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

2

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

3

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.

4

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.

5

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.

6

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.

7

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

8

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

9

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

10

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.

11

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.

18

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.

19