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THE SPE I MAGE LI BRARY SPE 2983

Adj ust ment of Reser voi r Si mul at i on Model s To Mat chFi el d Per f or mance

2983

Sl at er , G. E. , andDur r er , E. J . , Member s AI ME,Gul f Research and Devel opment Co. , Pi t t sbur gh, PA.

Sept ember 1971

ABSTRACT

Numer i cal si mul at i on model s descr i bi ng f i el dbehavi or r equi r e r el i abl e est i mat es f or var i ousr eservoi r parameters whi ch cannot be measur eddi r ect l y. A t r i al - and- er r or pr ocedur e, l i near and

nonl i near r egr essi on anal ysi s on a r andom sear ch,and el ect r i c anal ogue comput at i on ar e pr esent l yused i n or der t o obt ai n t hese est i mat es. Theysuf f er ei t her f r om l engt hy comput at i on t i mes orf r om t he necessi t y to bui l d a physi cal model f oreach r eser voi r .

Thi s paper descr i bes a bal anced er r or - wei ght edgr adi ent met hod t hat syst emat i cal l y reduces t hedi f f er ence bet ween observed and cal cul at ed r eservoi rper f or mance dat a, t her eby l eadi ng t o a hi st or ymat ch. The scheme r esembl es cl osel y t he mechani calbal anci ng of an el ect r i c anal yzer once one hasdet er mi ned quant i t at i vel y t he i nt er f er encer el at i onshi ps bet ween t he i ndi vi dual wel l r egi ons.These r el at i onshi ps ar e f ound by changi ng t her eservoi r par amet er of each r egi on i n t ur n by aconst ant val ue, whi l e al l ot her r egi onal val uesremai n at t hei r base l evel . Then t he i nt er f er encer el at i onshi ps ar e or der ed i n mat r i x f or m. Thedi agonal el ement s of t hi s mat r i x yi el d t he gr adi ent sf or t he r egi onal r eser voi r par amet er val ues andt her eby t he di r ect i on of t he change necessar y t oobt ai n a r educt i on i n t he mat chi ng er r or . The

magni t ude of change i n each r egi on i s t akenpr opor t i onal t o t he r egi onal er r or . Such a wei ght i ngof t he gr adi ent s enabl es one t o cope wi t h t hei nt er f er ence.

Par t i cul ar car has t o be exer ci sed i n def i ni ngwhat component s const i t ut e t he i nf l uent i al r eser voi rpar amet er s of a f i el d. Case st udi es of oi l and gasf i el ds yi el ded i nf or mat i on f or choosi ng t hese.

Ther ef or e, t he pr oposed pr esent at i on wi l l consi stof a det ai l ed descr i pt i on of t he mat chi ng pr ocedur eand i t s appl i cat i on t o sever al r eser voi r s, as wel las gener al gui del i nes f or f i el d hi st or y mat chi ng.

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THE SPE I MAGE LI BRARY SPE 2983

I NTRODUCTI ON

The par t i al di f f er ent i al equat i on

. . ( 1)

wher ek = per meabi l i t yh = r eser voi r t hi ckness

= vi scosi t y= por osi t y

c = compr essi bi l i t yp = pressur ex

= space coor di natesyt = t i me

Q = i nj ect i on, or pr oduct i on r at edescr i bes t he pr essur e behavi or i n an oi l or gasr eser voi r . Fi ni t e- di f f er ence t echni ques, var i at i onal ,and f i ni t e- el ement methods can be used t o obt ai n anumer i cal sol ut i on t o Eq. 1 as no anal yt i calsol ut i ons are known f or t he condi t i ons t hatadequat el y descr i be a r eser voi r . Onl y i f a cel l orel ement happens t o cont ai n a wel l i s a r oughest i mat e of t he l ocal k and val ue known. . Sever alt i mes t hr oughout t he ent i r e l i f e of t he r eser voi r t hest at i c r eser voi r pr essur e may be measur ed at t hewel l s.

However , k and ar e onl y poi nt measur ement swhen compar ed t o t he over - al l r eservoi r si ze.Ther ef or , cal cul at ed and observed pr essurebehavi or wi l l r ar el y agr ee i f t hose k and val uesar e used i n t he comput at i on of Eq. 1. Usual l y t heymust be adj ust ed t o yi el d a mat ch bet ween the t wopr essur e behavi or s. Onl y t hen r el i abl e pr edi ct i onscan be made concer ni ng t he f ut ur e r eservoi rbehavi or .

I n t he past , t he r eser voi r was mor e or l essar bi t r ar i l y di vi ded i nt o a cer t ai n number of r egi ons.

SPEJ

p. 295

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