The Effects of Multiphase Flow on The

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THE SPE I MAGE LI BRARY SPE 15537

The Ef f ect s of Mul t i phase Fl ow on t heI nt er pr et at i on of Pr essur e- Bui l dup Test s

15537

Ayan, Cosan SPETexas A and M U.Lee, W. J . SPETexas A and M U.

J une 1988

Summar y. A t wo- di mensi onal ( 2D) , t hr ee- phase, var i abl e- bubbl epoi ntr eser voi r si mul at or was devel oped t o si mul at e pr essur e- bui l dup t est si nvol vi ng mul t i pl e phases. The si mul at i on i ndi cat ed t hat nonuni f or msat ur at i on di st r i but i ons t hr oughout t he dr ai nage ar ea can causeer r oneous i nt er pr et at i ons when si ngl e l i qui d- phase t echni ques, as

modi f i ed by t he Per r i ne- Mar t i n t heor y, ar e used f or t he anal ysi s.

I nt r oducti on

Pressure- t r ansi ent t est s have pr oved to be one of t he most usef ulmet hods t o obt ai n r el i abl e i nf or mat i on about a pr oduci ng f or mat i onand t he condi t i on of a wel l bor e. One of t he most commonwel l t est i ng t echni ques used i n pr act i ce i s t he pr essur e- bui l dupt est . I nt er pr et at i on t heor y i s usual l y based on anal yt i calsol ut i ons of t he r adi al di f f usi vi t y equat i on. The assumpt i ons made t o

der i ve t he r adi al di f f usi vi t y equat i on i ncl ude si ngl e- phase l i qui df l ow, smal l and const ant l i qui d compr essi bi l i t y, const antvi scosi t y, smal l pr essur e gr adi ent s, const ant and i sot r opi cper meabi l i t y, const ant por osi t y, and negl i gi bl e gr avi t at i onalf or ces.

Fr equent l y, more t han one phase f l ows bef ore and dur i ng apr essur e- bui l dup t est . One of t he most common t echni ques used t oanal yze mul t i phase pr essur e- bui l dup t est s i s t he met hod pr oposed byPer r i ne. He suggest ed usi ng si ngl e- phase t heor y t o anal yzemul t i phase t est s af t er r epl aci ng si ngl e- phase mobi l i t y andcompr essi bi l i t y of t he r eser voi r f l ui ds. Mar t i n l at er j ust i f i ed

Per r i ne' s appr oach on a t heor et i cal basi s. Hi s der i vat i on ofmul t i phase f l ow equat i ons assumes negl i gi bl e gr avi t at i onal f or cesand negl ect s t er ms cont ai ni ng pr oduct s of pr essure and satur at i ongr adi ent s. St udi es by Wel l er and Ear l ougher et al . i ndi cat e t hat t hesecond- order t erms can be negl ect ed.

The wor k per f or med by Per r i ne, West et al . , and Wel l er i ndi cat et hat a gas zone f or ms around t he wel l bor e i n sol ut i on- gas- dr i ver eser voi r s i ni t i al l y above sat ur at i on pr essur e. Wel l er r ef er r edt o t he r esul t ant per meabi l i t y reduct i on ar ound t he wel l bor e as apseudoski n. Kazemi , i n a st udy si mi l ar t o our s, i nvest i gat edt he ef f ect of t he gas bl ock on oi l pr oduct i vi t y and t he i nf l uence

of gas sat ur at i on gr adi ent s on pr essur e- bui l dup cur ves. Chu et al .


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al so anal yzed t he ef f ect s of sat ur at i on gr adi ent s on t r ansi entwel l t est s. I n t hei r st udy, t hey i nvest i gat ed t he l i mi t at i ons oft he Per r i ne- Mar t i n t heor y wi t h a t wo- phase r eser voi r si mul at or .They concl uded t hat i f sat ur at i on gr adi ent s exi st , t he i ndi vi dualphase mobi l i t i es can be comput ed f or onl y a l i mi t ed set ofcondi t i ons. Fet kovi ch pr oposed a pseudopr essure f unct i onsi mi l ar t o t he r eal gas pot ent i al def i ned by Al - Hussai ny et al .Thi s pseudopr essure f unct i on al so cont ai ns a pr essure- dependent

r el at i ve per meabi l i t y t er m. I n a l at er s t udy, Raghavandemonst r at ed t he cal cul at i on and use of t hi s pseudopr essuref unct i on f or drawdown and bui l dup anal ysi s. Aanonsen expl ai nedt he use of pseudot i me f or mul t i phase f l ow pr obl ems. He showedt hat , dur i ng t he i nf i ni t e- act i ng per i od, t he di f f er ence bet weensol ut i on- gas dr i ve and si ngl e- phase l i qui d behavi or i s smal l i fpseudopr essur e and pseudot i me are used i n t he anal ysi s. The paperby Raghavan cont ai ns an overvi ew of t he l i t eratur e and someexampl es of t he t echni ques used f or anal ysi s of wel l t est si nvol vi ng mul t i pl e phases.

I n t hi s st udy, we anal yzed pr essur e- bui l dup t est s i n

sol ut i on- gas- dr i ve r eser voi r s under goi ng gas evol ut i on. Wedevel oped a thr ee- phase, 2D, var i abl e- bubbl epoi nt r eser voi rsi mul at or t o si mul at e t he bui l dup t est s. One- di mensi onal ( 1D)r adi al f l ow was si mul at ed t o det er mi ne t he ef f ect s of r at e changesand di f f erent degr ees of damage ( i mpr ovement ) around t he wel l . Weanal yzed t he ef f ect s of gr avi t at i onal f or ces and pr oduci ng t i me i nl ayer ed r eser voi r s wi t h cr ossf l ow wi t h 2D si mul at i ons. The st udyi nvest i gated t he consequences of bubbl epoi nt pr essur e, whi ch changedwi t h pr oduct i on. The st udy al so consi der ed t he ef f ect s of par t i alpenet r at i on on pr essur e- bui l dup t est s dur i ng mul t i phase f l ow.

Bef or e pr essur e- bui l dup t est s i n sat ur at ed r eser voi r s wer esi mul at ed, we si mul at ed t est s f or t he cor r espondi ng under satur at edsyst ems. The ski n f act or val ues obt ai ned f r om t hese t est s wer econsi dered t o be t he t r ue val ues. We compared t hese val ues wi t h t heski n f act or obt ai ned f r om pr essur e- bui l dup t est s conduct ed bel owt he bubbl epoi nt pr essure, whi ch we anal yzed usi ng t he Per r i ne- Mar t i napproach.

Si mul at i on and Anal ysi s of Pr essur e- Bui l dup Test s

To anal yze t he ef f ect s of mul t i pl e phases on pr essur e- bui l dupbehavi or , we devel oped a 2D, t hr ee- phase r eservoi r si mul at or .

Some f or mul at i ons of t hese si mul at or s have sever e sat ur at i oni nst abi l i t i es near t he wel l bor e. To mi ni mi ze t hese i nst abi l i t i esi n our si mul at or , we t r eat ed pr oduct i on, i nt er bl ock t r ansmi ssi bi l i t y,and capi l l ar y pr essur e t er ms i mpl i ci t l y, si mi l ar t o t he f or mul at i onof Let keman and Ri di ngs. The si mul at or al l ows bubbl epoi nt pr essuret o var y t hr oughout t he r eser voi r t o si mul at e t he ef f ect s of adi sappear i ng gas phase dur i ng a shut - i n per i od. The bubbl epoi ntpr essure f or mul at i on f ol l ows t he concept s of Thomas et al .The si mul at or sol ves t he syst em of di f f er ence equat i ons f or oi lpr essur e, wat er , and gas sat ur at i ons/ sat ur at i on pr essur essi mul t aneousl y wi t h a band mat r i x sol ver .

The si mul at or negl ect s f l ow i n t he t ubi ng. However , t he


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wel l bor e i s model ed as a par t of t he r eser voi r gr i d syst em. Thi ssi mpl i f i cat i on al l owed us t o si mul at e t he ef f ect s of backf l owdur i ng f l owi ng or shut - i n per i ods. We al so i ncl uded wel l bor est or age by assi gni ng hi gh por osi t y val ues t o t he wel l bor e cel l s.The si mul at or model ed a si ngl e wel l l ocat ed at t he cent er of acl osed cyl i ndr i cal r eser voi r t hr oughout our st udy. The si mul at ormodel ed al t er ed zones ( damage or st i mul at i on) f or i ndi vi dual t est swi t h gr adual l y i ncr easi ng ( decr easi ng) per meabi l i t i es away f r om t he

wel l bor e. I n al l r uns, wat er sat ur at i ons wer e sl i ght l y above t hei r r educi bl e mi ni mum val ue. We used t he same set of f l ui d and r ockpr oper t i es i n al l si mul at ed t est s. Tabl e 1 summar i zes t he basi cr eser voi r descr i pt i on.

We pr epar ed l og- l og pl ot s of pws - pwf vs. / ( + ) ( seeRef . 23) f or al l t est s t o i dent i f y t he begi nni ng of t he semi l ogst r ai ght l i ne by mat chi ng t he type cur ves present ed by Gr i ngar t en etal . We used Homer pl ot s ( semi l og gr aphs) of shut - i n bot t omhol epr essur e ( BHP) vs. l og[ ( + ) / ) t o anal yze each si mul at ed t est .Pressures and satur at i ons i n each cel l wer e aver aged wi t h r espectt o t i me dur i ng t he t est and f ur t her aver aged vol umet r i cal l y at t he

end of t he t est t o est i mate val ues of average pr essur e and phasesat ur at i ons. These val ues wer e t hen used t o cal cul at e t ot alcompr essi bi l i t y. Fr om t he semi l og st r ai ght l i ne obt ai ned, ski nf act or and phase ef f ect i ve per meabi l i t i es wer e cal cul at ed wi t hPer r i ne' s appr oach.

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