the ultimate fate of co2 - ccst @ mit · 11/14/2007 · • hesse, tchelepi & orr (in prep)...

The Ultimate Fate of COThe Ultimate Fate of CO22

Trapping TimescalesTrapping TimescalesMarc Hesse

13 - 14 Nov. 2007Stanford University

MIT - CSF VIIIThe State of Geological Storage

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CollaboratorsCollaborators

HamdiTchelepi

LynnOrr

BrianCantwell

AmirRiaz

All errors are undoubtedly the result of my failure to follow their advice.



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MenuMenu

Trapping Processes in CO2 storage

Dissolution Trapping- onset of convection- dissolution rate

Residual Trapping- Horizontal Aquifer- Sloping Aquifer

Summary



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Injected COInjected CO22 is buoyant!is buoyant!

from:

(Ide et al. 2007)

500 1000 1500 2000 2500 30000.3

0.4

0.5

0.6

0.7

0.8

20 C°/km25 C°/km30 C°/km

dens

ity C

O2 /

dens

ity b

rine

depth [m]



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COCO22 Trapping ProcessesTrapping Processes

2.2 mm

Residual Mineralized

rockgrain

water

CO2

(Benson et al. 06)

Dissolved

(Riaz, Hesse et al. 06)

unstable diffusiveboundary layer

brine

fingers of dissolved CO2NaAlCO3(OH)2



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States of COStates of CO22 in Subsurfacein Subsurface

dissolution of residual CO2

min

eral

trap

ping

mineralizedCO2

leakedCO2

dissolution

tapping

dissolvedCO2

residual trapping

residualCO2

injectedCO2

Dissolution TrappingDissolution Trapping



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Dissolved CODissolved CO2 2 Increases Brine DensityIncreases Brine Density

(Yang & Gu 2006)

linear relationship



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Important ScalesImportant Scales

Time and length scales:

1) Critical time:

2) Critical wavelength:

⇒ permeability K is the important factorhigh-K aquifers: tc ~ 1 yr, and λc ~ 1 m

KgKD

c1

07.02

∝Δ

=ρ

πμλ

( ) 22

2 1146KgK

Dtc ∝Δ

=ρ

φμ

(Riaz, Hesse et al. 2006)



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Numerical Resolution?Numerical Resolution?

10m x 13m

Mesh size: 3cm x 4cmgrid blocks: 80.000Onset time: 2yrs

(Lindeberg & Bergmo 2003)

supercritical CO2

brine

dissolved CO2

100m x 100m x 2m350.000100yrs

7km x 10km x 30m



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Open AquifersOpen Aquifers

τ = 7.3 τ = 14.6 τ = 22.0 τ = 29.0

CO2 Concentration Maps: Evolution of Dissolution Rate:



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Closed AquiferClosed Aquifer



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COCO22 Dissolution at Dissolution at SleipnerSleipner

(Chadwick et al. 2004)

+ large volume

400km x 50-100km100 – 200m

high permeability

φ ~ 0.3K ~ 3 Darcy

= efficient dissolution

(Lindeberg & Bergmo 2003)

5,000 – 50,000 years

Residual TrappingResidual Trapping



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Microscopic & Microscopic & MarcoscopicMarcoscopic

How much is left behind?⇒ residual saturation

How much of the aquifer iscontacted? ⇒ sweep

(Benson et al. 2006) (Doughty et al. 2006)



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DerivationDerivation

ttxxQtxQSxh ggwr ΔΔ+−=−ΔΔ )),(),(()1(φ grSxh φΔΔ−



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NonNon--Dimensional FormDimensional Form

( ) ( ) ⎥⎦

⎤⎢⎣

⎡∂∂

+−−

∂∂

=⎥⎦

⎤⎢⎣

⎡+−

−∂∂

+∂∂

ξη

ηηη

ξσ

ηηη

ξσ

τη

11M)1(

11M)1( Pe

⎩⎨⎧

>−≤

=0;10;1

τ

τ

ηεη

σ

Hh=η0Lx=ξ

)cos( 120 θκ

τHLt

=

θtanPe0

0

HL

=

Pe

∗

∗

=rw

w

g

rg

kk μμ

M

M M

wr

gr

SS−

=1

ε

ε



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Horizontal AquiferHorizontal Aquifer

Sgr = Swr = 0.2L0 = 2000 mH0= 200 mθ = 0°(M = 0)



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Volume Decay Horizontal AquiferVolume Decay Horizontal Aquifer

volume: V ∝ t3β-1

tip pos.: xtip ∝ tβ

height: h ∝ t2β-1

(Bear & Ryzhik 1998)



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Sloping AquiferSloping Aquifer



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Analytic model for large Analytic model for large PePe

M=20 M=0M=1

τ = 50, ε = 0, Pe = 2

M = 0M = 1

M = 4M = 12M = 20

( ) ( ) ⎥⎦

⎤⎢⎣

⎡∂∂

+−−

∂∂

=⎥⎦

⎤⎢⎣

⎡+−

−∂∂

+∂∂

ξη

ηηη

ξσ

ηηη

ξσ

τη

11M)1(

11M)1(

Pe0

analytical solution hyperbolic limitnumerical solution full equation



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Evolution of FootprintEvolution of Footprint

front

ξ: distance

τ: t

ime

back



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Volume Decay Sloping AquiferVolume Decay Sloping Aquifer



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Numerical SolutionsNumerical Solutions



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Residual Trapping in Alberta BasinResidual Trapping in Alberta Basin

(Bachu et al. 2002)

(Bac

hu&

Ben

nion

2007

)



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Summary: Dissolution TrappingSummary: Dissolution Trapping

vigorous convection in high permeability aquifers

linear dissolution rate in large open aquifers

dissolution likely to be important at Sleipner

convective dissolution is numerical challenge



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Summary: Residual TrappingSummary: Residual Trapping

power-law plume decay in horizontal aquifers

rapid plume decay in sloping aquifers

residual trapping likely to be important in Alberta

thin gravity tongues are numerical challenge



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DisclaimerDisclaimer

model reality

“All aquifers discussed in this presentation are fictional. Any similarity to real aquifers, intended for storage or not, is strictly a coincidence.”



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ReferencesReferences

Dissolution Trapping:• Hesse, Riaz & Tchelepi (2006) Resolving density fingering during CO2

sequestration: A challenge for reservoir simulation, Proceedings, CO2SC 2006

• Riaz, Hesse, Tchelepi & Orr (2006) Onset of convection in a gravitationally unstable diffusive boundary layer in porous media, JFM., 548, pp. 87-111

Residual Trapping:• Hesse, Tchelepi & Orr (in prep) Gravity Currents with residual trapping in

sloping aquifers• Hesse, Tchelepi, Cantwell & Orr (2006) Gravity currents in horizontal

porous media: transition from early to late self-similarity, JFM 577, pp. 363-383

• Hesse, Tchelepi & Orr (2006) Scaling Analysis of the migration of CO2 in saline aquifers, SPE 102796

the ultimate fate of co2 - ccst @ mit · 11/14/2007 · • hesse, tchelepi & orr (in prep)...

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