A coupled large-scale model for hydromechanical simulation of CO2 geological storage

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Submitted on 7 Jul 2011

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simulation of CO2 geological storage

Pierre Sochala, Vivien Desveaux, Darius Seyedi, Jeremy Rohmer

To cite this version:

Pierre Sochala, Vivien Desveaux, Darius Seyedi, Jeremy Rohmer. A coupled large-scale model for

hydromechanical simulation of CO2 geological storage. SIAM Geosciences 2011, Mar 2011, Long

Beach, United States. �hal-00606982�

A oupled large-s ale model for hydrome hani al simulation of CO

2

geologi al storage

P.So hala*, V.Desveaux*,J.Rohmer*,andD.Seyedi* *BRGM(Fren hGeologi alSurvey)

NaturalRisksandSafetyofCO2storage Orl

´

eans

SIAMGeos ien es2011 Mar h21-24,LongBea h

General introdu tion

Greenhouse gasemissions

⇒

Globalwarming

CO 2

inje tion

⇒

reservoiroverpressure

⇒

apro kdamageor faultrea tivation?

General introdu tion Hydrauli Me hani Hydrome hani almodelingofCO 2 sequestration

◮

Tough2-FLAC 3D

→

Rutqvistetal.

◮

ToughRea t-FLAC 3D

→

Taronetal.

◮

ModiedCODE_BRIGHT

→

Vilarrasaetal.

General introdu tion Hydrauli Me hani uidpressure stress Hydrome hani almodelingofCO 2 sequestration

◮

Tough2-FLAC 3D

→

Rutqvistetal.

◮

ToughRea t-FLAC 3D

→

Taronetal.

◮

ModiedCODE_BRIGHT

→

Vilarrasaetal.

General introdu tion Hydrauli Me hani uidpressure stress volume variation porosity Hydrome hani almodelingofCO 2 sequestration

◮

Tough2-FLAC 3D

→

Rutqvistetal.

◮

ToughRea t-FLAC 3D

→

Taronetal.

◮

ModiedCODE_BRIGHT

→

Vilarrasaetal.

Geohydrologi al system

◮

Two-phase

γ

(liquid,gaz)andtwo- omponent

χ

(water,CO 2

)ow

◮

Mass onservationof

χ

withasour e termS

χ

∂

t



ϕ

X

γ

ρ

γ

s

γ

ω

χ,γ



+ ∇ ·

 X

γ

ω

χ,γ

F

γ



=

S

χ

ϕ

porosity,

ρ

γ

density,s

γ

saturation,

ω

χ,γ

massfra tionof

χ

in

γ

◮

Dar y'slaw F

γ

= −ρ

γ

k i k r

,γ

µ

γ

(∇

p

γ

− ρ

γ

ge z

)

k i

porousmediaintrinse permeability,k r

,γ

relativepermeability

µ

γ

dynami vis osity,p

γ

pressure

◮

Hydrauli relations

→

Van-Genu hten80,Mualem76 Thermodynami equilibrium

→

Spy her

&

Pruess05

Me hani al equations

◮

Conservationof momentum

∇ · σ + ρ

ge z

=

0

σ

totalstress tensor,

ρ

averagedensity

◮

Ee tive stress on ept

σ = σ

′

−

bpI

σ

′

ee tivestresstensor,bBiot's oe ient,pporepressure

◮

Linearelasti ity

σ

′

=

E 1

+ ν



∇

u

+

t

∇

u

+

ν

1

−

2

ν

(∇ ·

u

)

I



Coupling onditions

◮

pore pressureequaltothemean-valueofthetwo-phasesystem p

=

X

γ

s

γ

p

γ

◮

permeability-porosityrelation

→

David05

k i

=

k 0 i

 ϕ

ϕ

0



m mempiri alparameter

◮

Biot's law

→

Biot41

d

ϕ =

bd

(

div

(

u

)) +

1 M

dp M Biot'smodulus

Tough2 and Code_Aster dis retization

Tough2

→

Lawren eBerkeleyNationalLaboratory

◮

Multi-phaseuidandheatow inporousandfra turedmedia

◮

Finite volumewithnitedieren e evaluationoftheuxterm IntegratedFiniteDieren e Method

→

Narasimham76

◮

Eulerimpli its heme

◮

NewtonRaphson Algorithm

Code_Aster

→

EDF(Fren hEle tri ityCompagny)

◮

Non-linearmodelsofme hani alphenomena

Transfer operator

T

FV

→

FE

for pressure eld step1- onstru tionofa dualmesh

M

FV









Transfer operator

T

FV

→

FE

for pressure eld step1- onstru tionofa dualmesh

M

FV









h 1 h 2 h 3 h 4











p0

,

0 p 1

,

0 p 2

,

0 p0

,

1 p 1

,

1 p 2

,

1 p0

,

2 p 1

,

2 p 2

,

2

∂Ω

M

d FV p 0

,

i

=

p 1

,

i

+

h 1 h

(

p 1

,

i

−

p 2

,

i

)

Transfer operator

T

FV

→

FE

for pressure eld step1- onstru tionofa dualmesh

M

FV









h 1 h 2 h 3 h 4











p0

,

0 p 1

,

0 p 2

,

0 p0

,

1 p 1

,

1 p 2

,

1 p0

,

2 p 1

,

2 p 2

,

2

∂Ω

M

d FV p 0

,

i

=

p 1

,

i

+

h 1 h 2

(

p 1

,

i

−

p 2

,

i

)

step2-linearinterpolation

•

x i









A 2 A 3 A 4 A 1 x i

,

1 x i

,

4 x i

,

2 x i

,

3 p FE

(

x i

) =

4

X

k

=

1 A k A p FV

(

x i

,

k

)

Transfer operator

T

FE

→

FV

for porosity eld Mean-valueof

ϕ

on

K

estimatedbyMC

•

•

•

•

•

•

•

•

•

•

•

M

FE



K

∗ ∗

∗

∗

∗

∗

∗

∗

∗ ∗ ∗

∗ ∗

∗ ∗ ∗ ∗

∗ ∗ ∗ ∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

randompoint

ϕ

FV

|

K

=

1 N N

X

j

=

1

ϕ

FE

(

x j

)

Time oupling

ConventionalParralelStaggeredalgorithm

→

Pipernoetal95

•

•

•

•

p n

−

1

γ

p n

γ

p n

+

1

γ

Tough2

•

•

•

•

ϕ

n

−

2

ϕ

n

−

1

ϕ

n Code_Aster n

−

1 n n

+

1 n

+

2 1 1

′

2 2

′

3 3

′

1

,

3

: T

FV

→

FE

(

p

)

1

′

,

3

′

: T

FE

→

FV

(ϕ)

Test ase presentation

◮

CO 2

inje tionbyhorizontalwellindeepaquifer

◮

2D geometry

Ω = [−

50km

,

50km

] × [

0

, −

2km

]

andT

=

5years

◮

S CO2

=

500t

/

m

/

year

◮

impa t ofasealingfaultneartheinje tionzone

Upper Capro k Aquifer Base z

=

0 z

= −

1400m z

= −

1450m z

= −

1550m z

= −

2000m x

=

0 x

= −

50km x

=

50km

•

CO 2 inje tion

Test ase presentation

◮

CO 2

inje tionbyhorizontalwellindeepaquifer

◮

2D geometry

Ω = [−

50km

,

50km

] × [

0

, −

2km

]

andT

=

5years

◮

S CO2

=

500t

/

m

/

year

◮

impa t ofasealingfaultneartheinje tionzone

Upper Capro k Aquifer Base z

=

0 z

= −

1400m z

= −

1450m z

= −

1550m z

= −

2000m x

=

0 x

= −

50km x

=

50km

•

CO 2 inje tion 5km

Overpressure (Pa)

t=1year

Overpressure (Pa)

t=2years

Overpressure (Pa)

t=3years

Overpressure (Pa)

t=4years

Overpressure (Pa)

t=5years

Overpressure in the aquifer (Pa)

Initial ase Perturbated ase

0

2e+06

4e+06

6e+06

8e+06

1e+07

1.2e+07

1.4e+07

1.6e+07

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

x (m)

Horizontal ee tive stress hange due to inje tion (Pa)

Initial ase Perturbated ase

-1.8e+07

-1.7e+07

-1.6e+07

-1.5e+07

-1.4e+07

-1.3e+07

-1.2e+07

-1.1e+07

-1e+07

-9e+06

-8e+06

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

x (m)

CO 2

plume

Initial ase Perturbated ase

-400

-200

0

200

400

x (m)

-1600

-1550

-1500

-1450

-1400

y (m)

Con lusion

◮

robustmethodtotransfereldsbetweendierent meshes

◮

e ientparalleltime ouplingalgorithm

◮

signi antin rease oftheoverpressuredue totheimpermeablefault

Furtherwork

◮

tensile andshearstressfailure riteria

→

sustainablepressure

◮

non-linear onstitutivelawofthegeologi alformation

◮