (11,2, 4)
LOCATE ID=OIL_OUT (12,2,18) to (12,2,18)
/
LOCATE ID=MORE_WATER (1,1, 1) to (999,999,6)
LOCATE ID=MORE_OIL (1,1, 7) to (999,999,999)
/
BOUN FLUX = 0 !All other faces set to no flow
SET P LINEar 9.0, -1.0, Z
SET S 0.9 in ID=MORE_WATER
SET S 0.1 in ID=MORE_OIL
/
/::::::::: Water is injected at a constant rate
/::::::::: Oil & Water are withdrawan based on local saturation
SOURce P ID=WATER_IN 0.1 ! Injection Well
SOURce P ID=OIL_OUT LINEar 0. -0.1 * S ! Recovery Well
SOURce P2 ID=OIL_OUT LINEar 0. -0.1 * S2 ! Recovery Well
/
DENSity of FIRSt phase = 1000 ! water
DENSity of SECOnd phase = 600 ! oil
VISCosity of FIRSt phase = 2.32E-04 ! water
VISCosity of SECOnd phase = 3.22E-04 ! oil
FLUId COMPressibility = 5.40E-6 FIRSt ! water 5.51e-10 1/pascal
FLUId COMPressibility = 1.87E-5 SECOnd ! oil 3.18e-9 1/pascal
/
FOR type(s) 1 thru 1 skipping 1
MATErial DENSity 2500
MATErial POROsity 1
HYDRaulic 1.0E-10 1.00E-03 1.00E-03 1.00E-03
/
MULTiphase VAN GENUCHTEN: n=2 alpha=10 SR=0.099 sg=0.1 M=0.5 KR=0.001
/
MULTiphase COND TABLe of 4 sets:
0.0 0.0
0.1 0.0
0.9 1.0
1.0 1.0
MULTiphase COND TABLe of 4 sets for SECOnd phase:
0.0 0.0
0.1 0.0
0.9 1.0
1.0 1.0
/
PROPerty P P2 MAXIMUM
/
DIAG TIME P S BP BP2 at (12,2,18) every 100 steps
/
SELECT (8,2,1) TO (13,2,999)
OUTPut XZ PLANES U W P P2 S S2 SELEct NARROW
/HISTORY on file '502.HIS' EVERY 100 STEPS PLOTS
/HISTORY at (11,2,4) (11,2,7) (11,2,10) (11,2,13), (11,2,16) (12,2,18)
/
CONVergence FIRSt 1.E-5 10 ! With Van Genuchten
CONVergence SECOnd 1.E-5 2 REFE ! With Van Genuchten
/
SAVE OFF EVERY TIME = 10000 UNITS '503.SAV'
/
SOLVe for 100000 dt=1 dt_increase_factor 1.01; dt_max = 100
/
END
/
/

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