Thin Bed Analysis

7/28/2019 Thin Bed Analysis

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S P W L A 4 2 nd A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 -2 0 , 20 0 1

D E T E C T I N G T H I N G A S B E D S I N F O R M A T I O N S U S I N GS T O N E L E Y W A V E R E F L E C T I O N A N D H I G H - R E S O L U T I O N

S L O W N E S S M E A S U R E M E N T S

X . M . T a n g a n d D . P a t te r s o n , B a k e r A t l a s, H o u s t o n , T e x a s , U . S . A

A B S T R A C TDetec t ing gas in format ions is an important task offormat ion eva lua t ion . Oftent imes, gas sa tura t ion isin smal l pocke ts or in th in / lamina ted beds of thefo rma t ion , w h ic h t e nd to be ove r looke d byc onve n t iona l me thods tha t ha ve a l ow e r ve r t i c a lresolut ion . Neverthe less, f inding such th in gasin te rva ls i s qui te s ignif icant , espec ia l ly fore nha nc ing p roduc t ion in he a vy o i l r e se rvo ir s . Th i spaper descr ibes the acoust ic de te rmina t ion of th ingas in te rva ls using Stone ley wave re f lec t ion andh igh - re so lu t ion s low ne ss me a su re me n t s .A gas-sa tura ted in te rva l has drast ica l ly d i ffe rentf lu id mob i l i ty a nd c ompre ss ib i l it y c ompa re d to thoseo f t he su r round ing fo rma t ion . D ur ing a c ous t i clogging across the in te rva l , the s ignif icant f lu idmob i l i t y / c ompre ss ib i l i t y c on t ra s t w i l l ge ne ra t e ame a su ra b le S tone le y w a ve re f l e c t ion a nd inc re a sethe t r a ve l t ime / s low ne ss o f c ompre ss iona l w a ve s .The o re t i c a l mode l ing show s tha t t he S tone le y -w a veref lec tance is pr imari ly contro l led by the f lu idproperty contrast and is sensi t ive , to a lesser extent ,to the in te rva l th ickness. Thus the Stone leyre f l ec t ion me a su re m e n t c a n be u se d fo r t h in ga s be dde te c t ion . The s low ne ss me a su re me n t , how e ve r , i sc on t ro l l e d by the th i c kne ss o f t he ga s be d . W i th arecent ly deve loped th in bed slowness ana lysis ,fo rma t ion c om pre ss iona l a nd she a r s low ne ss p ro f il e sc a n be de t e rmine d w i th a me a su re me n t a pe r tu redown to 0 .5 f t , a l lowing for the de tec t ion of th in gasin t erva l s . C om bin ing the S tone le y a nd s low ne ssme a su re m e n t s c a n p rov ide m u tua l ve r i f i ca t ion o f t heresul t and enhance the re l iabi l i ty of the de tec t ion .F ie ld e xa mple s w i l l be u se d to de mons t ra t e t heappl ica t ion resul ts .

I N T R O D U C T I O NIn format ion eva lua t ion , the th in gas-bed de tec t ion isimportant for hydrocarbon ident i f ica t ion , espec ia l lyin f ight format ions. I t i s a lso important fore nha nc ing re c ove ry f rom he a vy -o i l r e se rvo i r s .Acoust ic logging and in te rpre ta t ion techniques a reof ten used for th is purpose . The presence o f gas informat ions a ffec ts the e last ic wave ve loc i ty of aporous rock. For instance , a porous rock sa tura ted

with gas wi l l have a considerably lowerc ompre ss iona l (P ) -w a ve ve loc i ty tha n the sa me roc ksa tura ted wi th water , whi le the shear (S)-waveveloc i ty is re la t ive ly insensi t ive to the gas sa tura t ion .Actua l ly , th is change of P-w ave v e loc i ty wi thhydrocarbon property is of ten used as an e ffec t iveindica t ion of hydro carbon sa tura t ion of reservoirrocks (e .g . , Wil l iams, 1990; Brie e t a l ., 1995) . Forth in gas beds, however , the response wi l l be d i ff icul tto de tec t i f the bed th ickness is smal l compared tothe aper ture o f the acoust ic rece iver a rray on theacoust ic logging tool ( typica l ly 3 .5 f t) . In o therwords, the acoust ic s igna ture of the th in gas bed wi l lbe obscured, or smeared, i f acoust ic wave slowness,or ve loc i ty , i s obta ined using convent iona l a rrayp roc e ss ing t e c hn ique s .

The m a in foc us o f t h i s s tudy is t o i nve s t iga t e how touse acoust ic logging to de tec t th in gas beds informat ions. Figure 1 i l lust ra tes the scenar io of thelogging o f an acoust ic a rray tool across a th in gasbe d . Tw o a c ous t i c w a ve phe nom e na oc c u r a t t he ga sbed. The f i rs t i s the acoust ic wave re f lec t ion causedby the h igh a c ous t i c impe da nc e c on t ra s t be tw e e n thega s be d a nd the su r round ing fo rma t ion . The se c ondi s t he inc re a se o f c ompre ss iona l -w a ve s low ne ssacross the gas bed. We descr ibe two acoust ictechniques tha t can capture the acoust ic response ofthe th in ga s be d a nd c ombine the tw o re su l t s t oenhance the re l iabi l i ty of the de tec t ion . One suchtechnique is the recent ly deve loped acoust ic th in-bedslowness ana lysis (Zhang e t a l . , 2000) . Thistechnique obta ins the acoust ic wave slowness overthe in te r-rece iver spac ing (0 .5 f t ) of the acou st icarray , grea t ly enhancing the resolut ion of theresul t ing slowness prof i le . Another technique is theStone ley-wave re f lec t ion ana lysis (Tang, 1996) .Th i s t e c hn ique p roc e sse s the low - f re que nc yS tone le y w a ve a nd se pa ra t e s t he w a ve in tot ransmit ted and re f lec ted wave da ta . By t rac ing theorig in of the re f lec tion events presen t in the la t te rda ta , a format ion re f lec tor adjacent to the boreholecan be loca ted . A th in gas bed has a h igh f lu idmob i l i t y a nd c ompre ss ib i l it y t ha t a re d i f f e re n t f romthe su r round ing fo rma t ion . A pa ss ing S tone le y w a vewil l therefore in te rac t wi th the gas content in theth in bed, producing a re f lec ted wave tha t can be


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S P W L A 4 2 "d A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 - 2 0 , 2 0 0 1

m e a s u r e d b y a n a c o u s t i c l o g g i n g t o o l ( s e e F i g u r e 1 ) .Un f o r t u n a t e l y , a n a m b i g u i t y i n t h e S t o n e l e y - wa v eref lec t ion ana lys i s i s tha t many o ther fac tors , such asb o r e h o l e c h a n g e s ( wa s h o u t s ) , f o r m a t i o n l i t h o l o g yc h a n g e s , f r a c t u r e s , e t c . c a n a l s o p r o d u c e m e a s u r a b l eS t o n e l e y wa v e r e f l e c t i o n s ( Ta n g , 1 9 9 6 ; Ge l i n s k ya n d Ta n g , 1 9 9 7 ) . I d e n t i f y i n g t h e s o u r c e s o f t h er e f l e c ti o n e v e n t s i s a f o r m i d a b l e t a s k . Co m b i n i n g t h ea c o u s t i c t h i n - b e d a n a l y s i s wi t h t h e S t o n e l e y - wa v er e f l e c t i o n m e t h o d r e d u c e s t h e a m b i g u i t y i n e i t h e rs t a n d - a l o n e a n a l y s i s a n d e n h a n c e s t h e r o b u s t n e s sand re l i ab i l i ty of the in te rpre ta t ion .

I n t h e f o l l o wi n g , we wi l l t h e o r e t i c a l l y a n a l y z e t h eS t o n e l e y wa v e r e f l e c t i o n d u e t o a t h i n g a s b e d a n dg i v e s o m e n u m e r i c a l e x a m p l e s . W e wi l l t h e nd e s c r i b e t h e m e t h o d o f a c o u s ti c t h i n - b e d s l o wn e s sa n a l y s is . Th e a p p l i c a t i o n s o f th e t wo m e t h o d s t o t h i ng a s - b e d d e t e c t i o n wi l l b e d e s c r i b e d a n dd e m o n s t r a t e d w i t h f ie l d d a t a e x a m p l e s .T H E S T O N E L E Y W A V E M E T H O DTheoret ical founda t ion- Bo r e h o l e S t o n e l e y wa v e s i na p o r o u s f o r m a t i o n c a n b e m o d e l e d u s i n g B i o t ' sp o r o e l a s t i c wa v e t h e o r y ( Ro s e n b a u m , 1 9 7 4 ; Sc h m i t te t a l , 1988; Winkler , 1989; Tang e t a l . , 1991) . Nor r i s( 1 9 8 9 ) d e m o n s t r a t e d t h a t , f o r a p o r o u s r o c k o f g i v e np e r m e a b i l i t y a n d p o r o s i t y , t h e S t o n e l e y wa v ea t t e n u a t i o n a n d d i s p e r s i o n d e p e n d c r i t i c a l l y o n t h epore f lu id (or sa turant ) proper t i es , i . e . , v i scos i ty andc o m p r e s s i b i l i t y . ( Th e v i s c o s i t y e f f e c t c a n b ee x p r e s s e d u s i n g f l u i d m o b i l i t y , d e f i n e d a s' p e r m e a b i l i t y / v i s c o s i t y ' . ) Th e e f f e c t s o f p o r e f l u i da r e d e m o n s t r a t e d i n F i g u r e 2 , wh e r e t h e S t o n e l e ywa v e a t t e n u a t i o n ( F i g u r e 2 a ) a n d v e l o c i t y d i s p e r s i o n( F i g u r e 2 b ) i n a p o r o u s f o r m a t i o n ( s e e p a r a m e t e r s i nTa b l e I ) a r e c a l c u l a t e d f o r wa t e r - a n d g a s - s a t u r a t i o nc a s e s . ( Th e b o r e h o l e h a s a r a d i u s o f 0 . 1 m a n d i sf i l l e d wi t h wa t e r . ) Th e a t t e n u a t i o n i s e x p r e s s e d i nt e r m s o f t h e i n v e r s e q u a l i t y f a c t o r Q , a n d t h ev e l o c i t y i s n o r m a l i z e d t o b o r e h o l e f l u i d a c o u s t i cv e l o c i t y ( 1 5 0 0 m / s ) . Fo r t h i s m o d e r a t e l y l o wp e r m e a b i l i t y f o r m a t i o n , t h e wa t e r - s a t u r a t i o n c a s ep r o d u c e s a m i n i m a l e f f e c t o n t h e S t o n e l e ya t t e n u a t i o n a n d d i s p e r s i o n , a s c o m p a r e d t o t h e n o n -p e r m e a b l e c a s e ( z e r o a t t e n u a ti o n in F i g u r e 2 a a n dd a s h e d c u r v e i n F i g u r e 2 b ) . I n c o n t r a s t , t h e g a ssa tura t ion resul t s in a s igni f i cant drop in Stone leyv e l o c i t y a n d d r a m a t i c i n c r e a s e i n a t t e n u a ti o n . Th ed r a s t i c a l l y d i f f e r e n t S t o n e l e y wa v e c h a r a c t e r i s t i c sb e t we e n t h e t wo s a t u r a n t f lu i d s c a n c a u s e s i g n i f i c a n tS t o n e l e y wa v e r e f l e c t i o n a t t h e g a s - wa t e r c o n t a c t o ra t a th in gas bed in a format ion .

At t h e i n t e r f a c e b e t we e n t wo f o r m a t i o n s ( o n e wi t h ,a n d a n o t h e r wi t h o u t , g a s s a t u r a t i o n , a s d e n o t e d b ysubscr ip t s , g and O, respec t ive ly) , the re f l ec t ion of al o w- f r e q u e n c y S t o n e l e y wa v e i s g i v e n b y ( W h i t e ,1 9 8 3 )

r - 2 , ( 1 )kg + k o

wh ere r i s the re f l ec t ion co ef f i c ient and I II Id e n o t e st a k i n g t h e m o d u l u s v a l u e o f a c o m p l e x e x p r e s s i o n o rq u a n t i t y ; k i s t h e S t o n e l e y wa v e n u m b e r , wh i c h , i n ap e r m e a b l e f o r m a t i o n , i s a c o m p l e x q u a n t i t y g i v e n b y

O) O)k = ~ + i , (2 )V s r ( c o ) 2 O ( c o ) Vsr ( c o )w h e r e V s r ( W ) a n d Q ( c o ) a r e t h e S t o n e l e y - w a v ep h a s e v e l o c i t y a n d q u a l i t y f a c t o r a s a f u n c t i o n o ff r e q u e n c y ( s e e e x a m p l e s i n F i g u r e s 2 a a n d b ) , wh i c ha r e c o n t r o l l e d b y f o r m a t i o n p e r m e a b i l i t y , p o r o s i t y ,a n d p o r e f l u i d p r o p e r t y . Th e s i g n i f ic a n t l y d i f f e r e n tv e l o c i t y a n d Q v a l u e s b e t we e n g a s a n d wa t e rsa tura t ion s i tua t ions resul t in the d i f fe rence be tweenkg and k 0 in equ a t ion (1) , g iv ing r i se to Stone leywa v e r e f l e c t i o n a t t h e in t e r fa c e . F i g u r e 2 c s h o ws t h eref lec t ion coef f i c ient (dashed curve) for the in te r facea t t h e g a s - w a t e r c o n t a c t.In the case of a th in , gas -sa tura ted format ion l ayer ,r e f l e c t i o n o c c u r s a t t h e l o we r a n d u p p e r l a y e ri n t e rf a c e s . T h e t o t a l re f l e c ti o n c a u s e d b y t h e l a y e r i sg i v e n b y ( Ta n g a n d Ch e n g , 1 9 9 3 ) :

I" = 2 i (k 2 - k ~ ) s i n ( k g L )( k g + k o ) 2 e - ik `L - ( k g - k o ) 2 e ik~L ' ( 3 )wh e r e L i s t h e l a y e r t h i c k n e s s . I t c a n b e s h o wn t h a tt h e Ta n g a n d Ch e n g ( 1 9 9 3 ) r e s u l t i n e q u a t i o n ( 3 )r e d u c e s t o t h e W h i t e ( 1 9 8 3 ) r e s u l t i n e q u a t i o n ( 2 ) i nt h e l i m i t a s L - - - > ~ . Fi g u r e 2 c s h o ws t h e r e f l e c t i o ncoef f i c ient curve ( so l id curve) for a gas-sa tura tedlayer of 0 .1524 m (0 .5 f t) th ickness . Th e th in- layercurve osc i l l a tes a round the s ingle- in te r face curve ,i n d i c a t i n g t h e i n t e r f e r e n c e b e t we e n t h e r e f l e c t i o n sf r o m t h e u p p e r a n d l o we r l a y e r i n t e r f a c e s . W h e n t h el a y e r t h i c k n e s s i s a b o u t a q u a r t e r wa v e l e n g t h o f t h eS t o n e l e y wa v e , t h e t wo r e f l e c t i o n s t e n d t o a d dc o n s t r u c t i v e l y , p r o d u c i n g a h i g h e r r e f l e c t i o na m p l i t u d e ( e . g . , t h e m a x i m u m a r o u n d 1 . 2 k Hz ) .W h e n t h e l a y e r t h i c k n e s s i s a b o u t h a l f o f t h ewa v e l e n g t h , t h e t wo r e f l e c t i o n s t e n d t o c a n c e l ,resul t ing in a smal le r re f l ec t ion ampl i tude ( see the


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min imum a round 3 .8 kH z ) . H ow e ve r , t hecance l la t ion wi l l not be comple te because theampli tude of the upper re f lec t ion is a t tenua ted (seea t tenua t ion in Figure 2a) f rom t rave l ing through thelayer . Based on the above e labora t ion , i t can beconcluded tha t a th in gas bed in the format ion canproduce a s ignif icant Stone ley wave re f lec t ionbe c a use o f i t s h igh f lu id mob i l i t y a ndc ompre ss ib i l i t y c on t ra s t t o t he su r round ingformat ion. T he re f lec t ion is fur ther enhanced w henthe bed th ickness is on the order of a quar te r of theS tone le y w a ve le ng th . (Fo r a t yp ic al S tone le yve loc i ty o f a bou t 3 5 0 0 - 5000 ft /s a nd a c e nte rf r e que nc y o f 1 kH z , t he qua r t er w a ve le ng th i s a bou t0 .8 - 1 .25 f t , which can be re la ted to the resolut iono f t he th in -be d s low ne ss a na ly s i s t o be de sc r ibe dlater.)Synthet ic waveform examples- To de mons t ra t e t hein f lue nc e o f a t h in ga s be d on S tone le y w a ve fo rmcharac te r is t ics , Figure 3 shows the synthe t icS tone le y w a ve fo rms a c ross a t h in be d in t e rva l(L=0.1524m, or 0 .5f t ) . The ca lcula t ions a re made forwater (Figure 3a) and gas (Figure 3b) sa tura t ioncases, respec t ive ly . The waveforms are ca lcula tedfor a f ixed source- to-rece iver offse t of 12 .5 f t on anacoust ic tool . The waveform center f requency is 1 .5kH z . A c ous t i c l ogg ing i s s imu la t e d by mov ing thetool f rom 25 f t be low, to 35 f t above , the bedinte rva l . Because water sa tura t ion produces onlymin ima l c ha nge s on S tone le y w a ve a t t e nua t ion a ndve loc i ty fo r t h i s mode ra t e ly low pe rme a b i l i t yfo rma t ion ( se e F igu re s 2a a nd b ) , no me a su ra b leref lec t ions can be observed in Figure 3a . In contrast ,replac ing water wi th gas for the same bed in te rva lproduces qui te s ignif icant Stone ley wave re f lec t ionevents . The re f lec t ion events a re designa ted as adow n-go ing w a ve , ge ne ra t e d w he n the too l i s be lowthe be d , a nd a n up -go ing w a ve , ge ne ra t e d w he n thetool i s above , the bed in te rva l . The dow n- and up-going re f lec t ion waves form a "chev ron" pa t te rn , asi s c ommonly obse rve d in f i e ld a c ous t i c l ogg ingwaveform da ta . I t can a lso be seen tha t the or ig in ofthe down-going re f lec t ion is a t the bed loca t ion . Theo r ig in o f t he up -go ing w a ve i s o f f se t f rom the be dloca t ion by the source- to-rece iver d istance . Thismode l ing e xa mple show s tha t S tone le y -w a veref lec t ion da ta can be used to de tec t /charac te r ize th ingas beds in format ions.Stoneley-wave data processing- Fie ld S tone le y w a vedata a re processed using a wavefie ld separa t ionprocedure (Tang, 1996) in order to ana lyze theref lec t ion events present in the da ta . This proceduresepara tes the Stone ley-wave da ta in to t ransmit ted ,down-going re f lec ted , and up-going re f lec ted , wave

S P W L A 4 2 "d A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 -2 0 , 20 0 1data . Examp les of the la t te r two re f lec ted wav e da tawil l be show n respec t ive ly in Figures 5 and 6 . Afte rthe wave separa t ion , var ious re f lec t ion events in theda ta can be c lear ly t raced to the i r or ig in a t thebo re ho le . The me r i t o f t he w a ve -se pa ra t ion me thodis tha t i t p icks up a lmost a l l re f lec t ion events , la rgeand smal l , in the da ta . How ever , in te rpre t ing thecause of the re f lec t ion events i s a formidable taskbe c a use ma ny o the r f a c to r s , suc h a s bo re ho lechanges (e .g . , washouts/ rugosi ty) and l i thologica lboundaries, e tc . , a lso cause the Stone ley-wavere f le c t ion . N ume r i c a l mod e l ing i s u se d to r e duc e thea mbigu i ty in t he in t e rp ret a t ion (G e l in sky a nd T a ng ,1997) . The model ing can rea l is t ica l ly s imula te theS tone le y w a ve p ropa ga t ion to a c c oun t fo r t hebo re ho le a nd fo rma t ion c ha nge s a long the w a vepath , provided tha t these changes, as input f rom thelog da ta (e .g . , borehole ca l iper , shear andc ompre ss iona l s low ne ss , a nd de ns i ty logs ) , a reaccura te . In prac tice , however , because o f theresolut ion l imi ta t ion of the log da ta , sharp boreholea nd fo rma t ion c ha nge s a re o f t e n sme a re d a nd themode le d re f l e c t ion ma gn i tude t e nds to beunderest imated. In th is regard , combiningin fo rma t ion f rom o the r me a su re me n t s p rov ide s ause fu l t oo l fo r r e duc ing the a mb igu i ty a ndenhancin g the re l iabi l i ty of the in te rpre ta t ion . Thethin-bed slowness ana lysis , to be descr ibed be low, isa me thod tha t c a n be c ombine d w i th the S tone le y -wave re f lec t ion method for the th in gas beddetec t ion problem.T H E T H I N -B E D S L O W N E S S M E T H O D

Effect o f gas saturation on slowness- Forma t ion ga ssa tura t ion can signif icant ly change the P-waveslowness and can thus be de tec ted using thes low ne ss me a su re me n t . The s low ne ss c ha nge c a n bep re d ic t e d by G a ssm a nn ' s equa t ion

K - K a 4 ( 1 - K a / K~ )2O / K y + ( 1 - 0 ) / K ~ - K d / K 2 ' (4 )w he re K i s t he roc k bu lk modu lus , K s i s t he modu luso f t he roc k g ra in , Ka i s t he bu lk modu lus o f t he d ryrock, 0 is the porosi ty , and K i s t he modu lus o f t hepore f lu id . The e ffec t of pore-f lu id sa tura t ion on P-wave ve loc i ty is ca lcula ted by

Ve - ~ / (K + 4 # / 3 ) / p , (5 )wh ere p is the rock densi ty ; and /z i s the shearmodu lus tha t i s a ssume d una f fe c t e d by po re f lu id .For the acoust ic parameters used to ca lcula te Figures2 and 3 (see Table I ) , replac ing the K va lue o f w a te r


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S P W L A 4 2 "a A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 - 2 0 , 2 0 0 1

with tha t of gas can produce a 10% decrease in theP-wave ve loc i ty (or increase in s lowness) . This gas-induc e d c ha nge w i l l be more p ronounc e d fo r h igh -po ros i ty roc ks . A l though the p re se nc e o f ga s info rma t ions c a n s ign i f i c a n t ly inc re a se the P -w a veslowness va lue , de tec t ing th is e ffec t in th in gas bedsposes a problem. The problem is tha t , i f the layerth ickness is smal l compared to the rece iver a rrayaperture (see Figure 1) , i t i s d i f f icul t to de tec t thes low ne ss c ha nge f rom the s low ne ss log ob ta ine dusing a convent iona l a rray technique ( i .e . ,semblance , see Kimbal l and Marzze ta , 1986) . Thethin-bed slowness ana lysis offe rs a so lu t ion to th isp rob le m.Enhancing s lowness resolut ion- E n h a n c i n gre so lu t ion o f s low ne ss e s t ima te s f rom a n a r ra yacoust ic tool i s to u t i l ize over lapping subarraysa c ross t he sa me de p th in t e rva l w hose th i c kne ss i sequa l to the subarray aper ture . At some par t icula rdepth during logging, the acoust ic source on the toolis ac t iva ted and an a rray ( typica l ly e ight rece ivers)o f w a ve fo rm da ta i s r e c o rde d . Th i s p roc e du re i srepea ted whi le the tool i s pul led up a d istance equa lto one in te r-rece iver spac ing ( typica l ly 0 .5 f t ) .Consequent ly , the rece iver a rrays a t successivesource loca t ions a re over lapped. The th in-bedslowness ana lysis (Zhang e t a l . , 2000) usesre dunda n t i n fo rma t ion in ove r l a pp ing a r ra ys toimprove bo th the ve r t i c a l r e so lu t ion a nd thea c c u ra c y o f t he fo rma t ion a c ous t i c s low ne sse s t ima t ion . F igu re 4 show s tw o c o mm only u se ddata-ga ther ing configura t ions for an e ight-rece iverarray-acoust ic tool , where the subarray rece iversused in the da ta ga ther a re h ighl ighted . Thec on f igu ra tion in F igu re 4a ha s the h ighe s t r e so lu tionwith the processing aper ture equa l to the in te r-rece iver spac ing (0 .5 f t ) in the rece iver a rray . Thec on f igu ra tion in F igu re 4b ha s a p roc e ss ing a pe r tu reof 1 f t . Whether to use the 0 .5- or 1-f t aper turedepend s on a va l id i ty condi t ion , as wi l l be descr ibedlater.A pa i r -w i se w a ve fo rm inve r s ion sc he me i s u se d toop t imiz e the ma tc h be tw e e n the w a ve fo rm pa i r sacross the common depth in te rva l . For the 0 .5-f t -aper ture configura t ion ( two-rece iver subarray) , eachw a ve fo rm i s ma tc he d tw ic e , onc e by sh i f t i ng thew a ve fo rm i t se l f a nd a no the r by sh i f ti ng the o the rwaveform, across the same depth in te rva l .A l toge the r t he re a re 14 w a ve fo rm pa i r s a nd 28 t ime so f r e pe a te d w a ve fo rm usa ge fo r t he 0 .5 - f t -a pe r tu reconfigura t ion . Simila r ly , there a re to ta l 36 waveformpa i r s a nd 54 t ime s o f r e pe a te d w a ve fo rm usa ge fo rthe 1-f t -aper ture configura t ion . This techniquethe re fo re u t i l i z e s t he ma x imum poss ib l e numbe r o f

w a ve fo rms to ma x imiz e the r e dunda nc y o finformat ion for est imat ing the slowness over theprocessing aper ture . This method substant ia l lyenhances the resolut ion of the slowness prof i le asc omp a re d to the c onve n t iona l a r ra y p roce ss ing .Validity condition- The val id i ty of the th in-beds low ne ss ha s be e n ve r i f i e d by va r ious e xa mple s(Zhang e t a l . , 2000) wi th exce l lent resul ts . However ,t he re mus t be a l im i t be yond w h ic h the th in -be dme thod w i l l be c ome inva l id . (O bv ious ly , t h i sme thod c a n no t be a pp l i e d to w a ve s w i th ve ry longw a ve le ng ths . ) The va l id ity c ond i t ion fo r t h is me thodis tha t the processing aper ture ( i .e . , 0 .5 f t or 1 f t , asin Figure 4) should be no less than a quar te r of thewavelength for the acoust ic wave used (e .g . ,com pressio na l or (d ipole) shear waves) . A physica lexplana t ion for th is condi t ion is tha t , for the wave tobe st i l l recognizable as an osc i l la t ing wave across anobserva t ion in te rva l ( i .e . , the processing aper ture) ,the in te rva l must be grea te r than a quar te r of thewavelength . For the 0 .5-f t -aper ture , th is condi t ion issa t isf ied for most of the logging si tua t ions,espec ia l ly for P-wave da ta . (For example , for a 10kHz P-wave with a ve loc i ty of 10 ,000 f t / s , i t squar te r wavelength is 0 .25 f t , which is smal le r than0.5 f t . ) This condi t ion may occasiona l ly be v io la tedw i th low - f re que nc y d ipo le w a ve s w he n us ing the0.5-f t -aper ture configura t ion . In th is case , the 1-f t-aper ture configura t ion , as in Figure 4b, should beused.The th in -be d s low ne ss me thod c a n de t e c t s low ne sschange s over a th in gas-bed in te rva l . Th e gassa tura t ion wi th in the bed can a lso cause a substant ia lS tone le y -w a ve re f l e c t ion . The c ombina t ion o f t hetw o me thods , t he re fo re , p rov ide s a be t t e r a nd morere l iable approach for the acoust ic de tec t ion of th inga s be ds in fo rma t ions . Th i s w i l l be de m ons t ra t e d inthe fo l lowing f ie ld da ta examples.

F I E L D A P P L I C A T I O N E X A M P L E SHigh porosity gas beds- The th in -be d s low ne ssana lysis and the Stone ley wave re f lec t ion processingme thods w e re u se d to e va lua t e a h igh po ros i ty ,lamina ted gas reservoir . Figure 5 shows the ana lysisresul ts , toge ther wi th o ther log da ta to support there su lt s . Tra c k 1 o f t h i s f igu re show s the ga mm a - ra ycurve , w hich exhibi ts the lamina ted fea tures of thefo rma t ion . The c ompre ss iona l -w a ve da t a u se d fo rthe slowness ana lysis a re show n in t rack 4 . (Thep re se nc e o f ga s c a n be se e n by the s t rong a mpl i tudea t tenua t ion in the waveform da ta .) The da ta was f i rs tp roc e sse d u s ing the c onve n t iona l a r ra y t e c hn ique ,g iv ing the dashed slowness curve in t rack 2 .


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S P W L A 4 2 "d A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 -2 0 , 20 0 1

B e c a use o f t he l a c k o f r e so lu tion in th i s s low ne sscurve , the increase of the P-wave slowness acrossthe reservoir was over looked. The acoust icw a ve fo rm da ta w e re r e p roc e sse d u s ing the th in -be da na lys i s me thod w i th the 0 .5 f t -p roc e ss ing a pe r tu re(Figure 4a) . The resul t (so l id s lowness curve in t rack2) drast ica l ly enhances the resolut ion of theslowness prof i le , revea l ing the lamina ted fea tures ofthe reservoir . The drast ic increase of the P-waveslowness over a th in depth in te rva l indica tes thepresence of a gas-sa tura ted th in bed. Despi te thedrast ic var ia t ions on the th in-bed slowness curve , i t sde r ive d t r a ve l t ime c u rve t r a c ks the w a ve fo rm da taqui te wel l ( t rack 4) , g iv ing qua l i ty contro l andval ida t ion for the h igh-reso lut ion slown ess curve .The va l ida t ion is a lso confi rmed by the densi tycurve shown in t rack 2 ( le f t curve) . The densi ty inth is h igh porosi ty reservoir c lear ly shows thepresence of gas, a drop in densi ty corresponding toga s in p l ac e . B e c a use the de ns i ty me a su re me n t ha s acomparable depth resolut ion (on the order of 1 f t ) ,the densi ty fea tures can be d i rec t ly corre la ted wi ththose on the th in-bed slowness curve . Indeed, asharp decrease in densi ty is genera l ly correspondedto a sharp increase in s lowness, indica t ing thepresence of a th in gas bed in format ion.The monopo le da t a w e re f i l t e re d to ob ta in S tone le yw a ve da t a a round 1 kH z . Th e w a ve se pa ra tionprocessing was appl ied to separa te the da ta in tot r a nsmi t t e d , dow n-go ing re f l e c t e d a nd up -go ingref lec ted , waves. Display ed in track 3 a re the up-going re f lec ted Stone ley wave da ta , which is sh i f teddown by a d istance equa l to the source- to-rece iverspac ing (see Figure 319) to correspo nd to the loca t ionof format ion/borehole re f lec tors . Many re f lec t ionevents can be ident i f ied across the reservoir in te rva l ,as indica ted by a rrows in t rack 3 . The bot tomre se rvo i r se c t ion show s the bo re ho le w a shou t(X 780-X 840 m, a s c a n be se e n f rom the c a l ipe rc u rve ve r sus b i t s i z e ) . Th i s c a use s some a mbigu i tyin re la t ing the re f lec t ion events to th in gas beds.The upper sec t ion , where the borehole is in goodshape , shows m any re f lec t ion events tha t a reevident ly re la ted to the th in bed loca t ions ident i f iedfrom the th in-bed slowness prof i le .The re su l t show n in F igu re 5 c l e a r ly de mons t ra t e stha t gas sa tura t ion in th in beds increases the P-waveslowness and genera tes Stone ley-wave re f lec t ion ,g iv ing a good confi rmat ion of the above theore t ica lana lyses. A drawba ck of th is exam ple is tha t theS tone le y -w a ve re f l e c t ions se e m una b le to r e so lveeach individua l th in bed, as ident i f ied by the th in-bed slowness ana lysis . This i s in par t due to the poorS tone le y da t a qua l i t y c a use d by the s t rong

at tenua t ion in the gas format ion, and in par t due tothe fac t tha t the beds a re c lose ly spaced. Thefo l low ing e xa mple show s a be t t e r c o r re sponde nc ebetween the Stone ley and th in-bed slowness resul ts .Gas-saturated sand-shale sequence- W he n the ga s -induced slowess change is s t rong, the P-waveslowness a lone suff ices to indica te the gas e ffec t , asis the case for the h igh porosi ty gas example shownin Figure 5 . However , in many si tua t ions, such assand-sha le sequences, the gas- induced changes a recoupled wi th l i thology changes. In th is case , the useo f t he V p /V s ra t io , i n s t e a d o f P -w a ve s low ne ss , i nc ombina t ion w i th the S tone le y -w a ve a na ly s i s , ma yprovid e a be t te r gas indica t ion . This i s because , apo rous roc k sa tu ra t e d w i th ga s w i l l ha ve ac ons ide ra b ly low e r P -w a ve ve loc i ty tha n the sa merock sa tura ted wi th water , whi le the S-wave ve loc i tyis re la t ive ly insensi t ive to the gas sa tura t ion . Bytaking the Vp/Vs ra t io , the gas e ffec t s tands outre la t ive to the l i thologica l var ia t ion . As a resul t , ac ha nge in the V p /V s ra t io w i l l be more ind ic at ive o fthe pore f lu id e ffec t than the l i thologica l e ffec t.The e xa mple in F igu re 6 i s f rom a fo rma t ionconta in ing gas-sa tura ted , lamina ted gas-sha lese que nc es . Tra c k 1 show s the ga mma ra y a ndca l iper curves. The Stone ley -wave re f lec t ion(down-going) da ta a re d isplayed as a var iabledensi ty image in t rack 2 . The Stone ley re f lec t iondata a re of good qua l i ty wi th d iscernable individua lre f lec t ion events . The Vp/Vs ra t io in the same t rackis sca led from 1.2 to 2 , r ight to le f t , to approxim ate lyoverlay the curve wi th the or ig ins of the re f lec t ione ve n t s . Tra c k 3 show s mode le d S tone le y -w a veref lec t ion da ta and the P- and S-wave slownesscurves. The slowness curves were obta ined byp roc e ss ing , r e spe c t ive ly , t he monopo le a nd d ipo lea c ous t i c a r ra y da t a u s ing the th in -be d me thod w i ththe 0 .5-f t -aper ture (see Figure 4a) . The P- and S-w a ve s low ne ss c u rve s a re d i sp l a ye d f rom 80 to 360kts/ f t , le f t to f ight , to a l low for the d isplay of themode le d S tone le y w a ve da t a . The S tone le y -w a vemode l ing u se s the me thod de sc r ibe d in G e l in sky a ndTang (1997) , using the slowness curves and theca l iper curve ( t rack 1) as the input . This mod el ingcan he lp ident i fy Stone ley-wave re f lec t ions tha t a rec a use d by l i t ho logy a nd bo re ho le c ha nge s .The re su l t s show n in F igu re 6 c a n now beinte rpre ted . The Vp/Vs ra t io curve in t rack 2 showsma ny loc a l ly low a nd h igh va lue s . S inc e ga ssa tura t ion causes the Vp/Vs ra t io to drop, theloc a t ion w i th a l ow V p /V s ra t io va lue ma ypotent ia l ly be a gas bed. How ever , one can notexc lude tha t these low va lues a re not caused by


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S P W L A 4 2 "d A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 -2 0 , 2 0 0 1

l i tho log ic a l c ha nge s . C onf i rma t ion f rom S tone le yw a ve a na ly s i s c a n he lp r e duc e th i s unc e rt a inty . Th eme a su re d S tone le y r e f l ec t ion da t a i n t r a ck 2 show smore , a nd s t ronge r , e ve n t s t ha n the mod e le d da t a i nt rack 3 , suggest ing tha t the re f lec t ions a re morere la ted to gas-sa tura t ion than to l i thologica l e ffec ts .M ore in te rest ing , mos t Stone ley re f lec t ion eventso r ig ina t e f rom de p ths w he re the V p /V s ra t io c u rveshows 0oca l ly) low va lues (- - 1 .6-1 .7) . Since gassa tura t ion causes the Vp/Vs ra t io to drop, the lowVp/Vs-ra t io depth in te rva l wi th a re f lec t ion event i smost l ike ly the loca t ion of gas zones. Therefore , i tc a n be c onc lude d tha t t he ga s p roduc t ion fo r t hede p th r a nge show n in F igu re 6 c ome s mos t ly f romthe loc a t ions ind ic a t e d by low V p /V s ra t io a nd theStone ley re f lec t ion .Gas-pockets in heavy-oi l sand- Find ing l i gh thyd roc a rbons in he a vy -o i l r e se rvo i rs i s impor t a n t fo rre c ove ry e nha nc e me n t , be c a use i t p rov ide sin fo rma t ion fo r r e se rvo i r e ng ine e r ing / t r e a tme n tl e a d ing to p roduc t ion / re c ove ry op t imiz a t ion . Thel igh t hyd roc a rbons o f t e n e x i s t a s ga s poc ke t s i nhe a vy -o i l fo rma t ions . The c on t ra s t be tw e e n ga s a ndheavy oi l genera tes acoust ic responses tha t can bede te c te d u s ing the a bove -me n t ione d t e c hn ique s .F igu re 7 i s a n e xa mple o f de t e c t ing l i gh thyd roc a rbons in a he a vy -o i l sa nd c ompa r tme n t . Thefo rma t ion i s a h igh po ros i ty ( -30%) t a r sa nd w i th ave ry he a vy o i l . T ra c k 1 show s the ga mma ra y a ndc a l ipe r c u rves . The ga m ma - ra y c u rve show s tha t t here se rvo i r sa nd i s f a i r ly homoge ne ous , w i thou tsignif icant l i thologica l var ia t ions. The ca l iper curveshow s tha t t he bo re ho le i s i n f a i r ly good sha pe .Ta c k 2 show s the P - a nd S -w a ve s low ne ss c u rve sacross the reservoir sand. The slowness curves werep roc e sse d f rom the monopo le a nd d ipo le a c ous t i ca r ra y da t a u s ing the th in -be d me thod w i th the 0 .5 - f tprocessing aper ture . I t i s noted tha t the slownessc u rve s in t he uppe r po r t ion o f t he sa nd e xh ib it morevaria t ions than the low er port ion . I t i s a lso noted th a tthe P - s low ne ss c u rve , c ompa re d to the S - s low ne ssc u rve , show s more h igh -va lue f e a tu re s . The V p /V sra t io c u rve c ompu te d u s ing the P - a nd S - s low ne sscurves in t rack 2 , toge ther wi th the Stone ley-waveref lec t ion (down-going) image , i s shown in t rack 3 .The V p /V s ra t io i s sc a l e d f rom 0 .5 to 2 .5 , r i gh t t ole f t , to a l low for corre la t ing the curve fea tures wi ththe o r ig in s o f the r e f l e ct ion e ve n t s . The low V p /V sra t io va lue fea tures, as wel l as the h igh-slownessevents on the P-slowness curve , exhibi t a th in- layerbehavior . Indeed, these th inlayer fea tures/eventscorre la te wi th the Stone ley-wave re f lec t ion eventsvery wel l . Thes e re f lec t ion events could not becaused by the ca l iper and shear ve loc i ty var ia t ions

shown in t racks 1 and 2 , for the modeled re f lec t iona mpl i tude s (no t show n) a re a n o rde r o f ma gn i tudesmal le r than those shown in t rack 3 . Thesefea tures/events , as seen from the slowness andStone ley wave da ta , therefore , correspond to th inga s poc ke t s i n t h i s he a vy -o i l sa nd c ompa r tme n t .The y c a n be jo in t ly loc a te d by the low V p /V s ra t io(or h igh P-slowess) events and by t rac ing the or ig inof the Stone ley re f lec t ion events .C O N C L U S I O N SA thin gas-sa tura ted layer in a format ion cans ign i f i c a n t ly inc re a se the l a ye r ' s c ompre ss iona l -w a ve s low ne ss a nd p roduc e a me a su ra b le S tone le y -wave re f lec t ion . These acoust ic responses a rethe o re t i c a l ly mode le d a nd ha ve be e n c on f i rme d byfie ld observa t ions. The slow ness change in the th inlayer can be resolved using a th in-bed slownessana lysis , and the Stone ley-wave re f lec t ion can beob ta ine d u s ing a w a ve se pa ra t ion me thod . Jo in tin te rpre ta t ion of the resul ts of these twome a su re me n t s o f fe r s a more r e l i a b l e a nd robus tapproac h to th in gas- layer de tec t ion . Spec if ica lly , ath in gas layer can be ident i f ied as a h igh-va lue ( low-va lue ) e ve n t on the h igh - re so lu tion P -w a ve s low ne ss(Vp/Vs ra t io) prof i le . The layer can a lso be loca tedby the o r ig in o f t he S tone le y w a ve re f l e c t ion . Thea g re e me n t be tw e e n the tw o re su l t s e nha nc e s there l iabi l i ty of the de tec t ion . This appro ach has beensuccess ful ly appl ied to de tec t th in gas layers in h igh-porosi ty gas sand, sand-sha le sequences, and heavy-oi l format ions.A C K N O W L E D G E M E N T SW e tha nk Me t t e Munkho lm a nd Ma ss i e l R a nge l fo rthe i r par t ic ipa t ion in the da ta ana lyses and handl ing.W e a l so tha nk B a ke r A t l a s fo r pe rmiss ion to pub l ishth is paper .


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SPW LA 42 nd Ann ua l Logging S ympo s ium, Ju ne 17-20 , 2001R E F E R E N C E S

Brie, A., Pumpuri, F., Marsala, A. F., and Meazza,O., 1995, Shear sonic interpretation in gas-bearingsands: 1995 SPE annual technical conference andexhibition, Paper 30595.Gelinsky, S., Tang, X. M., 1997, Fast forwardmodel ing of Stoneley waves for i r regular boreholesand heterogeneous formation: 67th Ann. Intern.Mtg., Soc. Explor. Geophys., Expanded Abstracts,Dallas, TX.

Winkler, K. W., Liu, H. L., and Johnson, D. L.,1989, Permeability and borehole Stoneley waves:Comparison between experiment and theory:Geophysics, 54, 66-75.Zhang, T., Tang, X. M., Patterson, D., 2000,Evaluation of laminated thin beds in formationsusing high-resolution acoustic slowness logs, paperXX, in 41st Annual Meeting Transactions: Societyof Professional Well Log Analysts, Dallas, Texas.

Kimball, C. V., and Marzetta, T. L., 1986,Semblance process ing of borehole acoust ic arraydata: Geop hysics, 49, 274-281.Norris, A. N., 1989, Stoneley-wave attenuation anddispersion in permeable formations: Geophysics, 54 ,330-341.Rosenbaum , J . H. , 1 97 4, Synthet icmicroseismograms: logging in porous format ions :Geophysics, 39, 14-32.Schmitt, D. P., and Bouchon, M., and Bonnet, G.,1988, Full-waveform synthetic acoustic logs, inradially semiinfmite saturated porous formations:Geophysics , 53, 807-823.Tang, X. M., Cheng, C. H., and Toksoz, M. N.,1991, Dynamic permeabi l i ty and borehole Stoneleywaves: A simplified Biot-Rosenbaum model: J .Acoust. Soc. Am ., 90, 1632-1646.Tang, X. M., and Cheng, C. H. , 1993, BoreholeStoneley wave propagat ion across permeablestructures: Geophysical prospecting, 41, 165-187.Tang, X. M., 1996, Fracture hydraulic conductivityes t imat ion from borehole Stoneley wavetransmission and reflection data, paper HH, in 37thAnnual Meet ing Transact ions : Society ofProfessional Well Log Analysts.

A B O U T T H E A U T H O R SXiaoming Tang is a senior s taff sc ient is t wi thin theHouston Technology Center for Baker At las / INTEQand is project leader for acoustic processing andinterpretation development. He received his Doctorof Science degree from the Massachusetts Instituteof Technology in 1990, and then worked as ascientist at New England Research, Inc., from 1990to 1994. He joined Bake r Atlas in 1994. H is currentinterests include borehole acoustics, petrophysics,and rock mechanics . H e has authored or co-authoredmore than 50 technical publications and ten patents.He i s member of SPWLA and SEG.Doug Pat terson is the Acoust ic Program Managerwithin the Houston Technology Center for BakerAtlas / INTEQ where he focuses on development ofboth wirel ine and LW D devices. Doug received hisB.S.M.E. from M emphis Univers i ty in 1 97 8 andbegan his career with Schlum berger. His careercontinued with Gearhart in 1981, holding positionsin both sales and technical marketing. Morerecent ly, Doug joined Acutec Logging Services in1992, where he focused extensively on thedevelopment of downhole equipment , process ingsoftware, and interpretation methods. He was withAcutec unt i l May of 1996 when the company wasacquired by Western Atlas Logging Services (nowBaker Atlas).

White, J . E., 1983, Underground sound, ElsevierScience Publ ishing Co mpany, Inc .Wil l iams, D. M., 1 99 0 , The acoust ic loghydrocarbon indicator: paper W, in 31th AnnualMeet ing T ransact ions : Society of Profess ional W ellLog A nalys ts.


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S P W L A 4 2 "d A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 -2 0 , 20 0 1

Vp ( m/ s ) Vs (m/s) /9 (g/cc) /7 (cp) ~b (pu) K" (md ) Ks (GPa )Roc k 3000 1800 2.5 - 0 .1 10 37.9Wa ter 1500 - 1 1 - - -Gas 340 - 0 .14 0.022 - - -T ab l e I . F or ma t i on and f l u i d pa r ame t e r s used i n ca l cu l a t i ng F i gur es 2 and 3 . T he pa r ame t e r s a r e P - and S - waveve l oc i ti e s , dens i t y , v i s cos i ty , por os i t y , pe r meab i l i t y , and r ock g r a i n modul us .

G a s b e dHigh f lu idm o b i l i t y a n dcompressib i l i t , .

I n c r e a s e i nP - s l o w n e s s

L _ .D T P

Figure 1. Aco ust ic log ging across a thin gas-saturated depth interval . The presen ce of gas increases thecompr es s i ona l ( P ) wave s l owness . T he h i gh f l u id mob i l i t y and com pr es s i b i l i ty o f the gas bed g i ve r is e t o aS t one l ey- wav e re f l ec ti on . T he s l owness o f t he gas bed is ana l yzed wi t h a t h i n - bed me t hod , whe n t he bedt h i ckness i s sma l l e r t han t he r ece ive r a r r ay ape r t u r e . T he S t one l ey r e f l ec t ion i s ana l yzed us i ng a wav e sepa r a t i onm e t h o d .


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S P W L A 4 2 "d A n n u a l L o g g i n g S y m p o s i u m , J u n e 1 7 -2 0 , 2 0 0 10 . 5

AO 0 . 4

= 0 .3o

= 0 . 2

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Thin Bed Analysis