Frequency-dependent seismic reflection coefficient for discriminating gas reservoirs

Transcription

1 Journl of Geophyscs nd Engneerng 0, vol. 8, pp do:0.088/74-3/8/4/003 Frequency-dependent sesmc reflecton coeffcent for dscrmntng gs reservors Duo Xu,, Ynghu Wng, Qgn Gn, Jnmng Tng. Centre for Reservor Geophyscs, Imperl College London, UK. E&P Reserch Insttute of Southwest Petroleum Compny, Snopec, Chn Astrct The symptotc equton of wve propgton n flud-sturted porous med s vlle for clcultng the norml reflecton coeffcent wthn sesmc frequency nd. Ths frequency-dependent reflecton coeffcent s expressed n terms of dmensonless prmeter, whch s the product of the reservor flud molty (.e. nverse vscosty), flud densty, nd the frequency of the sgnl. In ths pper, we pply ths expresson to Xnchng gs-feld, Chn, where reservors re super tght snds wth very low permelty. We demonstrte tht the vrton n reflecton coeffcent t gs/wter contcts s oservle wthn sesmc frequency nd. Then we conduct sesmc nverson to generte ttrutes whch frst ndcte the exstence of flud (ether gs or wter), nd then dscrmnte gs reservor from wter reservor. Keywords: norml reflecton coeffcent, poroelstc med, gs/wter contct, chotc nverson. Introducton Hydrocron reservors s well s mny other sedmentry rocks re flud-sturted porous mterls, n whch the elstc propertes cn e descred y poroelstcty theory tht predcts the effects of pore flud movements reltve to the sold skeleton on sesmc wves propgtng through the rock. However, most of poroelstc studes re focused on velocty dsperson nd ttenuton, few reserchers consder plne-wve reflecton coeffcents n the porous med. In ths pper, we desgn gs/wter contct model sed on petrophyscl prmeters collected from Xnchng gs-feld, Southwesten Chn, nd nvestgte the potentl frequency-dependency of the norml-ncdent reflecton coeffcent wthn the sesmc frequency nd. The clssc theory of poroelstcty (Bot, 956,, Dvorkn, 993) s not sutle for the sesmc whch hs low frequency less thn 00 Hz. Its predcted wve ttenuton nd dsperson only ecome sgnfcnt t frequences comprle to the so-clled Bot s chrcterstc frequency, whch s usully 0. MHz or hgher (Gurevch, 004). The reltve flud movement t low frequences s neglgle nd the rock ehves lke n elstc sold wth the equvlent elstc modul gven y Gssmnn s (95) equton. In prctce, frctures my hve sgnfcnt mpct on the flow propertes of the reservors.

2 Dul-porosty model, proposed orgnlly y Brenltt et l. (960), consders the presence of frctures t dfferent scles of permelty. A connected system of frctures, due to reltvely smple geometry of the pore spce, s hghly permele for flud flow. The mtrx, due to the tortuous pores nd pore throts, s sgnfcntly less permele. At the sme tme, the totl volume of frctures s usully smll nd the mtrx locks contn most prt of the reservor flud. However, ccordng to Brenltt model, the flud flow n mtrx locks s locl: t only supports the exchnge of flud etween ndvdul locks nd the surroundng frctures. In lrge scle, flud flows through frctures only. Prde nd Berrymn (003 & ) proposed nother dul-porosty model whch supports lrge-scle flud flow n oth med. Ths model comned Brenltt model wth Bot s theory of poroelstcty nd hs the pplclty not lmted to frctured rocks (Goloshun, 006, 008). But to cses whenever the permelty of the rock hs two or more contrst scles. These scles must e dstruted n the medum n such wy tht every representtve volume comprses oth smll-volume hghly permele medum nd low-permele nlog of mtrx. In order to understnd nd to explore mplctons for reflectons from n nterfce etween two porous med, t s desrle to otn nlytcl expressons for the reflecton coeffcents. However, they re too complcted for rtrry ncdence ngles (Dennemn et l., 00). The prolem s gretly smplfed for the norml ncdence. Bsed on Bot-Brenltt poroelstc model, Sln nd Goloshun (006, 00) derved n symptotc expresson for the reflecton nd trnsmsson coeffcents. These symptotc expressons re pproxmte ut hve reltvely smple mthemtcl form. They re vld n the low-frequency end of the spectrum ncludng the sesmc frequency nd (0 00 Hz), for plne wve crossng permele nterfce t norml ncdent ngle. In ths pper, we nvestgte the potentl pplclty of ths norml-ncdence reflecton coeffcent to the gs/wter contct models n gs-feld.. Petrophyscl model of study re The study re s Xnchng gsfeld, Southwesten Chn (Gn et l., 008). Tle lsts petrophyscl prmeters n ths re. We collect these prmeters from rock physcs mesurements nd well-log dt. When we clculte the reflecton coeffcent, we ssume prmeters of skeleton to e sme for up nd down porous lyers. In Xnchng re, the reservors re tght snd wth very low permelty. The verge permelty of trget reservor s out 0.03 mlldrcy. The producton s mnly the nture gs, whch s mostly from frctures. When the frctures occur n the reservor, permelty wll ncrese drstclly up to decdes or hundreds fold of t. Therefore, n the followng numercl clculton, we desgn two permelty prmeters (0.03 nd 30 md) n the model. The permelty of 30 md corresponds to the cse wth frctures present. The petrophyscl model ncludes the followng prmeters: K g : ulk module of grns sold, K : the ulk module of the porous medum, : the sher module, : porosty, : permelty, g : the densty of grns, K f : the flud module, f : the flud densty, : the stedy-stte sher vscosty.

3 () Prmeters of the porous rock Tle. Propertes of the porous rock nd the smple pore flud. K g (GP) K (GP) (GP) (md) g (kg.m -3 ) Snd or () Prmeters of the pore flud K (GP) f f (kg.m -3 ) (P.s) Wter Gs Norml-ncdence reflecton coeffcent t gs-wter contct Consder two hlf-spced poroelstc med, leled y superscrpts nd (Fgure ), seprted y permele plne nterfce t z = 0. For n ncdent fst wve rrvng from the hlf-spce z < 0, there re four wves to e generted: reflected fst nd slow wves, nd trnsmtted fst nd slow wves. Fgure. A fst wve ncdentl from the hlf-spce z < 0 genertes four wves genertes four wves t plnr nterfce: reflected fst nd slow wves nd trnsmtted fst nd slow wves. The mss nd momentum lnce mply tht the skeleton dsplcement, the Drcy velocty of the flud, the totl stress, nd the flud pressure must e contnuous t the nterfce. The symptotc expressons of norml-ncdence reflecton nd trnsmsson coeffcents from ths nterfce re (Sln nd Goloshun, 00) R 0 R R, () T 0 T T, () 3

4 where R 0, T 0, R nd ntegrted prmeter defned s R re the zero- nd frst-order terms, nd s n / 4 f e. (3) whch comnes the flud densty f, the flud vscosty, nd the permelty. Note here tht we hve redefned prmeter n slghtly dfferent wy from Sln nd Goloshun (00), so tht we re le to present the expressons n lner form. In the symptotc expnsons, the zero-order terms re gven y Z Z R0, (4) Z Z where Z s modfed coustc mpednce Z Z T0. (5) Z Z Z M K, (6) v p expressed n terms of (Bot, 96) K g K K ( ), K f K g K K ( ) K g, v p 4 K 3. ( ) f g The coeffcents of the frst-order terms re defned y FS FS ( T R Z ) R, (7) Z Z FS FS ( R T Z ) T. (8) Z Z In these coeffcents, the slow-wve reflecton nd trnsmsson coeffcents re 4

5 R FS Z ( ) Z K K, (9) ( ) D Z Z K ( K ) T FS ZZ D( Z Z ) K K ( ( K K ), (0) ) where D M v f K K K K M v f K K K K, nd v f M / f. We use equton () to clculte the reflecton coeffcent t gs/wter contct n Xnchng gsfeld. As s the functon of frequency, the reflecton coeffcent s frequency dependent. We clculte the vrton of reflecton coeffcent versus frequency 0 y R 00 ( R( ) R 0 ) / R0 (n percentge), where R 0 R( 0) s the reflecton coeffcent for frequency 0. () () Fgure. The vrton (n percentge) of reflecton coeffcent t n nterfce etween gs-sturted porous medum nd wter-sturted medum n Xnchng gsfeld. () The permelty md. () The permelty 30 md. The clculton s sed on formul (). The ncdent wve s from gs-sturted porous medum. When the permelty s very low t 0.03 md, there s very smll chnge n reflecton coeffcent t the gs/wter nterfce (Fgure ). However, when there re frctures presented n porous medum, sometmes the permelty cn e very g ( to 3 mgntude orders hgher) wthn strongly frctured med n Xnchng re. When the permelty ncreses to 30 md, there s out % of the reflecton coeffcent chnge wthn sesmc frequency nd (Fgure ). The key fctor whch mkes the symptotc expresson of the norml ncdent reflecton 5

6 coeffcent work n sesmc nd s the consderton of dynmc nd non-equlrum effects n flud flow (Sln nd Goloshun, 00). Modfed Drcy s lw s W W u p f t () t where W denotes the Drcy velocty of the flud reltve to the skeleton, s prmeter hvng the dmensonlty of tme, nd p s the pressure of flud. The ddtonl term W / t to the Drcy s lw expresses dynmc nd non-equlrum effects n flud flow. Ths modfcton of Drcy s lw s equvlent to lnerzton of the dynmc permelty for perodc osclltory flow (Johnson et l., 987; Corts, 00; Crcone, 003). But derved symptotc expressons hve smple mthemtcl form whch s useful n prctce. Under the symptotc model, ncresng the frequency would enlrge the vrton of reflecton response t the nterfce etween two porous medums. So prolems of reflecton coeffcent t gs/wter contct wth low permelty such s Xnchng gsfeld wll prtlly suject to the development of hgh-resoluton sesmc explorton, nd to the enhncement of ny exsted sesmc dt sets, y hgh-fdelty sesmc nverse Q flterng (Gn et l., 008). 4. Sesmc nverson for flud dscrmnton The postve chnge n reflecton coeffcent n (Fgure ) provdes us n opportunty to nvert for the reflectvty sed on formul (). Here, we rewrte formul () s where the constnt R ( 0 ) R C ( ), () f C R. It reflects proportonlly the molty (nverse vscosty) of reservor flud, the densty of flud, nd the permelty. We use chotc optmzton lgorthm to nvert for prmeters R 0 nd C. The nverson oject functon s defned s J [ R ( R0, C, ) Ros( )], (3) where R os s the oserved feld dt n the frequency domn. Chos s unversl phenomenon s stochstc ut ergodc nd regulr (Lorenz, 993). One cn explot the ergodcty s mechnsm for glol optmzton, to effectvely vod the serch eng trpped n locl optmum. Ths s nonlner lgorthm serchng for n optml rndom vrle x whch s mde y Logstc mppng equton x ( k ) ( k ) ( k ) x ( x ), (4) where k s the terton numer, nd s constnt tht controls stochstc ehvor. If , the rndom vrle x s chotc. In our nverson here, we set 4. The 6

7 dmensonless x vlue s n the rnge (0, ). However, the followng three ponts (0.5, 0.5, 0.75), for whch the vrle x s unchngele should e excluded from the terton. If we hve n of unknown prmeters {x,,,, n} tht need to e nverted, we smply set dfferent ntl vlue for ech prmeter x. () () (c) Fgure 3. () A sesmc secton n Xngchng gsfeld. Ths secton crosses two wells, where the end of well A s gs reservor nd the end of well B s wter reservor. () Inverted C ttrute secton y chotc optmzton. (c) The ttrute vrton clculted y C C. Strong mpltude mens more molty. Gs reservor shows stronger mpltude thn wter reservor n the sme formton. 7

8 For ech terton k, gven ny rndom vrle ctul mgntude n ts physcl spce through (k ) x n the rnge (0, ), we scle-up to xˆ ( k ) 8 ( k ) ( ) x, (5) ( ) where x ˆ k s the ctul model prmeter n the model spce. The rnge of xˆ s n,, ( ) wth physcl unts model. We susttute ll n prmeters {ˆ x k,,,, n} smultneously to the ojectve functon wthn ech terton. Eventully, we cn fnd the soluton whch mnmzes the ojectve functon. Fgure 3 s the feld sesmc secton from Xnchng gs-feld, the reservor (the trough n Fgure 3) s reltve shllow wth low mpendence. Ths secton cross two wells: the end of well A s gs reservor, nd the end of well B s wter reservor. Fgure 3 s the nverted C secton. Ths ttrute secton hs dfferent fetures from Fgure 3. In sesmc secton (Fgure 3), we couldn t fnd the dfference t the locton of well A nd well B n the reservor. However, n Fgure 3, we cn oserve the dfferences: () The mpltude s stronger t well A thn t t the well B. () Menwhle, oth of them hve stronger mpltude thn other res. The g vlue of C mens strong molty of flud, when there s gs or wter present n the reservor, the mpltude of C wll ecome strong. In ddton, reltvely stronger mpltude ndctes the exstence of gs t well A. In order to hghlght the vrton n the ttrute C, we clculte weghted ttrute C C, where C s the dfference of the solute vlue C etween two djunct smples. As shown n Fgure 3c, the response of the gs reservor s clerer thn the response of the wter reservor. In summry, the strong mpltude n C ndctes the molty of flud (ether gs or wter), nd the strong mpltude n C ndctes the exstence of gs reservor. 5. Conclusons C The symptotc equton of sesmc reflecton s vlle for clcultng the norml reflecton coeffcent wthn sesmc frequency nd t gs/wter contct. The reflecton coeffcent s expressed s power seres wth respect to smll dmensonless prmeter, whch s the product of the reservor flud molty nd densty, nd the frequency of the sgnl. The functonl structure of these coeffcents provdes opportuntes for frequency-dependent sesmc nverson, to produce frequency-dependent sesmc ttrutes. We hve demonstrted tht n Xnchng gs feld where reservors re super tght snds wth very low permelty, the vrton n reflecton coeffcent t gs/wter contcts cn stll e oserved wthn sesmc nd. Further more, sesmc nverson generted ttrutes C ndctes the exstence of flud, nd weghted solute vlue C C dscrmntes gs reservor from wter reservor. Acknowledgments We re grteful to the sponsors of the Centre for Reservor Geophyscs, Imperl College London, nd Snopec, Chn, for supportng ths reserch. We lso would lke to thnk Mr. Neng-chun Jng for knd ssstnce on collectng nformton for ths reserch. References Bot M. A., 956. Theory of propgton of elstc wves n flud-sturted porous sold, I:

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