Joint inversion of crosswell seismic and EM data for CO2 saturation · 2009. 2. 3. · – Hertz-Mindlin & Hashin-Strikman (effective dry rock bulk modulus) – Dry frame K(P eff)

Earth Science DivisionERNEST ORLANDO LAWRENCEBERKELEY NATIONAL LABORATORYBERKELEY LAB 5/3/05

Joint inversion of crosswell seismic Joint inversion of crosswell seismic and EM data for COand EM data for CO22 saturationsaturation

G. Michael HoverstenG. Michael Hoversten11

Jinsong ChenJinsong Chen11

Tom DalyTom Daly11

John PetersonJohn Peterson11

Kevin DoddsKevin Dodds22

Ping ZhangPing Zhang44

Mike WiltMike Wilt44

Jeff LittleJeff Little 44

Shinichi SakuraiShinichi Sakurai33

Larry MyerLarry Myer11

Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory 11

CSIRO Australia CSIRO Australia 22

Texas Texas BeureaBeurea of Economic Geology of Economic Geology 33

SchlumbergerSchlumberger--EMI Technology Center EMI Technology Center 44


OutlineOutline

•• Input Geophysical DataInput Geophysical Data

•• ProcessProcess

•• RockRock--physics modelsphysics models

•• Individual estimation of SIndividual estimation of Sww

•• Joint inversionJoint inversion

•• DiscussionDiscussion

•• ConclusionsConclusions


Cross Well DataCross Well Data•• VVpp traveltravel--time tomographytime tomography

–– Contours of Contours of ∆σ∆σ are overlaidare overlaid

–– Large Large ∆∆VVpp @ @ --1510 coincides 1510 coincides with large +with large +∆σ ∆σ

•• EM inversionEM inversion–– ++∆σ ∆σ could be movement of could be movement of

brine or noisebrine or noise

•• Further work to tie to VSP and Further work to tie to VSP and logs is required to interpretlogs is required to interpret–– Possible fault induces upward Possible fault induces upward

migrationmigration

–– Possible movement of CO2 Possible movement of CO2 &/or brine up annulus of &/or brine up annulus of injection wellinjection well


Path from geophysics to reservoirPath from geophysics to reservoir

•• Geophysical estimates of VGeophysical estimates of Vpp, V, Vss, and , and σσ•• RockRock--physics model that relates geophysical physics model that relates geophysical

parameters to reservoir parametersparameters to reservoir parameters

•• Two approaches takenTwo approaches taken–– RockRock--physics transform (Vphysics transform (Vpp, V, Vss, s) , s) --> (S> (Sww, , φφ))

–– Bayesian inversionBayesian inversion


RockRock--PhysicsPhysics•• VelocityVelocity

–– HertzHertz--Mindlin & Mindlin & HashinHashin--StrikmanStrikman (effective dry rock (effective dry rock bulk modulus)bulk modulus)

–– Dry frame Dry frame K(PK(Peffeff))–– GassmannGassmann (fluid (fluid

substitution)substitution)

•• DensityDensity–– Mixing lawMixing law

•• Simplex inversion for Simplex inversion for model parametersmodel parameters–– Input (Input (φφ, S, Sgg, S, Sww, , P,T,oilP,T,oil API, API,

brine salinity)brine salinity)–– Output (grain Output (grain -- υυ,,ρρ,K,K, critical , critical

φ, φ, gas density)gas density)

Fixed ParametersFixed Parameters

Critical PorosityCritical Porosity 0.380.38

Oil APIOil API 28.528.5

Brine SalinityBrine Salinity 0.070.07

Gas GravityGas Gravity 0.590.59

Temperature©Temperature© 67.767.7

Regression FitRegression Fit

44.544.5Grain Shear Mod.Grain Shear Mod.

0.260.26Grain Poisson Grain Poisson

25122512Grain DensityGrain Density

4.14.1# Contacts/grain# Contacts/grain


Archie’s LawArchie’s Law

•• Logs determine porosity Logs determine porosity exponentexponent

•• No variable SNo variable Sww, so S, so Sww

exponent is unknownexponent is unknown–– Limited sensitivity to SLimited sensitivity to Sww

exponent at small exponent at small ∆∆SSww

–– At higher At higher ∆∆SSww unknown unknown exponent exponent --> 10% variation > 10% variation in estimatein estimate

•• Inversions run at SInversions run at Sww--1.81.8

Injection well


Prediction from RockPrediction from Rock--Physics Physics transformtransform

•• VVpp, V, Vss, , ρρ model used to model used to convert convert ∆∆VVpp to to ∆∆SSww

•• Archie’s Law used to convert Archie’s Law used to convert ∆σ∆σ to to ∆∆SSww

•• Seismic resultSeismic result–– 50% S50% Sww at at ObsObs. well. well

–– Nov 2 log average SNov 2 log average Sww = = 83%83%

•• EM resultEM result–– 90% S90% Sww at at ObsObs. Well. Well

–– Dec 2 log average SDec 2 log average Sww = = 80%80%


Bayesian Estimation ModelBayesian Estimation Model

( , , , | , , , ) ( , , , | , , , ) ( , , , )

w o b s b s w o

w o

f S S P k k f k k S S Pf S S P

φ ρ σ ρ σ φφ

∝Posterior PDFPosterior PDF

Prior PDFPrior PDF

Likelihood functionLikelihood function

( , , , | , , , ) ( | , , , ) ( | , ) ( | , , ) ( | , )

b s w o b w o s

w o w

f k k S S P f k S S P f k Pf S S f S

ρ σ φ φ φρ φ σ φ

=Likelihood can be simplifiedLikelihood can be simplified

wherewhere 1 2

3 4

( , , , ) ( , )( , , ) ( , )

b w o b s s

w o w

k g S S P k g Pg S S g Sρ σ

φ ε φ ερ φ ε σ φ ε

= + = += + = +

For example, if we assume For example, if we assume εεσσ has the Gaussian distribution; has the Gaussian distribution; 2

42

1 ( ( , ) )( | , ) e x p22

ww

g Sf SDD

σ φσ φπ

⎧ ⎫−⎪ ⎪= −⎨ ⎬⎪ ⎪⎩ ⎭

where, D is the standard deviation of the errorswhere, D is the standard deviation of the errors


MCMC Sampling MethodMCMC Sampling Method

•• MCMC methods use a variety of algorithms to MCMC methods use a variety of algorithms to update Markov chains, which are convergent to the update Markov chains, which are convergent to the true distribution true distribution –– chains are irreducible and aperiodic.chains are irreducible and aperiodic.

•• Traditional Monte Carlo (MC) methods (e.g., Bachrach Traditional Monte Carlo (MC) methods (e.g., Bachrach et al. [2004]) draw samples uniformly in entire feasible et al. [2004]) draw samples uniformly in entire feasible space, but MCMC methods sampling density is space, but MCMC methods sampling density is proportional to the true probability density function.proportional to the true probability density function.

•• For example, in Bachrach’s paper, the traditional MC For example, in Bachrach’s paper, the traditional MC methods need to draw 100,000 or more samples, but methods need to draw 100,000 or more samples, but MCMC methods only need to draw 2,400 samples with MCMC methods only need to draw 2,400 samples with the first 400 as burnthe first 400 as burn--in.in.


Joint inversion Joint inversion

C

BB

•• Estimated VEstimated Vpp and and σσ at the at the two times are used to two times are used to estimate Swestimate Sw

•• Joint estimation removes Joint estimation removes artifacts not common to bothartifacts not common to both

•• Predicted has a time smear Predicted has a time smear of 1 month due to time lag in of 1 month due to time lag in surveyssurveys

•• CC--sand Ssand Sww = 75= 75--85%85%–– Log ~ 80%Log ~ 80%

•• Indication of COIndication of CO22 reaching reaching the B sand abovethe B sand above–– SSww = 75= 75--85%85%


DiscussionDiscussion•• Processing is not completeProcessing is not complete

–– Refinement on seismic picks and sensor rotationRefinement on seismic picks and sensor rotation

•• EM inversions have not been exhaustiveEM inversions have not been exhaustive–– Data sensitivity analysis and further editing may Data sensitivity analysis and further editing may imporveimporve

•• Both seismic and EM inversions could benefit by Both seismic and EM inversions could benefit by crosscross--iterations where models are transformed to iterations where models are transformed to each other and used as starting pointseach other and used as starting points

•• Input from Final VSP models has not been Input from Final VSP models has not been incorporatedincorporated


ConclusionsConclusions•• Both timeBoth time--lapse EM and seismic see changes lapse EM and seismic see changes

realatedrealated to CO2 movement to CO2 movement –– Noise levels need to be reducedNoise levels need to be reduced

•• Both techniques suggest possible movement of fluids Both techniques suggest possible movement of fluids (CO2 and/or brine) up the injection well (CO2 and/or brine) up the injection well annulasannulas and and into upper formationsinto upper formations

•• Transformation of seismic alone via rockTransformation of seismic alone via rock--physics physics model yields lower Sw estimate in Novembermodel yields lower Sw estimate in November

•• Transformation of EM alone via rockTransformation of EM alone via rock--physics model physics model yeildsyeilds higher Sw estimates in Decemberhigher Sw estimates in December

•• Joint inversion estimates of Sw in C sand are very Joint inversion estimates of Sw in C sand are very close to logged valueclose to logged value

•• Joint inversion estimates of Sw indicate Joint inversion estimates of Sw indicate chanechane in B in B sandsand

•• Further work will improve all estimatesFurther work will improve all estimates

Documents

Joint inversion of crosswell seismic and EM data for CO2 saturation · 2009. 2. 3. · – Hertz-Mindlin & Hashin-Strikman (effective dry rock bulk modulus) – Dry frame K(P eff)