NUMERICAL MODELING OF PARTIAL SATURATION IN SANDS INDUCED
THROUGH TRANSPORT AND REACTIVITY
SUTRA-BUBBLE
Professor M. K. Yegian
Seda Gokyer, Ph.D. Candidate
NEESR Project: Induced Partial Saturation (IPS) Through Transport and
Reactivity for Liquefaction Mitigation
(Grant Number: CMMI-1134940)
SUTRA – BUBBLE
-
COMPUTER PROGRAM TO MODEL PARTIAL SATURATION IN SANDS INDUCED THROUGH TRANSPORT AND REACTIVITY
Injection of sodium percarbonate solution
Inj. Pres. =?
Inj. Conc. =?
Inj. Duration =?
Sand
S=100%
S = f (C)
S
Computer
simulation
kr = f (S)
kr
time
S
Injection nodes
S < 100%
X
Sand
Y
Z
Governing Equation
Fluid mass balance
Ideal gas law
Darcy’s law
S = f (x,y,z,t)
Degree of saturation
Moles of gas bubbles
Concentration of solute
Governing Flow Equation
time
time
S = f (C)
time
 k k r ρ 

 (1  Sbw )   P
(Sb )2  δρ 
ρ C
 εSw
 RTερ w 

 .  p-ρg    Qp
 r C   
Pb  MWsolute 
C t
 Pb   t
 μ 

Sw ρSop  ερSbw 
CONSTITUTIVE MODELS IN SUTRA-BUBBLE
- CONT’D
LABORATORY EXPERIMENTS FOR CONSITUTIVE MODELS
Rate of reaction for gas generation
Relative permeability of soil
k PS
k FS
k FS - permeability for fully saturated specimen
kr
kr  S δ
time
S
υ b (t)  1   υ b0  exp(  rt)
C(t)   C0  exp( rt)
Moles of gas bubbles
k PS - permeability for partially saturated specimen
Concentration of solute
kr 
time
CONSTITUTIVE MODELS IN SUTRA-BUBBLE - CONT’D
LABORATORY EXPERIMENTS FOR CONSITUTIVE MODELS
Relative permeability of soil
kr 
kr 
k PS
kr  S δ
k FS
k PS - permeability for partially saturated specimen
k FS - permeability for fully saturated specimen
Relative permeability,
kr ( kPS / kFS)
1.0
0.8
Fitted line
-S
2
0.6
0.4
0.2
Lower bound S for
IPS – 40%
Fredlund relation 3
for clean sands - S
0.0
0.0
k PS
 S2 - used in SUTRA-Bubble model
k FS
0.2
0.4
0.6
0.8
Degree of Saturation, S
1.0
FS5-1
FS5-2
FS5-3
FS5-4
PS3-1
PS3-2
PS3-3
PS3-4
PS2-1
PS2-2
PS2-3
PS2-4
PS4-1
PS4-2
PS4-3
PS4-4
Specimen 1 Fully
Saturated (FS)
Specimen 2 Partially
Saturated (PS)
Specimen 3 Partially
Saturated (PS)
Specimen 4 Partially
Saturated (PS)
Degree of
Saturation
Gradient, i
Permeability,
cm/s
Void Ratio
1.00
1.00
1.00
1.00
0.90
0.90
0.90
0.90
0.64
0.65
0.66
0.66
0.49
0.49
0.49
0.49
0.83
0.63
0.40
0.22
0.89
0.66
0.43
0.23
0.64
0.44
0.22
0.89
1.17
0.90
0.66
0.43
0.056
0.053
0.050
0.044
0.048
0.050
0.049
0.048
0.028
0.029
0.024
0.027
0.016
0.020
0.019
0.023
0.71
0.71
0.71
0.71
0.77
0.77
0.77
0.77
0.80
0.80
0.80
0.80
0.75
0.75
0.75
0.75
kR
(kPS/kFS)
1.00
1.00
1.00
1.00
0.77
0.80
0.79
0.76
0.41
0.42
0.35
0.40
0.28
0.35
0.33
0.39
CONSTITUTIVE MODELS IN SUTRA-BUBBLE
- CONT’D
LABORATORY EXPERIMENTS FOR CONSITUTIVE MODELS
Moles of gas bubbles
Electrical Conductivity
(microsiemens/cm)
time
Exp Data Set 1
2500
Fitted Line - Data Set 1
2000
Exp Data Set 2
Fitted Line - Data Set 2
1500
Fitted gas bubble generation relation in
SUTRA-Bubble
1000
500
r0.76% = 0.000133 (1/sec)
1.2
0
0
250
500
750
1000
Time, min
1250
0.8
r = 0.000083 (1/sec) - Ceqv=0.38%
0.6
r = 0.000133 (1/sec) - Ceqv=0.76%
0.4
Exp Data Set 1
Fitted Line - Data Set 1
Exp Data Set 2
Fitted Line - Data Set 2
1200
1
1500
Generation of Oxygen Bubbles in Sand
Ceqv =0.38%
1600
Electrical Conductivity
(microsiemens/cm)
time
3000
Generation of Oxygen Bubbles in Sand
Ceqv =0.76%
(t) / b0
Concentration of solute
Rate of gas generation
0.2
0
0
800
400
r0.5% = 0.0000833 (1/sec)
0
0
250
500
750
1000
Time, min
1250
1500
500
Time, min
1000
1500
VALIDATION OF SUTRA-BUBBLE WITH LABORATORY EXPERIMENTS
LARGE SAND SPECIMEN IN A GLASS TANK
EXPERIMENTS FOR VALIDATION OF SUTRA-BUBBLE
Test 1 and Test 2
Measurements made to validate SUTRA-Bubble:
•
Inflow/Outflow rates and pore water pressures
•
Rate of transport of chemical solution during injection – using Electrical Conductivity Probes
•
Degree of saturation in soil – using Electrical Conductivity Probes
EXPERIMENTAL TEST SET UP
Mariotte’s
Bottle
(MB)
12 EC Probes and 5 PPT’s
Injection tube
with relief valve
Glass Tank
Electrical
conductivity
meters
Data acquisition
system to read PPT’s
Picture shows the experimental set up with measurement
instruments including electrical conductivity meters and data
acquisition system
EXPERIMENTAL TEST SET UP - CONT’D
2.3 cm in
diameter
Pore pressure
transducers –
PPT
Injection
Tube
Electrical
Conductivity –
EC Probe
Kulite XCL– 11-250
Druck PDCR 81
EC Probe
Two electrodes
measuring electrical
resistance
Meters to read the
EC probes
Final locations of instruments for both Test 1 and Test 2
PPT - Pore pressure transducer
EC - Electrical Conductivity Probe
Each square side is 5 cm
Injection tip
Table of parameters of injection
Test 1
e = 0.70
Test 2
e = 0.72
Depth of
Inj. pressure –
Inj.
Inj.
inj. tube
H (TIP)
duration
concentration
Water inj.
25.5 cm
26 cm
5 min
0%
IPS inj.
25.5 cm
26 cm
13 min
1% (by weight)
Water inj.
25.5 cm
26 cm
5 min
0%
IPS inj.
25.5 cm
26 cm
13 min
0.5% (by weight)
RESULTS AND DISCUSSIONS
Results from TEST 1
Inflow and pressure measurements
Cumulative flow of sodium percarbonate solution
Test 1
Cumulative flow of water
Test 1
16000
qave = 1944 gr/min
end of injection
8000
qave = 1892 gr/min
4000
Inflow, gr
Outflow, gr
0
0
1
2
3
4
5
6
7
Time, min
8
9
12000
8000
4000
H = 20.5 cm
30
Hydrostatic
pressure
20
PPT 1
PPT 2
10
0
1
2
3
4
5
6
Time, min
7
8
9
30
Hydrostatic
pressure
0
1
2
9
12
15
H (TIP) = 26 cm
40
10
10
6
Injection of sodium percarbonate solution
PPT 3
PPT 4
PPT 5
20
3
Time, min
3
4
5
6
Time, min
7
8
9
10
PPT 1 & PPT 2
50
PPT Pressure, cm
40
Outflow, gr
0
10
PPT 3, 4 & 5
50
PPT Pressure, cm
PPT Pressure, cm
50
Inflow, gr
0
Injection of water - Test 1
H (TIP) = 26 cm
PPT 1 & PPT 2
end of injection
13 min
40
H = 20 cm
30
Hydrostatic
pressure
20
PPT 1
PPT 2
10
0
3
6
9
Time, min
PPT 3, 4 & 5
50
12
15
PPT Pressure, cm
12000
Cumulative flow, gr
Cumulative flow, gr
16000
PPT 3
PPT 4
PPT 5
40
30
20
Hydrostatic
pressure
10
0
3
6
9
Time, min
12
15
RESULTS AND DISCUSSIONS
Results from TEST 1
Outflow measurements
24000
Cumulative flow, gr
20000
Volume of gas
16000
12000
8000
4000
Inflow
0 – 10 hours
Outflow
0
0
1
2
3
4 5 6
Time, hrs
7
8
9 10
TEST 1
SAVE in the zone of partial saturation using outflow measurements:
(Outflow - Inflow) @ 360 minutes = (Vwater )  (Vbubble ) = 4292 cm3
(Vv )  27310 cm3 for total specimen
Partial saturated zone 55% of the total volume
(Vv ) for partially saturated zone = 27310 * 0.55 = 15021 cm3
(SAVE ) = (Vv  Vbubble ) / Vv  (15021-4292)/15021 = 0.71
RESULTS AND DISCUSSIONS
Results from TEST 1
Transport of chemical solution – Electrical Conductivity measurements
•
Solution arrives at the locations of probes EC1 to EC9.
•
Solution transports ~ 25 cm away from injection.
TEST 1
EC11
Each square side is 5 cm
EC9
EC7
EC6
EC1
EC3
EC4
EC2
EC5
EC8
EC10
EC12
Electrical Conductivity, mS/cm
4.0
EC - Electrical Conductivity
Probe
End of
Injection
3.5
EC1
EC2
3.0
EC3
EC4
2.5
EC5
2.0
EC6
1.5
EC8
EC7
EC9
1.0
EC10
During
injection
0.5
0.0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Time, min
EC11
EC12
RESULTS AND DISCUSSIONS
Results from TEST 1
Degree of Saturation – Electrical Conductivity measurements
TEST 1
4.0
1/
S= Degree of Saturation
n=Saturation exponent close to 2
=Porosity
a= Tortuosity factor
Electrical conductivity of brine
m=Cementation exponent
P
Electric Conductivity
Assumption: From P to R only change in the
Archie’s Law if due to change in S
R
Electrical Conductivity, mS/cm
Archie’s law :
3.5
EC1
EC2
3.0
EC3
EC4
2.5
EC5
EC6
2.0
EC7
EC8
1.5
EC9
EC10
1.0
EC11
EC12
0.5
0.0
0
1
13 min. injection
Time
2
3
4
5
Time, hrs
6
7
8
9
10
RESULTS AND DISCUSSIONS
Results from TEST 1
Degree of Saturation – Electrical Conductivity measurements
~ 60% - 70% degree of saturation achieved in the zone of partial saturation
TEST 1
Degree of saturation results EC probes in the zone of
influence (EC 1-9)
100
1.0
Degree of Saturation, %
EC1
0.62
0.63
0.66
0.65 0.67
0.59
0.73
0.60
0.68
1.0
0 – 10 hours
90
EC2
EC3
80
EC4
EC5
EC6
70
EC7
EC8
60
EC9
50
0
1
2
3
4
5
6
Time, hrs
7
8
9
10
RESULTS AND DISCUSSIONS
Results from TEST 2
Inflow and pressure measurements
TEST 2
Cumulative flow of sodium percarbonate solution
TEST 2
Cumulative flow of water
16000
Cumulative flow, gr
qave = 2400
gr/min
8000
end of injection
4000
qave = 2420
gr/min
Inflow, gr
3
8000
6
9
12
Time, min
9
12
15
H (TIP) = 26 cm
PPT Pressure, cm
20
Hydrostatic
pressure
3
PPT 3, 4 & 5
PPT 1 & PPT 2
50
50
30
2
6
Injection of sodium percarbonate solution
40
1
3
Time, min
PPT 3
PPT 4
PPT 5
0
Outflow, gr
0
15
PPT 3, 4 & 5
10
Inflow, gr
0
Injection of water - Test 2
H (TIP) = 26 cm
50
end of injection
13 min
4000
Outflow, gr
0
0
12000
PPT Pressure, cm
12000
PPT Pressure, cm
Cumulative flow, gr
16000
40
30
20
Hydrostatic
pressure
PPT 1
4
5
6
7
8
9
10
40
30
20
Hydrostatic
pressure
PPT 2
10
Time, min
PPT 3
PPT 4
PPT 5
10
0
3
6
9
Time, min
12
15
0
3
6
9
Time, min
12
15
RESULTS AND DISCUSSIONS
Results from TEST 2
Outflow measurements
Cumulative flow, gr
20000
16000
Volume of gas
12000
8000
4000
0 – 16 hours
Inflow
Outflow
0
0
2
4
6 8 10
Time, hrs
12 14
16
TEST 2
SAVE in the zone of partial saturation using outflow measurements:
(Outflow - Inflow) @ 600 minutes = (Vwater )  (Vbubble ) = 1483 cm3
(Vv )  28311 cm3 for total specimen
Partial saturated zone 40% of the total volume
(Vv ) for partially saturated zone = 28311 * 0.40 = 11324 cm3
(SAVE ) = (Vv  Vbubble ) / Vv  (11324-1483)/11324 = 0.87
RESULTS AND DISCUSSIONS
Results from TEST 2
Transport of chemical solution – Electrical Conductivity measurements
•
Solution arrives at the locations of probes EC1 to EC9 except EC8
•
Solution transports ~ 20 cm away from injection.
TEST 2
EC - Electrical Conductivity
Probe
EC11
Each square side is 5 cm
EC9
EC7
EC6
EC1
EC3
EC4
EC2
EC5
EC8
EC10
Electrical Conductivity, mS/cm
4.0
End of
Injection
3.5
EC2
3.0
EC3
EC4
2.5
EC5
2.0
EC6
1.5
EC8
EC7
EC9
EC10
1.0
During
injection
0.5
0.0
EC12
EC1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Time, min
EC11
EC12
RESULTS AND DISCUSSIONS
Results from TEST 2
Degree of Saturation – Electrical Conductivity measurements
TEST 2
Archie’s law :
P
Electric Conductivity
Assumption: From P to R only change in the
Archie’s Law if due to change in S
R
Electrical Conductivity, mS/cm
1/
S= Degree of Saturation
n=Saturation exponent close to 2
=Porosity
a= Tortuosity factor
Electrical conductivity of brine
m=Cementation exponent
4.0
3.5
3.0
EC2
EC3
2.5
EC4
2.0
EC6
1.5
EC8
EC5
EC7
EC9
1.0
EC10
EC11
0.5
EC12
0.0
0
Time
EC1
0 – 18 hours
2
13 min. injection
4
6
8
10
Time, hrs
12
14
16
18
RESULTS AND DISCUSSIONS
Results from TEST 2
Degree of Saturation – Electrical Conductivity measurements
~ 60% - 75% degree of saturation achieved in the zone of partial saturation
TEST 2
Degree of saturation results EC probes in the zone of
influence (EC 1-9)
100
0 – 18 hours
0.65
0.71
0.77 0.77
0.69
Degree of Saturation, %
1.0
0.54
0.71
0.75
0.65
EC1
90
EC2
EC3
80
EC4
EC5
EC6
70
EC7
EC8
60
EC9
1.0
50
0
2
4
6
8
Time, hrs
10
12
14
16
SUTRA-BUBBLE PREDICTIONS FOR GLASS TANK TEST
Modeling of injection tube
Mesh for test specimen
Free surface boundary
55 cm
25.5 cm
Injection tube
13.5 cm
Source of flow boundary
Injection nodes
Sand
91 cm
Injection tube
Permeability
(m2)
25.5 cm
SUTRA-BUBBLE PREDICTIONS FOR GLASS TANK TEST
Parameters used in SUTRA-Bubble runs
TEST 1 and TEST 2
Size of model
Specimen height
Depth of Injection tip
Porosity
Mean Average Permeability
Dispersivity (Long. & Trans.)
Diffusion coefficient
Coefficient of density change
ρ
)
C
Initial pressure
Initial concentration
Actual concentration of H2O2
solution (CH 2 O 2 )actual
(
Injection pressure
Duration of injection
Total duration of the model
Time increment
Mesh size
Number of nodes
Number of elements
Solver for pressure
Solver for pressure
TEST 1
91 cm (L) x 13.5 cm (W)
55 cm
25.5 cm
0.41
1.5 E-10 m2 *
1E-4 m
1E-9 m2/s
TEST 2
91 cm (L) x 13.5 cm (W)
55 cm
25.5 cm
0.42
1.75 E-10 m2 *
1E-4 m
1E-9 m2/s
4052 (kg/m3)
4052 (kg/m3)
Hydrostatic pressure
0 (kg/kg)
Hydrostatic pressure
0 (kg/kg)
0.002468 (kg/kg)
0.001234 (kg/kg)
H (TIP) = 26 cm
13 minutes
360 minutes
10 seconds (for 15 minutes)
60 seconds (15 to 105 minutes)
360 seconds (105 to 360
minutes)
0.5 cm (hexahedral)
571872
543510
Iterative – GMRES
Tolerance – 1E-13
# of iterations - 1600
Iterative – GMRES
Tolerance – 1E-13
# of iterations - 1600
H (TIP) = 26 cm
13 minutes
600 minutes
10 seconds (for 15 minutes)
60 seconds (15 to 105 minutes)
360 seconds (105 to 600
minutes)
0.5 cm (hexahedral)
571872
543510
Iterative – GMRES
Tolerance – 1E-13
# of iterations - 1600
Iterative – GMRES
Tolerance – 1E-13
# of iterations - 1600
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 1
Inflow/Outflow and pressure measurements
TEST 1
Inflow of solution -SUTRA-Bubble Input
TEST 1
24000
Cumulative flow, gr
Cumulative flow, gr
16000
12000
8000
Measured q
assigned every 2.5
minutes
4000
0
3
6
9
12
15
PPT 1 & PPT 2
PPT Pressure, cm
PPT Pressure, cm
30
PPT 1
PPT 2
PPT 1&PPT 2-Model
10
0
3
6
9
Time, min
16000
Inflow
12000
8000
Inflow-Exp
Inflow-Model
Outflow-Exp
Outflow-Model
0
12
15
1
2
3
Time, hrs
PPT 3, 4 & 5
50
40
Hydrostatic
pressure
Outflow
Exp
0
Time, min
20
20000
4000
0
50
SUTRA-Bubble
PPT 3
PPT 4
PPT 5
PPT 3-Model
PPT 4-Model
PPT 5-Model
40
30
20
Hydrostatic
pressure
10
0
3
6
9
Time, min
12
15
4
5
6
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 1
Transport of chemical solution
SUTRA-Bubble output of concentration
TEST 1- 15 minutes
Ceqv (H
EC11
EC9
EC6
EC7
EC1
EC2
EC5
EC3
EC8
EC4
EC10
EC12
2O 2 )
(kg/kg)
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 1
Transport of chemical solution
SUTRA-Bubble output of concentration & electrical conductivity measurements
Arrival of Solution - EC 1 & EC2
Arrival of Solution - EC3, EC5 & EC6
1.2
0.8
Exp
SUTRA-Bubble
0.4
Concentration-EC1&EC2-Model
Conductivity-EC1-Exp
Conductivity-EC2-Exp
0.2
0.0
0
2
4
6
8
10
Time, min
12
14
16
1.0
0.8
0.6
Exp
SUTRA-Bubble
0.4
Concentration-EC3,EC5&EC6-Model
Conductivity-EC3-Exp
Conductivity-EC5-Exp
Conductivity-EC6-Exp
0.2
0.0
18
0
2
4
6
8
10
12
14
16
15 cm away from injection
1.0
0.8
Exp
0.6
SUTRA-Bubble
0.4
0.2
Concentration-EC7-Model
Conductivity-EC7-Exp
0.0
0
18
2
4
6
Time, min
Arrival of Solution - EC4 & EC9
1.2
~ 20 cm away from injection
1.0
0.8
0.6
SUTRA-Bubble
Exp
0.4
Concentration-EC4&EC9-Model
Conductivity-EC4-Exp
Conductivity-EC9-Exp
0.2
0.0
0
2
4
6
8
10
Time, min
12
14
16
18
8
10
12
Time, min
Arrival of Solution - EC8
1.2
Normalized to peak value
0.6
Arrival of Solution - EC7
1.2
10 cm away from injection
Normalized to peak value
Normalized to peak value
1.0
Normalized to peak value
Normalized to peak value
1.2
25 cm away from injection
1.0
0.8
0.6
Exp
SUTRA-Bubble
0.4
ConcentrationEC8-Model
ConductivityEC8-Exp
0.2
0.0
0
2
4
6
8
10
Time, min
12
14
16
18
14
16
18
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 1
Degree of Saturation
SUTRA-Bubble output of degree of saturation
TEST 1 – 360 minutes
S
EC11
1.0
EC9
EC6
EC7
EC1
0.62
EC2
0.66
EC5
EC3
0.65 0.67
EC8
0.59
EC4
EC10
0.68
EC12
0.63
0.73
0.60
1.0
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 1
Degree of Saturation
SUTRA-Bubble output of degree of saturation & Experiment (EC measurements)
EC1 & EC2
70
Exp
60
EC1-Exp
EC2-Exp
EC1&EC2-Model
50
40
0
1
2
3
Time, hrs
5
Exp
80
SUTRA-Bubble
70
60
EC3-Exp
EC5-Exp
EC6-Exp
EC3,EC5&EC6 - Model
50
40
6
0
1
2
3
Time, hrs
EC4
100
Degree of Saturation,%
4
90
Exp
80
SUTRA-Bubble
70
60
EC4-Exp
EC4-Model
50
40
0
1
2
3
Time, hrs
4
5
6
4
5
6
Exp
SUTRA-Bubble
80
70
60
50
EC9-Exp
EC9-Model
40
0
1
2
3
Time, hrs
Exp
80
SUTRA-Bubble
70
60
50
EC7-Exp
EC7-Model
40
0
1
2
5
6
4
5
6
25 cm away from injection
90
Exp
SUTRA-Bubble
80
70
60
50
EC8-Exp
EC8-Model
40
4
3
Time, hrs
EC8
100
21 cm away from injection
90
15 cm away from injection
90
EC9
100
18 cm away from injection
Degree of Saturation,%
SUTRA-Bubble
10 cm away from injection
90
EC7
100
Degree of Saturation,%
80
Degree of Saturation,%
@ Injection
90
EC3, EC5, & EC6
100
Degree of Saturation,%
Degree of Saturation,%
100
0
1
2
3
Time, hrs
4
5
6
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 2
Inflow/Outflow and pressure measurements
TEST 2
Inflow of solution -SUTRA-Bubble Input
TEST 2
20000
SUTRA-Bubble
Cumulative flow, gr
Cumulative flow, gr
16000
12000
8000
Measured q
assigned every 1
minute
4000
0
0
3
6
9
12
15
Exp
16000
Outflow
12000
Inflow
8000
Inflow-Exp
Inflow-Model
Outflow-Exp
Outflow-Model
4000
0
Time, min
0
1
2
3
4
5
6
Time, min
50
Exp
PPT Pressure, cm
PPT Pressure, cm
PPT 3, 4
PPT 1 & PPT 2
50
40
30
SUTRA-Bubble
20
Hydrostatic
pressure
PPT 1
PPT 2
PPT 1&PPT 2 - Model
10
0
3
6
9
Time, min
12
15
PPT 3
PPT3-Model
40
30
PPT 4
PPT4-Model
Exp
20
Hydrostatic
pressure
10
0
3
SUTRA-Bubble
6
9
Time, min
12
15
7
8
9
10
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 2
Transport of chemical solution
SUTRA-Bubble output of concentration
TEST 2- 15 minutes
Ceqv (H
EC11
EC9
EC6
EC7
EC1
EC2
EC5
EC3
EC8
EC4
EC10
EC12
2 O2 )
(kg/kg)
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 2
Transport of chemical solution
SUTRA-Bubble output of concentration & Electrical conductivity measurements
Normalized to peak value
Exp
SUTRA-Bubble
0.6
0.4
Concentration-EC1&EC2-Model
0.2
Conductivity-EC1-Exp
Conductivity-EC2-Exp
0.0
0
2
4
6
Time, min
8
10 cm away from injection
1.0
Exp
0.8
0.6
SUTRA-Bubble
0.4
Concentration-EC3,EC5&EC6-Model
Conductivity-EC3-Exp
Conductivity-EC5-Exp
Conductivity-EC6-Exp
0.2
0.0
10
1.2
0
12
2
4
6
8
10
15 cm away from injection
1.0
0.8
Exp
0.6
SUTRA-Bubble
0.4
Concentration-EC7-Model
0.2
Conductivity-EC7-Exp
0.0
0
12
2
Time, min
~ 20 cm away from injection
0.8
Exp
SUTRA-Bubble
0.4
Concentration-EC4&EC9-Model
Conductivity-EC4-Exp
Conductivity-EC9-Exp
0.2
0.0
0
2
4
6
Time, min
8
6
Time, min
8
10
1.2
1.0
0.6
4
Arrival of Solution - EC8
Arrival of Solution - EC9
1.2
10
12
Normalized to peak value
0.8
Normalized to peak value
Normalized to peak value
@ Injection
1.0
Arrival of Solution - EC7
Arrival of Solution - EC3, EC5 & EC6
1.2
Normalized to peak value
Arrival of Solution - EC 1 & EC2
1.2
25 cm away from injection
1.0
0.8
SUTRA-Bubble
0.6
0.4
Exp
ConcentrationEC8-Model
0.2
Conductivity-EC8Exp
0.0
0
30
60
90
Time, min
120
150
12
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 2
Degree of Saturation
SUTRA-Bubble output of degree of saturation
TEST 2 – 600 minutes
S
EC11
1.0
EC9
EC6
EC7
EC1
0.65
EC2
0.71
0.77 0.77
0.54
EC5
EC3
0.69
0.71
EC8
EC4
0.75
EC10
EC12
0.65
1.0
VALIDATION OF SUTRA-BUBBLE PREDICTIONS
TEST 2
Degree of Saturation
SUTRA-Bubble output of degree of saturation & Experiment (EC measurements)
Exp
60
EC1-Exp
EC2-Exp
EC1&EC2-Model
50
0
1
2
3
4 5 6
Time, hrs
7
8
9
80
SUTRA-Bubble
60
EC4-Exp
50
EC4-Model
1
2
3
4 5 6
Time, min
60
EC3-Exp
EC5-Exp
EC6-Exp
EC3, EC5 & EC6-Model
50
0
1
2
3
4 5 6
Time, hrs
7
8
9
7
8
9
10
70
Exp
60
EC7-Exp
50
EC7-Model
0
10
21 cm away from injection
SUTRA-Bubble
80
1
2
3
4 5 6
Time, hrs
Exp
60
EC9-EXp
EC9-Model
7
8
9
10
EC8
100
90
50
SUTRA-Bubble
80
EC9
70
15 cm away from injection
90
40
40
40
0
SUTRA-Bubble
100
Exp
70
70
10
18 cm away from injection
90
Exp
80
40
EC4
100
10 cm away from injection
90
EC7
100
Degree of Saturation, %
SUTRA-Bubble
40
Degree of Saturation,%
Degree of Saturation, %
80
Degree of Saturation,%
Degree of Saturation, %
@ Injection
90
70
EC3, EC5, & EC6
100
Degree of Saturation,%
EC1 & EC2
100
25 cm away from injection
90
Exp
80
SUTRA-Bubble
70
60
EC8-EXp
50
EC8-Model
40
0
1
2
3
4
5
6
Time, min
7
8
9
10
0
1
2
3
4 5 6
Time, min
7
8
9
10
Findings:
•
•
•
•
Computer program SUTRA-Bubble was developed to model partial saturation induced through transport and
reactivity.
Parameters for constitutive models were determined experimentally.
• Relative permeability - kr = S2
• Rate for gas generation – r = 0.0001333 (1/sec) for C = 0.76%
r = 0.0000833 (1/sec) for C = 0.38%
Measurements from two glass tank tests (Test 1 and Test 2) were compared with SUTRA-Bubble outputs of:
• Flow and pore water pressure measurements
• Concentration of solution – Transport of solution
• Degree of saturation
Observations and Conclusions from the comparisons of glass tank experimental and SUTRA-BUBBLE results:
• Outflow matches well - representing average degree of saturation in zone of flow
• Pressure outputs do not match as well as the other parameters – pressures are very sensitive to soil
permeability, assumption of uniform permeability may be rigorous
• Transport of solution matches very well – arrival time of the solution matches very well at each electric
conductivity probe location
• Degree of saturation matches quite well
• The shape of the zone of partial saturation achieved matches quite well
• At each probe location the final degree of saturation matches well
• In general, the match is better for TEST 1 results compared to TEST 2 results.
• The two experimental tests helped validate SUTRA-BUBBLE