#1 effect of wellbore storage and damage on the transient pressure behavior of vertically fractured...

8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf

1/8

S

SPE6752

EFFECTOFWELLBORETORAGENDDAMAGE

ONTHETRANSI ENTRESSUREEHAVI ORF

VERTI CALLYRACTUREDELLS

by HeberCi nco- Leyand Fe?nandoSamanl egoV. ,

Members SPE-AIME, I nstf tutoMexi canodel Petrol eo

s Copyright1977,AmericanInstit uteof Mining,Mst aihrrglcal .nd PetroleumEn;meera,Inc.

Thispaperwaspresent edatt he52ndAnnualFallTechnicalConferencendExhibit i onof theSocietyof PelroleumEflgineersf AIME,heldin Denver,Colorado,Ott. 9-12,1977.Thematerialc ‘ i ’bj ect’ t o

correct iony theauthor.Permiss ionto copy is restr ic tedoan abstrac tof notmoret han300words. Wri te :6200 N. Centra lExpy,Dal laa,Texas75206.

ABSTRACT

wellborestorage,and suggesteda matchingtechniue

8for analyzingpressuredata. Recently,Raghaven2

-A modelrecentlyp?esentedby Cincoet al.for discussedpressureanalysistechniquesfor

the transientpressurebehatiorof wellswith finite

verticallyfracturedwells,includingthe effectsof

conductivityverticalfractureswas moafled to

wellborestorageand skin.

He assumedthe fracture

includethe effectsof wellborestorageand fracture

to be of uniformflux,andpresentedgeneral

damage.

An infinitesimalskinwas consideredaround

characteristicsf the pressuretransientbehavior

thefracture,end it was handledas a dimensionless

for tinesesystems.

factordefinedas (aK/2)wd/Xf)[(k/kd) 1].

The puxposeof this studyis to preL3ent

It was foundthatthewellbehavioris

solutionsfor the transientwellbme pressm:e

importantlyaffectedby the fracturedamage.

When

behaviorof swell crossedby a finiteconductivity

plottedas a functionof log ~D vr3lot tD for short

times,resultsshowflat,almosthorizontallines

verticalfracture,consideringthe effectof a

dsmagedzonearoundthe fracture.nd wellbore

that laterbecomeconcaveupwardcurvesasymptotic-

storage. It is alsointendedto showthe general

ally approachingthe curvefor undamagedfractures,

flow characteristicsf thesefracturedsystems.

Thisbehavioris shownevenby slightlydamaged

fractwes. It alsowas foundth&t important

MATHFMKJTCALMODELSANDMEWHOLBOF SOLUTION

iidlmmation

aboutthe fracturecharacteristicsay

—.

not be determinedwhenwellborestorageeffectsare

The transientflow towardawell with a finite

present.

conductivityverticalfracturesurroundedby a

INTROIUCTCON

damagedzonewas studiedby usinga modifiedversio

of the modelpresentedby Cincoet al.lg The

followingassumptions\;ereconsidered.

It has been shownthat the increasein the

productivityofswell createdby hydraulic

1. An infinite,homogeneou~,isotropic

fracturingdependson fracturecharacteristics,l-k

reservoirof permeabilityk, porosityo, and

suchas fractureconductivity,ength,penetra-

thicknessh.

tion,5?6and alsoon a possibledamageto the

formationimmediatelysurroundingthe fracture.sfy

2. The formationis producedthrougha

Duringthe last few years~therehas been a

verticallyfracturedwell.

‘fhewellboreis inter-

continuouslyincreasinginterestin thedetermination

sectedby a fullypenetratingvertical.ractureof

of the characteristicsnd orientationof fractures

permeabilitykf?porosityof, widthw, and half-

by meansof trsnsient’pressurenaIYSiS,6-20Mostof

lengthxf. All productionof fluidis via the

tkse methodsconsiderthe fractureto be of

fracture.

infiniteconductivityor of uniformflu%;others

3. Therejs a zoneof reducedpermeability

considerfiniteconductivityractures.

Generally,

thesemethodsassumethatthereis no skindamage

causedby fracturingfluidloss aroundthe fraoture

This regionhas a permeabilityksandwidthws.

aroundthe fracture.

Evens14proposeda pressure

analysistechniqueconsideringfractureSW damage.

4.

The porousmediumconttis a slightly

He assumedthe flowfromthe formationto the

compressibleflulclof viscosity and cmpresslbili

fractureto be linear,passingthroughtwo porous

c.

mediain series,onebeingthe damagedzonearound

5,

All formation,fractureend fluidproperti

the fractureand the otherthe undsmagedformation.

are independentOf pressure.

Ramey end Gringarten17discussedthe transientwell

behaviorof verticallyfracturedwellgwith large

6. Gravityeffectsare negligibleend pressus

Referencessnd W&trations at end of paper.

gradientsare smalleverywhere.

..


2/8

E~~EcTOFwELLB ORE” sTORA GEA NDD~AGEONTHE”

2

TRANSI ENT PRESSUREBEHAVI OROF VERTI CALLYFRACTUREDWELLS SPE 6752

‘ ?.

Initially,the pressureis uniformthrough-

out the system.

k h (pi- Pwf)

8. Thewellborehas a finitestoragecapacity.

Pw =

141.2qB~ * “ “ “ “ “ “ “ “

D

The systemabcvedefinedis shownin Figs. 1

aiid2, andwas dividedintofourparts:

(1)well-

bore,(2)fracture,(3)damagedzonef~d (4)WI-

~ =o*ooo264kL , , . . .

damagedformation.

D

6P Ct Xfz

The followingdescribesthe flowmodelsfor

eachof the systemcomponents.

WellboreStorageModq&

The transientpreseurebehaviorof a well when

~=n fects are

presentcan be obtainedfromthe

‘D

‘wD(tD) = Jo [1 - CD

d ‘~.(’)] [~ ‘tD

D

T ] dT ,. . . . . . . * .

1

wherepwn

endpD areth(.cibwensionl.essellborepres-

V

sureswith andwithoutwclLborestorageeffects?

respectively.tDis the dimensionlessime,andCD

representsthe wellborestoragecoefficientin

dimensionlessorm.

A discretizationofthe integralinEq. 1

allowsus to solveforpw as follows.

u“

I

p (tD)=

.

‘D n

CD PD (tD - ‘Dn ,)

[(1+ (~ -:

- )]

Dn Dn ,)

and

c

cD=2Tt hctxf2 -”” ““”’”’”

FractureFlowModel

The fractureis consideredas a porousmediu

of heighth, half-length~, widthw, and with

propertiesas statedbefore. Thewell flowrate

is simulatedby a planesourceof lengthw and

heighth locatedat thewellborecenter. i??uidi

enterin fromthe formationto the fractureat a

f

ate qf x?t)

per unitof fracturelengthfas show

in Fig.3.

The pressurealong%he fracturemay”~ecompu

from

kh (pi- pf)

141.2 q B u

‘Pf XD, t D,

A, Bf,

c

D

wherepf is definedby Eq. 3 of Ref. 19;~ is t

D

dimensionlessdistancealongthe fracture;tD is

dimensionlessimedefinedin E@. 4, and A sndB

the correlatingparametersof the solutiondefin

Cincoet

EQ. 19:

{CID,PD (tD ) -::: (qD - qD

w @ff Cft

)PD(tD-tD )

xf~ct

. . .

.

n i i+l

n

i +- 1

Pw (tD ) kfffct.

- qD

pD :tD- tD

n-1 y

)+[l+cDg-~J

B4=

~“ “ “ “ “ ” “ “ “ “ “ “ “

n-2

n n-1

n

n-1

Fq. 6 includesA andB’becausethepressurebehav

“-PD@Dn- ‘Dn-l

)}, . . . . . . . . .

of the systemdependsupon thepropertiesof boti

. . (2)

fractureend the formation.

where

[PWD ‘ D “D~-~]

tD)-P

.

‘Di

1

- CD

.

‘Di - ‘Di-l

pwD(tDi)~dPD(tDi) me the ~mensiofless’press~es

&t dimensicxil.essimet ..

%

The limitationsof thismodelare discussedby

CincoandSsmsniego.22It was foundthatresults

accurateenoughfor matchingpurposescan he obtained

by-usingthismethodof solution.

When thistechniqueis appliedto the case of

fracturedwell,the dimensionlessariablesare

definedas

“..,.-.

It is convenientto exyressthe flowrateof

fluidgoingfromthe formationto the

fraC W?? q

in dimensionlessorm?qf ? as

D

2 qf Xf

q.-

(xDttD) =-

‘D

q ‘“

“ “ “

“’”

Desnajzed-ZonelowModel

F??actures consideredto be surroundedby a

zoneof widthW9 and permeabilityk= lessthanth

formationpermeebilityk. Sincethe fluidflowi

from the formationto the.fracturehas to go thr

thtszone,

a>


3/8

SPE 6752

HEBERCINCI - LEY AND FERNANDOSA 4ANI EGOV;

3

damaged zone. Fq. 10 may be obtainedby combining

19 Or.cethe fl

roceduredescribedbyCinco et al.

two equationsfor pressuredropacrossthiszone;

rateqf as a functionof ~~d~D is known,the

the firstone considersthe undamagedformation

characteristicsnd the secondone usesthe proper-

dimensi%lesspressuredropat the wellborepf (~

ties of thedamagedregion.

O, t ) canbe computed.

8

Wellborestorageeffe%s

Eq. 10 in dimensionlessormbecomes

incl ded in the solutionby apply+nglkI.2 to the

wellborepressurepf

(~ = o, tD .

kh~p

IT ‘d k

D

llpD=

s

——

= qfD(xD* ‘D) 2 Xf

~

- , 1

141.2 q BP

Discussionof Results

s

**.*** *****. O****>

(11) To studythe generalcharacteristicsf the

transientflowbehaviorof swell intersectedby a

Althoughthisequationwas obtainedby con-

finiteconductivitydamagedfracture,severalcas

sideringstead~stateflow~it can be ueed %0 compute

were solved.

the extrapress~e

op caused

by the damagedregion

in the transientflow towarda fracturewhen the

Figs. 5, 6,

7 showgraphsof logof

damaged-zoneidtinis small. Thisis becausedura-

dimensionlessellborepressurepw vs logof dim

tionof transienteffectsin thisregionere a func-

?

ticvlof wd*

sionlesstime tD, for valuesof (w f)/(fix+c)qua

0.2, 2, :nd 100,respectively. Resultsarepre-

~. 11 showsthata zoneof va..iableidth end

sentedin eachof thesefiguresfor severalvalue

a veriableflow rate alongthe fracturemay be

of fractu?edemagefactorsfs.

In thesecases,t

handled.

widthof the damagedzonewas takenas uniforman

the valueof the damagefactorconsideredwere0,

FormationFlowModel

0.01,0.02,0.1,0.2 and 1. It canbe seenfrom

of thesegraphsthat,for shorttimes,the curves

The reservoiris of infiniteextentin the behaveas horizontallines,and for largevalues

radialdirection;the characteristicsf the forma-

time,thesecurvesapproachasympototicel~rthe

tionwccementionedbef?re. The flow towardthe

undamagedfracturecasefrom above;thisbehavio

fracturecan be simulatedby a planesourceof flux similarto the resultspresentedby Raghavanfor

qf (x~t)and lengthxf as shownin Fig.4.

case of uniformfluxfractureswith skindamage.

low fractureconductivity(Cr. 0.2)the valueso

Thepressureat anypointin thereservoircan

p ~ 3n the horizontalregionof the curvesare sl

be calculatedby the equation:

g~eaterthan the fracturedamagefactor;however

kh (pi-

for highfractureconductivity(Cr>100) thepwD

P(X,y, t))

141. 3 q B IJ

= P* xD, YD1 tD *

valuefor thisperiodis equalto the fractureda

(12)

factor. Thisis becausefor shorttimesfluxis

.*,**.* *.**** *****=

unifermalonga highlyconductivefracture. Anot

where~andyD=e the fimensiotiessbscissaand

interestingfeature

s

thatthe log-loggraphsof

the solutionsshowcurvesof differentshapesfor

ordinate,respectively.

and high conductivityfractures;thus,if format

permeabilityis known,and the transientpressur

The PD functionof ~. 12was definedby Eq. 5 datafor a longperiodof timeaxe available,a

in Ref. 19

roughestimate’ofthe fractureskindamagefacto

may be obtainedby a type-curvematchingtechniq

Methodof Solution

A furtheranalysisofthe results(notshownhere

showsthat if the solutionsarepresentedin a gr

The reservoirand fractureflowmodelscan be

of p~D vs log t~t straightlinesof slope1.151a

coupledby consider.

Y

thatthepressuredrop elong

obtaznedfor largevaluesof tw

Thus,the comm

the fractureApf(X,t

is equalto the pressuredrop

semilogerithmicethodscanbe used to analyzelo

alongthe plane sourceAp(x, y = C, t in the reser-

1

timepressuredata.

Resultsalso showthatthe

voir,pla3 the preesuredropAp5(x,t causedby the

extradimensionlessressuredropat thewellbor

damagedzone. Thismaybe expressedin dimeneion-

causedby the fractureskindamageis constantfo

lessformas

largetimes,andit is greaterthanthe fracture

Pfd(xDt

tD, A, B) = PD XD, YD

factordefinedbefore.

=o, tD)-i-qf(xDrtD)sf~ ,.. ,,, ,.(13)

It is of interestto know the effect”offrac

D

skindamageon the stabilizedflux distributiona

the fracture. Figs.8 snd 9 showthiseffect. I

where

canbe seenfrom thesegraphsthat,in general,f

IT

w~(xD) k

ture skindamagemakesthe flux distributionmore

%=T

Xf (~- ‘)’

uniform*

Fig. 8 showsresultsfor Cr = 0.2tand

9 presentsresultsforCr= 100.

By doingthis;the damagearoundthe fracture

““

It shouldbe pointedout, as mentionedbefo

has been hendledas an infinitesimalskin. It csn

that the

results

for transientpressurebehavior

be Seen from the E@. 3 end 5 inRef, 19 thatpf, m

d

.fracturedellswith skinckmagepresentedhere a

pD are functionsof qf

D (~~ ‘D); thuss~“ 13 D

+ A comple;esetof graphsfor eeverelVZIUeSof

constitutesan equationwith orlyone unknown:

(wkf)/(fix+c)anbe obtainedupon requestto the

clfD(~, LD).

Thisequationcanbe sol:’edy the

authors.


4/8

.

EFFECTOF WELLBORESTORAGEAND DAMAGEON THE

4

TRANSI ENT PRESSUREBEHAVI OROF VERTI CALLYFRACTUREDWELLS SPE

valid onlywhen thewidthof the damagedzoneis very

small.comparedwiththe fracturelength. The preseurt

behaviorwhen the widthof thedamageis largewillbc

diecussedlater.

The effectof wellborestorageon the transient

behaviorof a fracturedwell is ehownin Figs. 10 and

11, Fig. 10 showsa graphof log pwDvs log tD for

the caseof undamagedfractmes. Resulte=e

presentedfor valueeof the dimensionless

llbore

storageconstant

c f ewd ~ O lo-4t 10- t lo-2f

?

nd I&l. Cincoe_ sl.20presentedthisgraphfor

CM = O and tD 2 10_~snd suggeeteda ~.pe-c~e

matchingtechniqueto analyzetransientpressuredata

however,if pressuredataof fracturedwellsin low-

permeabilityformation,or wellswith very largefrac-

tures haveto be analyzed,datafor very emallvalues

of dimensionlessimeare necessary.

It csnbe seen

fromFig. 10 thatfor smallvaluesof tD, for the

caseof cDf

= O, thepressure.-timeurvesgive

straightlinesof slopeequalto one-fourth.

Analysi:

of thiefact showsthatthisbehaviorcorrespondsto

the periodwhen almostall fluidgoingto thewell-

borecomesfromthe formationend fracturetip effect

are not felt.

CincoandSsmeniego23presenta rigor-

ous analyticalproofof thisbehaviorandconclude

thatpressuredatafromthisperiodmaybe usedto

determinefracture-formationharacteristics.How-

ever,if wellborestorageinfluencesthe test,this

kind of informationmay,notbe obtained.

A comparisonof thebehaviorof damagedend

undemagetfractureschowsthat fractureskindamage

may be detectedwhenthe slopeof the log-logcurve

of nressuredata,at smallvaluesof time?is less

thanone-fourth.Althoughthe curvesfor undamaged

fractureswithintermediatevaluesof Cr (1s CrS50

approachthe infiniteconductivitysolutionfrmm

above~as do the curvesfor damagedfractures,they

neverhave a slopeless thanone-fourthat small

valuesof time. However,if short-timepressuredata

for a testarenot available,

erroneous

conclusions

may be reachedsincea finiteconductivityfracture

may be takenas an infiniteconductivityfracture

with a skindamage.

Resultsin Fig. 10 alsoshow thatthe half

slopeperiodlengthfur highlyconductivefractures

(C{> 100)dependsor~Crvelues. This graphindi-

ca es thatwellborestoragegreatlyM.fectsthe

transientpressurebehaviorof fracturedwells. For

shorttimesthereis a wellborestoragedominated

‘flowperiodcharacterizedy etraightlinesof slope

one;followingthereis a transitionperiodwhose

durationdependson the Cr andCDf values,andlater,

the pressurebehavioris not effectedby wellbore

storage. In genwal the curveshave different

shapes;thus,Fig. 10 can be ueedto

anslyze,tran-

sientpressuredataby atype-curvematchingtech-

Kique.

Problemsof uniquecharacterizationay

arisewheninsufficientpressuredatamatchthe type

curvein the regionof lineeof one-fourthslope;

however,the graphmay givethe timewhenwellbore

storageeffectswe negligible.

Transi.entreseurebehaviorfor the casesof

fractureddemagedwel.lith wellborestoragea??’

presented

on Fig. 11,*

It shouldbe realizedthat

~Ful.1-scaleraphsof logpwn Vs log t,D,including

wellborestorageand fractureskin,maybe obtained

upon request‘W the authors.

therearemanypossiblecasesfor the differe

combinationsof Cr, Sfs, andCDf so to showt

generalbehavior,onlycasesfor Sfs equalto

and for Cr equalto 0.2 and 100 are shown.

Fo

times,as elwsyeoccur,thereie a wellborest

dominatedperiod

after

whichmayor may not be

periodstronglyinfluencedby the fractureski

damagedependinguponthe valueof Sfs.

Up to now, discussionof resultshas cons

a damaged

zone

aroundthe fractureof smallwi

on the contrary,when thewidth

zon e i s l ar ge

well behavesat shorttimesas a fracturedwel

withouta fractureskinend a fractureconduc

Cr lessthenthe realvalue. Later,thewell

as a fracturedwellwith en increasim?fractu

ductivity(flat

port ion ;

end,finall~,for la

timee,thepressurebehaviorof thissystembe

equalto the infinitesimal.ractureskinsolu

Thiskindof behavioris similarto thewellb

for finiteandinfiniteimel skindiscuseedby

9

Wattenbargerand Ramey.4

CONCLUSIONS

Fromtheresultspresentedin thiswork,

followingcommentsare important.

1.

The transientpressurebehaviorfor.

fracturedwell is importantlyaffectedby well

storageand fractureekindamage.

2. Resultswhenplottedas a functionaf

~D vs log tD showthatevensmallfracturesk

affectsthe pressuretimebehaviorat shortti

producingflat,almosthorizontalcuxvesthat

approachthe curvefor undamagedfractureasym

ellyfromabove.

3. Fractureskindamagemakeethe stabi

fluxdistribution

long

the fracturemoreunif

4. Fracturedamagecenbe estimatedrou

from short-timedataby a type-curvematching

niqueif fracturepermeabilityis knownandwe

sLorageis negligible.

50

Pressuretimebehaviorin alogpwfDv

tDpb% for a fracturedwellwith en undamage

turemay exhibita one-fourthslopestraightl

wellborestorageeffectsare negligible.

6. For intermediatevaluesof time,the

sientbehaviorof a wellwith a fracturecond

Cr between1 end 50 is similarto the behavio

wellwith a damagedinfiniteconductivityfra

thus,erroneousconclusion aboutthe fractux

systemcan be reachedif short-or long-timep

data-e not available.

i’. Tnw=ve - @s f orms- e

dat

the influenceof wellborestoragecan leadto

uniqueinterpretationnlyif pressuredatado

matchthe curveein the one-fourthslopestre

region,

8. For a bettercharacterizationf the

turedeystem,it is of primeinterestto have

estimateof the formationpermeability.


5/8

CDK ~7K9

UCRCD PTNf’fLl CV ANn CCQNllNllfl RAMANTFMI V

R

NOMENCLATURE

I

A = fracturestorageparameter,dimensionless

B? =

ratioof diffusivitiesf fractureend forma-

tion

B=

formationvolumefactor,bb@TE

CDf . dimensionlessellborestorageconstant

c compressibility,si-l

h = formationthickness,ft

k = permeability,d

p = pressure,psi

qf =

fractureflux density,STB/D-ft

cl=

wellflowrate,STB/D

i .

time,hours “

. fracturewidth,ft

w: = damagezonewidth,ft

x,y = spacecoordinates,ft.

~ =half fracturelength,ft

: =

viscosity,cp

= porosity,.raction

D = dimensionless

f

. fracture

i = initial

S . damagedzone

t = total

w = wellbore

1.

McGuire,W. J. end Sibra, V. J.:

l~~eEffect

of Vertical.ractureE..{

Well Productivity,”

Trans.,AIME (1960)~, 401-403.

2. —

an Poollen,H. K., Tinsley,J. M., and

Saunders,C. D.:

Wydraulic Fracturing-

FractureFlowCapacityvs Well Productivity,”

Trans.,AIME (19%) ~, 91-95.

?. m. M.:

wEffectof VerticglFractureson

Reserbir Behatior-IncompressibleluidCase,”

Sot.Pet.liim.J. (June1961)105-11’7.

4. Jefigs, A. R. ~dLord~ DC L.: “Fracture

FlowC~pacity

- A Key to SustainedProduction

AfterHydraulicFracturing,”paperSPE6127

presentedat theWE-AIME 51stAnnualFall

TechnicalConferenceend Exhibition,New

Orleans,La.,Oct.3-6, 1976.

5. Tinsley

J.

M.,Williams,J. R., Tiner,R. L.,

~d M~one, W. T.: ~WerticelFractureHeight-

Its Effecton Steady-StateProduction

Increase,’~. Pet.Tech. (MSY1969)633-638.

6. Raghavsn,R.,Uraiet,A., end l%omastG. W.:

l~vertics,l.ractureHeight: Effecton Tran-

sient FlowBehavior,”paperSPE 6016presented

at theWE-AIME 51stAnnualFall Technical.

Conferencesndl?xhibition,ew Orleans,La.,

oct. 3- 6, w76.

7. van Poollen.H. K.:

w~oductitityVS perme-

abilityin H@raulicsllYReduced-Fractures~” I

&L1l.”sndfiod. Prac.,-AF I1957)103-110.-

8. Scott,J. 0.:

fr,~~efect of VerticalFrac-

tureson TransientpressureBehaviorof Wells,”

J. Pet. Tech.(Dec.1963)1365-1369.

9. Rusell.D. G. and Truitt,N. E.: “Transient

Press&e Behaviorin VerticallyFractured

Reservoirs,~l’J.et.Tech.(Oct.1964) “1159-

1170.

10. Lee,W. J., Jr.:

wAnalyeisof Hydraulically

FracturedWellsWith PressureBuildupTests

paperSPE 1820presentedat theSPE-AIME42

AnnualFall TechnicalConferenceand Exhibi

tion,Houston,Tex.,Oct.

1- 4, 1967.

110 cl ~k, K. K. : YTransientPressureTestingo

FracturedWaterInjectionWells,’8. Pet.Te

(June1968)639-643.

12. Wattenbsrger,. A. end Ramey H. J., Jr.:

‘WellTestInterpretationf VerticallyFra

~pd Gas Wells,”J. Pet.Tech.(May 1969)6

.

13. van Everdingen,A. F. and Meyer,L. J.:

wfmlysis of BuildupCurvesObtainedAfterW

Treatments,”. Pet.Tech.(April1971)513

524.

14, ~m9, J. G.: lTheUse of R’e99LU’euildup

Informationto AnalyzeNon-Respondenterti

callyFracturedOil Wells?”paperSpE3345

presentedat ths SPE-AIMERockyMowtti

RegionalMeeting,?2illings,ont.,June 2-3

1971.

15.

Gringarten,A. C., Rsmey7H. JtsJr.9 and

Raghaven,R.:

t ~e99We A.nal.ysieor Frac-

tWed wells,~~aperSPE 4051presentedat ‘

S?&AIMEAnnusl.Fall TechnicalConferencee

Exhibition,San Antonio,Tex.,Oct. 8-11,

1972.

,16.Gringsrten,A. C., RemeypH. J.v Jr.p and

Raghaven,R.:

f?APPliedeseure Adysis ‘

~r;&ed Wells,”J. Pet. Tech. (J@J 1975)

-*

. .

17. Ramey,H. J., Jr. and Gringarten,A. C*:

t ~fectof High VolumeVerticalFractures

O

GeothermalSteamWell Behavior, ’aperpre-

sentedat the SecondUnitedNationsSympos

on theUse and Developmentof Geothermal

EnergyrSan Francisco,Celif.,May 20-29,

1975.

18. Locke,C. D. snd Sawyer,W. K.: “Constant

PressureJnjectionTestin aFractiared

Reservoir-HistoryatchUsingNumericalSim

tionsnd~e CurveAnalysis,’taperSPE 55

presentedat the SPE-AIME50thAnnualF~

TechnicelConferenceand~bition, Dalla

Tex.,Sept.@-Oct. 1, 1975.

19.

Cin~o-Ley,H6ber,Ssmeniego-V.?., and

Rmunguez-A.,N.:

lt~~eient PressureBeha

for a WellWith a FiniteConductivityVerti

Fracture,”paperSPE6014 presentedat theS

AIME Annuali%ll TechnicalConferenceend

lMhibition,New Orleans,La.,Oct. 3-6, 197

20. Raghavan,R.:

tlsome~actica Considerat

in theAnslysisof PressureData,”J. Pet.

Tech.(Oct.1976)1256-1268.

21. ~-al, R.”G.,A1-HussainY,R.t end mey~

H, J*t Jr.:

Wk Investigationf Wellbore

Storue endSkin Effectin UnsteadyLiq~d

Fiow:-1. AnalyticalTreatment,”Sot. Pet

*R. J. (Sept.1970) 291-297,

22. Cinco-Lev.H6ber and Samaniego-V.,ernand

f?A Sbpl&’Numerical.

Wellbore-Storageimul

tor,”to be published.

23. Cinco-Ley,H6ber and Semaniego-V.,prnsnd

tlWellTestAnalysisfor VerticallyFractur

Wells,l’o be published.

24. WattenbergerfR. A. and RameytH. J., Jr.:

.

~ ~ Investigation of WellboreStorage and

Skin Effectin Unste&@Liqtid Flow: 11.

FiniteDifferenceTreatment”SOC=Pet.

J (Sept.1970)

279-290.


6/8

WELLBORE

P

MPERMEABLE

BOUNDARIES

L

T

II

I

I

I

.-

—~ -

----

>

,FRACTURE

FIG, 1- FINITE CONDUCTIVITYERTICALFRACTUREN AN

iNFINITE SLAS RESERVOIR,

Q x. t)

PLANE SOURCE [WELLI

FIG, 3- FRACTURE FLOW MODEL,

FI NI TECONDUCTIVI TY FRACTURE

r—

NW

FIG, 2- FRACTURED WELL WITH A DAMAGED ZONE AROUND THE

FRA CTURE ,

af(x, f)

Y

PLANE SOURCE FRACTURE

* X

~

FIG, 4 - RESERVE FLOW MODEL,

1

cd

I

r’

.-4

0-3

0-2 .-1

0.000264

kt ‘

10

lo~

‘o= Pc,xf

..

FIG,

5- DIMENSIONLESS PRESSURE DROP VERSUS DIMENSIONLESS TIME FOR A FRACTURED WELL WITH

FRACTURE SKIN DAMAGE (WKF/~XFK =

0.2),


7/8

10

1

Id

lo”~

JO-4

IO-8

10-~

10-[

J

0.000264 kt

I

10

‘o’ flxc xf

lot

lo~

FIG,

6-

DIMENSIONLESS PRESSURE DROP VERSUS DIMENSIONLESS TIME FOR A FRACTURED WELL WITH

FRACTURE SKIN DAmAGE (WKF/17XFK =

2 ,

10

I

,0-3

to-d

Io-~

10-2

Jo-1

0.000264 k

I

to=

10

102

10

4FC, x?

FIG, 7- DIMENSIONLESS PRESSURE DROP VERSUS DIMENSIONLESS TIME FOR A FRACTURED WELL WITH

FRACTURE SKIN DAMAGE (WKF/IIXFK E

100),

3

\

bo”e

1

sf,’** +-1

A

\

I

r \\

I

-r

*

9

.2 .4 ,6 .8 j

x+

FIG, 8- STABILIZEDLUX DI STRI BUTION” FOR DI F-

FERENT FEA CTURE SK IN DAM Ac i E (WKF/7XFK ={0,2

es

o

-.

FIG,9-

STABILIZED FLux[.isTRIBuTIgN [o;o;;F-

FERENT FRACTURE SKIN QAMAGE (WKF/17XFI( .


8/8

.

lot

8

t

1

1

1 I

I

I

@ .

to=

0.000264 kt

+ r etXf

Fi g. 10-

Dimensionless

fracture

ski n damage).

pressurevs.

di mensi onl essti me for swel l w th a ful l y penetrati ngverti cal f racture

1

~o-l

10-2

10-3

10-4

1

to =

0.000264 kt

01 v Ct

Xf ’

Fi g. 11 . - Di mensi onl esswel l bore pressureversus di mensi onl esst i me fora vert i cal l yf racturedwel l w th

f racture skin damage and wel l bore storage.

#1 effect of wellbore storage and damage on the transient pressure behavior of vertically fractured...

Documents