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1 2 3 4 5 6 7 8 9 10

CHAPTER 4: VARIABLY SATURATED FLOW PROBLEMS

Shortcuts:


CASE 4.01 - Vertical Infiltration with Rainfall

CASE 4.02 - Philip's Infiltration Problem

CASE 4.03 - T-106 Single-Shell Tank Benchmark Problem


************************************************************************
TITLe CASE 4.01 - Vertical Infiltration with Rainfall
************************************************************************
/
GRID NODEs 3 BY 16
/
COORdinate Y MINImum =-30, max 0
GRAVITY COMPONNENTS: 0., -9.81
/
ROCK DENSity 1, POROsity = 0.52
HYDRAULIC PROPS SS = 1.E-7, (KX,KY,KZ) --> 3*3.125
PROPERTY OPTIONS: GEOMETRIC MEAN
/
MULTIPHASE FLOW: COREY & BROOKS, LAMDA=0.2, HREF=5.4
/
SET P -130.54
/
BOUNDARY at Y+ FLUX of P = +1.4125 cm/hr !! flux in
/
DIAGNOSTIC NODE AT 2,2 PRINT EVERY 10 STEPS
DEBUG GEOMETRY OFF
CONVergence for FLOW: 1.E-5
CONVergence for P: LOCAL MODE; VALUE=0.00001 MAX ITERATIONS = 20
/
SELEct window from 2,1 to 2,100
OUTPut for SELEcted window
/
MATRIX SWEEPS ONLY Z DIRECTIONS
RELAX S=0.5
SOLVE UNTIL TIME = 2.55 hrs IN STEPS OF .050 hrs
SAVE OFF
/
OUTPut V,S,H for SELEcted window
/
END
/
/

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************************************************************************
TITLe CASE 4.02 - Philip's Infiltration Problem
************************************************************************
**** INEL VERIFICATION TEST CASE VT1
**** 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 3 BY 101
COORdinate Y MINImum = -15.0, max = 0.0
GRAV 0., -7.57E-5 cm/hr/hr
/
ROCK POROsity = 0.371
HYDRaulic properties: SS=1.0E-7, K = 3*0.04428 cm/hr
/
SET P -601.76
BOUNdary conditions for P: index Y+, value = -1.
/
MULTiphase: properties: TABLE of 40 sets
/ water retention data, theta_star vs. head(cm), from code havuns.f by swen
1.000000E+00 1.000000E+00
9.999987E-01 1.193777E+00
9.999787E-01 1.425103E+00
9.998922E-01 1.701254E+00
9.996592E-01 2.030918E+00
9.991683E-01 2.424462E+00
9.982769E-01 2.894266E+00
9.968125E-01 3.455108E+00
9.945745E-01 4.124627E+00
9.913377E-01 4.923882E+00
9.868568E-01 5.878016E+00
9.808738E-01 7.017039E+00
9.731257E-01 8.376777E+00
9.633558E-01 1.000000E+01
9.513271E-01 1.193777E+01
9.368355E-01 1.425103E+01
9.197246E-01 1.701254E+01
8.998998E-01 2.030918E+01
8.773401E-01 2.424462E+01
8.521053E-01 2.894267E+01
8.243405E-01 3.455108E+01
7.942727E-01 4.124627E+01
7.622030E-01 4.923884E+01
7.284926E-01 5.878016E+01
6.935460E-01 7.017039E+01
6.577902E-01 8.376779E+01
6.216551E-01 1.000000E+02
5.855545E-01 1.193777E+02
5.498704E-01 1.425103E+02
5.149411E-01 1.701255E+02
4.810531E-01 2.030918E+02
4.484382E-01 2.424462E+02
4.172730E-01 2.894267E+02
3.876823E-01 3.455109E+02
3.597437E-01 4.124627E+02
3.334934E-01 4.923884E+02
3.089335E-01 5.878016E+02
2.860377E-01 7.017040E+02
2.647588E-01 8.376780E+02
2.450330E-01 1.000000E+03
MULTiphase CONDuctivity: TABLE of 40 sets
/ conductivity data, sstar vs. krel, (from havuns.f by swen)
1.000000E+00 1.000000E+00
9.999987E-01 9.891384E-01
9.999787E-01 9.851983E-01
9.998922E-01 9.798578E-01
9.996592E-01 9.726440E-01
9.991683E-01 9.629444E-01
9.982769E-01 9.499826E-01
9.968125E-01 9.328031E-01
9.945745E-01 9.102802E-01
9.913377E-01 8.811700E-01
9.868568E-01 8.442308E-01
9.808738E-01 7.984354E-01
9.731257E-01 7.432708E-01
9.633558E-01 6.790770E-01
9.513271E-01 6.073118E-01
9.368355E-01 5.305920E-01
9.197246E-01 4.523984E-01
8.998998E-01 3.764860E-01
8.773401E-01 3.061892E-01
8.521053E-01 2.438840E-01
8.243405E-01 1.907710E-01
7.942727E-01 1.469766E-01
7.622030E-01 1.118462E-01
7.284926E-01 8.428317E-02
6.935460E-01 6.303055E-02
6.577902E-01 4.686268E-02
6.216551E-01 3.468850E-02
5.855545E-01 2.559204E-02
5.498704E-01 1.883443E-02
5.149411E-01 1.383584E-02
4.810531E-01 1.015013E-02
4.484382E-01 7.438855E-03
4.172730E-01 5.447817E-03
3.876823E-01 3.987545E-03
3.597437E-01 2.917550E-03
3.334934E-01 2.134054E-03
3.089335E-01 1.560635E-03
2.860377E-01 1.141116E-03
2.647588E-01 8.342749E-04
2.450330E-01 6.098922E-04
/
PROP using GEOMetric option
/
CONVergence criteria: 1.E-5, iterations = 200
/
Diagnostic node 2,100 print every 100 steps
DEBUG GEOMETRY OFF
SELEct window (2,1) to (2,999) interval (1,5)
OUTPut for SELEcted window IN NARRow mode
/
SOLVE until time = 2.0 hrs IN steps of 0.01, factor = 1.001, max = .1
/
END
/
/

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************************************************************************
TITLe CASE 4.03 - T-106 Single-Shell Tank Benchmark Problem
////////////////////////////////////////////////////////////
**** INEL BENCHMARK TEST CASE BT5
**** 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
************************************************************************
/
****** Set up for 2D simulation on PC by AKR/ switch to 3D for real stuff
GRID NODEs IS 36 BY 36 BY 1 $ 2-D simulation
!!!<in> GRID NODEs IS 36 BY 36 BY 39 $ 31958 nodes for 3D
****** ******** ********* *********** ******
/
COORdinate X NODEs at:
0,12,22,28,32,36,40,42,44,46,48,50,52,54,56,58,60,62,64,66,
68,70,72,74,76,78,80,82,84,86,88,92,100,110,124,130
/
COORdinate Y NODEs at:
0,12,22,28,32,36,40,42,44,46,48,50,52,54,56,58,60,62,64,66,
68,70,72,74,76,78,80,82,84,86,88,92,100,110,124,130
/
/COORdinate Z
/ 143,147,152,157,161,164,167,170,173,176,178,180,181,182,183,
/ 184,185,185.5,186,186.5,187,187.5,188,188.5,189,189.5,190,190.5,191,
/ 191.5,192,192.5,193.5,195.5,199,202,203.5,204.5,205.
/
ZONE 1 1,1,33, 36,36,39 $ LAYER ONE IS A ZONE
ZONE 2 1,1,18, 36,36,32 $ LAYER TWO IS A ZONE
ZONE 3 1,1,13, 36,36,17 $ LAYER THREE IS A ZONE
ZONE 4 1,1,7, 36,36,12 $ LAYER FOUR IS A ZONE
ZONE 5 1,1,1, 36,36,6 $ LAYER FIVE IS A ZONE
ZONE 6 18,18,33, 28,28,35 $ ZONE 6 REPRESENTS T106 TANK
/
/ FLUID PROPERTIES
/
DENS 9.98E5 GM PER M CUBE
FLUId SPECific heat = 4.2 J/gm C
FLUId thermal CONDuctivity = 1.
/
DECAY half life for C (RUTHENIUM) is 365 days
gravity vector 0, 0, -1 (relative values)
/
/ SOIL-ROCK MATRIX PROPERTIES
/
FOR zones 1 through 6
SOIL DENSity: 1.6E6
/
FOR zone 1: $ AP-1G
SOIL POROsity: NE: 0.2585, NT: 0.2885, NC: 0.2785
HYDR SS=0.2485 KX=1.07 KY=1.07 KZ=0.54 $ M/DAY
TRANSPORT KD=0, DM=1.E-5 SQ M PER SEC, ALPHAL=1., ALPHAT=0.1
MULTiphase flow VAN, MUALam N: 2.9224, ALPHA: 10.08
/
FOR ZONE 2: $ AP-2
SOIL POROsity: NE: 0.521, NT: 0.627, NC: 0.617
HYDR SS=0.511 KX=0.52 KY=0.52 KZ=0.26 $ M/DAY
TRANSPORT KD=0, DM=1.E-5 SQ M PER SEC, ALPHAL=1., ALPHAT=0.1
MULTiphase flow VAN, MUALam N: 3.1071, ALPHA: 9.091
/
FOR ZONE 3: $ AP-4G
SOIL POROsity: NE: 0.409, NT: 0.456, NC: 0.446
HYDR SS=0.3986 KX=1.62 KY=1.62 KZ=0.81 $ M/DAY
TRANSPORT KD=0, DM=1.E-5 SQ M PER SEC, ALPHAL=1., ALPHAT=0.1
MULTiphase flow VAN, MUALam N: 2.6751, ALPHA: 6.658
/
FOR ZONE 4: $ AP-5
SOIL POROsity: NE: 0.428, NT: 0.451, NC: 0.441
HYDR SS=0.418 KX=0.04 KY=0.04 KZ=0.02 $ M/DAY
TRANSPORT KD=0, DM=1.E-5 SQ M PER SEC, ALPHAL=1., ALPHAT=0.1
MULTiphase flow VAN, MUALam N: 1.3945, ALPHA: 1.180
/
FOR ZONE 5: $ AP-1G
SOIL POROsity: NE: 0.2585, NT: 0.2885, NC: 0.2785
HYDR SS=0.2485 KX=1.07 KY=1.07 KZ=0.54 $ M/DAY
TRANSPORT KD=0, DM=1.E-5 SQ M PER SEC, ALPHAL=1., ALPHAT=0.1
MULTiphase flow VAN, MUALam N: 2.9224, ALPHA: 10.08
/
FOR ZONE 6: $ SINGLE SHELL TANKS
SOIL POROsity: NE: 0., NT: 0., NC: 0.
HYDR SS=0. KX=1.E-30 KY=1.E-30 KZ=1.E-30 $ M/DAY
TRANSPORT KD=0., DM=1.E-30 SQ M PER SEC, AL=1.E-30, AT=1.E-30
MULTiphase flow VAN, MUALam N: 3.0, ALPHA: 1.E-7
/
/ BOUNDARY AND INITIAL CONDITIONS
/
BOUN FOR P: at X- gradient = 0
BOUN FOR P: at X+ gradient = 0
BOUN FOR P: at Y- gradient = 0
BOUN FOR P: at Y+ gradient = 0
/BOUN FOR P: at Z- value = 4.
/BOUN FOR P: at Z+ gradient = 0
/
BOUN FOR C: at X- gradient = 0
BOUN FOR C: at X+ gradient = 0
BOUN FOR C: at Y- gradient = 0
BOUN FOR C: at Y+ gradient = 0
/BOUN FOR C: at Z- gradient = 0
/BOUN FOR C: at Z+ gradient = 0
/
SET C IS 0.0 EVERYWHERE
/
/ INITIAL CONDITION FOR 0.5 CM/YR RECHARGE
/
SELEct subdomain (1,1,39) to (36,36,39)
SET H = 205.21 in SELEcted region
SELEct subdomain (1,1,38) to (36,36,38)
SET H = 204.21 in SELEcted region
SELEct subdomain (1,1,37) to (36,36,37)
SET H = 203.21 in SELEcted region
SELEct subdomain (1,1,36) to (36,36,36)
SET H = 201.71 in SELEcted region
SELEct subdomain (1,1,35) to (36,36,35)
SET H = 198.71 in SELEcted region
SELEct subdomain (1,1,34) to (36,36,34)
SET H = 195.21 in SELEcted region
SELEct subdomain (1,1,33) to (36,36,33)
SET H = 193.21 in SELEcted region
SELEct subdomain (1,1,32) to (36,36,32)
SET H = 192.23 in SELEcted region
SELEct subdomain (1,1,31) to (36,36,31)
SET H = 191.73 in SELEcted region
SELEct subdomain (1,1,30) to (36,36,30)
SET H = 191.23 in SELEcted region
SELEct subdomain (1,1,29) to (36,36,29)
SET H = 190.73 in SELEcted region
SELEct subdomain (1,1,28) to (36,36,28)
SET H = 190.23 in SELEcted region
SELEct subdomain (1,1,27) to (36,36,27)
SET H = 189.73 in SELEcted region
SELEct subdomain (1,1,26) to (36,36,26)
SET H = 189.23 in SELEcted region
SELEct subdomain (1,1,25) to (36,36,25)
SET H = 188.73 in SELEcted region
SELEct subdomain (1,1,24) to (36,36,24)
SET H = 188.23 in SELEcted region
SELEct subdomain (1,1,23) to (36,36,23)
SET H = 187.73 in SELEcted region
SELEct subdomain (1,1,22) to (36,36,22)
SET H = 187.23 in SELEcted region
SELEct subdomain (1,1,21) to (36,36,21)
SET H = 186.73 in SELEcted region
SELEct subdomain (1,1,20) to (36,36,20)
SET H = 186.23 in SELEcted region
SELEct subdomain (1,1,19) to (36,36,19)
SET H = 185.73 in SELEcted region
SELEct subdomain (1,1,18) to (36,36,18)
SET H = 185.23 in SELEcted region
SELEct subdomain (1,1,17) to (36,36,17)
SET H = 184.48 in SELEcted region
SELEct subdomain (1,1,16) to (36,36,16)
SET H = 183.48 in SELEcted region
SELEct subdomain (1,1,15) to (36,36,15)
SET H = 182.48 in SELEcted region
SELEct subdomain (1,1,14) to (36,36,14)
SET H = 181.48 in SELEcted region
SELEct subdomain (1,1,13) to (36,36,13)
SET H = 180.48 in SELEcted region
SELEct subdomain (1,1,12) to (36,36,12)
SET H = 178.36 in SELEcted region
SELEct subdomain (1,1,11) to (36,36,11)
SET H = 176.36 in SELEcted region
SELEct subdomain (1,1,10) to (36,36,10)
SET H = 174.36 in SELEcted region
SELEct subdomain (1,1,9) to (36,36,9)
SET H = 171.36 in SELEcted region
SELEct subdomain (1,1,8) to (36,36,8)
SET H = 168.36 in SELEcted region
SELEct subdomain (1,1,7) to (36,36,7)
SET H = 165.36 in SELEcted region
SELEct subdomain (1,1,6) to (36,36,6)
SET H = 163.71 in SELEcted region
SELEct subdomain (1,1,5) to (36,36,5)
SET H = 160.71 in SELEcted region
SELEct subdomain (1,1,4) to (36,36,4)
SET H = 156.71 in SELEcted region
SELEct subdomain (1,1,3) to (36,36,3)
SET H = 151.71 in SELEcted region
SELEct subdomain (1,1,2) to (36,36,2)
SET H = 146.71 in SELEcted region
SELEct subdomain (1,1,1) to (36,36,1)
SET H = 139.00 in SELEcted region
/
/ these values are actually changed slightly from John Smoots version to
/ reflect correct values for assumed equilibrium with a flux rate of
/ 5 cm/year
/
/ FiXED zone for tank
/
SELEct subdomain (18,18,33) to (28,28,35)
SET C is 5.1E9 in SELEcted domain
FIXEd C in SELEcted domain
/
/ SOURCE-SINK TERMS: M^3, DAYS, MICROCURIES
/ volumetric source is spread over the entire 2.0m thick element.
/ This means source has to be 0.05 m/yr / 365 days/yr / 2.0m element
/
********************** 2D 2D 2D 2D 2D 2D 2D 2D 2D *********************
SELEct subregion from 1,36,38 to 36,36,38 !! infiltration zone for 2D
SOURCE for P: = 6.849E-5 (m3/day)/m3 VOLUmetric SELEcted region $(5 cm/yr)
/
SELECT 18,17,32 to 28,17,32
SOURCE P TABle of TIME 4 sets (0, 0) (2, 2.8) (52, 2.8) (54,0) SELEcted
SOURCE C TABle of TIME 4 sets (0, 0) (2,1.7E9) (52,1.7E9) (54,0) SELEcted
************************** END OF 2D SOURCES **************************
/
********************** 3D 3D 3D 3D 3D 3D 3D 3D 3D *********************
/LOCAte subregion from 1, 1,38 to 36,36,38 !! infiltration zone
/SOURCE for P: = 6.849E-5 (m3/day)/m3 VOLUmetric SELEcted region $(5 cm/yr)
/
/SELECT 18,18,32 to 18,18,32
/SOURCE P TABle of TIME 4 sets (0, 0) (2, 2.8) (52, 2.8) (54,0) SELEcted
/SOURCE C TABle of TIME 4 sets (0, 0) (2,1.7E9) (52,1.7E9) (54,0) SELEcted
/
/SELECT from 18,19,32 to 18,19,32 !! leak source
/SOURCE P TABle of TIME 4 sets (0, 0) (2, 2.8) (52, 2.8) (54,0) SELEct
/SOURCE C TABle of TIME 4 sets (0, 0) (2,1.7E9) (52,1.7E9) (54,0) SELEct
/
/LOCAte subregion from 18,20,32 to 18,20,32 !! leak source
/SOURCE P TABle of TIME 4 sets (0, 0) (2, 2.8) (52, 2.8) (54,0) SELEct
/SOURCE C TABle of TIME 4 sets (0, 0) (2,1.7E9) (52,1.7E9) (54,0) SELEct
************************** END OF 3D SOURCES **************************
/
/ SOLUTION OPTIONS & OPERATIONAL CONTROL
PROP GEOM
MATRix for P using ADI, 200, 3.E-11
MATRix for C using ADI
CONVergence for FLOW: 1.E-5
CONVergence REFErence variable P, local mode: 0.005,10
DIAGnostic node (18,18,32) every 5 steps
DEBUG GEOMETRY OFF
!!!<in> HISTory at (18,18,12) (18,18,8) (18,18,5) (20,18,8) (22,18,8)
SELEct window from (1,18,1) to (36,18,39)
OUTP C,H BY XZ planes every 10000 steps for SELEcted window
/
FLUX BALAnce for C every 100 steps
/
SOLVE FOR 1.0 DAYS IN STEP OF 0.05 DAY, MULT=1.0, MAX=2.
!!!<in> SOLVE FOR 9.0 DAYS IN STEP OF 0.1 DAY, MULT=1.0, MAX=2.
/
!!!<in> SOLVE FOR 40.0 DAYS IN STEP OF 0.2 DAY, MULT=1.0, MAX=3.
!!!<in> SAVE P,C,S NOW
/ 50 days total
/
!!!<in> SOLVE FOR 50.0 DAYS IN STEP OF 0.4 DAY, MULT=1.0, MAX=3.
!!!<in> SAVE P,C,S NOW
/ 100 days total
/
!!!<in> SOLVE FOR 265.0 DAYS IN STEP OF 1.0 DAY, MULT=1.00, MAX=5.
!!!<in> SAVE P,C,S NOW
/
END
/
/

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