Well Testing AnalysisBasis for Grade:Homework 20%Examinations (3) 45%Final Examination 25%Class Participation/Pop Qi!!es"0%total # "00%Grade Cutoffs: (Percentages)$% & '0(% )'*'' to )0 C% +'*'' to +0 ,% -'*'' to -0F% & 5'*''.ntro/ction to 0ell 1estin2ObjectivesList the more common objectives of well testing.Describe the diffusivity equation by explainingits purpose and applications assumptions made in its derivation and how it is derivedits form for one-dimensional radial flow.List, define, give the units for, and specify typical sources for each of the variables that influence responses in a well test.Compute the total compressibility for different reservoir systems undersaturated oil, saturated oil, gas!.What Is A Well Test" tool for reservoir evaluation and characteri#ation$nvestigates a much larger volume of the reservoir than cores or logs%rovides estimates of permeability under in-situ conditionsnear-wellbore conditionsdistances to boundariesaverage pressureHow .s $ 0ell 1est Con/cte/3qtqtpWell is allowed to produce normallySensor is lowered into wellProductionremains constantPressure stabilizesHow .s $ 0ell 1est Con/cte/3q = 0tqtpSensor is lowered into wellWell is shut inProduction drops to0PressurerisesFn/amental ConceptsApplications and objectives of well testingDevelopment of the diffusivity equationDefinitions and sources for data used in well testing 14pes an/ Prposes o5 0ell 1ests%ressure transient tests&e generate and measure pressure changes with timeDeliverability tests&ell controlled production%roduction "nalysis!'se of production data for goals usually achieved by well testingPro/ction /ata anal4sis(eservoir properties permeability, s)in factor, fracture half-length, etc!.(eservoir pore volume estimated using long-term production performance!.*stimated ultimate recovery *'(!+movable fluid volumes.0ell 1est $pplicationsDefine reservoir limitsEstimate average drainage area pressureDiagnose productivity problemsCharacterize reservoirEvaluate stimulation treatment effectiveness0ell 1est 678ecti9es :in2le;< =ltiwell 1estsqWell is allowed to produce normallySensor is lowered into well:in2le;< =ltiwell 1estsWell is shut in, pressure is measuredWell is shut inSensor is lowered into offset well. . . pressure is measured at offset well(s):in2le;< =ltiwell 1ests>in/s o5 0ell 1estsqtPwfProduce well at constant ratePlot pressure responseower sensor into wellProduce well at constant rateShut in wellower sensor into welltPwsPlot pressure response>in/s o5 0ell 1eststp!n"ect fluid into well at constant ratePlot pressure response>in/s o5 0ell 1eststp!n"ect fluid into well at constant rate#easure pressure responseq=0Shut in well>in/s o5 0ell 1ests=ltiwell 1ests. . . measure pressure response at offset well(s)Produce one well at constant rate . . .tp. . . measure pressure response at offset well(s)$lternately produce and shut in one well . . .tpq=ltiwell 1estsP1$% :in2le;0ell 1estsone well in which the pressure response is measured following a rate change pressure buildup test shut in after controlled productiondrawdown or flow test !specific drawdown tests" are called reservoir limits testspressure falloff test similar to a pressure buildup test# e$cept it is# conducted on an injection wellinjectivity test %nject into the well at measured rate and measure pressure as it increases with time analogous to pressure drawdown testingP1$% =ltiwell 1ests&low rate is changed in one well 'ressure response is measured in one or more other wellsDirectional variations of reservoir properties !orientation of natural fractures('resence or lac) of communication between two points in the reservoir*atio of the porosity+compressibility products of the matri$ and fracture systems=ltiwell tests%$nterference tests ,he active well is produced at a measured, constant rate throughout the test-ther wells in the field must be shut in so that any observed pressure response can be attributed to the active well only.!%ulse tests,he active well produces and then, is shut in, returned to production and shut in again(epeated but with production or shut-in periods rarely exceeding more than a few hours%roduces a pressure response in the observation wells which usually can be interpreted unambiguously even when other wells in the field continue to produce!,eli9era7ilit4 tests (,1)production capabilities of a well under specific reservoir conditionsprimarily for gas wellsabsolute openflow!A,&( potentialinflow performance relationship !%'*( or gas bac)pressure curve,1% Flow;$5ter;Flow 1ests !referred to as gas bac)pressure or four+point tests( producing the well at a series of different stabilized flow rates measuring the stabilized bottomhole flowing pressure at the sandface typically# with a sequence of increasing flow rates ,1% :in2le;Point 1estslow+permeability formationsflowing the well at a single rate until the bottomhole flowing pressure is stabilizedrequired by many regulatory agenciesrequires prior )nowledge of the well-s deliverability behavior !from previous testing or from correlations with other wells producing in the same field under similar conditions(,1% .soc?ronal 1ests.pecifically# the isochronal test is a series of single+point tests developed to estimate stabilized deliverability characteristics without actually flowing the well for the time required to achieve stabilized conditions/he isochronal test is conducted by alternately producing the well# then shutting in the well and allowing it to build up to the average reservoir pressure prior to the beginning of the ne$t production period.ssesDevelopment 0ells vs E$ploration 0ells'roducing 0ells vs %njection 0ells.hallow 0ells vs Deep 0ells.timulated 0ells vs 1nstimulated 0ellsEffects of *eservoir 'roperties2ow 'ermeability vs 3igh 'ermeability &ormations.ingle 4ones vs 5ultiple 4ones.afety and Environmental Considerations.weet 6as vs .our and Corrosive 6ases,ther environmental Concerns Pro/ction /ata anal4sis*eservoir properties !permeability# s)in factor# fracture half+length# etc(*eservoir pore volume !estimated using long+term production performance(Estimated ultimate recovery !E1*(7movable fluid volumesEn/ o5 Class1?e ,i55si9it4 E@ationDescribes the flow of a slightly compressible fluid having constant viscosityin a porous mediumat constant temperatureDerived from basic relationships ofcontinuityflow equation !Darcy8s law(equation+of+state1?e Continit4 E@ation! "v A v A #(Av$"(Av$!Flow E@ation (,arc4As Baw)or# in differential form#Lp kAqxp kuxxE@ation o5 :tate 5or a :li2?tl4 Compressi7le Bi@i/op p coe1?e ,i55si9it4 E@ationtpkcrprr rt.%ne&dimensional, radial form'Formation Colme FactorsurfresVVBsurfresoVVB(or oil'surfreswVVB(or water'surfresgVVB(or )as'Ciscosit4A fluid8s resistance to flow6asoline7low viscosity9aseline7high viscosity Fli/ Compressi7ilit4pVpVVcln .Porosit4Permea7ilit4p AL qkPore Compressi7ilit4plnpcf.%hale%andDet Pa4 1?icknessh&h!h"h'(*o perforationsin this sand)h = h1 + h2 + h3Det Pa4 1?ickness+ertical well, horizontal formation,e-iated well, horizontal formation,e-iated well, slanted formation+ertical well, slanted formation:atrations0ell7ore Ea/isr(1otal Compressi7ilit4g g w w o o f tc S c S c S c c)odeling *adial +lo(.nstrctional 678ecti9es.tate the Ei+function solution to the diffusivity equation# and list all the assumptions on which it is based.tate practical rules for determining the numerical values of the Ei+function6iven formation and fluid properties# be able to calculate the radius of investigation at a given time and the time necessary to reach a given radius of investigationDescribe the effects of reservoir properties on the radius of investigationEa/ial Flow Eeser9oir =o/elhrr(Bul,for#ationEi;Fnction :oltionto t?e ,i55si9it4 E@ationktr cEikhqB. p pti/0123 45xuuuex Ei0*00" 0*0" 0*" " "0 "00-.024--/i(-.$Ei;Fnction Frap?0og a11ro.i#ation/i-function dro1s to 2ero:?ort;1ime $pproximation 5or Ei;Fnction :oltionip p.5012/>ktr ctA11lies (hen(large radius or s#all ti#e$Bon2;1ime $pproximation to Ei;Fnction :oltionktr clogkhB q. p pti/.5.3223 .3/A11lies (hen5. 5012/.ktr ctIsin2 Horner 1ime Eatio0it? $/8ste/ 1imeaa ptt tHTR +Don;,arc4 Flow&low equations developed so far assume Darcy flow&or gas wells# velocity near wellbore is high enough that Darcy8s law failsHon+Darcy behavior can often be modeled as rate+dependent s)in$pparent :kin FactorgDq s s + -Estimatin2 Don;,arc4 Coe55icientFrom =ltiple 1ests024-)"00 2 ( )DDDDDtptptln => DDDtpt,eri9ati9e 14pe Cr9et5HC5474""44"446444t5HP5C5e!s3474"C5e!s3"484C5e!s3"445ifferences in curve sha1es #a,e #atching easierPressre J ,eri9ati9e 14pe Cr9est5HC5474""44"446444P5Co#bining curves gives each ste# value t(o distinctive sha1esPressre/,eri9ati9e 14pe Cr9et5HC5474""44"446444P5WB% Transition *adial +lo(/arly Ti#e *egion )iddle Ti#e *egion?nit %lo1e 0ineFori2ontal 5erivativePressre J ,eri9ati9e 14pe Cr9et5HC5474""44"446444P50o( s,inFigh s,in>o s,inE@i9alent 1ime For P(I 1ests( )11]1

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sr cktkhqBpw tGCK> ormEa/ial Flow( ) b t m p + logAeneral >orm( ) ( )E>Eorm< B t m b p :p?erical Flow< B t m b p Aeneral >ormDerivative( )< B< BractureAeneral >ormB Bb t m p + A B(ilinear FlowAeneral >ormB Bb t m p + A BDerivative( )A BA BABt mtb t mttptBB B+ (ilinear Flow.lapsed time (t ), hrsPressure chan)e (p ) and deri-ati-e (p ), psiPressure in fractured, undama)ed wellPressure in fractured,dama)ed wellPressure deri-ati-e"',ia2nostic Plot.lapsed time (t ), hrsPressure chan)e (p ) and deri-ati-e (p ), psiWellborestorage%1herical flo(*adialflo(*echarge/sti#ating Average *eservoir PressureEstimatin2Eeser9oir PressreDiddle ,ime (egion DethodsDatthews-;rons-Ca#ebroe) Dethod(amey-Cobb DethodLate ,ime (egion DethodsDodified Dus)at Dethod"rps-:mith Dethod=i//le;1ime Ee2ion =et?o/s;ased on extrapolation and correction of D,( pressure trend"dvantage'se only pressure data in the middle-time regionDisadvantagesEeed accurate fluid property estimatesEeed to )now drainage area shape, si#e, well location within drainage areaDay be somewhat computationally involved=att?ews;(rons;Ha!e7roekProducing time prior to shut-in, tp = 482 hrPorosity, = 0.15 Viscosity, m = 0.25 cpTotal compressiility, ct = 1.!15 " 10-5#rainage area, A = 1500 " $000 %t &a 2"1 reser'oir(12Cr9es 5or :@are ,raina2e $rea;"0"2345-0*0" 0*" " "0t1A51)BF5Cr9es 5or 2x" Eectan2le;"0"2345-0*0" 0*" " "0t1A51)BF5Cr9es 5or 4x" Eectan2le;2;"0"23450*0" 0*" " "0t1A51)BF5=att?ews;(rons;Ha!e7roek2400245025502!502)501 10 10210$10410510!*orner time ratio+hut-in ,ell pressure, psiap*=2689.4m=26.7+tep 1- Plot pressure 's. *orner time ratio +tep 2- ."trapolate slope m to /nd p*( ) ( ) ( )( ) ( ) ( )( ) ( )E=>E>>> B=>> B> CB=B B=>AG< =F >>>>>>=" cktttpp"D " cktttpp"D>>>+tep $- 0alculate dimensionless producing time=att?ews;(rons;Ha!e7roek+tep 4- 1n appropriate 23* cur'e, /nd p23*#=att?ews;(rons;Ha!e7roek-101234560.01 0.1 1 10p23*#tp4#tp4# = 0.$52"1 rectangle2.05( )( )C=E>> B=>> B> CB=B B=>AG< =F >>>>>>=" cktttpp"DEame4;Co77:tep 6F >ind the Diet# shape factor -A for the drainage area shape and well location+hape %actor CA = 21.8$!6( ) ( )CEFE=> GG>t! cktf tD !f>>kccktft fffD f tD !h! cCCfrff fcDCk!k w$ ff frk!k wC&racture flow2inear?ilinear&ormation flow2inearElliptical'seudoradialFlow Ee2imes in FractresFractre Binear FlowTransient#oves do(n fracture lengthTransient has not #oved into reservoirTransient has not reached end of fractureFractre Binear Flow5imePressure(0og-log 1lot$(Too early for 1ractical a11lication$D ! fDcDDft$p BC>B>>< D !cDft$Elliptical FlowPse/ora/ial FlowPse/ora/ial Flow6#fLts . .r cktlogkhqB .pw t230 5 /6 63 .3//,ept? 65 .n9esti2ationba.////)(!x/ / /) ! LfLf+or linear flo(6 1seudosteady-state flo( e.ists out to a distance b at a di#ensionless ti#e given by,ept? 65 .n9esti2ation>>b cktttbD BbDt< B>1]1tcktb 5e1th of investigation for a linear syste# at ti#e t,ept? o5 .n9esti2ation< B>1]1tcktb < >BB ( )f f fsssw h k ! qBp< >>BB s fpqBkhs >>F>G>( ) ,_,_f f fssw h k ! qBqBkh< >>BB>>F>G> f fssfw k k!sH4/ralic Fractre 0it? Fractre Face ,ama2ekwfkfkswsLfFractre Face :kin Factork"! qBp>>BB ( ),_ k k ! hw qBps f fssB BA >>BBs fpqBkhs >>F>G>( ),_,_,_k k ! hw qBqBkhs f fsB BA >>BB>>F>G> ./s fsfkkLws(ilinear Flow $nal4sisProce/re%dentify the bilinear flow regime using the diagnostic plot 6raph pwf vs tB@A or pws vs t?eB@A &ind the slope m? and the intercept p> of the best straight line Calculate the fracture conductivity w)f from the slope and the fracture s)in factor sf from the intercept(ilinear E@i9alent 1ime11 .1 . 1 .t t t t tp p Bep Bet t 0 t tp p Bet t 0 t t(ilinear Flow $nal4sisE@ations=> >>F>G>p pqBkhsi f ( )wf fp pqBkhs >>>F>G>Buildu15ra(do(n(ilinear Flow $nal4sis143!8'!7' 1si#38&79 1siHhr"H'1(f3!8!978 1si1s!844!8>BC( and beginning of pseudoradial flow !t2fD J E(*equires independent estimate of ) 6ives estimate of 2f and sf Cannot be used to estimate w)fPse/ora/ial Flow $nal4sisProce/re%dentify the pseudoradial flow regime using the diagnostic plot 6raph pwf vs log!t( or pws vs log!te( &ind the slope m and the intercept pBhr of the best straight lineCalculate the formation permeability ) from the slope and the total s)in factor s from the interceptEstimate fracture half+length from total s)in factorPse/ora/ial Flow $nal4sisE@ationsBuildu15ra(do(nmhqBk CBCDistance to boundary# ftAnalysis assumed net pay ft from 0ell O?P'?1 test interpretation indicates nearest boundary K>> ft awayCan these inconsistencies 1ossibly be resolvedWhat could have caused this #uch error in the distance esti#ate:orces o5 .npt ,ata2og interpretation&luid properties*eservoir and well properties,ata From Bo2 .nterpretation'orosity0ater saturationHet pay thic)nessCases o5 Error in Bo2 .nterpretation&ailure to calibrate the logging tool&ailure to ma)e necessary environmental corrections&ailure to calibrate the log+derived properties against core measurements&ailure to select appropriate cutoffs for net pay estimationError in Bo2 .nterpretation ,ataPara#eter 5eviation0it?ot 0it? correction correctionPorosit4 t"5 % t 5 % 0ater satration t 40 % t "0 % Det pa4 t50 % t "5 % Fli/ Properties ,ata&ormation volume factorCompressibility9iscosityError in Fli/ Properties ,ataPara#eter 5eviationBg 5rom compositiont "*"% to t 5*)% Bg 5rom composition t "*3 % to t +*3%(as mc? as 2+% i5imprities are i2nore/)cgDe2li2i7le at low pressre g t 2% to t 4%< g & " p to 20% low< g K "*5From Fas Properties CorrelationsError in Fli/ Properties ,ataPara#eter 5eviationBo, p K pb t "0%Bo, p pb t 5%co, p K pbIp to 50% low at ?i2? pressre(est near pbco, p pbt "0%< p K 500 psi t 20%< p & 500 psio 6r/er o5 ma2nit/e onl4From 6il Properties Correlations6t?er .npt ,ata&low rate0ellbore radius&ormation compressibility/otal compressibilityError in 0ell an/ Eeser9oir ,ataPara#eter /rrorFlow rate Failre to recor/ rate 7e5ore (I test.naccrac4 in estimates< a9era2es0ell7ore ra/isPoor c?oice o5 measrementFormation compressi7ilit4 Estimation errors1otal compressi7ilit4 Cariations in 5li/ satrations$7normall4 pressre/ reser9oir6il compressi7ilit4From =easrement or Calclations1otal Compressi7ilit4g g w w & & f tcccc c + + + Eac? p?ase o5 5li/times its compressi7ilit4Formation compressi7ilit4E55ects o5 Errors9ertical well.ingle+phase flow3omogeneous reservoir?oundaryHo+flow# linear constant pressure# closed/estDrawdown# buildup# injection# or fall+offDuration long enough to identify boundaryErrors in Ciscosit4 %f input ; < true /hen" kcalc ; < ktrueHothing else will be affectedErrors in Porosit4 %f input ; < true# /hen" scalc ; strueM >=ln!=ln!=ln!E=?oundary# BFF ft:oltion 1o Pro7lem 2.eismic interpretation indicates boundary E>> ft from 0ell O?P'?1 test interpretation indicates nearest boundary K>> ft awayTotal co#1ressibility could be off by a factor of "4Boundary could be a factor of & too far a(ay:mmar4'ermeability is most affected by errors in viscosity# net pay# and flow rateDistances to boundaries and drainage area are most affected by errors in compressibility.)in factor is not affected to a large degree by any input variable(on/e/ Eeser9oir (e?a9iorCations*ecognizing may be as important as analyzing5any reservoir models may produce similar pressure responses%nterpretation model must be consistent with geological and geophysical interpretationsC?aracteristics?oundaries control pressure response following middle+time regionEquivalent time functions apply rigorously only to situations where either'roducing and shut+in times both lie within middle+time region.hut+in time is much less than producing time?oundaries affect pressure responses of drawdown and buildup tests differently:?apes o5 cr9esDurations of flow regimes e$plain shape of drawdown pressure responses .hape of buildup derivative type curve depends on how the derivative is calculated and plotted.hut+in timeEquivalent time.uperposition time:perposition in spacePro/cin2 wellsEa/ial 5low pattern$pparent no;5low 7on/ar4 7etween wellsPro/cin2 well:perposition in space*eal no;5low 7on/ar4.ma2e wellE@al /istances 5rom no;5low 7on/ar4:perposition in spacePro/cin2 well.ma2e well .ma2e wellDo;5low 7on/ar4Pro/cin2 wellDo;5low 7on/ar4:perposition in space:perposition in space.n5inite;actin2 reser9oir0*0"0*"""0"00"EJ03 "EJ04 "EJ05 "EJ0- "EJ0+ "EJ0) "EJ0'5i#ensionless ti#e5i#ensionless 1ressure,raw/own 14pe Cr9e.n5inite;actin2 reser9oirDo 7on/aries encontere/0*0"0*"""0"00"EJ03 "EJ04 "EJ05 "EJ0- "EJ0+ "EJ0) "EJ0'5i#ensionless shutin ti#e5i#ensionless 1ressuretp,#"0)tp,#"0+tp,#"0-tp,#"05,raw/own(il/p Eesponse5erivative (ith res1ect to shut-in ti#e.n5inite;actin2 reser9oir:?ape /epen/s on /ration o5 pro/ction time prior to s?t;in 5i#ensionless shut-in ti#e(il/p Eesponse5erivative (ith res1ect to eBuivalent ti#e.n5inite;actin2 reser9oirDot a55ecte/ 74 pro/cin2 time"00"0"EJ030*0"0*"""EJ04 "EJ05 "EJ0- "EJ0+ "EJ0) "EJ0'5i#ensionless 1ressure5i#ensionless eBuivalent ti#etp,#"05tp,#"0-tp,#"0+tp,#"0)0*0"0*"""0"00"EJ03 "EJ04 "EJ05 "EJ0- "EJ0+ "EJ0) "EJ0'5i#ensionless ti#e function5i#ensionless 1ressuretp,#"05>$ estimated value may indicate reser*&ir storage instead of 0?.wb wbc V C +luid-filled (ellbore *ising liBuid levelgg "Ccwbwb CB==BAA:kin Factor2i)ely estimates by completion typeHatural completion >Acid treatment +B to +E&racture treatment +E to +C6ravel pac) M= to MB>&rac pac) +< to M