towards basin-scale modeling of geological … · · 2007-11-20towards basin-scale modeling of...

Carbon Sequestration Forum VIIIStanford, California, November 13-14, 2007

Ruben Juanes

MIT

TOWARDS BASIN-SCALE MODELINGOF GEOLOGICAL CO2 STORAGE:

UPSCALING OF CAPILLARY TRAPPING

R. Juanes, Nov 2007 Carbon Sequestration Forum VIII 2

SUMMARY OF RESULTS

, Trapping of CO2 leads to safer sequestration scenarios:immobilization and further dissolution

, How to maximize trapping:" Inject deeper" Inject at higher rates" Inject water slugs"Horizontal, smart wells

, Word of caution: models will tend to overestimatesweep, trapping and dissolution

, We present a new model to upscale capillary trappingto the basin scale


, Potential leak of the CO2 into the atmosphere"Activation of faults (overpressurization)"Existing wells (abandoned)"Regional groundwater flow

, Essential to predict the migration and distribution ofthe CO2 in the subsurface – at the basin scale

, Need proper monitoring to assess the success of thesequestration project – at the basin scale

RISKS OF CO2 STORAGE

(IPCC Report, 2005)


, Mechanisms for CO2 immobilization

"Structural trapping: impermeable cap rock

"Solution trapping: dissolution into the brine

"Mineral trapping: geochemical binding to the rock bymineral precipitation

"Capillary trapping: disconnection of the CO2 phaseinto immobile blobs during two-phase flow

STORAGE MECHANISMS


, Trapping mainly due to snap-off during imbibition

, During CO2 injection (drainage-like process): no trapping

, When/where does trapping occur?

"after injection

"at the trailing edgeof the plume duringupwards migration(water displacing CO2)

BASIS FOR CAPILLARY TRAPPING

(Juanes et al, 2006)


CAPILLARY TRAPPING MODEL

, Most relative permeability hysteresis models are basedon the trapping relation proposed by Land (1968)

, Land’s model yields amonotonically increasing initial-residual curve

"Higher initial gas sathigher trapped gas

gi

gigr SC

SS

⋅+=

1


NUMERICAL STUDY

, Reservoir model

"Realistic three-dimensionalheterogeneous reservoir(PUNQ-S3 synthetic model)

"Anticline structure

"8 injectors

(Juanes, Spiteri, Orr and Blunt: WRR 2006)


RESERVOIR DESCRIPTION

, Relative permeability

"Data taken from Oak (1990)"Data result in a Land trappingcoefficient C ~ 1

, PVT properties

"Typical of CO2 at reservoirconditions


EFFECT OF HYSTERESIS

, Compare Case 1 (no hysteresis) and Case 2 (with hysteresis), CO2 saturation after 200 years

, The model that accounts for hysteresis predicts"Almost all the CO2 is trapped"Spread-out distribution of trapped CO2, as opposed toa concentrated distribution of mobile CO2


EFFECT OF INJECTION RATE

, Compare Case 2 (10 years) and Case 3 (50 years), CO2 saturation after 200 years

, Lower injection rate leads to more mobile CO2 at the top


EFFECT OF WATER INJECTION

, Compare Case 2 (CO2 injection) and Case 4 (WAG injection), CO2 saturation after 200 years

, Alternating water injection induces more trapping(enhanced imbibition) and reduces the amount of CO2

that accumulates at the top


EFFECT OF WATER INJECTION

, Impact on bottom-hole pressure

, Alternating water injection increases the operating BHP"Water injection rate is higher than that of CO2

"Compressibility of water is much smaller


SUMMARY OF SIMULATION RESULTS

, Accounting for trapping and hysteresis of the nonwettingCO2 phase is essential. Trapping occurs at the trailing edgeof the plume after injection stops

, Trapping of CO2 leads to safer sequestration scenarios:immobilization and further dissolution

CO

2

wat

er , How to maximize trapping:

" Inject deeper" Inject at higher rates" Inject water slugs"Horizontal, smart wells

(Juanes, Spiteri, Orr and Blunt: WRR 2006)


SCALING OF CAPILLARY TRAPPING

, Typical simulation models do not capture:"Gravity override"Channeling and viscous fingering

, Simulations are therefore grid dependent, Coarse-grid simulations overestimate trapping!


, Dependence of megascopic trapping coefficient on

"Mobility ratio"Gravity number"Subgrid heterogeneity

PREDICTIVE THEORY

, Grid dependence of block-effective trapping coefficient

, The same can be done for dissolution, geochemistry, etc.

log h

Ceff


, Mathematical models that capture gravity override

UPSCALING OF CAPILLARY TRAPPING

brine

mobile gasgasinjection

brine

mobile gas

trapped gas

waterinjection

brine

mobile gas

trapped gas

waterinjection

"Need to model the injection period"Effect of regional groundwater flow


, Main features of the mathematical model

"Sharp interface approximation"Vertical equilibrium (Dupuit approximation)

" Incompressible flow

MATHEMATICAL MODEL – INJECTION

hg

gasinjection HQ

⎩⎨⎧

>−Δ++<−−

=hzzhgphzzhgp

pI

I

if ),()( if ),(

ρρρ

0)( ≠=−+=+ QhHuhuQQ gwggwg


*rgk

, Formulation

"Darcy’s law – endpoints ofrelative permeabilities

"Fractional-flow formulation

"Mass balance

MODEL – INJECTION PERIOD

( )xh

fhgkQfQ gggggg ∂

∂−Δ−= )1(*λρ

0))1((

=∂

∂+

∂

−∂

xQ

thS ggwcφ

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂−

∂∂

−=xh

gxpk

ku gI

g

rgg ρ

μ

*


, Dimensionless parameters

"Plume height:

"Time:

"Length:

"Viscosity ratio:

"Effective gravity number:


Hh

h g=

timeinjection , == TTt

dτ

φξ

HQTL

Lx

== ,

w

gMμμ

=

h

v

g

rggd k

kHQT

HHQgkk

Nφμ

ρ⋅

Δ=

*


, Equation in dimensionless form

"This is a nonlinear advection–diffusion equation


hgas

injection Q

0)()())1((=⎥

⎦

⎤⎢⎣

⎡∂∂

−∂∂

+∂−∂

ξξτhhDNhfhS

gdd

wc

fractional flow function gravity diffusion function


, Now we can have drainage or imbibition

, Dimensionless parameters

"Time:

"Effective gravity number:

MODEL – POST-INJECTION PERIOD

brine

mobile gas

trapped gas

waterinjection

h

UH

UHQTT

Tt

cc

i == ,τ

ggdgi NUHQNN ==

*rwk


, Equation in dimensionless form

, Seemingly the same equation, but:

"Scaling of gravity forces is different"The constitutive relations are discontinuous!


0)()())((=⎥

⎦

⎤⎢⎣

⎡∂∂

−∂∂

+∂

∂ξξτ

θ hhDNhfhhgi

i

brine

mobile gas

trapped gas

waterinjection

h

UH


, Storage coefficient:

, Fractional flow function, and Gravity diffusion function


brine

mobile gas

trapped gas

waterinjection

h

UH

⎩⎨⎧

<∂∂−−>∂∂−

=0 if ),1(0 if ),1(

)(igrwc

iwc

hSShS

hττ

θ


, Full analytical solutions are possible for

" Injection period

"Early post-injection period (detached fronts)

ANALYTICAL SOLUTIONS


, Analytical solutions to the hyperbolic model

"Late post-injection period (continuous drainage/imbibition)

ANALYTICAL SOLUTIONS

, For the full model, we resort to numerical solutions

0)()())((=⎥

⎦

⎤⎢⎣

⎡∂∂

−∂∂

+∂

∂ξξτ

θ hhDNhfhhgi

i

0


, High-viscosity gas(M = 0.5, Ng = 0)

NUMERICAL SOLUTIONS

, Low-viscosity gas(M = 0.05, Ng = 0)


, ξmax depends on M, Ng (for a given trapping coefficient C)

, When does the plume stop? Critical length scale

"Vertical

"Horizontal

, In our analysis, we chose

FOOTPRINT OF THE PLUME

σρgkBo

BorL t

vΔ

== ,max,

σμ UCa

CarL wt

h == ,max,

max,hL

max,vL

01.0max, <=H

Lvvε


, We want to match thefootprint, but cannotresolve gravity override

, Equivalent to solvinga stable flow (M = 1),with different values ofthe megascopic trappingcoefficient <C>


<C> = 1

<C> = 5



, Calibration curve ξmax vs megascopic trapping coefficient <C>


MEGASCOPIC TRAPPING COEFFICIENT

, From ξmax(M,Ng) and the calibration curve ξmax(<C>),we obtain the response surface <C>(M,Ng)

Almost insensitiveto Ng for values of

M < 0.1


, What is Ceff if we partially resolve gravity override?

"Reduced gravity number"More favorable viscosity ratio

BLOCK-EFFECTIVE TRAPPING COEFF

N z= 1

5

20

100

500

2000

1000

0

N z= 1

520100

2000

1000

0 500


, The trapping coefficient is larger for coarse grids"Highly refined grids laboratory measurement Clab

"Very coarse grids megascopic value <C>

BLOCK-EFFECTIVE TRAPPING COEFF

M = 0.1, Ng = 10, C = 1

<C>

Clab


VALIDATION WITH EXPERIMENTS


M = 0.1, Ng = 10, C = 1

<C>

Clab

VALIDATION WITH SIMULATION


THE BASIN SCALE

, When all is said and done, this is the important scale(100’s – 1000’s km)

, An order-one scientific problem"Open boundaries! Natural recharge–discharge areas"The issue is not (only) where the CO2 goes,but where the displaced brine goes

"Need to upscale, upscale, upscale (injection & trapping)

(www.bgs.ac.uk)

100 km


BACK-UP SLIDES


HUMAN IMPACT

, Human activities are interactingwith the planet at a global scale

, Atmospheric accumulation of CO2and other greenhouse gases(CH4, NO2)

"Global warming"Reduction of pH of upper ocean

, Reductions in emissions are neededto stabilize concentrations ata level double the pre-industrial level

, Challenge: balancing emissions and meeting energy demands

(IPCC Third Assessment Report, 2001)


NO SILVER BULLET

, A portfolio of technologies must bedeployed to meet this challenge(there is no silver bullet)

" Improved efficiency(cars, buildings, power plants)

"Nuclear energy"“Renewable” energy sources(solar, wind, biofuels)

"Forestation"Accelerated ocean uptake"Carbon capture and storage(“putting the carbon back”)

, Carbon capture and storage is oneof the “stabilization wedges”

(Pacala & Socolow, Science 2004)


, What is CO2 sequestration?Capture (at the surface) and storage (in the subsurface)of anthropogenic CO2

, Target formations for geological CO2 storage

Depleted oil and gas reservoirs

Coal-bed methane formations

Deep (saline) aquifers

GEOLOGICAL CO2 STORAGE

Ocean sediments


STORAGE IN OIL AND GAS RESERVOIRS

, Familiar scenario for the oil industry

, In oil and gas reservoirs, CO2 is injected for storage and EOR

"The CO2 is injected,displacing the oil

"Well-to-well flow frominjector to producer

"Typically, miscible floods(high local displacement eff.)

"Fingering, channeling andgravity override limit sweep Source: IPCC Report, 2005


Well-defined regulatory structure

Considerable experience in CO2 floods for enhanced oil recovery (EOR)

Opportunity to co-optimize EOR and CO2storage (water-alternating-gas strategies)

Extension of the life of the field –possibility to offset costs

The CO2 has low viscosity compared to oil – subject to viscous fingering and permeability channeling

Dissolution of the CO2 in both the resident oil and formation water

Oil and gas reservoirs are not always near the areas where anthropogenic CO2is generated

Detailed reservoir characterization is available

Unless it is damaged by prior operationA geologic seal exists

DisadvantagesAdvantages

STORAGE IN OIL AND GAS RESERVOIRS


STORAGE IN COAL BEDS

, Storage mechanism of CO2 in coal" In many coalbeds, CH4 is adsorbed onto the coal surface"When CO2 is injected, it replaces the CH4

"This allows for methane recovery (ECBM)

Source: Seto, 2004



, Adsorption in coal"CO2 and N2 adsorb preferentially (compared with CH4)"All gases display hysteresis – CO2 adsorption is stable

Source: Kovscek, 2004



, Transport of CO2 in coal

"Dual porosity system"Fast flow through fractures,slow diffusion into matrix

Source: Orr, 2004

Source: Seto, 2005



Storage volumes are uncertainUnminable coalbeds may be available near coal-fired power plants

Possibility to co-inject with other contaminant gases

ECBM predictive modeling and field experience are limited

Enhanced coalbed methane recovery –possibility to offset costs

Physics of coalbed systems not very well understood – complex interplay of flow, permeability variation, diffusion and adsorption

Stable adsorption–desorption isotherm: “permanent” storage



Costs cannot be offset by by-products (as in EOR and ECBM)

Opportunity to optimize the CO2injection scheme (injection location and rate; water-alternating-gas strategies)

Regulation is still not well-defined

The CO2 has low viscosity compared to water – may limit the reservoir volume contacted by CO2

Success story: Sleipner

Detailed reservoir characterization is usually not available

Several trapping mechanisms may immobilize the CO2 – including capillary trapping

A geologic seal may not exist;potential leakage through faults and abandoned wells

Deep saline aquifers are widely distributed


STORAGE IN SALINE AQUIFERS


, Structural trapping"The CO2 remains mobile atthe top of the formation

, Solution trapping"Diffusion of CO2 into brine creates denser brine at the top"Gravity-driven fingers develop, enhancing mixing


Source: Hesse, 2005

Source: Riaz et al, 2006


, Mineral trapping

"CO2 dissolution in water produces a weak acid

"This acid reacts with rock minerals, leading toprecipitation of solid carbonate minerals

" It is arguably the most permanent form of storage



, Deep saline aquifers are prime candidates for CO2 storage

"Huge storage capacity, widely distributed"Predominantly water-wet

injection period post-injection period


water

CO2 andconnate water

imbibition

drainage


, Fluid arrangement according to wettability

"CO2 in thepore centers

"Water in thepore crevices

A LOOK AT THE PORE SCALE

(Lenormand et al, 1983)


, CO2 displaces waterin a piston-like fashion,one duct at a time

, This process is called“invasion percolation”

, Water remains at porecrevices, coating the solid

, Both water and CO2

form connected clusters,so they are mobile

THE DRAINAGE PROCESS


CO2 water


, Now water displaces CO2

, Initially also piston-like,one duct at a time

, But water films swell anddisconnect the CO2

(“snap-off”)

THE IMBIBITION PROCESS


CO2 water


, Now water displaces CO2

, Initially also piston-like,one duct at a time

, But water films swell anddisconnect the CO2

(“snap-off”)

, Clusters of CO2 are leftbehind, immobile

, Residual (or capillary)trapping of CO2

RESIDUAL CO2


CO2 water


, At the pore scale, the CO2

is disconnected by snap-offduring imbibition

, Macroscopically, this leads tohysteresis (residual CO2) in:

"capillary pressure Pc

" relative permeability kr of CO2

CAPILLARY TRAPPING

Pc

residual (trapped)saturation

drainage

imbibition


LAND’S HYSTERESIS MODEL

, The basis for Land’s hysteresis model is to express theimbibition relative permeability at a given saturationas the drainage relative permeability evaluated at adifferent flowing saturation

, At any bulk saturation Σν:

, The trapped saturation DΣν isequal to the maximum trappedminus what is flowing but willeventually be trapped

( ) ( )( ) ( )i drn n rn nfk S k S=

n n nfS S SD = -

( ) ( )n nr ni nr nfS S S S SD = -


GEOPHYSICAL MONITORING

, Appropriate space resolution is a challenge

Time-lapse seismicdata at Sleipner(IPCC report, 2005)


ARE WE DONE?

, Some outstanding issues

"Small (well) scale

" Intermediate (pilot/reservoir) scale

"Large (basin) scale


THE WELL SCALE – INJECTION

water

CO2 andconnate water

, CO2 injection is an inherently unstable process:

"CO2 is less dense (gravity fingering)"CO2 is less viscous (viscous fingering)"Heterogeneity variations (channeling)

, Leads to a patchy, nonuniform,finger-like distribution of CO2

,Can we capture theaverage behavior with acoarse numerical model?


THE WELL SCALE – POST-INJECTION

, Where is trapping taking place?

"Leading (top) edge– counter-current flow

"Trailing (bottom) edge– co-current flow

, How much is trapped?

"Depends on degree ofpatchiness/instability

"No model exists currently

, Need for experiments!

counter-current flow?

co-current flow?

CO2 fingers


THE BASIN SCALE – CAN WE SOLVE IT?


(terpsichore.stsci.edu)


, Capacity of different target formations

"Very uncertain"Lack of geophysical information and laboratory data"Depend on the economic model

ISSUES IN CO2 STORAGE

100001000Saline aquifers

2003-15Coal seams

900675Oil and gas fields

Upper estimate (GtCO2)

Lower estimate (GtCO2)

Geologic formation

Source: IPCC Report on Carbon Capture and Storage, 2005


, The time scales of the various mechanisms can bevery different

tstruct ~ tcapil << tdissol << tminer

(10’s yrs) (100’s yrs) (1000’s yrs)


(IPCC Report, 2005)


SETUP OF NUMERICAL SIMULATIONS

, The formation is initially filled with brine. A total of 0.15 pore volumes of CO2 are injected

, Four different scenarios

, Three “observation points”"Block (13,18,1) near the top"Block (7,21,1) slightly lower"Block (11,11,1) slightly lower still

5 – 1 – 5 – 1 yrsHysteresis - WAG4

50 yrsHysteresis3

10 yrsHysteresis2

10 yrsNo hysteresis1

Injection timeDescriptionCase number


EFFECT OF HYSTERESIS

, Evolution of CO2 saturation at observation points

, When hysteresis is ignored"Accumulation of CO2 at the top of the formation"CO2 travels through without leaving residual saturation

, When hysteresis is included"Lower CO2 saturation at the top of the structure"CO2 migrates leaving residual saturation


EFFECT OF INJECTION RATE

, Evolution of CO2 saturation at observation points

, Higher injection rates"Larger areal extent of the CO2 plume at the end of injection"More trapping during the vertical ascent of the plume

towards basin-scale modeling of geological … · · 2007-11-20towards basin-scale modeling of...

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