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SSociety of Petroleum Engineers

675Skin ffects ue to Formation amageFines Migration

.A. Ohen, Core Laboratories Div. of Western Atlas IntI., and Civan, U of OklahomaE Members

Copyright 1991, Society of Petroleum Engineers, Inc.This paper was prepared for presentation at the Production Operations Symposium held in Oklahoma City, Oklahoma, April 7 9 1991.This paper was selected for presentat ion by an SPE Program Committee following review of information contained in an abstract submitted by the author s . Contents of the paper,as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correct ion by the author s . The material, as presented, does not necessarily ref lectany position of the Society of Petroleum Engineers, itsofficers, or members. Paperspresented at SPE meetingsare sUbject to publication reviewby Editorial Committeesof the Societyof Petroleum Engineers. Permission to copy is restricted to an abstractof not morethan 300words. Illustrations may not be copied. The abstractshould contain conspicuous acknowledgmentof where and by whom the paper is presented. Write Publicat ions Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL.

STR CTmong the important issues concerning for mation damage assessment and control s tudiesare to understand and describe ef fect ivelythe physicochemical and hydrodynamic fac torscont rol l ing near wellbore damage dur in g we lldevelopment and re servo i r explo it a ti on . Theproblem i s twofold. Firs t the mechanismsresponsible for formation damage requirecomplicated mathematical models. Secondi s d i f f i cu l t to s imu la te nea r wellbore flowcondit ions in a laboratory core flow t e s t .In a paper present ed prev ious ly ef for t

has been made by the authors to solve thef i r s t problem. The present work i s aimed a tproviding solutions to the second problem.Laboratory core d ata and the Ohen and C iv anmodel have been employed to determine theparameters tha t control formation damage forgive n r oc k f luids systems and operat ingcondit ions . A mathematical technique hasbeen developed to scale t he l abor at or yresponse to near we ll bo re condit ions-thereby simUlating th e a ctu al radia l flowcondit ions tha t exis t in the near wellboreregion. The radius and permeabil i ty of thedamaged zone are computed a s f un cti on s ofexposur e t ime of the zone of in te res t to thedamaging f lu ids . A fac tor herein re ferredto as the skin factor i s computed as a mea-sure of the overal l effec t of formation dam-age on p roduc ti vi ty o r in jec t iv i ty .

The major benef i t of th i s work i s theabi l i ty to design dr i l l ing and completionoperat ions to optimize the t ime the pay zonei s exposed to the damaging f luid. The val idi ty of the model has been demonstrated in anea r l i e r publication. A typica l example i spresented in th i s study to demonstrate thecapabi l i ty of the radia l flow simulator toassess formation damage in the near wellboreReferences and figures a t end of paper.

region. The s imulato r p resent ed in th i sstudy can be used in the design of welldevelopment and r e se rvo i r exp lo i ta ti on pro-grams with reduced formation damage as wellas cleanup operations .INTRODUCTION

The petroleum industry has been searchingfor methods to reduce the loss of revenuedue to permeabil i ty impairment in the formof abnormal decline in productivity duringhydrocarbon production and loss of in jec t iv i ty during expensive supplementa l waterin jec t ion projec ts . Permeability impairmentwhich can occur dur ing any stage of welldevelopment and r e se rvo i r exp lo i ta ti on ema-nates from adverse chemical and/or physicalreact ions between reservoi r rock andformation/ extraneous f luids operat ing con-di t ions including temperature pressure andflow ra tes . All rock forming minerals havethe potent ia l to damage a formation when thephysical and chemical equilibrium betweenthem and the pore f luids is adverselyal tered . However the type and degree ofdamage depend on the following

1. Type morphology and lo ca tio n o f res i d en t c la y m in era ls.2. In -s i tu and extraneous f luids composi-t ion.3. Well development and reservoi rexploi tat ion pract ices .To ef fect ively assess and control thepotent ia l formation damage problems r esu l t ing from o i l f ie ld operat ions d r i l l ingworkover acidizat ion polymer flooding andpar t icu lar ly water in jec t ion and hydrocarbonproduct ion a systematic approach is neces-sary. This approach should involve the useof core data to evaluate r igorously boththe rock mineralogy and the chemistry of

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supplemental w a t e r I n j e c t i o n Related Prolm l.LTh e well known dominant form ation dammechanism as s o ciated with supplemental win jec t ion i s sol id plugging. A g r e a t d e awork h as been done by th e i nd ustry toimprove th e water q ua lit y i nje ct ed in toformation. However t h e r e a re o th er damamechanisms which have more effec ts on int iv i ty than sol id plugging. Among th e do

nant mechanisms a re in s i tu m o b i l i z a t i o nmigration o f c la y and/or s i l i c e o u s finepar t i c l es . Swelling o f sm e c t i t i c clay merals is another. These problems a re a sc ia te d with th e c o n t r a s t between i o n i cst r e n g t h sal ini ty an d pH o f th e i n j e c t i oand formation f lu ids . This c r e a t e s a tedency f o r in s i tu clay minerals to e f l ol a te and r el ea se f in es tha t migrate andflow p ath s . Swelling o f au th ig en ics m ectite a n d / o r mixed l a y e r i l l i t e / smet i t e may a l so reduce pore e n t r y r ad iu s aimpair p er m eab ili ty .Frequently th e sa l in i ty l e v e l o f in jt ion f lu id s adequate to p re v en t d e fl o c

la t ion an d y e t formation damage occurs uc o n t a c t o f th e i n j e c t e d w a t e r with th er e s e r v o i r roc k. This type o f damage inmost cas es stems from i l l i t i c pluggingwhich happens when f lu id whose i o n i c coms i t ion i s high in polyvalent c a t i o n s b u tdevoid o f potassium comes in c o n t a c t witi l l it e b ear ing formation. The potassiumr em ov ed f ro m th e crysta l l a t t i c e l e a d i n gd i s i n t e g r a t i o n o f th e i l l i t e la t t ice .Th e interdependency between sa l in i ty asal ini ty c o n t r a s t pH an d i on ic s tr e ng thbeen demonstrated by some r es ear ch er s 15

D r i l l i n g an d completion Related ProblemsTh e formation damage problems mostly ac ia te d with dri l l ing an d well completionformation plugging from sol id par t iclesth e dr i l l ing / completion fluids an d f i lt r a te invasion. These problems a re unavoab le s i n c e some degree o f f i l t ra t ion i snecessary in dr i l l ing o p e r a t i o n s to b u i l df i l t e r cake an d reduce flu id lo ss. The bconcern o f t h e r e s e r v o i r an d productionengineers i s to ensure tha t such damageminimized. An understanding o f th e b a s icf a c t o r s tha t c on tro l t he degree an d deptdamage during well development o p e r a t i o nth e ke y to minimizing th e above mentioneformation damage mechanism. These f a c t o rinclude1 formation pore morphology amouo f p r es s u r e overbalance a p p l i e d to th e pazone during dr i l l ing time o f c on ta ct o fdr i l l ing / completion f l u i d s with th e zonin te res t rock mineralogy mud par t i c l e

dis t r ibut ion i n co n tact with form ation ps iz e d is tr ib u ti on th e chemistry o f th ed r i l l i n g / c o m p l e t i o n f l u i d s f i l t r a t e an dcircula t ion rate .

2

A g en er alized phenomenological model tha tcompletely q u an ti fi es t he known mechanismso f formation damage has been p r e s e n t e d byOhen an d civan14 The c o n t r o l l i n g paramete r s o f t h e model a r e determined based on asystem response a n a l y s i s o f lab o r ato r y c o r e .The work presented i n th i s paper fac i l i t a testh e use of estimated model parameters tos c a l e th e response o f l ab or at or y core flowt e s t s to n e a r wellbore flow co n d itio n s . Th eb e n e f i t s o f th i s type o f a n a l y si s includeth e abi l i ty to design well d ev el op me nt a ndr e s e r v o i r e x p l o i t a t i o n programs with reducedformation damage using l ab o ra to ry d a taex tr ap o lated to n e a r well bore co n d itio n s .I n doing th i s however i s important tounderstand t ha t t he c o n tr o ll in g formationdamage mechanisms a re different fo r w a t e rin jec t ion dr i l l ing well completion an dhydrocarbon production and must t h e r e f o r e b ei n v e st i g a t e d different ly .

2 PREDICTING SKIN EFFECTS DUE TO FORMATION DAMAGE BY FINES MIGRATION SPEformation/ extraneous f lu ids . A complete I n th e following a br ief review o f sop etr o g r ap h ic a na ly sis o f rock mineralogy o f th e is s u es involved in well developmeut i l iz ing scanning e l e c t r o n m icroscopy and r e s e rv o i r e x p lo i ta t io n programs a reSEM), thin s e c t i o n petrography TSP) and p r es en ted .X-ray diff rac t ion XRD provides informat ion on t h e type abundance l o c a t i o n an dmorphology o f th e r e s id e nt pesky claym i n e r a l s . A p l a u s i b l e s ys te ms a pp ro ac h mustcombine a v a i l a b l e mineralogical d ata withw a t e r an d hydrocarbon a n a l y s e s an d coreflow tes ts d ata to as s es s formation damagepotent ia l an d design non-damaging dr i l l ingw e l l completion water i n j e c t i o n an d hydrocarbon production programs.

Several lab o r ato r y s t u d i e s2- 6 have beencarr ied o u t th e p a s t to determine format ion damage du e to f i n e s movement sol idinvasion and c l a y sens i t ivi ty. A number o fm athematical models have a l so been d ev eloped7- 11 to study th e phenomenon. A reviewo f th e v ar io u s modeling effor ts s p r e s e n t e dby Ohen12 The e ng in ee r f ac e s th e followingtw o major problems when attempting to employt h e s e models to study an d as s es s formationdamage.1. Formation damage mechanisms involvecomplex physicochemical an dhydrodynamic processes o f d iv er s en a t u r e . Th e e xis ting models7- 11 a redeveloped to study in d iv id u al ra therthan th e c olle ctiv e e ff ec ts o f th es emechanisms. Civan e t a l . 13 showed thatt h e degree o f p e r m e a b i l i t y impairmentcan only be q u a n t i f i e d by consideringt h e combined effec ts o f foreign f i n e sinvasion in s i tu f i n e s m o b i l i z a t i o nan d c l a y s w e l l i n g .

The above ci ted formation damagemodels7- 11 13 were developed to simul a te l inear c o r e flow t es t s i n l a b o r a t o r y se t t ings o r i n a few cas es a tsimulated r e s e r v o i r c on di tio ns . Inrea l i ty however near wellbore flow i sb e s t simulated in radia l ra ther thanl inear geometry. A complete formationdamage model should s c a l e lab o r ato r ymeasurements to near wellbore radia lflow co n d itio n s .

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SPE 21675 HENRY A. OHEN AND FARUK CrYAN 3

1

I t has been shown tha t the ra t io of divalentions to the t o t a l cation concentrat ion inin ject ion f lu ids plays a major ro le in thede f locculation tendencies of c lay minerals .Apart from the col lo idal process controlformation damage problems discussed above,there are hydrodynamically controlled f inesmigration problems associated with the mobil iza t ion of formation f ines l ike authigenickaol in i te and i l l i t e .Inorganic scaling i s a dominant formationdamage mechanism encountered during supplemental water in ject ion. Even tpough i sone of the most troublesome damagemechanisms, inorganic sca l ing has not yetbeen addressed adequa te ly in the petroleuml i t e ra ture . A disturbance in thermodynamicand chemical equilibrium in oi l f i e ld br inere su l t s in th e b rin e becoming saturated r e l -at ive to the soluble minerals in solut ion.The re su l t i s the depos it io n o f scaleswithin the pore system.A problem frequent ly encountered insupplemental water in jec t ion i s tha t concerning mixing of waters from d i f f e r en t

sources. The scale index may indicate tha teach water i s free of scal ing tendencies ,ye t when the waters come in contact , ser iousscaling problems may re su l t . The s i tuat ioni s more c r i t i ca l when waters containing su l -fate ions are i nj ec te d in to a formation conta in ing wat er w it h barium ions.

Therefore, in addit ion to specifying thef i l t ra t ion level of in ject ion water , a nondamaging water floo d d esign should specifythe safe sa l in i ty pH t o t a l and divalenti on ic s t rength s of the f i l t e r t rea ted injec-t ion water. This can only be achieved byconsidering the overal l system i . e rockmineralogy, chemistry of pore and in jec t ionwaters .For many years, the industry has been concerned primari ly with formation damage whichoccurs when fresh water contacts a rock tha thas previously been e ~ o s e to high sal ini tybr ine. Recent s tudies 7 have shown tha twhen reservoir containing carbonate cementsis contacted wi th ext raneous brin e, thecements could be dissolved by the sa l inesolution to free the mineral par t ic les tomove and block the pore throat . Therefore,knowing the mineral at t r ibutes of the format ion i s important to the ef fect ive design ofdr i l l ing completion and i n je c ti on f lu i ds tomeet sa l in i ty requirements.

Hydrocarbon Production Related ProblemsStudies2 have shown tha t fin es are carr iedin the phase tha t wets them and the mosttroublesome f ine par t ic les found in oi l f i e ldoperat ions are typical ly water wet. I t i sconceivable therefore tha t when o il andwater flow simultaneously, tpe ~ t e r couldmobilize the water-wet f ines resul t ing inf ines migration problems. I t i s important tounderstand tha t under unfavorable hydrodynamic condi t ions when i n t e r s t i t i a l ve loc i -t i e s are h ig he r th an the c r i t i ca l veloci ty

to oi l f ines can be mobilized even whens ingle phase o il i s being produced.An important formation damage problem

e n o ~ n t e r e du:ing o il production i s organicsca11ng. Organ1c components - paraff ins andasphal tenes could precip i ta te a s orga nicscales near the wellbore and impair permeabi l i ty . Emulsion and water b lo ck s are for-mation damage problems frequent lyencountered during hydrocarbon production.Water blocks may be formed when water i st rapped within the pores of a low permeabili ty formation re su lti ng in high capi l larypressures and the reduct ion in the re la t ivepermeabi l i ty to the economic f lu id . A low .permeabi l i ty clayey reservoir i s a strongcandidate for water b lo ck . When f ine par-t i c l e s crude o i l and shear ex is t simultaneously, a suff ic ient condi t ion for theformation of s table emulsion i s createdleading to emulsion block.

Evidently formation damage problems akinto d i f f e r en t well development and reservoirexploi ta t ion programs are not only differentbut are too complicated to lend themselvest o t he o re ti ca l modeling. The be st s ol ut io ntherefore , l i e s in a system responseapproach in which laboratory core data areused to determine the response of the ent i resys tem inc lUding the rock, the reservoirf lu ids the extraneous f lu ids and operat ionvar iables . This type of phenomenologicalmodeling has been present ed p rev ious ly byOhen and C iv an14 . Mathematical scal ing oflaboratory measurements to f ie ld condi t ionsusing the Ohen and Civan model i s presentedin th i s paper .MATHEMATICAL MODELING

Permeabili ty impairment due to f ines movement and clay swelling can be quant if ie d a sposit ive skin. I f skin i s viewed as a zoneof f in i t e th ickness with permeabi l i ty kssee Fig. 1 then for radia l f low a roundthe wellbore, the following re la t ionship18may be used to compute a f in i t e th icknessskin factor .S= :: l }n r s r Although well tes t ing procedures can beused to est imate the skin factor , s r s andks can not be estimated independently. Themodeling e f fo r t presented in th i s paper provides a means of determining these paramet e r s . The l inear flow v ers io n of th i s model

has been presented and discussedelsewherel2 ,14. The a pp li ca ti on o f the modelto near-wellbore damage require tha t themodel equations in radia l geometry are con-sidered. The bas is for th i s modeling technique i s tha t the parameters estimated froml inear core flow t es t s can be used to scalet he l abo ra to ry response to f ie ld condit ions.This i s feas ible only becau se the modelparameters, when estimated under simulatedreservoi r condi t ions NOB and temperaturecondit ions , are not dependent on flow geomet ry .

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4 PREDICTING SKIN EFFECTS DUE TO FORM TION D M GE Y FINES MIGRATION SPE 2Radial Flow Equations

The model equations fo r rad ia l flow fol lows from the same development for l inearflow presented previously14. The developmentof the rad ia l flow model and simulator i sbr ief ly summarized below. D etails of thesimulator development i s presented elsewhere continuity Equations

Considering the l iquid and par t icles astwo different phases, the following par t ia ldi f feren t i a l equations can be writ ten fo rrad ia l flow.Liquid material Balance; : :o/rp1u l )+ ot(PISI< +S=O (2 )

In Eq. 2, represents mass rate of f lu idabsorption by the swelling clay and S I represents the volume fract ion of flu id in theflowing stream. gp in Eq. 3 represents thealgebraic sum of the par t icles los t fromsuspension by t rapping, smooth surface depos i t ion , and par t icles gained into the suspension by i n - s i tu mobil izat ion,deflocculation and chemical precip i ta t ioninorganic scal ing . f i s a f ac to r r ep re s en ti ng t he par t icles flow capacity of theporous media. The sign convention applicableto Eq. 3 requires t ha t p a rt ic le s gained havenegative sign and those los t have ~ o s t vsigns. The previous paper defined1 massconcentrat ion of par t icles , pp,/and t o t a lvolume flux of suspension, u, Eqs. 3 , 4and 5 in reference 14 .Particles Transport Equation

The t ranspor t of suspension of par t iclesthrough the porous media i s represented bythe following equation.

Up = uS p

Pm=Pp,j+PI I.O-pp.j/p p)..I.m = 1 1 1.0 - Pp. j /p p/,5

Volume FluxesUl-US I

where

Equation for Mass Rate of Liquid dsorptio.5=I3(PI-P p. j PI /P p -p l ,so) l , [ tRate Equations

The following a,s a summary of the rateequat ions derived and presented elsewhere I2 ,14.

UpP pU=PP. jThe non Oarcy om ntum Equation- op l ox = ..I.mu1k Pm 3jUwhere

non-Darcy numberjnd= 1.0+Pml3 j uk l ..l.m

To completely descr ibe formation damagdue to par t icu la te processes, equations foformation swell ing, f ines mobilization anddeposition are required. These equationsh ave b een presented l4 and are summarizedfollows.Mass Concentration of f ines and VolumeFluxesMass Concentration pf FinesPP . /= 1 .0 -S I p p

3Particles material BalanceI ; : : o / r j ppu p)+ ot(ppSp< +g p=O

I ; : :o / r jpp, ju + ot(PP.j< +op+op=o Clay swelling Model4

= { - a . O ~ [ 1.0 - r exp -k 3 K)](6F)ot 0 i j6F 5.0.0

Pressure EquationAs plugging of the flow path progresses,i ner t i a effec ts begin to se t in due to thef lu ct ua ti on s i n in te r s t i t i a l veloci t ies high a t the pore throats and low in the porebodies . Therefore, the Forchheimer equationhas been used in th i s stUdy to descr ibe thevarying flow regimes from Darcy to non-Darcyflow. As shown previously14, a combinationof the non-Darcy equat ion, l iquid mater ia lba lance equa t ion Eq. 2) and par t iclesmater ia l ba lance equa ti on Eq. 3) yie ldsthe fol lowing equa ti on t ha t descr ibe thevar ia t ion of pressures and ve loc i t i e s in thedamaged near-wel lbore region.

- ~ [ r r k o p J = o< > a p a ~ .5ro r ..I.m or ot Pp PI 5

where

{ 3 1.0 - exp - U - U c

3= 0 i jUU c

i j 6F>O

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SPE 21675 HENRY A. OHEN AND FARUK CrYAN 5as a function of f ines deposi t ion and clayswell ing i s given as:where/ : ) F = _ o P _ _ O P )x cr 20) 29 )

21 whereC/J=C/Jo- C1 p C1sw /p p 30

31

32)

Eq. 4 can then be wri t ten as:Oo v j p p , f U ) + j U P p , f+ r w e x p u)

Numerical Treatment o f Model Equations inRadial GeometryA t ransformation is required fo r radial flow toemploy the same numerical solut ion presentedby Ohen12 fo r l i nea r flow. Only the par t i c l et ranspor t pressure 7quat ions requi ret ransformat1on from rad1al to l inear geomet ry be amenable to l i nea r flow solut iont7chn19lle. The t ransformation using th ed1mens10nless spa t i a l var iable i s given by:

v = n[ J

22 )

23)

24)

a = e x p k - k s p i T )F ines Depo si ti on Hodel

C1p = { k 1UPP,fC/J-k C1 /: .F i j / : F>O.Oot k1Pp,fC/Ju i j / : F ~ O . O

s ize exclusion HodelThe v ariab le f in the par t i c l es t r anspor t equation represen t s th e f ract ion of theflow path t ha t may allow par t i c l est ranspor t . A mathematical an d s t a t i s t i ca lprotocol fo r determining t h i s var iabledescr ibed in our previous paper14 are summarized below.

Model for plugging by ize Exclusion In Y/d, 2-o.S f b P dj = 1.0 - E f e dyap 2ns dY

33

o [FkOP]ou 11m ou

Eq. 5 can in the same manner be wri t tenas:

[ oC J +0 Jr ~ e x p 2 u - p - - p ot Pp P tAn impl ic i t f in i te difference approximat ion of the coupled system of non- l inear

equat ions p re sen ted above has been obtainedan d a simultaneous solut ion of the equationsha ve b een carr ied out to obtain12 the fo l lowing information:1 . Change i n o rig in al pore volume pe r un i tbUlk volume du e to clay swell ing an df ine deposi t ion.2. Radius of damaged zone as a functionof t ime.3. Ratio of damaged to undamaged permeab i l i ty as a function of t ime.4. The d is t r ibu t ion of i n t e r s t i t i a l veloc i t i e s an d pressures in the damagedzone as a function of t ime.5 Skin faqtor as a function of t ime ofcon tac t of extraneous f lu ids with th ezone of i n t e r es t .Input ParametersTo determine the skirr fac to r, th e phenome-nological model parameters must bedetermined as wel l as some measurable inputvar iables . The measurable quan t i t i e s an dmethods of measurement are shown in Table 1 .

26)

27 )

28

25)

In Y/d, 2-O.S j bP e sdd - dy = 0t a p J2ns d yDimensionless TimeThe d imension le s s t ime i s d efin ed a s:

/: .ptt d = ;f fect ive porosi ty and PermeabilityAnalysis of porosi ty-permeabi l i ty r e l a

t ionship using Hagen-poi seu i ll e equat ionsmay yield a porosi ty-permeabi l i ty r e la t ion .However, the Kozeny-Carman t yp e c on st an tin such equat ion12 i s only appl icable toun i t s with the same hydraul ic proper t ies 19 t i s inadequate to use a s ingle value fo rthe constant to compute skin in a damagedzone whi ch may conta in severa l hydraul icun i t s . A power law type r el at io n s hi p p r evious ly used by civan e t a l . 13 was found torepresent accura te ly the range of dataemployed in th i s study. The simple empir icalre la t ionship which i s used to es t imate l oca lpermeabil i ty var ia t ion around the wellbore

ap an d bp are the lower and upper bounds ofthe pore s iz e d i st ri b ut io n an d it i sobtained by th e simultaneous so lu tio n of th efollowing non- l inear in teg ra l equations. In Y/d, 2-O.S f b P e d1 .0- dy=Oap 2nSdY

whered t o - = - Y C 1 .ot pI

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6 PREDICTING SKIN EFFECTS DUE TO FORM TION D M GE BY FINES MIGRATION SPE 2The phenomenological model parameters havebeen obtained b i the method described in ourprevious p ap er s 3 ,1 4. The model parametersare the rate constant for smooth surfaced epos it io n, k I, rate constant for par t i c l esre-entrainment, k2 , rate constant for l iquidadsorption, swelling constants , t 1 andt2rate constant for change in por e w ith deposi t iona l morphology, VCorrection constant fo r measu red and

computed equivalent pore throat s i z ~ ,def locculat ion constant, k3 , f ines mobil izat ion constants , k4 and k5' The methodemployed i s an automatic parameterestimation technique based on a systemresponse analys is in which l inea r core dataare used as system response to obtain themodel parameters. A deta i led descript ion ofth i s technique i s presented elsewhere13 ,14.DETERMINATION OF SKIN

The procedure for the use of th i s technique to predic t skin as a function of t imei s presented in Fig. 2 flow d iagram . Todemonstrate the usefulness of the approach,the Gruesbeck and Co ll in s d at a7 (case 2apresented previously12) have b een u sed asinput fo r a simulation run. In th i s example a hypothetical case of a well of diamet e r 3 inches in the cen ter o f a reservoi r ofradius about 400 f t has been used toin troduce damaging f lu id into a pay zone.The const i tu t ion of the damaging f lu id thelaboratory derived data and parameters es t i -mated by the automatic parameters estimationtechnique are as shown in Table 2.

The simulated pro f i le s of local to i n i t i a lpermeabil i ty r a t io versus dimensionlessradius of the damaged zone i s shown in Fig.3. From th i s f igure , the radius of damagedzone, r s and permeabil i ty of the damagedzone, ks , can be est imated. In th i s par t icu-la r case , assuming permeabil i ty r a t io equalto or less than 0.995 i s considered damaged, i s shown tha t the dimensionless radius ofdamaged zone under prevail ing condit ions andt ime of exposure to the damaging f lu id i sabout 4 .2 from the w ellbore. This can beseen more vividly in Fig. 4 which i s a p lo tof damage r a t io versus dimensionless radiusof damaged zone.

A p lo t Fig. 5) of dimensionless radiusof damaged zone versus dimensionlesstime , can be used as an indicat ion of thedepth and degree of damage a f t e r a givenperiod of in jec t ion . This information i svery important for formation damage controlduring dr i l l ing and completions as may beused to determine the maximum time t ha tdr i l l ing or completion f lu ids can be l e f t ina wel l o pp os ite a pay zone wit hout c au si ngconsiderable damage. I f the time of exposurei s known, the corresponding skin fac tor canbe determined from Fig. 6.REM RKS

The Ohen and C iv an model has been employedto predic t the skin fac tor during o i l production21 However, a two phase flow model

i s more germane for predict ing f inesmovement during o i l product ion. c r i t i c a lv e lo ci ti es t o single phase o i l are in mocases high enough to preclude formation dage during th e production of water f ree oHowever, when o i l i s produced .i n presencemobile water phase, water wet f ines aremobilized a t some re la t ive ly low c r i t i c a lveloci ty . Local disturbances created by tphase flow reduces the prospect of bridgiand hence the par t icles are car r ied somedis tance to near wellbore and are depositthere to cause skin e f fec t . I t i s evidentherefore , t ha t prudent modeling of sk indamage during hydrocarbon production andcleanup must consider issues in multiphasflow.CONCLUSIONS1. A systematic method of ut i l i z ing labortory core measurements to determine thparameters tha t control near wellboredamage has been developed. A simUlatorwhich can be used to assess and contron ea r w ell bore damage i s also descr ibe

The capabi l i ty of the s imu lato r inc ludthe abi l i ty as a function of t ime, tocompute r s and ks and determine skin ftor .2. Validation of the system response analmodel has been presented by Ohen andCivanl4 The re su l t s presented in th i sstudy demonstrate the appl icabi l i ty ofmodel under f ield operating conditionsTyp ical d es ign plots have b een presentto aid in the apr ior i determination ofoperat ing var iables f or t ak in g m it ig ats teps agains t formation damage.3. Prudent modeling of skin damage duringhydrocarbon production and/or cleanupshould consider issues in multiphase fCurrently , work i s being car r ied out ith i s area.NOMENCL TUREThe dimensions are given in the Darcy ufor consistency with laboratory core t e s t

Basic Dimensions[1 ] Dimensionless[L] Length un i t [cm]e Temperature uni t [Kelvin]

[M] = Mass uni t [grams][T] = Time uni t [sec]Alphanumeric Symbolsap = Lower bound of pore s iz e d is tr ib u ti o ]bp = Upper bound of pore s iz e d is tr ib u ti o[L ]

Total Clay Content [ML-3]Equiva len t pore t hr oa t s iz e [L]Plugging Efficiency [1 ]F ra ct io n o f non-plugging flow path

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SPE 21675 HENRY A. OHEN AND FARUK CrYAN 7 - Non-Darcy n um ber [L _1 ]nd

c r c r i t i c a l1 L iq u idl =Liquid in flowing f l u i d

l s L iq u id i n flowing f l u i dm Mixture0 I n i t i a l c o n d i t i o n sp P a r t i c l e sp f P a r t i c l e s i n suspensionsw = Swellin gS u p e r s c r i p t s I n - s i t u f i n e sACKNOWLEDGEMENTS

Th e authors g r a t e f u l l y acknowledge th e U. SDepartment o f Energy g ra nt f o r p a r t i a l s u p p o r t o f t h i s work u n d er th e c on tra ct No. DEFGO l- 87 FE6 11 46 . The s u p p o r t o f th e School o fPetroleum an d G e o lo g ic a l E n gi ne e ri n g an d th eCo lleg e o f E n g in eerin g computing f a c i l i t i e sa t th e U n i v e r s i t y o f Oklahoma i s apprec i a t e d . Th e a u t h o r s a l s o would l i k e t o thankth e American F i l t r a t i o n S ociety fo r th epermission t o rep ro d u ce F igs. 3, 5 an d 6from o ur p re vi ou s paper21 f o r i l l u s t r a t i o n .REFERENCES1 Amaefule, J . o. an d Kersey, D.G: dvancesin Formation amagessessment and ontrols t r teg ies An i n t e r n a l p u b l i c a t i o n o fCore L a b o r a t o r i e s , A d i v i s i o n o f WesternA t l a s I n t e r n a t i o n a l .2 Muecke, T. W : II Formation Fines an d Fact o r s C o n t r o l l i n g t h e i r Movement i n PorousMedia 1I JP T F eb., 1979) p . 144-1503 Moore, J . E . : II C la y M i ne r al og y Problemsin o i l Recovery,1I P e tr o le u m E n g in e e r , Vol.32, 78 1960).4 Egbogah, E . O : II An E f f e c t i v e Mechanismfo r Fines Movement Control i n Petroleum

Reservoirs,1I CIM 8 4- 35 -1 6, J un e 19845 J o n e s , F.O. : II Influence o f Chemical Comp o s i t i o n o f Water on C la y B lo ck in g o f P e r m e a b i l i t y , II JPT, 19646 H a r t , R .T ., F ek et e, T. And F loc k, D .L .: IITh e Plugging E f f e c t s o f B ac te ria in Sandstone System, II Canadian M in ing a nd Metall u r g i c a l B u l l e t i n , 53, 1960), p . 495-501.7 Gruesbeck, C. And C o l l i n s , R.E. : IIEntrainment and Dep o sitio n o f Fine P a r t i c l e s in Porous Media 1I SPEJ, Dec. 1982)p . 847-8508 K h i l a r , K.C. And Fogler, H.S. : II WaterS e n s i t i v i t y o f Sandstones,1I SPEJ, Feb.

1983) p . 55-64.9 Wojtanowicz, A.K K r i l o v , Z. And L a n g l i n a i s J . P . : II s t u d y on th e E ffe ct s o fPore Blocking Mechanisms on FormationDamage 1I Paper SPE 16233 presented a t SPEp r o d u c t i o n s ym p os iu m, O kl ah om a c i t y March8 -1 0 , 1987.10 Sharma, M.M. And Yortsos, Y. C. : II T r a n s p o r t o f P a r t i c u l a t e Suspension in PorousMedia: Model Formulation ll AICHE J o u r n a l ,v o l . 33, no. 10 Oct. 1987), 1636-1643

Radius o f th e damaged zone [L]Radius o f th e wellbore [L]Sk in f a c t o r [1 ]Stan d ard deviation [1 ]Volume f r a c t i o n [L3/L3]Mass r a t e o f l i q u i d absorption p e r u n i tb u l k volume [ML-3T-1]Time [T]

= Rate c o n s t a n t fo r l i q u i d a b s o r p t i o n [T-1/2]= C o r r e c t i o n c o n s t a n t fo r measured an dcomputed e q u i v a l e n t pore t h r o a tRate c o n s t a n t f o r change in pore withd e p o s i t i o n a l morphology [1 ]

T]

v

= V is co sit y o f th e continuous phase [ ML1T-1]

P o r o s i t y [1 ]p Mass c o n c e n t r a t i o n o r d e n s i t y [ ML-3]a E f f e c t i v e change in o r i g i n a l pore v ~ume p e r u n i t b u l k volume expressed interm s o f mass [ML-3]SUbscripts

L

r

t

r

Thickness o f zone o f i n t e r e s t [L)P ermeabili ty [L2]Rate c o n s t a n t fo r smooth s u r f a c e depos i t i o n [L-1]

= Rate c o n s t a n t fo r r e -e n tr a in m e nt o ff i n e s [L2 T M-1]k3 = Rate c o n st a nt s w el li ng o f ,clay p a r t i c l e s [L3 T1/2 M-1]

= Rate c o n s t a n t fo r m o b i l i z a t i o n o f fi n e s[L2 T M-1]= Rate c o n s t a n t f o r s u rf a ce e ro si on [L3 eM-1]

T e s t core l e n g t h [L]P ressure [ MT-2L-1]Radius [L]F r a c t i o n o f t o t a l a u t h i g e n i c c l a y t h a ti s s m e c t i t i c [1 ]

= Radius o f th e undamaged zone [L]

p

T Temperature [ u Volume flux [ LT-1]v Dimensionless r a d i a l d i s t a n c e from

wellbore [L]Greek Symbols

405

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8 PREDICTING SKIN EFFECTS DUE TO FORM TION D M GE BY FINES MIGR TION SPE 211 Kumar, T. And Todd, A.C. : A NewApproach fo r Mathematical Modeling o f Formation Damage Due to Invas ion o f S olidSuspension, Paper SPE 18203, presen ted a tth e 63 th annual Technica l Conference andExh ib iti on o f th e Socie ty o f PetroleumEngineers , Houston, Texas, (Oct. 2-5 ,1988) .12 Ohen, H.A. : Model in g a nd Simula t ion o fth e E ff ec ts o f Clay Swel l ing and FinesMigra t ion on Formation Damage. Ph D Diss e r t a t i on , Univer s i ty o f Oklahoma, Norman,Oklahoman, (1989).

13 Civan, F . , Knapp, R.M, and Ohen, H.A. :Altera t ion o f P e rme ab il it y by Fine Pa r t i c u l a t e Processes , Journal o f PetroleumScience and Engineer ing, vo l . 3, nos 1/2 .(1989) p . 65-7914 Ohen, H.A. And Civan F .: Simula t ion o fFormat ion Damage in Petroleum Reservo i r s ,p resen ted a t th e 9th SPE Symposium on For mation Damage Cont ro l , Lafayet te , Lou i s i ana , Feb. 22-23, 1990.15 Vaid ja , R.W. And Fogle r , H.S. : FinesMigrat ion and Formation Damage: In f luenceo f pH and Ion Exchange, presen ted a t th e9th SPE symposium on Formation Damage Cont r o l , Lafayet te , Louisiana , Feb. 22-23,1990.

16 Scheuerman, R.F. And Bergersen, M.B. In jec t ion-water Sa l i n i t y , Formation Prt rea tment , and Wel l -opera t ions Flu id-Sl e c t ion Guidel ines , JPT (July, 1990) p836-845.17 Reed, M.G. : Formation Permeabil i tyage by Mica Altera t ion and Carbonate Dso lu t ion , JPT, ( 1979)p. 1056-1067 .18 Hawkins, M F . : Notes on The Skin

Ef fec t s , Trans . , AIME, 207, (1965) p .356-35719 Amaefule, J .O . , Keelen, D.K, Kersey, Dand Marschal l , D. : n Integrated Core nalysis pproach to Reservoir Descr ipt i on , An i n t e rna l pUbl ica t ion o f Coreora to r i e s , A div i s ion o f Western At lasI n t e rna t iona l .20 Harv i l l e D.G. And F reeman D .L . : Th eBenef i t s an d Appl ic at io n o f Rapid MineAnalys i s Provided by Four ier TransformIn f r a r ed spectroscopy, Paper SPE 1812presen ted a t th e 63 t annual Technica lConference and Exh ib it io n o f th e Socieo f Petroleum Engineers , Houston, Texas

(Oct. 2-5, 1988) .21 Ohen, H.A. And Civan F. : Fines Genet i on , Migrat ion and Permeabil i ty Impa iment Near Product ion and Injec t ion WeAdvances in F i l t r a t i on and Separa t ionTechnology, vol . 1 , ( 1990 )p . 161 -164 .

Table Laboratory Measurable Quantit iesLaboratory Mea Methods o f Measurementsured qu n t i t i sr r i t i c a l p re ss ure S in gle phase c r i t i c a lfo rce to mobi l ized veloc i ty t e s t 1f ine s , o p o )c r

~ o t a l c l ay conten tWour ier Transform au th igen ic and ~ n f r a r e d (FTIR) Spect ros -~ e t r i t a l C ~ o p y 2 0 (Minera log)~ o t a l au th igen ic ~ o m p l e t e pet rograph icclay con ten t , analysis1 XRD, TSP,. ~ E M .Wraction o f t o t a lclay t h a t i s

~ w e l l l e smecI ~ i t e mixed l aye ri l l i te - sm ec t i t e ) , r

~ h i n sec t ion petrography

~ r i t i c a l Pore V o l - ~ a t e r sen s i t i v i t y t e s t[ume o f i n j ec t edf lu id fo r th epnse t o f swel l ing ,Per

4 6

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~ a l e x npu t ata and Estimated Parame~ e r s 1 2 1 4Inpu t Values Est imated ValuesData Parameters

c o 0.476 k l l /em) 5.73X10- 3ko 153 k2 em 2 0 .0MD see /g

t.p Atm 1.36 k1 em3 0 .0see /2 /g ) 1 .0 k4 em 2 0 .0ep) see /g

L em) 15.2 k5 em3 ke l - 0 .0y in /gP , g/ 0.019.3x.LU vee) em 4 / g)p J,g/ee 1 .0 0 .0

( 1 /

p g /ee 1 .0 165.d em) 3.81 cr 50ee)

2 .0 sd i ; er a tm / em 0

SPE 216

WELL RE

Figure 1. Schematic of damaged zone.

7

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Obtain fines concentration in suspension ( Eq. 32)and pressure distribution (Eq. 33)

Compute change in pore volume due to ;Clay swelling Eq 17)Fines deposition Eq 23

Compute In-situ fines generation (Eq. 19)determine fraction of non-pluggingpathway Eqs. 24-27)

Compute Instanteneous : Porosity Eq 30)-Permeability Eq 29)

Yes

\ : ~ t 6 7

Obtain Radius of Damaged Zoner @ k/kO >0.9995

Compute Skin factor,s (Eq. 1. )

( stop ~ 1 Make design plots Figs. 3,4,5 8)F i g u r e 2 . Simulat ion flow diagram.

Start

INPUT DATA IPetrographic data;J:tt:r ~ ~ ~ i g e n l c finesFraction of smectitic clay mineralsCore Data:length and diameterIInltlal porosity and permeability

Test Fluid dataLiquid viscosityConcentration of solidsParticles size distributionParticles and liqUid densitiesTest Conditions:Injection pressureBack PressureTime and rate of Injection

FLOW TESTSystem response; K vs throughput- Fines production vs throughput

Obtain Model Parameters using the linearf low model and the automatic parameter

12estimation routine

Reservoir/Well DataRadius of Reservoir and wellboreWellbore temperature, T SCALE TO NEAR WELLBORE CONOITIONS

r - - - - - - - - - - - - - - - - - - - - -Initialization:-S t initial conditions around the wel lborek, p,T,etc

t O- o

Figure 2. Simulat ion Flow Diagram continued

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C

jm 0Erf:s 0g

CII0

0

4 6

SF E 2 6 75

Figure 3imensionless radial distance

Permeabi l i ty impairment prof i l e s reproduced from Ohenan d Civan l with permiss ion f rom AFS .

2 4 6 8

imensionless T meF ig ur e 4 . Damaged f ron t t racked with t ime.

4 9

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Xc:i

I :i3.sD c:id

o

3.0 3 3.4 3.6 3.8 4.0 4

Figure 5 .imensionless adius of amage Zone

Permeabi l i ty impairment as a f un ct io n o f damaged radius reproduced from Ohen an d Civan l with permission fromAFS)

2 4 6 8

Figure 6imensionless TimeSkin f a c to r as a f un ct io n o f contac t t ime r e pr o du c ed fromOhen an d Civan 21 with permiss ion f rom AFS .

4