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Training and Research on Probabilistic
Hydro-Thermo-Mechanical (HTM) Modeling
of CO2 Geological Sequestration (GS) in
Fractured Porous Rocks
Project DE-FE0002058
Marte Gutierrez, Ph.D.
Colorado School of Mines
U.S. Department of Energy
National Energy Technology Laboratory
Carbon Storage R&D Project Review Meeting
Developing the Technologies and Building the
Infrastructure for CO2 Storage
August 21-23, 2012
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Presentation Outline
• Benefit to the program (Program goals
addressed and Project benefits)
• Project goals and objectives
• Technical status – Project tasks
• Technical status – Key findings
• Lessons learned
• Summary – Accomplishments to date
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Benefit to the Program
• Program goals being addressed.
– Develop technologies that will support industries’
ability to predict CO2 storage capacity in geologic
formations to within ±30%.
• Project benefits statement.
– The project is developing and validating an advanced
simulation and risk assessment model for predicting
the fate, movement and storage of CO2 in
underground formations. The model has the following
capabilities: 1) takes into account the full coupling of
physical processes, 2) describes the effects of
stochastic hydro-thermo-mechanical parameters, and
3) focuses on porous fractured rocks.
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Project Overview: Goals and Objectives
1. Develop a rigorous procedure for coupled hydro-
thermo-mechanical (HTM) modeling of CO2 GS in
fractured porous rocks.
2. Develop a hydro-mechanical (HM) model for fractured
porous rocks with random fracture geometries.
3. Develop Monte-Carlo-based risk assessment procedure
for CO2 GS in fractured porous rocks.
4. Perform comprehensive study on the effects of
stochastic HM parameters on CO2 GS in fractured
porous rocks.
5. Validate models using an inverse analysis procedure.
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Technical Status – Project Tasks
P , S , T
p S P
Geomechanical Simulation
ij ij p T ijd d dp A dT
ij ijkl kld C d= , v ijtr d
0 1ve
k k
Non-isothermal Multiphase Fluid
Flow Simulation
1n n nm nm n n
i i i in m
tM M A F V q
V
Fig. 1. Coupling of geomechanics and non-isothermal multiphase fluid flow
(1) Rigorous Procedure for Coupled Hydro-Thermo-Mechanical (HTM) Modeling using
TOUGH2 and FLAC.
Length Histogram
0
50
100
150
1 8
15
22
29
36
43
50
Length [m]
Fre
qu
en
cy
0 %
50 %
100 %
150 %
JRC Histogram
0
50
100
150
200
250
300
5 8
11
14
17
20
Joint Roughness Coefficient
Fre
qu
en
cy
0 %
20 %
40 %
60 %
80 %
100 %
120 %
Mechanical Aperture
Histogram
0
50
100
150
200
0.0
0
0.0
3
0.0
6
0.0
9
0.3
0
1.0
0
4.0
0
Mechanical aperture [mm]
Fre
qu
en
cy
0 %
50 %
100 %
150 %
-0.04 -0.02 0.00 0.02 0.04
Permeability in x-direction (mD)
-0.04
-0.02
0.00
0.02
0.04
Perm
eabili
ty in y
-direction (
mD
)
Increasing effective stress
Fracture Fluid and Geomechanical
distribution thermal properties properties
Coupled HTM Model
Pre
sure
Time
Pressure Injected Risk of
histories volumes leakage
h Fig. 3 – Monte Carlo method for probabilistic
modeling of CO2 flow, transport, storage and leakage (3) Monte-Carlo Risk Assessment
Procedure.
(2) Hydro-Mechanical (HM) for Fractured Porous Rocks
(4) Validation.
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Coupled Hydro-Thermo-Mechanical (HTM) Modeling Using TOUGH2 and FLAC
2F
2F
2a
2b
y
x
0
0.2
0.4
0.6
0.8
1
1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized time, T=ct/a 2
no
rmali
zed
po
re p
ressu
re,
p/p
0
Analytical
Monolithic
Modular (FE-FE)
Modular (FE-FD)
Porosity
Technical Status – Key Findings
Verification of Mandel-Cryer Effect.
-5
-4
-3
-2
-1
0
1
-14000 -9000 -4000 1000 6000 11000
distance (m)
vert
ical
dis
pla
cem
en
t (m
)
Subsidence
Compaction
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
1971 1976 1981 1986 1991
time (year)
vert
ical
dis
pla
cem
en
t (m
)
Subsidence
Compaction
measured data
0
10
20
30
40
50
60
-4000 -2000 0 2000 4000 6000
distance (m)
pre
ssu
re (
MP
a)
1 year
5 year
10 year
15 year
-1.5 -1 -0.5 0 0.5 1 1.5
x 104
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
x axis
y a
xis
-5
-4
-3
-2
-1
0
1
-14000 -9000 -4000 1000 6000 11000
distance (m)
vert
ical
dis
pla
cem
en
t (m
)
Subsidence
Compaction
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
1971 1976 1981 1986 1991
time (year)
vert
ical
dis
pla
cem
en
t (m
)
Subsidence
Compaction
measured data
0
10
20
30
40
50
60
-4000 -2000 0 2000 4000 6000
distance (m)
pre
ssu
re (
MP
a)
1 year
5 year
10 year
15 year
-1.5 -1 -0.5 0 0.5 1 1.5
x 104
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
x axis
y a
xis
Verification of Nordbergum Effect.
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Hydro-Mechanical Model (HM) for Fractured Porous Rocks
Technical Status – Key Findings
Oda’s permeability tensor
where
1c
ij kk ij ijk P P3
1
1v
mk k
ij i j
k
P Tr t n nV
0.00
1.25e-17
2.50e-17
0
30
60
90
120
150
180
210
240
270
300
330
D = 1.70
D = 2.21
D = 2.75
0.0
7.5e-18
1.5e-17
0
30
60
90
120
150
180
210
240
270
300
330
NFS
= 2
NFS
= 5
NFS
= 100
2e-16
2e-18
2e-200
30
60
90
120
150
180
210
240
270
300
330
n = 1.15
n = 1.25
n = 1.35
Fracture apertureFracture length
Fracture orientationSelection of an REV
(Representative Element Volume)
Examples of Fracture Geometry Realizations
Permeability Polar Plots
SLR
1e-5 1e-4 1e-3 1e-2 1e-1 1e+0
Mea
n o
f k
1, m
2
1e-17
1e-16
1e-15
1e-14
1e-13
1e-12
Mea
n o
f k
3, m
2
1e-12
1e-16
1e-20
1e-24
1e-28
1e-32
k1
k3
Inflection point
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Stochastic analysis of permeabilities to establish REV of fractured porous
rocks.
SLR
1e-5 1e-4 1e-3 1e-2 1e-1 1e+0
Mea
n o
f k
1,
m2
1e-14
1e-13
1e-12
Mea
n o
f k
3,
m2
1e-13
1e-17
1e-21
1e-25
1e-29
1e-33
Inflection point
k1
k3
FIT, m-1
1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1 1e+2
RE
V, m
2
1e-7
1e-5
1e-3
1e-1
1e+1
1e+3
1e+5
1e+7
REV of k1
REV of k3
-2 -2.05
2
REV=0.16×10 ×
0.97
FIT
R( )
( )
1
1vm
k
k
FIT rV
Technical Status – Key Findings
Hydro-Mechanical Model (HM) for Fractured Porous Rocks
REV for Fractured Rock Mass
Permeability
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Hydro-Mechanical Model (HM) for Fractured Porous Rocks
Technical Status – Key Findings
0.00
0.25
0.50
0
30
60
90
120
150
180
210
240
270
300
330
NFS = 1
NFS = 3
NFS = 100
0.0
2.5
5.0
0
30
60
90
120
150
180
210
240
270
300
330
0
10
20
0
30
60
90
120
150
180
210
240
270
300
330
(a) Young’s modulus (GPa) (b) Poisson’s ratio (c) Shear modulus (GPa)
L SLR
0.0 0.2 0.4 0.6 0.8 1.0
Ex,
Pa
1.3e+10
1.4e+10
1.5e+10
1.6e+10
1.7e+10
1.8e+10
xy
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
Constant range
Ex
xy
l
MOV, m-1
1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0
RE
V,
m2
1e-3
1e+0
1e+3
1e+6
1e+9
1e+12
1.790.06
20.81
REV MOV
R
1 1 1δ δ δ δ
4
f
ijkl ijkl ik jl jk il il jk jl ik
n s s
S F F F F FK K K
( ) ( ) ( ) ( )
1
1v
mk k k k
ij i j
k
F A r n nV
( ) ( ) ( ) ( ) ( ) ( )
1
1v
mk k k k k k
ijkl i j k l
k
F A r n n n nV
max /MOV r Area
Oda Compliance Tensor
( )
where and fracture stiffness along normal and shear direction, Kronecker delta,
and fourth and second rank tensors, volume of rock, fracture length, fracture surface area
n s ij
ijkl ij
v
K K
F F V r A
m total number of fractures, directional cosine of the normal to the fracture orientationin
Elastic Moduli as Function of Sampling Volume
Polar Plots of Elastic Moduli
REV for Elastic Moduli
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Hydro-Mechanical Model (HM) for Fractured Porous Rocks
Technical Status – Key Findings
σ3σ3
σ3
σ3
ε1
ε1 FLAC (Version 6.00)
LEGEND
10-Aug-11 15:45
step 40000
-6.667E+00 <x< 6.667E+00
-6.667E+00 <y< 6.667E+00
Boundary plot
0 2E 0
Effective Principal Stress
Max. Value = 5.642E+00
Min. Value = -3.538E+02
0 2E 3
Displacement vectors
max vector = 7.748E-04
0 2E -3
-5.000
-3.000
-1.000
1.000
3.000
5.000
-5.000 -3.000 -1.000 1.000 3.000 5.000
JOB TITLE : PRINCIPAL STRESS AND DISPLACEMENT
FLAC (Version 6.00)
LEGEND
10-Aug-11 15:44
step 40000
HISTORY PLOT
Y-axis :
1 sigmav (FISH)
X-axis :
2 epsilonv (FISH)
10 20 30 40 50 60 70
(10 )-06
0.500
1.000
1.500
2.000
2.500
3.000
(10 ) 02
JOB TITLE : STRESS-STRAIN CURVE
Angle of inclanation, (degree)
0 20 40 60 80 100 120 140 160 180
Un
iaxi
al s
tren
gth
, f/c
j
5
10
15
20Simulation
Analytical
Model Prediction vs.
Analytical Solution
Angle of inclination, (degree)
0 10 20 30 40 50 60 70 80 90
Maj
or p
rin
cip
al s
tres
s at
fai
lure
, 1f
(M
Pa)
0
100
200
300
400
500Simulation
Experiment
27.6
55.2
0.0
3 (MPa)
Model Prediction vs.
Experimental Results
Axial strain, %
0.0 0.5 1.0 1.5 2.0 2.5
Dev
iato
ric
stre
ss, M
Pa
0
1
2
3
4
5
6
7
Experimental
Calculated
α 15 ,105
α 45 ,135
α 30 ,120
α 0 ,900.5m
0.5
m
α°
0.125m
Compression
Normal stress (σn)
Sh
ear
stre
ss (τ)
Tension
c
ϕ
(+) No-fa
ilure
(-) Im
possible
f(σn,τ)=0
1 1 12 14
2 2 22 24
3 3 32 34
12 12 42 44
σ =σ λ tan λ
σ =σ λ tan λ
σ =σ λ tan λ
λ tan λ
N I s s
N I s s
N I s s
N I s s
S S
S S
S S
S S
Elasto-plastic Model for Fractured Rocks
Model Prediction vs. Experimental Results from
Biaxial Test.
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2000 4000 6000 8000
-150-100
-50
CO2 saturation migration at time 30 days
0
0.1
0.2
2000 4000 6000 8000
-150-100
-50
CO2 saturation migration at time 1 yr
0
0.2
2000 4000 6000 8000
-150-100
-50
CO2 saturation migration at time 2 yrs
0.10.20.3
1000 2000 3000 4000 5000 6000 7000 8000 9000
-150-100-50
CO2 saturation migration at time 10 yrs
y direction (m)
z d
ire
ctio
n (m
)
0
0.5
2000 4000 6000 8000
-150-100
-50
0
0.5
2000 4000 6000 8000
-150-100
-50
0.10.20.30.40.5
2000 4000 6000 8000
-150-100
-50
0
0.2
0.4
2000 4000 6000 8000
-150-100
-50
0
0.2
0.4
2000 4000 6000 8000
-150-100
-50
y direction (km)
z d
ire
ctio
n (m
)
0
0.5
CO2 saturation profiles at different times for
a single realization.
CO2 saturation profiles at 10 years of
injection for 5 realizations.
Technical Status – Key Findings
Monte-Carlo Simulation of CO2 GS – Injection Phase
12
CO2 saturation profiles at different times for
a single realization CO2 saturation profiles at 10 years of
injection for 5 realizations.
5 10 15
-150-100
-50
CO2 saturation migration at time 10 yrs
0
0.5
5 10 15
-150-100
-50
CO2 saturation migration at time 31.71 yrs
00.20.40.60.8
5 10 15
-150-100
-50
CO2 saturation migration at time 63.42 yrs
0
0.5
5 10 15
-150-100
-50
CO2 saturation migration at time 95.13 yrs
y direction (km)
z d
ire
cti
on (
m)
0
0.5
5 10 15
-150-100
-50
0.20.40.60.8
5 10 15
-150-100
-50
0.20.40.60.8
5 10 15
-150-100
-50
00.20.40.6
5 10 15
-150-100
-50
0
0.5
5 10 15
-150-100
-50
y direction (km)
z d
ire
cti
on (
m)
00.20.40.60.8
Technical Status – Key Findings
Monte-Carlo Simulation of CO2 GS – Migration Phase
13
Migration Phase
Total flow rate at production well
(kg/s) for all realizations.
CO2 saturation profiles at different
times for a single realization.
CO2 saturation at the surface for
all realizations at 10 years.
CO2 saturations at 31.71 years
for 5 realizations
Injection Phase
Technical Status – Key Findings
Monte-Carlo Simulation of CO2 GS
0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
CO
2 s
atu
rati
on a
t th
e s
urf
ace
of
the
dom
ain
y direction (km)
14
Storage capacity at different times for different
realization. Storage capacity at different times in terms of
fluid phase behavior.
Technical Status – Key Findings
Monte-Carlo Simulation of CO2 GS
0 20 40 60 80 1000.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
Time (year)
Sto
rage
cap
aci
ty f
acto
r
0 20 40 60 80 1000.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Time (year)
Sto
rage
cap
aci
ty f
acto
r
gas-like phase
liquid phase
total storage factor
Simulation conditions for
forward analysis.
15
Simulation
parameters
Values
Temperature 40°C
Initial pore
pressure 107 Pa
Injection rate 2.0 cm3/min
Porosity 0.21
Absolute
permeability 0.039 Darcy
Assumed
water/gas
irreducible
saturation Swr/Sgr
0.30/0.00
Water/CO2
viscosity 0.65/0.07 cp
Pore volume for
the sample 16.2827 cm3
Van Genuchten
exponent 2.464
Van Genuchten
parameter 6.63×10-4 Pa
Experimental model
1-D simulation FDM model
Technical Status – Key Findings
Inverse Analysis and Model Validation
16
Comparison of saline water production. Comparison of differential pressure.
Comparison of relative permeability curves. Capillary pressure vs. CO2 saturation
from inverse modeling.
Inverse Analysis and Model Validation
Technical Status – Key Findings
Lessons Learned
• Rigorous coupling between geomechanics and two-phase fluid
flow achieved using a staggered solution technique allowing for
use of two existing computer programs (TOUGH2 and FLAC).
• Coupled geomechanics and fluid flow simulation tested against
poroelastic effects predicted by Mandel-Cryer, and Nordbergum.
• Stochastic permeability and mechanical properties of fractured
rocks established from fracture properties and distribution using
Monte-Carlo Simulations.
• REV for both permeability and mechanical behavior defined from
fracture distribution and geometry.
• Significant uncertainties observed in both simulated CO2 injection
and migration due to random input parameters.
• Models rigorously validated using an inverse analysis procedure.
17
Lessons Learned
Effects of uncertainties on simulation of CO2 GS in
fractured porous reservoirs:
• During migration, CO2 saturation profiles are less random
compared to other quantities such as block-to-block flow rate, well
flow rate and CO2 mass fraction.
• Uncertainty in CO2 saturation profiles during injection is more
significant than during migration.
• Uncertainty in intrinsic permeability has the strongest influence in
CO2 flow during in the injection process.
• Uncertainty in porosity cannot be neglected particularly in
evaluating the storage capacity factor in the injection process.
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Summary - Accomplishments to Date
– Monte-Carlo-based risk assessment procedure
developed.
– Hydro-mechanical (HM) model for fractured porous rocks
developed and implemented in a simulation program.
– Comprehensive study on the effects of stochastic fracture
distribution on the elastic compliance, permeability and
REV of fractured rock masses completed.
– Comprehensive study on the effects of stochastic hydro-
mechanical (HM) parameters on CO2 geological
sequestration completed.
– Back-analysis procedure using inverse analysis to
validate stochastic models against experimental data
completed.
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