#1 effect of wellbore storage and damage on the transient pressure behavior of vertically fractured...
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8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf
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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.
..
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8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf
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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>
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8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf
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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.
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8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf
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.
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.
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8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf
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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-
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J. Pet. Tech.(Dec.1963)1365-1369.
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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.
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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),
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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( .
-
8/9/2019 #1 Effect of Wellbore Storage and Damage on the Transient Pressure Behavior of Vertically Fractured Wells.pdf
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.
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