Copyright 2000, Offshore Technology Conference

This paper was prepared for presentation at the 2000 Offshore Technology Conference held inHouston, Texas, 1Ð4 May 2000.

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Abstract4D seismic has become a widely accepted technique tointerpret changes between successive 3D seismic surveys interms of fluid substitution and pressure depletion in aproducing reservoir. However, most time-lapse studies havebeen mostly qualitative and based on simplified reservoirrepresentation in order to adjust to the time constraints oftoday's oil market.In this paper, we present how reservoir simulation constrainedby stochastic characterization and non-linear optimization canbe used in an integrated series of tools to refine 4Dinterpretation.Because of its direct relationship with pore fluid content andproperties, we use seismic impedance rather than seismicamplitude as the primary data between the various steps of our4D interpretation loop. Non-linear inversion of the 3D seismicdata sets allows a preliminary interpretation. Stochasticsimulation of the lithology and porosity, constrained by these"observed" impedance volumes and by well logs, provide thestatic reservoir characterization for the reservoir simulator.Once simulated production matches the recorded productionhistory, empirical or Biot/Gassmann-type petrophysicalmodels are used to calculate the "simulated" impedancevolume from the fluid saturation and pressure distributioncalculated by the reservoir simulator. Non-linear optimizationis used iteratively to improve first the production historymatch and next the agreement between "simulated" and"observed" impedance volumes over time. This optimization isperformed over a limited set of poorly constrained parametersin the permeability calculation and petrophysical models. Inthe case study presented here, the analysis of a turbiditereservoir in the South Timbalier 295 field, our results show

how stochastic characterization helps reproducing thecomplexity of reservoir fluid dynamics while the results of theoptimization underlines the robustness of the 4D interpretationdespite the large amount of unknowns.

IntroductionTime-lapse, or 4-D, seismic monitoring is an integratedreservoir exploitation technique based on the analysis ofsuccessive 3D seismic surveys. Differences over time inseismic attributes are directly related to changes in pore fluidsand pore pressure during the drainage of a reservoir underproduction. The detection of areas with significant changes orwith unaltered hydrocarbon-indicative attributes, can be usedto determine drilling targets where hydrocarbons remaintrapped after several years of production. Making sure thatseismic differences are related to fluid flows is critical for acomplete time-lapse seismic study. Noise associated withdifferences in acquisition can generate seismic differencesbetween surveys that are not related to the reservoir drainagepattern.

In this paper, we describe how reservoir simulation can beused to generate independent impedance maps to validate orconstrain 4-D impedance maps obtained from the inversion ofsuccessive legacy data sets. A complete 4D analysis is aniterative loop where the original interpretation can be refinedalong the later steps. First, we summarize the steps precedingthe reservoir simulation, including the 3D seismic processingand inversion, and the preliminary time-lapse interpretation.We then describe the elastic models, the properties ofreservoir fluids and the reservoir characterization that can beused to link the impedance volumes to fluid and lithologydistributions in the reservoir. The results of the simulation arefinally used to generate impedance maps that can be comparedwith seismic inversion results. Because of the large number ofpoorly constrained parameters used to describe complexreservoirs, the different steps of the interpretation have to beoptimized to match at best simulation results and observations.The first optimization loop is applied to the reproduction ofthe production history by the simulator, using parameters suchas relative permeability or aquifer support. The second stageof optimization is in deriving impedance maps from simulatedsaturation, which involves the choice of an elastic formulation

OTC 12102

Optimization of Reservoir Simulation and Petrophysical Characterization in 4D SeismicGilles Guerin, Wei He, Roger N. Anderson and Liqing Xu, Lamont-Doherty Earth Observatory, and Ulisses T. Mello, IBMWatson

2 G. GUERIN, W. HE, R.N. ANDERSON, L. XU, U.T. MELLO OTC 12102

and the reservoir fluid properties. To illustrate the differentsteps of the entire procedure we use the case study of the K8reservoir, South Timbalier 295, offshore Louisiana.

The 4D seismic loop:Non linear inversion of successive 3D datasetsSince its emergence, time-lapse analysis has been usuallyapplied to changes in seismic amplitudes. However,amplitudes are only proportional to seismic reflectivity, whichdepends on the relative variability in the elastic properties ofthe formation, not on the value of these properties.In contrast, seismic impedance, the product of density (ρ) andcompressional velocity (Vp) is directly related to the elasticproperties of the sediments. ρ is the volumetric average of thedensity of the different phases (fluids and solids) and Vp canbe explicitly expressed as a function of their density andcompressibility. Also, unlike amplitudes, a simple algebraicsubtraction between the impedance volumes at two dates canbe directly converted into fluid or pressure changes. Thereforea 4D analysis based on impedance volumes instead ofamplitudes allows a direct qualitative interpretation of seismicchanges in terms of fluid substitution or migrations. We use aconstrained non-linear inversion technique to estimate theacoustic impedance volumes from each 3D survey1.

Preliminary 4D interpretation of the K8 sandThe K8 reservoir in the South Timbalier 295 field, offshoreLouisiana (Fig. 1). It produced about 350,000 m3 of oil and150 millions m3 of gas between two 3D surveys shot in 1989and 1994. The K8 sand is a complex combination ofchannelled mid-fan sheet sands lapping on a paleo-high in theeast and gently dipping to the South West (Fig. 2). Fig.3shows the results of the inversion of the two surveys shot in1989 and 1994 over K8. The difference between the twoinversions (Fig. 3c) shows a global decrease in impedance(red) in most of the shallower layers and updip (NE) from thetwo producing wells in the deeper layers. Impedance hasmostly increased (blue) in the deeper layer of the reservoirbetween the two surveys. Because the reservoir was originallyfilled with oil, and the replacement of oil by gas or waterrespectively decreases or increases the density and the sonicvelocity of the formation, oil might have been replaced mostlyby gas in the shallower layers of the reservoir and by water inthe deeper layers. The substitution of oil by gas exsolutionupdip is controlled by the pressure decrease induced by theproducing wells while the replacement of oil by water in thedeeper layers is assisted by the presence of an aquifersupporting the reservoir2.

Independently of the nature of the pore fluid, the bulk ofthe impedance of such medium porosity sediments (40%maximum) is mostly controlled by the porosity and lithologydistributions. To relate quantitatively the observed changes inimpedance with the nature and the volume of the pore fluids, itis necessary to have a complete representation of the sedimentmatrix, and to define the relationships between the differentcomponents of the system and its elastic properties.

Petrophysical characterization of reservoirsElastic models. Explicit relationships relating pressure, porefluid, porosity, matrix materials and the elastic properties ofmarine sediments have been the topic of various theoretical3,4

or empirical5,6 studies. They are all limited in application bythe infinite number of parameters affecting the elasticproperties of sediments and no approach can offer acomprehensive formulation. We review in the Appendix somecommonly accepted models and relationships that could beused to link the changes observed in our impedance maps withchanges observed in the reservoirs.

Fluid properties. For any of these eleastic models, thechanges observed in impedance over time will depend on theelastic properties of the pore fluid, which are the primaryparameters responsible for changes in impedance duringproduction.Properties of fluid mixtures. The properties of the pore fluidthat affect the elastic properties of a reservoir are in fact theproperties of a fluid mixture, which is a function of theproperties of the various fluid phases. The three primary typesof pore fluid in a reservoir are hydrocarbon gas (gas)hydrocarbon liquid (oil), and brine. The density (ρfl) and thecompressibility (1/Kfl) of the mixture are respectively theweighted averages of the density and of the compressibility ofthe three phases

Elastic properties of reservoir fluids. Physical properties ofreservoir fluids are dependant on composition, pressure andtemperature7. Unless thermal recovery techniques are used, thevariations of temperature in a reservoir are negligible duringits production history, and pressure and composition are thedominant parameters affecting the changes observed betweentwo surveys. In addition to the relationships defined in thelitterature7, we also use simple linear relationships betweenpressure and elsatic properties in our optimization, based onavailable laboratory data (Gas and oil gravities, reservoir GasOil Ratio) and a few rules: density and velocity of gas andbrine decrease with decreasing reservoir pressure, velocity anddensity of oil decrease with decreasing pressure while pressureis above bubble point, and increase below bubble point aslighter component come out of solution

Stochastic reservoir characterization. The final linkbetween impedance volumes, fluids properties, saturations andpressure distribution resides in the characterization of thereservoir porosity and lithology distribution. We usegeostatistical simulations for this characterization, assumingthat within an individual reservoir petrophysical and acousticproperties are closely related and can be associated withcalibrated cross-correlation functions1. Sixteen wells providedthe hard data used to constrain the reservoir characterization ofK8 (Fig. 4). Both porosity and shale distributions show a highlevel of heterogeneity, illustrating the channelled deposition ofthe reservoir. The bulk of the porosity is located immediately

OTC 12102 OPTIMIZATION OF RESERVOIR SIMULATION AND PETROPHYSICAL CHARACTERIZATION IN 4D SEISMIC 3

downdip from the two producing wells and in the South Eastcorner of the study area.

From saturations to impedances. The completedcharacterization of fluid and reservoir characterizationproperties allows to use any of the petrophysical models tocalculate the impedance volumes when pressure and fluiddistributions are known, such as before the beginning ofproduction in 1988, when oil/gas and oil/water conatcts can beassumed horizontal . In Fig. 5, the crossplots of the differentmodels with the 1988 impedance allow to compare theirrespective validity. In all these figure, a perfect formulationshould result in an identical linear fit with the inverted values.The KT and Gassman+KT impedances (Figs 5a and 5b)display the highest level of scattering and consequently thepoorest agreement with the inversion results. The Han andGassmann+Han impedances present the best agreement withthe inversion, with regression coefficients higher than 0.80. Itis necessary, however, to make a similar comparison aftersimulation to evaluate how fluid substitution affects thecomparison between the calculated and the invertedimpedance.

Comparison with vertical sweep. This preliminary validationof the elastic formulations can be used to illustrate the need foran accurate understanding of the reservoir dynamics that time-lapse seismic can provide. A traditional view of the fluidmovements within a producing reservoir is of a uniformbuoyancy-driven movement of the different phases, thecontact surfaces between adjacent phases remaininghorizontal. Assuming that the GOC and WOC have beensimply sweeping uniformly along dip, and that the reservoir isstill globally in hydrostatic equilibrium at any time, we havecalculated the pressure and fluid distribution that would existin 1994 if an horizontal gas cap had formed down to 3280mbsf and the WOC had moved up to 3320 mbsf. Theimpedances calculated from these values using theGassmann+Han formulation are shown in Fig. 6. Comparisonwith Fig. 3 shows that the impedances calculated presentstrong similarities with the 1994 inversion results. Theimpedance changes over time (Figures 3.4c and 3.8c) alsodisplay some global similarities: decrease in impedance updipfrom the wells, and increase downdip. However, the patternand the absolute values of the observed impedance changesare much more heterogeneous in Fig 3c than in this simpleÔgravitational sweepÕ. The bright areas in the observedimpedance changes correspond to isolated impedancedecreases, that could indicate areas with low connectivitywhere hydrocarbon, mostly gas, would remain trapped as thereservoir pressure decreases. The comparison of Figs 3.4c and3.8c shows that after a few years of intense production, therepresentation of a GOC as a continuous horizontal surface ismerely irrelevant. The fact that the impedances calculatedafter the reservoir sweep compare reasonably well with theinversion results in 1994, despite the major differences in thechanges over time (Fig. 3c vs. Fig 6c), shows how crucial it isfor each inversion to be the most accurate, as differentiating

between the inversions of successive surveys is much moresensitive to errors than either inversion.

Reservoir SimulationThe entrapment of hydrocarbons is mostly the result of theheterogeneity in the reservoir and in the permeabilitydistribution. Assuming that our inversion results are correct,the heterogeneity observed in the impedance difference overtime suggests a migration process more complex than thesimple gravitationnal sweep. Numerical simulation of themigration of the different phases can be used to identify theactual behavior of the reservoir under production.

Permeability distribution. In addition to porosity, theprimary control on the reservoir drainage is the permeabilitydistribution. While permeability is directly related to porosity,it can also be affected considerably by the presence of shales.The effective permeability of shaly sandstones can becalculated from porosity and shale fraction (γ) by:

k = kss.(1 - γ)m = αexp(βΦ). (1 − γ)mÉÉÉÉÉ(1)where m is an exponent dependant on the aspect ratio of theclay minerals8. α and β can be measured on clean sandsamples. The permeability distribution in K8 is shown in Fig.7.

Multiple-phase fluid flows in porous media. Reservoirsimulation is based on solving the mass conservation equationof multiple-phase fluids in porous media, using DarcyÕs lawfor multi-phase fluid flows in porous media:

r r rq k S

kP g

o g w

r= − ∇ −[ ]∑=

., ,ϕ

ϕ ϕϕ

ϕϕ ϕρ

µρ ÉÉÉÉÉ(2)

where q is the three-phase fluid velocity, the subscript ϕ refersto the attributes of each phase: saturation (S_), pressure (P_),density (ρϕ), viscosity (µϕ) and relative permeability (kr_). k isthe absolute permeability of the formation and

rg the gravity

acceleration.The relative permeability of each phase (oil, water, gas)

increases with its saturation and can be calculated in threephases fluid as a combination of the relative permeabilities oftwo-phases fluid mixtures:

kS k S S k

S S Srog rog w wco row

g w wco

=+ −+ −( ) ÉÉÉÉÉ(3)

where krog and kr o w are the oil relative permeability forsystems with oil and gas only and oil and water only,respectively. Swco is the connate, or irreducible, watersaturation. The variations of krg and krog, as a function of gassaturation and of krw and krow as a function of water saturation,called saturation functions, are rarely available. No relativepermeability measurements were available for K8 and sincethis absence has to be expected in most reservoir, relativepermeabilities are one of the adjustable parameters within theoptimization of the production history match.

Simulator description. The code used to solve Eq (2) isECLIPSE, a commercial three phase, three dimensional finite

4 G. GUERIN, W. HE, R.N. ANDERSON, L. XU, U.T. MELLO OTC 12102

differences simulator using a corner point geometry grid thatallows to define highly distorded nodes to represent thereservoir geometry9.Since the only actual measurable effects of the reservoirdrainage are the volumes of hydrocarbons collected at thesurface, the production history recorded on the rig floor is theprincipal constraint on the simulator. It is expressed in termsof daily production rate of oil or gas for each well, andaveraged monthly. This imposed production is translated intopressure gradients between the wellbores and the formation,which are echoed in the reservoir at each time step of thesimulation.

In addition to the perforated well intervals the only flowsallowed in and out the reservoir model are from eventualaquifers, in order to simulate possible aquifer support. Thestrength of this support is defined in water influx per unitpressure difference. All other model boundaries are consideredimpermeable, either lithologically (shaled out) or structurally(sealing faults).

Simulation resultsHistory match. Fig. 8 shows how the simulator was able toreproduce the production history of K8, starting from theinitial conditions in 1988. Dots represent observed productiondata and the lines the simulation results. Because oilproduction was the imposed control mechanism, the perfectmatch for this production iss expected. The optimization of theproduction history was done on two parameters: the exponentin the gas relative permeability, and the location of the aquifersupport, wethere from the west, or directly underneath thereservoir. The comparison of the different figures shows thatthe best match in the gas and pressure histories are with a 0.9exponent in gas relative permeability and an aquifer supportunderneath the reservoir.

Even without matching the exact production history, thesimulation helps to understand the dynamics in the reservoir.Fig. 9 shows the simulated oil and gas streamlines in May1993, while the two wells are producing at their peack. Thedifferences between the various figures, and the differences inproduction matching results show how reservoir simulationsuccess can be is sensitive to a limited number poorlyconstrained parameters

Fluid saturations and impedance. The oil and gasdistributions at the end of the simulation (Fig. 10) have to becompared with the uniform values of 70% oil and no gas at theorigin of the simulation. Fig. 11 shows the impedancevolumes and change over time calculated with these valuesusing the Gassmann+Han formulation. The simulatedimpedance distribution in 1994 seems very similar to theinversion results at this date (Fig 3b), but to confirm that thisrelationship still offers the best representation of the reservoirproperties after fluid substitutions, we also calculated theimpedances after the simulation with the other petrophysicalformulations. A similar crossplot analysis as conducted in1988 shoews that the Gassmann+Han models still presents thebest comparison with the inverted impedance after fluid

substitutions.

End of the 4D loopImproving the present results and, more generally, theoptimization of the 4D interpretation loop can take severalforms. We have developped a procedure to automaticallyoptimize the production history and the impedance maps, afteridentifying various numerical parameters and 'loose' reservoirproperties. These procedures can be applied authomatically tosuch parameters as grain or frame moduli, fluid properties orempirical parameters in the experimental relationshipsdescribed in the appendix

Recurrently missing properties and numerical parameterssuch as relative permeability functions, critical saturations,capillary pressures, aquifer strength or permeability factorscan be varied between successive simulations in order to finda better history match. Upscaling the reservoir modeldimensions for shorter computation times, it is possible toautomate the variation of some of these arbitrary numericalparameters or loosely constrained properties to minimize thedifference between measured and simulated productionhistory.

To complete the loop, the impedance volumes calculatedfrom the reservoir simulation results have to be fed into a 3Dseismic waves propagation elastic model to try to reproducethe observed datasets. For this purpose, we have built toolsallowing to remesh the simulation grid within the original datavolume10 and developed a full elastic 3D finite differencemodel to simulate the propagation of seismic waves andgenerate a synthetic seismic amplitude volume. Thecomparison of the simulated amplitudes with the originaldatasets can be used as a simple validation of the reservoirsimulation, but it can also be used to re-evaluate the inversionor the reservoir characterization results when data are missingor unreliable

ConclusionsThese are mere possibilities for the 4D interpretation toproceed from reservoir simulation to get an exactunderstanding of the reservoir dynamics. Because theexploration, production history and the configuration of eachreservoir are unique, there is no exhaustive procedure fortime-lapse monitoring. We have tried to develop an integratedseries of tools allowing to apply our general methodology toany reservoir, but its flexibility requires a clear understandingof the possible sources of errors in order to use the iterativeprocedure to minimize them.

At the junction between complex theoretical methods(non-linear seismic inversion, 3D elastic modelling orstochastic simulation) and the most primary field data,reservoir simulation provides the link between the observedchanges in seismic attributes, the hydrocarbons produced onthe rig floor and the actual fluid dynamics within a reservoir.Because it should ultimately indicate where to drill to recovertrapped hydrocarbon, and the volumes to expect, it can helpunderstand the passed history of a reservoir, but moreimportantly, how to make the best of its future. In the case of

OTC 12102 OPTIMIZATION OF RESERVOIR SIMULATION AND PETROPHYSICAL CHARACTERIZATION IN 4D SEISMIC 5

the K8 sand, the good agreement between simulation andinversion indicate that the final optimization should be only arefinement of the present results.

References:1. He, W., 1996, 4-D Seismic Analysis and Geopressure Prediction

in the Offshore Louisiana, Gulf of Mexico. Ph.D. Thesis,Columbia University.

2. Mason, E.P., 1992, Reservoir geology and productionperformance of turbidite sands at South Timbalier 295 field,offshore Louisiana, i n transactions of the Gulf CoastAssociation of Geological Societies, Vol XLII, 267-278.

3. Gassmann, F., 1951, Elastic waves through a packing ofspheres, Geophysics, 16, 673-685.

4. Kuster, G.T., and M.N. Toks�z, 1974, Velocity and attenuationof seismic waves in two-phase media, 1, Theoreticalformulation, Geophysics, 39, 587-606.

5. Han, D-H., A. Nur and D. Morgan, 1986, Effects of porosityand clay content on wave velocities in sandstones, Geophysics,51(11), 2093-2107.

6. Ramamoorthy, R., W.F. Murphy and C. Croll, 1995, Totalporosity estimation in shaly sands from shear modulus, Trans.SPWLA 36th Logging Symposium, paper H.

7. Batzle, M., and Z. Wang, 1992,Seismic properties of porefluids, Geophysics, 57(11):1396-1408.

8. McCarthy, J.F., 1991, Analytical models of the effectivepermeability of sand-shale reservoirs, Geophys. J. Int., 105,513-527.

9. Ponting, D.K., 1989, Corner Point Geometry in ReservoirSimulation, proc. Joint IMA/SPE European Conference on theMathematics of Oil Recovery, Cambridge.

10. Mello, U.T., P.R. Cavalcanti, A. Moraes and A. Bender, 1998,New developments in the 3D simulation of evolving petroleumsystems with complex geological structures, AAPG internationalconference and exhibition abstracts, AAPG Bulletin, 82(10), p.1942.

11. Hamilton, E. L., 1971, Elastic properties of marine sediments, J.Geophys. Res., 76, 579-601.

12. Hamilton, E. L., Bachman, R. T., Berger, W. H., Johnson, T. C.,and Mayer, L. A., 1982, Acoustic and related properties ofCalcareous deep-sea sediments, J. Sed. Pet., 52(3), 733-753.12.

13. Guerin, G., and D. Goldberg, 1996, Acoustic and elasticproperties of calcareous sediments across a siliceous diageneticfront on the eastern U.S. continental slope, Geophys. Res. Lett.,23(19), 2697-2700.

Appendix - Elastic models for sediments propertiesMost models define relationships for the elastic moduli of theformation instead of the impedance. The bulk modulus (K) isthe inverse of its compressibility and the shear modulus (G) ameasure of its shear strength. Compressional and shear (Vs)sonic velocity can be expressed as functions of these moduliand of the density of the sediments:

V K Gp = +

1 4

3ρÉÉÉÉÉÉÉÉÉ.(A-1)

and VG

s =ρ

ÉÉÉÉÉÉÉ.ÉÉÉÉÉÉ..(A-2)

and the impedance (Z)can simply be re-writen

Z V K G K Vp s= = +

= +ρ ρ ρ ρ4

3

4

32 2 ÉÉ.(A-3)

Theoretical formulations. Gassmann (1951) expressed thebulk modulus of fluid-saturated sediments as a function of thebulk moduli of the dry frame (Kf), of the pore fluid (Kfl) andof the grains (Kg)

K KK Q

K Qg

f

g

=++

with QK K K

K K

w g f

g w

=−( )−( )Φ

ÉÉÉ.(A-4)

Empirical relationships for Kf as a function of porosity havebeen established for several types of lithology11,12. Using hisresults for clay, silts and fine sands, we use a single formulafor clastic sediments:

log (Kf) = log(Kg) - 4.25Φ or log(Kf/Kg) = -4.25Φ.....(A-5) The grain modulus of a shale/sand mixture can be calculatedby a Voigt-Reuss-Hill average of the grain moduli of sand (Ks)and clay (Kc)

11:

K K KK K

K Kg c ss c

s c

= + − ++ −

1

21

1γ γ

γ γ( )

( )ÉÉ..(A-6)

where γ is the shaliness or volumetric shale fraction. We referto it as the Gassmann/Hamilton model13.

The theory of sonic waves scattering and propagation hasalso been used to calculate the effective elastic moduli of atwo phase medium made of spherical inclusions in a uniformmatrix4:

K KG K K K G K I

K K K G Im

m i m i m m c

i m i m c

=+ −( ) +( )( )[ ]

− −( ) +( )[ ]1 4 3 4

1 3 3 4É..(A-7)

and

G GK G G K G I G I G

K G G K G I G I Gm

m m i m m c m c i

m m m m m c i c m

=+( ) + +( ) −( ) +[ ]+( ) + +( ) −( ) +[ ]

6 12 9 8 1

9 8 6 12 1-

(A-8)where the i and m subscripts refer to the inclusion and thematrix properties, respectively, and Ic is the volumetricfraction of the inclusion.

Experimental relationships. Underlining the practical limitsof these theoretical relationships, the following linearrelationships have been established between ultrasonicvelocities, porosity and clay content5:

Vp = 5.59 - 6.93Φ - 2.18γ....ÉÉÉÉÉÉ.(A-9)Vs = 3.52 - 4.91Φ - 1.89γ...........................(A-10)

Using in situ data from shear sonic geochemical logs thefollowing relationship has been drawn for the shear modulusof shaly sediments6:

G = Ggrain(1 - 3.48Φ + 2.19Φ2)É..ÉÉÉ(A-11)With Ggrain = (0.039log10(_) + 0.072)-1 ÉÉ.(A-12)

Ggrain is the effective grain shear modulus.

6 G. GUERIN, W. HE, R.N. ANDERSON, L. XU, U.T. MELLO OTC 12102

85

5001000

1500

2000

95˚W 94˚ 93˚ 92˚ 91˚ 90˚ 89˚ 88˚

26˚

27˚

28˚

29˚

30˚

31˚N

N

2500

3000

295

4.8 km

NewOrleans

K8

SouthTimbalier

Figure 1 Location map of the K8 firld, South Timbalier Block 295. The grey areas shows

the actual overlap between successive surveys that were used in the 4D analysis.

3160

3180

3200322032403260

3280

3300

3320

A12

A22

0 500 m 3330 3150Depth (mbsf)

N

Figure 2 Structure of the top of the K8 reservoir. The reservoir dips slightly to the SouthWest and leans on a paleohigh to the east. A12 and A22 are the two wells producing between the 1988 and 1994 surveys

OTC 12102 OPTIMIZATION OF RESERVOIR SIMULATION AND PETROPHYSICAL CHARACTERIZATION IN 4D SEISMIC 7

4.6

4.8

5.0

5.2

5.4

5.6

5.8

4.6 4.8 5.0 5.2 5.4 5.6 5.8

y = 0.534 + 0.902x R= 0.7214.6

4.8

5

5.2

5.4

5.6

5.8

4.6 4.8 5.0 5.2 5.4 5.6 5.8

y = 0.221 + 0.962x R=0.735

4.6

4.8

5

5.2

5.4

5.6

5.8

4.6 4.8 5.0 5.2 5.4 5.6 5.8

y = 0.727 + 0.867x R= 0.8544.6

4.8

5

5.2

5.4

5.6

5.8

4.6 4.8 5.0 5.2 5.4 5.6 5.8

y = 0.835 + 0.846x R= 0.834

4.6

4.8

5

5.2

5.4

5.6

5.8

4.6 4.8 5.0 5.2 5.4 5.6 5.8

Mod

el I

mpe

danc

e (1

06 kg.

m.s

-1) a) KT b) Gassmann + KT

c) Han d) Gassmann + Han

e) Gassmann + Ramamoorthy

1988 Impedance (106 kg.m.s-1)

y = - 0.356 + 1.071x R=0.783

1988 Impedance (106 kg.m.s-1)

1988 Impedance (106 kg.m.s-1)

1988 Impedance (106 kg.m.s-1) 1988 Impedance (106 kg.m.s-1)

Mod

el I

mpe

danc

e (1

06 kg.

m.s

-1)

Mod

el I

mpe

danc

e (1

06 kg.

m.s

-1)

Mod

el I

mpe

danc

e (1

06 kg.

m.s

-1)

Mod

el I

mpe

danc

e (1

06 kg.

m.s

-1)

Figure 5: Comparison of the predictions of the various petrophysic models with the impedance inversion of

1988, before production. (a) KT, (b) Gassamnn+KT, (c) Han, (d) Gassmann+Han and (e) Gassmann+Ramamoorthy.

Equations of the linear fits and regression coefficients (R) are given in each figure.

0

1000

2000

3000

4000

5000

6000

7000

8000

3000

4000

5000

6000

7000

8000

9000

Oil A12Oil A22Gas A12Gas A22

Pressure

Pressure (psi)

Oil P

rodu

ctio

n (b

l / d

ay)

Gas

Pro

duct

ion

(103 s

cf /

day) Gas Relative permeability exponent: 0.6 - Aquifer support from west

0

2000

4000

6000

8000

10000

12000

14000

3000

4000

5000

6000

7000

8000

9000

Pressure (psi)

Oil P

rodu

ctio

n (b

l / d

ay)

Gas

Pro

duct

ion

(103 s

cf /

day) Gas Relative permeability exponent: 0.6 - Aquifer support underneath

Oil A12Oil A22Gas A12Gas A22

Pressure

0

1000

2000

3000

4000

5000

6000

7000

8000

3000

4000

5000

6000

7000

8000

9000

Pressure (psi)

Oil P

rodu

ctio

n (b

l / d

ay)

Gas

Pro

duct

ion

(103 s

cf /

day) Gas Relative permeability exponent: 0.9 - Aquifer support from West

Oil A12Oil A22Gas A12Gas A22

Pressure

0

1000

2000

3000

4000

5000

6000

7000

8000

3000

4000

5000

6000

7000

8000

9000

1990 1991 1992 1993 1994 1995

Pressure (psi)

Date

Oil P

rodu

ctio

n (b

l / d

ay)

Gas

Pro

duct

ion

(103 s

cf /

day) Gas Relative permeability exponent: 0.9 - Aquifer support underneath

Oil A12Oil A22Gas A12

Gas A22

Pressure

Figure 8: Production history match for different reservoir configurations - the optimizingprocedure is applied to the gas relative permeability exponent and to the aquifer position.In all figures, discrete symbols (square and circle) represent measured data and lines represent simulation results.

8 G. GUERIN, W. HE, R.N. ANDERSON, L. XU, U.T. MELLO OTC 12102