A successful seismic-based reservoir properties estimation

Transcription

1 Comining rock physics nlysis, full wveform prestck inversion nd high-resolution seismic interprettion to mp lithology units in deep wter: A Gulf of Mexico cse study RAN BACHRACH, MARC BELLER, CHU CHING LIU, JUAN PERDOMO, DIANNA SHELANDER, nd NADER DUTTA, Schlumerger Reservoir Services/Dt nd Consulting Services, Houston, Texs, U.S. MARCELO BENABENTOS, Repsol YPF, The Woodlnds, Texs, U.S. A successful seismic-sed reservoir properties estimtion effort hs three steps: ccurte seismic inversion in 3D to otin relevnt reservoir prmeters, rock physics trnsformtion to relte reservoir prmeters to the seismic prmeters, nd mpping these prmeters in 3D. This prolem is nonunique nd thus ny ville informtion specificlly geologic interprettion should e used to improve our ility to infer the reservoir properties of interest with confidence. Moreover, uncertinty ssocited with the different predicted vlues (i.e., confidence intervl nd estimte of misclssifiction proility) must e provided s well, so tht proper decisions cn e mde. Thus, it is evident tht this involves interdisciplinry effort tht includes rock physics, geologic interprettion, nd seismic inversion technology. However, for quntittive description of reservoir properties, one must derive wy to quntify the errors nd uncertinties ssocited with the process. In this pper we present unified workflow tht ddresses this issue using well-known Byesin estimtion theory. The outcome of this integrted workflow is 3D mp of reservoir properties with ssocited proilities nd uncertinties. We illustrte this pproch using n exmple from the deepwter Gulf of Mexico. Recently, Mukerji et l. (GEOPHYSICS, 2001) nd Avseth et l. (GEOPHYSICS, 2001) hve shown how comining rock physics nlysis with sttisticl rock physics cn e used to predict lithology units nd the proility of their occurrences (or, in other words, the confidence ssocited with the prediction). The unified workflow implemented in this cse study extends their pproch to propgte dt/nlysis from the different disciplines nd integrtes them to produce reservoir properties mp tht reflects ll known informtion. Figure 1 presents schemtic digrm of the workflow. Well-log dt nd petrophysicl nlysis provide the sic input for the rock physics nlysis nd the genertion of different lithology clsses. Seismic dt inverted into elstic ttriutes nd geologic interprettion provide different scle nd sptil coverge of the dt. We use oth to generte the seismic-scled proility density functions (pdfs) to e used in our Byesin clssifiction scheme. We integrte them with geology y defining interprettion priors which re n initil estimte of the possile rnges of lithology ssocited with different geologic fetures interpreted on the 3D volume nd consistent with our geologic model. Finlly we provide the lithology unit estimte with the uncertinty ssocited with our prediction. The prcticl spects of this workflow re discussed in detil elow. Geologic setting nd seismic dt interprettion. The deepwter field studied lies in n intrslope slt withdrwl sin (Cogswell, AAPG 2001) in western Gulf of Mexico, where wter depths re out 4800 ft. Gs, which ws discovered t ft suse, comprises the mjority of the field, with nrrow oil rim long the down dip edge. Column height for the gs cp is more thn 1000 ft, while the column height for Figure 1. Generl workflow for 3D lithology nlysis nd prediction. Figure 2. () Seismic-well tie. Gmm-ry log in lue, resistivity log in red. Aritrry seismic line is extrcted from 3D volume pssing etween three wells in the gs, oil, nd wter legs. () Verticl profile showing the interprettion of snds (yellow) nd shles (lue) t the reservoir level of ft. The high-resolution seismic (Q-dt) resolve thickness s smll s 5 m in the snds. 378 THE LEADING EDGE APRIL 2004

2 the oil rim is only out 250 ft. An extensive quifer occurs sinwrd. Dips re 5 to 10 to the southest. A strtigrphic trp formed to the northwest where the snds pinch out on the flnk of slt dome high. The Lower Pleistocene reservoir intervl, known s the A-50 snd, is mde of fine- to very fine-grined, unconsolidted, turidite snds tht were deposited in deepwter environment. Averge reservoir permeility is out 800 md, nd porosity is more thn 30%. Gross reservoir thickness rnges from roughly 100 ft to the north, to pproximtely 50 ft to the southern, more distl portion of the field. High resolution seismic dt (Figure 2), with ed resolution s thin s 15 ft, revel tht snd eds re often thin nd comprtmentlized y lyers of low permeility silts nd shles. The seismic mplitudes of the gs ering snds re chrcterized s right spot, while wet snd re low-impednce events. Flt events, dignostic of fluid contcts, re lso visile long much of the downdip edge of the field. The high-resolution seismic dt llow detiled interprettion, which will e used lter to constrin lithology nd fluid clssifiction. Note: similr snd lyer, the A-70 snd, exists elow the A-50 nd is seprted y 100-ft thick shle-to-shly-snd rrier. This ed is esily identifile on gmm-ry logs nd seismic dt. Wells drilled into the A-70 hve penetrted mostly rine-filled snds, however potentil for hydrocrons exist updip from those loctions. c d Rock physics nlysis nd model spce definition. Figure 3 shows well-log dt from the 500-ft intervl identified s potentil py. In well-log dt we cn generlly identify two types of fields. Seismic fields represent sediment properties tht ffect seismic wve propgtion in the susurfce. Nonseismic fields re other sediment properties tht re of interest for seismic reservoir description ut do not ffect directly the seismic wve propgtion. In this cse, the seismic fields re the well-log compressionl nd sher velocities nd the density log, nd the nonseismic fields re well-log estimtes of porosity, wter sturtion (S w ) nd cly content (V cl ). Rock physics nlysis is the key to relting the two. Plotting compressionl nd sher velocity s function of porosity with the Hshin-Shtrikmn ounds shows tht the sediments re poorly consolidted, soft, nd with high porosities (Figure 3) s the dt points re closer to the lower ound. Plotting sediment response in the porosity-ulk nd porosity-sher moduli (Figure 3c) with cly content s the color r shows distinct trnsition etween shles, shly snds, nd clen snds. The sher modulus is not very sensitive to cly content ut shows distinct stiffness-porosity trend. Plotting ulk nd sher moduli ginst porosity with S w s the color r (Figure 3d) shows distinct fluid effect in the ulk modulus domin. We thus conclude tht we hve Figure 3. Rock physics nlysis. () Petrophysicl nlysis provided porosity, wter sturtion, nd cly volume estimtes. () Plotting compressionl nd sher velocity s function of porosity with the Hshin-Shtrikmn ounds shows tht the sediments re poorly consolidted soft nd with high porosities. (c) Plotting sediment response in the porosity-ulk modulus (left) nd porositysher modulus (right) with cly content. The color r shows distinct trnsition etween shles, shly snds, nd clen snds. The sher modulus is not very sensitive to cly content ut shows distinct stiffness-porosity trend. (d) Plotting ulk nd sher moduli ginst porosity with wter sturtion. The color r shows distinct fluid effect in the ulk modulus domin. From this nlysis we identify the potentil signture of cly content porosity nd pore fluids. strong signture for cly content nd sturtion. In this study we were interested in predicting the lithology within the reservoir zone. Therefore, sed on this nlysis, four lithology clsses re defined s the model spce (or lithology clsses): shles, shly snds, hydrocron snds, nd rine snds. Anlysis of lithology clssifiction in well-log ttriute spce. In this cse study, hyrid inversion technology (Mllick nd Benentos, TLE 2002) is used to derive seismic ttriutes. This is sed on using comined full wveform prestck inversion or FWPI (Mllick, GEOPHYSICS 1995) nd AVO inversion. Therefore, the forwrd model in this cse is sed on liner elsticity formultion, where we lso ssume tht the mteril is isotropic. In such medi, ll physicl seismic ttriutes (e.g., coustic impednce, sher impednce, Poisson s rtio, nd others) re relted to three independent APRIL 2004 THE LEADING EDGE 379

3 Figure 4. () All clsses in the V P, V S, nd density spce. () Projection of discrete dt in V P - density spce. (c) Nonprmetric pdfs derived from the dt. c Figure 5. FWPI results. () Synthetic exmple shows results otined y forwrd modeling rel well log nd inverting the seismic trces. () Rel dt exmple. A correltion coefficient of.98 is otined etween synthetic nd model dt; for rel dt, the correltion coefficient is.79. The lck log is the est estimte. Red log is the true model. The yellow envelope represents error estimtes (±1 STD) susurfce prmeters: compressionl velocity (V P ), sher velocity (V S ), nd density. Figure 4 shows vrious lithology units in the 3D spce defined y V P, V S, nd density sed on wireline well-log dt. We suggest tht the vriility in the dt cn e cptured y using pdfs. Figures 4 nd 4c show how nonprmetric pdfs cn e derived in the seismic ttriute spce. Nonprmetric pdfs re proility density functions tht re estimted directly from the dt, without ssuming ny prior sttisticl model. Note tht when using pdfs to cpture the nturl vriility within the zone of interest, the degrees of freedom in the inference prolem (of lithology clssifiction in this cse) re set. Thus, s pointed out y Tkhshi (1999), liner or nonliner trnsformtion of this set of ttriutes into nother set of ttriutes will not reduce the degrees of freedom in this inference prolem. This is well known result from sttisticl inference theory known lso s dt processing inequlity. Nonuniqueness will e ddressed y deriving the proilities for successful identifiction of given lithology. Seismic inversion resolution. In the cse of FWPI, the lyer thickness is typiclly within 1/4 to 1/10 of the wvelength. This mens tht the velocity nd density estimtes within ech lyer represent vlue within the effective medi theory. Recll tht for lyered medi, the effective seismic response of thin-edded mteril cn e represented y the Bckus verge. If we use the lyer thickness s the length of Bckus verging opertor, we cn derive theoreticlly error free estimte of the expected inversion result on the well log. Bchrch et l. (SEG 2003 Expnded Astrcts) showed tht clssifiction results of the Bckus verged well log, which represent n error free mesurement within Bckus long-wvelength pproximtion, improves s the frequency content of the inversion increses (or lyer thickness decreses). In mny cses, high SNR will improve the resolution of the seismic inversion results. Seismic inversion ccurcy. FWPI is nonunique inversion. The process not only yields est estimte of the prmeters, ut lso quntittive mesure of uncertinty from the inversion process. Figure 5 shows synthetic exmple of results otined y forwrd modeling rel well log nd inverting the seismic trces using FWPI. Ech prt of the figure shows (left to right) input gther, inverted gther, V P, Poisson s rtio, nd density estimtes. For ech of the three fundmentl seismic ttriutes, we otin the est estimtes (the lck log), nd yellow envelope tht represents the error estimte ssocited with the lgorithm convergence. From comprison with the well log nd the error estimte ssocited with the FWPI, we cn stte tht, on the verge, inversion results for V P re within ±8%, inversion results for V S re within ±10%, nd inversion results for density re within ±15%. Propgting inversion ccurcy into well-log nlysis. The ccurcy of seismic inversion cn e integrted with the welllog dt pdfs y deriving n error filter tht will correspond to the expected ccurcy of the seismic dt. This error filter cn e then convolved with the well-log-generted pdfs to generte new pdfs tht will represent the uncertinty nd overlp etween the different lithology clsses s derived y the seismic mesurement. Figure 6 shows this process y presenting 1D well-log-derived V P pdfs nd the V P pdfs fter ccounting for the inversion ccurcy (the seismic pdfs). It is clerly seen tht the vrince of the pdfs hs incresed t ech estimted point. Therefore, clssifiction with the well log pdfs (Figure 6, top) is less miguous thn clssifiction with the low-ccurcy pdf (Figure 6, ottom). Such n error filter cn e generted for ny pdfs of ny dimensionlity. Seismic inversion: ccurcy nd resolution. The two topics we re considering when upscling well-log mesurements to seismic ttriutes re resolution (i.e., the well-log dt hve higher verticl resolution thn the seismic dt) nd ccurcy (i.e., the well-log dt re typiclly more ccurte thn the seismic dt). Byesin estimtion. The Byesin frmework enles us to ssemle initil knowledge out model efore oserving the inversion ttriutes ATR (we refer to the comintion of the seismic inversion ttriutes s ATR). We define this knowledge s prior (i.e., efore seismic inversion results re derived) nd define it in terms of the proility of ech lithol- 380 THE LEADING EDGE APRIL 2004

4 sion ttriutes ATR given lithology, nd p(atr)=σ i p(lithology i )p(atr lithology i ). Byes s rule provides frmework for comining the proilistic prior informtion with the informtion contined in the oserved dt to updte the prior informtion. The updted distriution is the posterior conditionl model distriution given the dt nd reflects wht we know out the model fter we hve comined the seismic inversion results nd the prior informtion. Figure 6. (top) Originl pdfs. (ottom) Pdfs fter ccounting for seismic errors (8% in this cse). Integrtion: From interprettion to lithology clssifiction nd uncertinty estimtion. So fr the pdfs we hve generted cn e used to generte the conditionl proility for given lithology p(atr lithology n ). Our gol is to generte the posterior proility estimte of lithology for given ttriute p(lithology n ATR). Byes s theorem cn e used to generte this posterior clss. To use Byesin estimtion, one must pply lithology prior ssocited with the oserved seismic ttriutes. Choosing prior in Byesin estimtion is not trivil tsk. In the sence of ny knowledge, n equiprole prior cn e used for ech lithology clss (in this cse noninformtive mens tht ech of the four lithology units hs n equiprole 25% chnce of occurring t ny point in the susurfce). However, the geologic interprettion provides dditionl independent informtion tht could e dded to improve our estimte of the lithology. In our cse, the seismic interprettion of the top of the A50 snds nd the ottom of the A70 snds cn e considered s n independent understnding of the geology of the reservoir snds. Figure 7 shows the interprettion prior ssocited with the lyers. These interprettionl priors will e used to normlize the seismic pdfs to reflect the knowledge gined from the structurl interprettion. The methodology to incorporte geologic interprettion into the lithology estimtion is executed s follows: 1) Pick horizons nd identify mjor sequences. 2) Assign prior proility for different lithology units within sequence. 3) Derive interprettionl indictor to e used s sptil filters for clssifiction proility. 4) Clssify the seismic dt ccounting for the prior informtion. The results of this clssifiction re discussed in the following section. Figure 7. Sudivision of the sequence defined etween the top A50 snd (interprettion in yellow) nd ottom A70 snd (interprettion in red) into three lithounits (snd, shly snd, shle) long the seismic inline crossing well. The percentges re verge vlues resulting from similr nlysis performed t the following three wells. We do not ssume prior knowledge of pore fluid within ech sequence. ogy unit p(lithology n ). Then Byes s rule sttes (Ky, 1993; Houck, 1999): where p(lithology n ATR) is the posterior pdf, p(atr lithology n ) is the conditionl proility of hving set of seismic inver- Results: Clssifiction nd uncertinty quntifiction. We use the new pdfs derived y the well logs nd downscled to their proper seismic ccurcy, nd then we cn use seismic ttriutes nd generte the proility of the lithology given the ttriute p(lithology n ATR), scled with the initil interprettionl prior. The most likely fcies is chosen using the mximum posteriori (MAP) rule (Ky, 1993), nd we lso generte n imge of the proility for ech clss. Thus, we cn consider how likely our MAP estimtor is, nd show the risk ssocited with the MAP estimtor. Figure 8 shows selected lines from the input dt which consist of 3D volumes of P-Imp, S-Imp nd Poisson s rtio. Figure 8 shows the 3D pdfs used to generte the ttriutes, nd Figure 8c shows the MAP lithology imge. The uncertinty ssocited with these predictions is shown in Figure 9 where we plot the 3D hydrocron proility mp. Note tht in Figure 9, the APRIL 2004 THE LEADING EDGE 381

5 c Figure 8. () Seismic input P-Imp, Poisson s rtio, nd S-Imp. () The 3D pdfs used for clssifiction. (c) MAP estimte of lithology clsses from three input ttriutes. Figure 9. Proility of hydrocron (HC). () 3D view of HC shows distinct delinetion of gs-oil nd wter lgs within the reservoir. () Good greement etween gs proility mp nd well log. HC pdfs re consistent with interprettion of gs-ering sediments, oil-ering sediments, nd rine-ering snds. Good greement etween the sturtion log nd the gs proility is shown in Figure 9. Summry nd conclusion. Becuse the prolem of seismic reservoir chrcteriztion is nonunique, s shown in the welllog dt nlysis, SRD effort must ccount for ll ville prior informtion. The uncertinty ssocited with the SRD process, nd seismic inversion ccurcy must e ddressed in consistent mnner. In this cse study, we used n integrted workflow tht quntittively ccounted for the inherent uncertinty in rock properties inversions nd the uncertinties ssocited with the seismic inversion ccurcy. High-resolution seismic 382 THE LEADING EDGE APRIL 2004

6 dt (lyers with thickness smller thn 12.5 m were delineted nd interpreted) enled the genertion of detiled interprettion mps tht were used to further reduce the uncertinty ssocited with this lithology prediction effort. The finl gs proility mp showed very good greement with oth well-log dt nd interprettion. 3D sptil mps of py enled identifiction of the gs-, oil-, nd rine-ering res of the reservoir. The interdisciplinry pproch used here provided quntittive wy to propgte knowledge from different disciplines into finl product tht is consistent with ll disciplines. Suggested reding. Seismic reservoir mpping from 3-D AVO in North Se turidite system y Avseth et l. (GEOPHYSICS, 2001). Propgting seismic dt qulity into rock physics nlysis nd reservoir property estimtion: Cse study of lithology prediction using full wveform inversion in clstic sins y Bchrch et l. (SEG 2003 Expnded Astrcts). Long-wve elstic nisotropy produced y horizontl lyering y Bckus (Journl of Geophysicl Reserch, 1962). Din sin development A prgmtic pproch to the exploittion of two deepwter GOM fields y Cogswell (AAPG 2001 Astrcts). Elements of Informtion Theory y Cover nd Thoms (Wiley, 1991). A vritionl pproch to the elstic ehvior of multiphse mterils y Hshin nd Strickmn (Journl of Mechnicl Physics Solids, 1963). Estimting uncertinty in interpreting seismic indictors y Houck (TLE, 1999). Foundmentls of sttisticl signl processing: Estimtion theory y Ky (Prentice Hll, 1993). Model sed inversion of AVO dt using genetic lgorithm y Mllick (GEOPHYSICS, 1995). Reservoir description using full wveform prestck inversion y Mllick nd Benentos (TLE, 2002). The Rock Physics Hndook y Mvko et l. (Cmridge, 1998). Mpping lithofcies nd pore fluid proilities in North Se reservoir: Seismic inversions nd sttisticl rock physics y Mukerji et l. (GEOPHYSICS, 2001). Sttisticl rock physics; comining rock physics, informtion theory, nd geosttistics to reduce uncertinty in seismic reservoir chrcteriztion y Mukerji et l. (TLE, 2001). To Byes or not to Byes y Scles nd Sneider (GEOPHYSICS, 1997). Quntifying Informtion nd Uncertinty of Rock Property Estimtion from Seismic Dt y Tkhshi (PhD thesis, Stnford University, 1999). TLE Acknowledgments: Mrcelo Benentos ws formerly with Schlumerger Reservoir Services. Corresponding uthor: rchrch@sl.com APRIL 2004 THE LEADING EDGE 383