SPESPE 14237

Case Study of a Low-Permeability Volatile Oil Field UsingIndividual-Well Advanced Decline Curve Analysis

by M.J. Fetkovich,Phillips Petroleum Co.; M.E. Vienot,Phillips Petroleum Co. Europe-Africa;and R.D. Johnson and B.A. Bowman, Phillips Oil Co.

.CPE Marnha..“. - . ..”..,””.”

Copyright 1985, .%xiety of PetroletFrn-Engineers

This paper waa prepsred for presentation at the 60th Annual Technical Conference and Exhibitionof the Society of Petroleum Engineera held in LasVegaa, NV September 22-25, 1985.

This paper was selected for presentation by an SPE Program Committee followingreview of informationcontained in an abstract aubmiwedby theauthor(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correctionby theauthor(a).Tha material, as presented, does not necessarily reflect any positionof the Society of Petroleum Engineera, ita officers,or members. Paperspresented at SPE meetings are subject to publicationreview by Editorial Commitfaes of the Sodety of Petroleum Engineers. Permiaaicmto copy isrestrictedto an abetract of notmore than 300 words. Illustration may notbe copied. The abatractshouldcontainmnapicuoua acknowledgmentofwhereand by whom the paper ia presented. Write PublicationsManager, SPE, P.O. Sox 833836, Richardson, TX 750S34S36. Telex, 730389 SPEDAL,

Am.7. .*TAD> I KIW I

rMTnnnlm*TTn.t111 I Kuuub I lull

This paper presents a detailed case history study In solution gas drive reservoirs, decline curve

of a low permeability volatile oil field located analysis of rate-time data for predicting futurein Campbell County, Wyoming. The field was anal- -production and determining recoverable reserves for

yzed on an individual well basis using advanced a fairly large number of wells is conwnonlydone

decline curve analysis for 40 individual well com- using the Arpsl empirical equations and a compu-pletions. Well permeabilities, skins and original terized statistical approach to arrive at answersoil in place are calculated for each well from rate- fairly quickly. For wells in high permeabilitytime analysis using constant wellbore pressure type reservoirs producing essentially wide-open$ wfthout

curve analysis techniques. future backpressure changes and without futurestimulation treatments, the results obtained should

Original oil in place values calculated from rate- be reasonably good providing the limits of thede-

time analysis for individual wells are used with cline exponent b of between O and 1.0 are honored.recoverable reserve projections from the declineanalysis to obtain fractional recoveries for each At the other extreme in analyzing rate-time datawell. Gas-oil ratios versus fractional recovery for predicting future production and recoverable

curves are also made for each well using historical reserves, a reservoir simulation study could be

cumulative production and the calculated oil in undertaken. However, this approach could take as

place values. Ultimate fractional recovery numbers much as a year to accomplish and normally would notand GOR vs fractional recovery curves, plotted for be considered acceptable, particularly for time-

each well, are shown to suggest different rock types constrained property acquisition or sales situations

and reservoir fluids. Multi-well decllne curve where few of the detailed reservoir parametersanalysis shows the validity of the varfables s necessary for a simulation study are available.

(skin), k, OOIP, ultimate fractional recovery andGOR vs fractional recovery evaluated from each Many of the newer oil and gas fields being discov-

well’s type curve evaluation. These variables must ered and produced are in the low permeability class-

all give consistent and reasonable numbers when ification, where transient behavior can last for

compared with each other. A single well analysis years, and therefore are not amenable to analysis

can easily give results that are not recognized as using the Arps equation alone. Also, a model studybeing invalid unless compared with other wells in of such low permeability reservoirs would require a

the field. very fine grid system to correctly simulate andmatch the early transient rate-time decline data.

The study also illustrates flowing and pumping wellbackpressure changes in a well’s decline, the method An approach to the problem of analyzing low petme-

of handling such changes, and their effect on ulti- ability wells and total field rate-time decline has

mate recoverable reserves predictions. Conventional been given in papersz 3 q 5 6 that illustrate

decline curve analysis can not handle backpressure methods of handling both the transient and depletionchant-m. haeaii.n of ~~~ .-nq.+o..+n+ +k.+ A..* ---+--I-

,.-,.=-- “-----=stages Of ‘atQ-tjme decline.*v,=bI91111,briat. WIIaI. Lurlbrui>

#.ah414A.-..K!l? ~t?rmcautl Ibles,

the decline in the past will also continue in the skins from stimulation treatments and original oil

future. in place or original gas-in-place can be calculatedfor each well from rate-time data using constantwellbore pressure type curve analysis techniques.

References and 111ustratlons at end of paper.

CASE STUDY OF A LOW PERMEABILITY VOLATILE OIL FIELDUSi?K iNDIViWAIL-klELL ADVA

With a field case study of the School Creek Field inCampbell County, Wyoming, a low permeability vola-tile oil field, we will present a stepwise procedurefor doing a total field study using individual welladvanced decline curve analysis techniques. Orig-inal oil in place values calculated from rate-timeanalysis for individual wells are used with recover-able reserve projections from the decline analysisto obtain fractional recoveries for each well.Gas-o~l ratio versus fractional recovery curves arealso made for each well using historical cumulativeproduction and the calculated oil in place values.Ultimate fractional recovery values and GOR versusfractional recovery curves, plotted for each well,are shown to suggest different rock types and reser-voir fluids. Multi-well decline curve analysisshows the validity of the variables s (skin), k,OOIP, ultimate fractional recovery and GOR versusfractional recovery evaluated from each well’s typecurve match point.–-These variables must all giveconsistent and reasonable numbers when compared witheach other. A single well analysis can often giveresults that are not recognized as being invalidunless compared with several other wells in thefield. The study also includes and illustratesflowing and pumping well backpressure changes in awell’s decline, the method of handling such changesand their effect on ultimate recoverable reservespredictions. Conventional decline curve analysisapproaches do not consider backpressure changes andtheir effect on projected recoverable reserves.

School Creek Field - Wyoming -.

The School Creek Field is located on the easternflank of the south central portion of the PowderRiver Basin in Campbell and Converse Counties,Wyoming. Following deposition of the underlyingSkull Creek Shale, the lower Cretaceous sea recededfrom the area of the Powder River Basin. Subse-quently, a wide-spread drainage system developed andcarved its pattern into the Skull Creek Shale. Asthe lower Cretaceous sea transgressed east, Muddydeltaic sediments buried the previously depositedchannel sediments as the sea continued to inundatethe basin. Continuous basin fill by deposition of+k- -.,fi-l..i--h“”,. Ck.la m.ae,,7+aA ;“ the ~W,~~~Gil= UVCI IJITIY IW.IWIJ .I,,-,C , C=UtbCU ,,, b,,

reservoir sands being ideally “sandwiched” betweentwo marine hydrocarbon source shales.

In the School Creek Area, a north-south paleodrain-age pattern was developed upon the underlying SkullCreek Shale and controlled the distribution of theproductive tidal channel and point-bar sands of thelower Muddy formation. Younger upper Muddy marinefacies units were then deposited as the Cretaceoussea transgressed east resulting in some well devel-QPQd Productive rnarjneoffshore b?!’Se!l(!s‘ithin tk

field area.

In the School Creek Field, the Lower Muddy channelsands have 35 well completions with an average of 11net feet of pay per well and an average porosity andwater saturation of 13.6% and 39%, respectively.Upper Wddy bar sands have 5 well completions withan average of 12 net feet of pay per well and anaverage porosity and water saturation of 22% and14%, respectively. Production has also been estab-lished in secondary objectives, which include theSussex, Turner, and Dakota formations. These wells---are iiOtincluded iiithis Study.

rn llrn lNC @llDllE ANhl vCTCLLIJLJLL lIIL bUnVL ,_lllAL1.lAtiCDF 1A9274, b .T*-,

Figure 1 is a plat showing the well locations, theirrelationship to the Channel Sand and Bar Sand andthe three wells from which PVT samples were taken.Figure 2 is a type log for a School Creek FieldMuddy formation completion.

The School Creek Field was discovered in 1980 whenthe Matheson E-1 well was drilled to 10,000 feet andcompleted in the Muddy formation. The initial res-ervoir pressure was approximately 3700 - 3600 psi.Basic fluid properties are given from three differ-ent PVT studies in Table 2 and Figure 3. Two quitedifferent fluid samples were obtained in the ChannelSand: the Federal EE-1 sample with a bubble pointpressure of 3400 psi, GOR of 1557 SCF/BBL and theMatheson E-1 sample with a bubble point pressure of2705 psi, GOR of 736 SCF/8BL. Based on reportedinitial producing gas-oil ratios, the Federal EE-1sample was used to represent wells in the southernportion of the field while the Matheson E-1 samplewas used for wells in the northern portion of thefield. The Federal J-1 sample was only usedl~~ rep-resent the five Bar Sand well completions.bubble point pressure was 2838 psi with a gas-oilratio of 1189 SCF/BBL.

Basic Decline Analysis Equations

The Arpsl empirical decline equations that can beused for analysis and forecasting future productionwhen depletion is clearly indicated are, for

b>Oqi

q(t) = . . . . . . . . . . ..o... (lj[1 + b~it]l/b

and for b = O (exponential)

q(t) . _l!I-eDit

where the limits of b

For type curve aiialys’

q(t)qDd = —

qi

and

tod = Djt

.............0..(2)

are between O and 1.

s

. . . . . . . . . . ...0..(3)

. ..0............(4)

~p~fi 1,-.-1-”+,,- -,,”..a “1=+,.h;m” +hc. ,n.+.h a+ ~~eI“Y-,WJ t,J@ L“, .C ,WZkb,,,,ty, L,,C ,,,(11.b,, “,

rate-time data yields b, t - tDd$ and q(t) - qDd.From these values qi and Di are evaluated and canthen be used in the predictive equatiorrs1 or 2above to forecast future production and to obtainultimate recoverable reserves.

As given in reference 3, we can also evaluate theproductivity factor from q(t) - qod match point, thesame match point as would be used with the above~ equations.

~E 14237 M. J. FETKOVICH M. E. VIENOT, I

kn

‘“’<[n (;)-:j ‘;::: .’: ...(.,

where rw’ is the effective wellbore radius incorpor-ating the skin term, r ‘ = rw e-s.

YThe skin term

can also include the e feet of a shape factor CA.See reference 7. If re/rw’ can be defined from anatch of early transient data, we could then evalu-ate k and s of the well.

To evaluate pore volume3, Vp, from the match point,we have

Zh$ .m t q(t)

‘P=m re .—. — ...(6)

(Met)F(TR - pwf) t~ qod

R

which gives the pore volume at the start of the de-cline analysis.

In the above equations, (m) is normally evalu-ated at average pressure (FR + pwf)/2 while_(uct)is evaluated at reservoir shut-in pressure p .

R, equa-In terms of an oil pseudo pressure, m(p)oi

tions 5 and 6 can be written as

kh 141.2 q(t)= ● —

in(E) -11 ‘@R)-‘(pwf)/ rwY 2j

1and Vn =

p ( Llct)T [(m(TR)-m(pwf)l

R

Usingfinedcientwould

....(7)

qDd

t q(t).—. — ●..(8)tDd q~

Ia simple, practical engineering m(p)oil de-from inflow performance relationships, suffi-for decli~e curve analysis, (see Appendix), wehave for pR~pb (bubble point pressure)

kh141.2 (2FR)(LId- q(t)

P-

2FR (6)F t q(t)

and Vp = R ● —* —

(Ct)F (TR* - Pwf*) ‘Dd qDd

R

. ..(9)

. ..(lO)

D. JOHNSON, and B. A. BOWMAN

Note that~~ is now evaluated at reservoir shut-inr.”aec.,,”a se ‘iel..#..\~lC23UlC, ~K, (Z>

S.ah’i,.h +ha” SIlm.,e ,..”—la \p* j, WIIILI1 Lllclt al tuna Lall-

!cellation of the viscos ty terms in equation 10.

For cases where pwf < pb and~R > pb, as is the casefor most of the School Creek Field wells in thisstudy, the productivity factor is evaluated from

kh 141.2 (P6)1 q(t)

.-.. (11)

.()]f

‘ein — -~

~R - 1Pb)+(pb2-pwf2) qDd

rw’ 2 2pb

and

(B)E t q(t)

~ .—.—.~ (12)‘P

1(et)- (TR -

1pb)+(pb2 - pwf2) ‘Dd ql)d

P“R L

Equat~ons 11when pR < pbAppendix~.

To calculatewe have

and 12 reduce to a simple APZ form(see for example equation A-9 in the

a drainage radius from the pore volume,

d“p x5.615re =

nh$

and oil in place atysis is

Vp(1 - Sw)

OIP =

...................(13)

the start of the decli’neanal-

..........00.......(14)

R

Finally, the original oil in place is determinedfrom

~~!p = ~~p + !$ flK\P .......*............4-.

where Np is the cumulative production to the startof the decline analysis.

Changes in Backpressure

Since many of the wells in the School Creek Fieldwere evaluated under flowing conditions with morethan one change in backpressure occurring, we haveextended the single backpressure change superpo-sition equation given in reference 20 Expressed interms of m(p)oil, for simplicity, we have

—

.’ .

CASE STUDY OF A LOW PERMEABILITY VOLATILE OIL FIELD} USING INDIVIDUAL-WELLADVA

(71 ~ .m i.. . ~-lkh cm{p/R

111\~wt ]J

q(t) = 1

[() ]

1141.2 In 3 - —

t-w’ 2

qDd (tD~)

m(pwfl)-m(Pwf2) m(pwf2)- m(pwf3)qDd(tD@odl) +

+ m(~R)-m(p~l) m(FR)- m(pwfl)

m(Pwfn-l)-m(Pwfn)“ q~(t~ - tDd2) + ... +

m(FR)-(pwfl)

● qf)d(tod‘tDdn ~)-1 . . . . . . . . . . . . . ..(16)

The rate change Aq for any backpressure change isa constant fraction of the initial rate at the sameinitial transient tfme period, as the rate changeretraces the original q~ - t~ curve. The samevalue of the decline exponent b is used for all ratechange superposition calculations.

[

m (Ptil) - m (pwf2)Aql = q2 = ql 1......(17)

m (FP) - m (Pwfl)— .. .

[

m (pwf2) 1-m(pwf3)and Aq2 = q3 = ql . . ..00.(18)

m (TR) - m (pwfl)

Note that the ql/[m (TR) - m (pwfl)] is the initialproductivity index in BOPD/psi or BOPD/psi2, which-ever is appropriate, times a Ap or A(p2) term forsuccessive flowing pressure changes.

For the more general expression used in this studyfor pressure above and below the bubble point pres-sure-

Aql “ qz s

and

Aq2 =q?J=

AI [Pti$::l ““”””””(19)

P~2*”Pq21 ......(20)

ZPb J

ED DECLINE CURVE ANALYSIS SPE 14237

If nd when~R < pb the expression reduces to the9A(p ) fOr’M. Siiiiilarlywhen p f > pb the Ap form

is obtained. YThe Ap form wou d be appropriate foruse with decline exponent values of b = O and AP2~orm for b values greater than zero. For A(P2),PRSPbt the first backpressure change relationshipbecomes

q (PM12 - Pwf22)Aql= qz = ● ...(22)

(~R2 - Pwf12)

For Ap, pwf > pb, the first backpressure changerelationship becomes

q (Pwfl - Pwf2)Aql . . . . ..(23)

= ‘2 = (FR - Pwf)

Successive rate changes would be handled as shown inthe previously given equations.

One should note that if (n) were correctly evalu-ated from m(p)oil using the inflow performance rela-tionship discussed in the Appendix, all the declinecline curve analysis could be done directly inpressure terms i.e.

(IF) =FR - Pwf

...............(24)m (FR) - m (pwf)

A detailed example illustrating two backpressurechanges is given for the Federal A-1 well, Figures 9and 10 and Tables 9 and 9A. The example is carriedout using the type curve match point and the basfcArps form of the decline equation. The procedure isquite simple using the concept of superpositiongiven by equation 16.

A convenient equation8 that can be used for calcu-lating the total Aq as a result of n pressurechanges is,~a Ap case,

ITR- PwflP~n = P@l -

I

[Aql + Aq2 +...+ Aqn] (25)ql ..,.,

SPE 14237 M. J. FETKOVICH, M. E. VIENOT,

for lll(p)~il

/

i

(2~R Pb-Pb2-Pwf12)(Aq1 z+ Aq +... Aqn)Pwfn= Pwf12-

ql

......(26)

The Aq values are all specifically defined at acommon point in time with respect to the initialrate ql; 1 day or 1 month, for example. A one monthtime period is used in this study. The Federal A-1example illustrates this point. (See Figure 9).One can also back calculate intermediate flowingpressures and rate changes Aq while performancematching knowing the initial flowing pressure andrate, and the final flowing pressure. This alsowill be discussed with the Federal A-1 example.

METHOD OF DECLINE ANALYSIS

Log-Log Data Plots

The first step in approaching the rate-time log-loganalysis in the study of the School Creek Field wasto make a log-log plot of all the rate-time datafor each well. We next ex~ned each well’s plot tofind when it actually started on decline. The rate-time data was then reinitialized at the point ofdecline to t = O and a new log-log plot for eachwell was prepared. We have thus eliminated theconstant rate or excess capacity time period whichactually represents the constant rate solution in-stead of the constant wellbore Dressure solution.For log-log type curve analysis: we can’t-do-deciineanalysis until the well is actually on decline.

Based on the assumption that each well was drainingits 160 acre spacing and that all wells had beenequally stimulated - i.e. re/rw’ would then be thesame for each well, a School Creek Field Type Curvewas constructed by ~v~rl~vino @ach we~~ls ~q-lnn* . ..= -----

curve, with the axis all kept parallel, until a-=single curve was obtained. Figure 5 represents thisattempt to obtain a total field type curve usingdata from 19 wells that exhibited a clear decline intheir data. Wote the “apparent” long transientperiod demonstrated by wells D-1, RA-1, and K-3. Ifthis field type curve were valid, we would have asimple and quick method of preparing an oil produc-tion forecast and of determining ultimate recover-able reserves for these wells and the remainingcompletions. I&would take the reinitialized log-log plot for each well, find the best match on thefield +..l..a,.,-----...A4..-,..- 1 4 . . 4.L.-.. *L- J.*. J----

k~pe QUI v=, aIIU ur aw a I Irle brrr-u brws udcd sown

the depletion stem of b = 0.30. Future rates would

be read directly from the real time plot. Ultimaterecovery would then be a summation of forecastedrates plus the cumulative production to the start ofdecline, plus any additional production as a resultof placing the well on pump, where applicable.

Ta Aa+.s-.lms 46 +h,. .-,..-.-..+ ● . . ...-4--- ---- . ..- -.-IIv Ucbcrllllllc 1 I LIIC appaf CIIL LI arl>lerlb >Lem was real ,

wells D-1, BA-1, and K-3 were all evaluated for kand skin (s) from a log-log type curve match on thec@stant w~~~h~r~ nraccllr~ cnl!!tinn /FimIr.nc ~ A- ~

-“,-”,”,, {, ,Yul=- w,

The evaluation of the match-pointsof reference 3)0 “-”--’lead to unreasonable values of permeability and,more specifically skins for all three wells, Noneof the wells were massively hydraulically fractured.

. D. JOHNSON, and B. A. BOWMAN

Wel1 k-red s

D-1 0.017 -7.6BA-1 0.040 -8.2K-3 0.024 -8.0

It was therefore concluded that the data for thesethree wells was not really transient and should beplaced in the early depletion period of the totalfield type curve. Figure 6 is our final SchoolCreek Field Type Curve that does not exhibit a longtransient stem. The field type curve is primarily adepletion type curve with a b = 0.30. (We willlater discuss the b = 0.30 selected for this study.)Blind matching of log-log data to a type curve andextrapolation can sometimes lead to erroneous pro-duction forecasts. An evaluation of the matchpoints to obtain reservoir variables for all wellsbeing studied should give consistent and reasonablenumbers when compared with each other thus confirm-ing the validity of the forecast and the ultimatereserves numbers developed. The elimination of theapparent transient stem in this case is a good exam-ple of such a checking procedure. The compositetype curve, Figure 4 of reference 2, was used forall match point evaluations performed in this study.

Basic Well and Reservoir Data

Table 1 lists basic individual well information andthe match points obtained from a log-log type curveevaluation for 40 well completions. Three of thewells are commingled. The table lists first produc-tion, the start of decline analysis and the cumula-tive production to the start of the decline analysis.Initially, virtually all wells came on flowing withseveral on curtailed or restricted production beforestarting on decline. Many wells, because of earlyhigh gas-oil-ratios and gas disposition problems,were shut in for as much as a year before beingreturned to production. This accounts for thedifference in time of as much as one year betweenfirst ~f’ndll~ti~nand start of rlnel+na with li++la~. ---- . . . . .!!-, “ , “o, , , ““ , =cumulative production for some wells during thisinterval.

Reservoir shut-in pressures, TR, were generallyassumed to be close to the original pressure ofapproximately 3600 psi except in a few cases wherebottomhole pressure surveys were available to indi-cate otherwise. Flowing pressures were estimatedfrom general pressure surveys conducted on 10 wellsin late 1982 and early 1983. Fluid levels shot onpumping wells indicated a minimum bottomhole flowingpressure of approximately 100 psi.

Porosity, thickness and water saturation for eachwell were furnished by a log analyst. Figure 4 is apermeability-porosity plot developed from 43 plugsamples taken on four wells in the field. The coreporosities, in general, are significantly less thanthe average values determined from log analysis.This will be discussed further under calculated re..-7.,--vamue>.

The final four columns of the table list the matchnninte nhtstnad frm ~~e Ifi–-I,w. +..-,. -.,---- .-.I...:-r“.,,-.. -“-=,,,=- IVS-IUy I,ypc LUI ve aflalysl>

for each of the well completions in terms of t - tDdand q(t) - q~ obtained using the composite typecurve (Figure 4 of r~f~r~n~~ ~) and a ~ecline ~xPo-nent b = 0.30.

CASE STUDY OF A LOW PERMEABILITY VOLATILE OIL FIELOI USING INDIVIDUAL-WELL ADVA

PVT Data

PVT properties required for evaluation of reservoirvariables from the type curve match points are pre-sented in Table 2 and also Figure 3. These are U,B and~t, all evaluated at reservoir shut-in- pres-sure, pR. The total compressibility term, et, was

3 ~ ,O-liP5,-{calcula ed us”ng a water compressibility, Cw, of

and pore volume compressibility, Cf,obtained from Hall’s13 correlation. The product(~) was “mechanically” evaluated at the averagepressure (pR + p~)/2.

Initially only two PVT samples were avaflable forthis study, the Federal EE-1 bottomhole sample torepresent Channel Sand completions and the FederalJ-1 bottomhole sample to represent Bar Sand comple-tions. The Matheson E-1 PVT surface recombinedsample became available only after our inftialstudies were virtually complete. This sample, be-cause of the vastly different gas-oil-ratio (763SCF/B versus 1557 SCF/B for the Federal EE-1 well)and because of being a surface recombined sample,had been labeled an unrepresentative sample.Inspection of initial GORS plotted for each welland a gas-oil-ratio versus fractional recoverycurve, based on original oil in place developed fromthe match point evaluations, clearly suggested thatthe Matheson E-1 sample was valid. The final sum-mary of the evaluation of reservofr variables fromtype curve analysis was made using the Federal EE-1PVT data for all wells south of and including wellsLL-1, H-1 and R-3. See Figure 1 and Tables 3 and 4.For weiis to the north of these wells we used thePVT data from the Matheson E-1 well sample.

Because the study had been vfrtually completed whenthe Matheson E-1 sample results became available, wehave Included the results of all channel sand wellsevaluated usfng both fluid samples. Basfc patternsof evaluation results remained essentially the samebetween the northern and southern wells, i.e.,higher percentage recoveries for the sc!!!thernwellsthan the northern wells since their actual rate-timeperformance was based on the real fluid present, notwhat we selected to use for the ffnal evaluationsummary. The more undersaturated a well was, theless recovery would be obtained as compared wfth awell with a fluid saturated at its fnitfal shut-inpressure, all else being equal. Tables 5, 6, 7, and8 summarize the~esults of the match point evalua-tiOtIS based on (pR - pwf)/(~) and m(p)oilevaluation.

Calculated Results From Decline Curve Analysis

The final results of the type curve evaluation fnterms of calculated reservoir varfables are pre-sented in Tables 3 and 4; the wells have beenarranged on the basis of PVT areas. ~ m(P)oilevaluatioflwas used for all results gfven in Table3 and a (pR - pwf)/(ZK) evaluation for allvalues fn Table 4.

Pore Volume (Vn)

The pore volume calculations are based on equatfons6 and 12, where

ED DECLINE CURVE ANALYSIS SPE 14237

,— .[Y8) t ‘“’

Vp=q(t)

.—* — . . ...(6)(llct)_ (FR - Pwfl) tDd qDd

PR

and

(t3)F t q(t)

.~. . ●

‘P

[ 1— (12)

(ct)F (TR-Pwf)+(Pb*-Pq2) tDd qDd

R 2pb

Equation 6 would most certainly apply to reservoirswhere the single phase liquid solution is applica-ble, i.e., where the decline curve exponent b = O.The introduction of the (~) term evaluated at~R + Pwf)/2 with the Ap form is simply an attemptto account for solution-gas drfve or two phase flowbehavfor. A rigorously derived (~) from m(p)concepts, as discussed previously, would be theapproach to make equation 6 and 12 equivalent.

For solutfon gas drive reservoirs, reference 2demonstrates that the A(p2) form of IPR (ofl wellbackpressure curve with n = 1.0) used with a non-linear~R versus Np material balance relationshipproduces a decline exponent b = 0.33. Levine andPrats~,fn thefr simulation study of a solutiongas drive reservoir producing under a constant well-bore pressure condition, presented a log qD - log tDtype curve. (See their Ffgure 11. ) The depletfonstem of thefr type curve basically ffts a declineexponent b s 0.33. Figure 7 illustrates one ofseveral wells in the School Creek Field that ex-hibited rate-tfme data fn a sufficient stage ofdeclfne to help us establish a single declfne expon-ent h . tl ‘M ~~~ ~~~ Anel+na -II-M- .ma~y~j~ ~fi~-..” - - “.””. “.=.-n ,81.= GUI v= all

rate predictions were based on matchfng and fore-casting on b = 0.30 for all wells. All forecastsfor this study were done~ graphical nrntoc+:nn-~.-u-””.”.,.

Figure 8 fs a plot of percent recovery versusbottomhole flowing pressure for the Federal A-1well. Usfng equations 6 and 12, the bottomholeflowing pressure was varied between 1600 psi to 100psi and the pore volume Vp and OOIP calculated.Ultfmate recovery was fixed at 36,000 60 for bothAp/(fi) and Alll(p)ojl cases to arrive at a percentrecovery. Note the lack of sensftfvfty in percent-age recovery for the Alll(p)ojl case with the varia-tion of bottomhole flowing pressure. Sfnce theAm(p)oil case is effectively a difference in pres-sures squared effect, we do not see a propO@ionalincrease in rate with drawdown as in the (UB) caseeven though (~) was evaluated at each flowing-pressure. Thfs is virtually fdentical with theeffect found for gas wells. The precfse determin-ation of flowing pressure, p~, may not then greatlyaffect our final results.

Oil in Place

Oil in place fs calculated directly from Vp usingequatfon 14

SPE 14237 M. J. FETKOVICH, M. E. VIENOT, R. O. JOHNSON, and B. A. BOWMAN

Vp(1-SW)OIP = . . . . . . . . . . . . ..(14)

(B)T

R

The calculated oil in place is at the start ofdecline which, when added to the cumul~ produc-tion up to the start of the decline analysis, yieldsthe original oil in place, OOIP, equation 15. Theoriginal oil in place is later used to calculatefractional oil recoveries, Table 10, and GOR versusfractional recovery, in an attempt to help identifyor confirm different fluid properties used in thefield analysis and also to possibly identify differ-ent rock types.

Calculated Drainage Radius (rP)

A “calculated” drainage radius is determined from Vpwith equation 13

IIVp X 5.615re = ................(13)

nh$

The calculated value of re is not only a function ofpore volume Vp determined from the type curve anal-ysis match point but also of porosity $ and thick-ness h. In this type of reservoir, with indicatedthin “dirty” sands and possible limited arealextent, the value of average h used as determinedfrom the logs may be too high. This would resultin a calculated re value in some cases much lessthan re = 1490 feet for 160 acres. Also, very fewof the core sample plugs obtained from wells in thefield (see Figure 4) appear to approach the averageporosity values reported from the log analysislisted on Table 1. If one were to build a simula-tion model of the School Creek Field, outlined inFigure 1, based on the log derived values of +, h,and 160 acre spacing for each well, we would haveto cut the pore volume to match the type curveanalysis derived reservoir variables, specificallyoil in place, that have already been history matchedto the rate-time decline data.

To come up with calculated values of re approachingon average the 160 acre field spacing, the $h pro-duct would have to be decreased. Otherwise, therather tenuous conclusion that many wells are notdraining the existing spacing could lead to a con-sideration of infill drilling.

Productivity Factor (P.F.)

The productivity factors for each well are calcu-lated from equations 5 and 11,

where (m) is evaluated at average pressure(PR + Pwf)/2

and

141.2 (Pf3)5

. . . . . . . ..(11).........,--,

Since there is a lack of early time transient ratedata to sufficiently define an re/rw’ stem, uniquevalues of permeability and skin cannot be calculatedfor each well. We know that all completions wereinitially stimulated. The core data indicates anarithmetic average permeability of 0.650 md and ageometric average of 0.195 md, with a range of 0.2md to 7 md. We also had one buildup test conductedon the KK-1 well where the final flowing pressureprior to shut-in was above the bubble point pressure.The analysis yielded a value of k = 2.5 md and s =

-3.4.

A range of values of skin from O to -4 was selectedto evaluate permeabilities for each well. When wefix rw’ on the basis of skin, rw’ = r e-s, andhaving previously calculated re from !he pore volumecalculation we can then calculate kh and k from equa-tions 5 and 11.

The ranges of values of k listed on tables 3 and 4for various values of skin are surprisingly narrowwithin a given table and even between the two meth-ods of calculation used. It should be pointed outthat the values of permeability and skin calculatedfrom the decline curve analysis are those at thestart of the decline analysis.

If a good correlation from the core derived $ - kplot had been obtained and if log derived averageporosities were considered reasonably reliable, wecould have used it to determine k and then its cor-responding skin from the tables for each well.Based solely on the KK-1 build-up analysis resultsand the fact that all wells were stimulated, onecould also select the -3 skin columns on Table 3 or4 to arrive at specific values of permeability atthe start of decline for each well. There are nounreasonable values of permeabilities listed oneither table. Nearly all lie within the range ofthe core permeabilities shown on Figure 4. Valuesof permeabilities in the 10s or 100s md on any wellwould, of course, be suspect.

Example of Effect of Backpressure Change on Recoveryand Decline

The equations to calculate the change in producingrates with backpressure changes have been givenpreviously as equations 16 - 26. The Federal A-1

CASE STUDY OF A LOW PERMEABILITY VOLATILE OIL FIELDUSING INDIVIDIJAL-WELLADVA

well produced against three different flowing pres-sures that resulted in two rate changes. Figure 9is a log-log plot of the rate-time data with thesolid line through the points calculated from thetype curve match points used with the Arps hyper-bolic decline equation. Only the first and lastflowing pressures of 1400 psi and 100 psi, respec-tively, were known. Equation 26, solved in termsof Aq total with pwf3 = 100 psi yielded a totalAq = 747 BOPM. A trial and error calculation wasthen made varying Aql until a best fit of bothrate changes was obtained. This resulted in a pwf2= 1069 psi.

Tables 9 and 9-A illustrate in detail the method ofdeveloping a forecast with two backpressure changesusing the m(p)oi~ approach. Note specifically thatsince the rate-time decline is undergoing depletion,the Arps equation is used for all the calculations.One does not have to deal with the reservoir vari-ables, kh, s, re/rw’, obtained from the match evalu-ations. This, however, would not be the case for atransient situation. Theoretically, the rates forthe first few months should be calculated at themid-point of the time intervai, i.e., 0.5, 1.5,2.5, to represent average monthly production rates.For simplicity of presentation of the superpositionexample, the rates have been evaluated at full monthtime intervals.

Table 9-A column 2 lists the rates for the initialf~owingpressure, pwfl, calculated from ~rps’ equa-tion wlttlb = 0.3, qi = 4545.5 t+lJtJMana LJi= O.ZiZ

- -----

me-l. The rate change as a result of a choke changeto pwfz = 1069 psi is listed in column 3. It issimply a constant fraction of the initial declinerates. The second backpressure change, when thewell was placed on pump to pwf3 = 100 psi, istreated similarly. For superposition, columns 3and 4 are retabulated at a time 1 month past theactual time of the pressure change. Total rate isthen the sums of columns 2,5,and 6. Adding thecumulative production to the start of declineanalysis (2633 go), we have

Nn Ultimate, BOAh(p)njl A(p)

No backpressure change 30,347 30,347First backpressure change 32,667 34,668Second backpressure change 35,858 47,226

The Ap numbers in the above table were generatedfor comparison by recalculating Aql and Aq2 onthe basis of a Ap superposition using equation 23.From this approach, a procedure using actual produc-tion data (and its projected rates for a knowninitial flowing pressure) could be developed todetermine the effect of a backpressure change onuitimate recovery, as foiiows.

Determine Np at pwfl to t = T, where T = total timeof rate-time forecast,

T- ~ (a pwf

Aql E2

thenANP1 = — “

q actualql tl.

FIl llFCi TNF CIIRVF ANAIYSIS SPE 14237-------- ... . . . . . .. ... Q----

T-t@ pwf3Aq2

andANP2 = — “ L q actual

ql t=l

where q actual may also be actual production plusthat projected for the initial flowing pressure,Pwfl ●

Ultimate Recoverable = Np + ANpl + ANP2

Similarly, actual early time production rates in-stead of calculated values can be used to generatethe rate-time superposition as illustrated in Table9-A. This in essence would have the effect of in-cluding a downtime if any early time rate variationswere due to downtime.

Figure 10 illustrates one more point about backpres-sure changes with regard to the decline exponent.As has been previously pointed out in references 2and 3, the sum of two forecasts, both having thesame vaiue of deciine exponent b, will rarelyresult in a total forecast having the same declineexponent. In general, the total forecast declineexponent will be larger. Reinitializing the rate-time data after the second backpressure changewhich also has b = 0.3 resulted in a declineexponent b = 0.40.

Finaiiy, uniess aii weiis are piaced on pump at thesame time, a backpressure change can cause a well’sdrainage radius to increase with respect to offsetwells. The given superposition example implicitlyassumes that re remains constant.

Commingled Wells

There are three wells in the School Creek Fieldwhere Bar Sand production and Channel Sand produc-tion are presently commingled. Figures 11 and 12-. LL. P. , . ,,.~or tne teaeral K-1 weii illustrate the method ofanalysis used to evaluate these wells. A differencecurve was developed between the forecast rates ofthe Channel Sand production only and the connningledproduction which came on production later. Separateforecasts were then made and added together.

Surmnaryof School Creek Field OOIP and UltimateRecoverv

Table 10 summarizes the results of the calculatedoriginal oil in place and ultimate recovery forecastfor each well based on anm(p)oil and a AP/(ti)evaluation. The superposition of rates as a resultof backpressure changes using equations 19 and 23have also been included where appropriate.

Channel Sand completion results are divided into thenorthern and southern areas of the field based onthe two PVT samples discussed previously. Bothevaluation methods indicate a much lower percentagerecovery for wells in the northern portion of thefiald dC r~ndPad With wane +. th~ =~,ith~m~ ~er~fefi-. . . . . . “., u“.,,~”, -“ “,”., “=, ta ,,, !.am= a“ubtac, ,,

Wells in the southern portion have percentage recov-eries near twice those of wells to the north. Thiswould be consistent solely on the basis of thedifferences in bubble point pressures between the

‘3PE14237 M. J. FETKOVICH, M. E. VIENOT\

two fluid samples. Values of percentage recoveriesare always lower for the m(p)oil evaluation method.With regard to the additional recoverable reservesthat could possibly be obtained by placing all wellson pump to a final bottomhole flowing pressure of100 psi, the following table summarizes those re-sults. (Nearly half of the wells were initially ator near 100 psi bottomhole flowing pressure at thestart of decline.)

Reserves Increase of Increase offor m(o}..+l hoi(ZJ

Initial R&&~~&-r,\l-w,

ReservesFlowing to pwf to pwfPressure of 100 psi of 100 psi

% %STB STB Increase STB Increase

NorthernWel1s 223,900 15,594 7% 51,361 23%

SouthernWel1s 312,105 19,220 6% 67,605 22%

TotalField 819,484 68,354 8% 230,346 28%

If, in fact the inflow performance relationshipbased on Ap~ applies, the percentage increase asa result of placing all wells on pump to a finalflowing pressure of 100 psi would be approximately8% or 68,000 BO. If the inflow performance rela-tionship were to follows Ap (PI) behavior, theanticipated increase in reserves would be 28% or230,000 BO. Perhaps the real increase in reservesdue to lowering the final bottomhole flowing pres-sure lies somewhere between these two limits.

Individual Well Gas-Oil-Ratio Performance

Figures 13 thru 16 reflect gas-oil-ratio performanceof individual wells in the field based on expressing~~~ Pa?-#l”a.”f.t-+tl. +“ +ame m+ a..h I.m.11 Is ~c~,da~, -“”.=,J ,“GI,”, ,,, l.=,,,,= “, cat.,, “c, ,

cumulative production divided by the OOIP calculatedfrom the m(p)oil evaluation. Either method of cal-culating OOIP should show similar trends. Gas andoil rates are metered separately for each well andare not based on allocation from tests.

Figures 13 and 14 are on an expanded gas-oil-ratioscale in an attempt to help identify rock types fneach area of the field. If one assumes the fluidsare the same for each area, three different rocktypes and/or initial water saturations are possiblyindicated in the southern portion of the field.

Figures 15 and 16, prepared on a scale where theentire gas-oil-ratio performance of each well canbe shown clearly, indicate two different fluids,based mainly on the wells’ peak gas-oil-ratio alonewhich is not a function of the method of calculatingan OOIP number. Note that the gas-oil-ratio hasturned over on several wells. The peak gas-oil-ratios for the northern wells is generally muchlower than those of the southern wells. These gas-oil-ratio curves could be used in developing a gasforecast to go with the oil rate forecast developedfrom the decline curve analysis.

. D. JOHNSON, and B. A. BOWMAN

CONCLUSIONS

Original oil in place values can be calculated fromrate-time analysis for individual wells and canalso be used with reserves projections developedfrom the decline analysis to obtain fractionalrecoveries for each well in a field. These frac-tional recovery numbers should be reasonable,considering the fluid type and the permeability ofthe reservoir.

Each well’s evaluation of the r~s~rv~ir Variab~eSk, s (skin), OOIP and fractional recovery, obtainedfrom individual well rate-time decline analysis,should give consistent and reasonable numbers whencompared with other wells in the field. A singlewell analysis can give results that are not recog-nized as being invalid unless compared with otherwells in the field.

Failure to consider a future lowering of a well’sflowing bottomhole pressure from that causing awell’s initial rate-time decline can result inunderestimating ultimate recoverable reserves.

A method of treating future backpressure changesbased on the superposition principle and an oilNell inflow performance relationship is easilyapplied to decline curve analysis. An oil wellinflow performance relationship can be utilizedOver an entire production forecast, not only atan instant in time.

NOMENCLATURE

b=

8 =

Cf =-Ct .

Cw =Di =~.h .k =

kro =!(p)oil =

n .

oh’ :

OOIP =

M=PR =

Pwf =

!

.J: .

re =rw =

rw’ ==

s: =t =

tod =T=

“~ ;

‘$=

reciproca’fo~:;;:n

of decline curve exponent

volume factor,res vol/surface vol

effective rock compressibil ty, psi-ltotal compressibility, psi-1water compressibility, p i-linitial decline rate, t-!nat!lral lrmarithm haca 9 71Q9Q,,..””, “, ,“~”, , “,,,,, ““== G., S“CU

thickness, fteffective permeability, mdrelative permeability to oil, fractionoil pseudo pressure, psi/cpexponent of backpressure curvecumulative oil production, STBoil in place at start of decline

analysis, STBoriginal oil in place, STBbubble point pressure, psiareservoir shut-in pressure, at start

of decline, psiabottomhole flowing pressure, psiadecline curve dimensionless ratesurface rate of flow at time texternal boundary radius, ftwellbore radius, fteffective wellbore radius, ftskin factor, dimensionlesswater saturationtime, mo.decline curve dimensionless timetotal time of forecast, mreservoir pore volume, ft!!”viscosity, Cpporosity, fraction of bulk volume

CASE STUDY OF A LOW PERMEABILITY VOLATILE OIL FIELDo USING INDIVIDUAL-WELL AOVANCED DECLINE CURVE ANALYSIS SPE 142:

ACKNOWLEDGEMENTS

We wish to thank Phillips Petroleum Company forpermission to publish this paper. We also wish tothank U. G. Kiesow, M. D. Bradley, and S. D. Dunstalfor their timely assistance in parts of this study.

REFERENCES

1.

2.

3.

40

5.

6.

7.

8.

9.

10.

11.

12.

13.

Arps, J. J.: “Analysis of Decline Curves,”TRANS, AIME (1945) 160, 228-247.

Fetkovich, M. J.: “Decline Curve AnalysisUsing Type Curves,” J. Pet. Tech (June 1980)1065-1077.

Fetkovich, M. J. , Vienot, M. E.,Bradley, M. D., and Kiesow, U. G.: “DeclineCurve Analysis Using Type Curves: CaseHistories,” paper SPE 13169 presented at the59th Annual Fall Meeting of SPE of AIME,Houston, Texas, September 1984.

Carter, R. D.: “Characteristic Behavior ofFinite Radial and Linear Gas Flow Systems -Constant Terminal Pressure Case,” SPE/DOE 9887presented at the 1981 SPE/DOE Low PermeabilitySymposium, Denver, CO, May 27-29, 1981.

Carter, R, D.: “Type Curves for Finite Radialand Linear Gas-Flow Systems: Constant TerminalPressure Case,” SPE 12917 presented at the 1984Rocky Mountain Regional Meeting, Casper, WY,May 1984.

Da Prat, Giovanni, Cinco-Ley, Heber andRamey, H. J., Jr.: “Decline Curve AnalysisUsing Type Curves for Two-Porosity Systems,”Sot. Pet. Eng. J (June 1981) 354-362.

Fetkovich, M. J. and Vienot, M. E.: “ShapeFactor, CA, Expressed as a Skin, SCA,” J. Pet.

Tech. (February 1985) 321-322.

Bradley, M. D.: Personal communication.

Levine, J. S. and Prats, M.: “The CalculatedPerformance of Solution Gas Drive Reservoirs,”Sot. Pet. Eng. J. (Sept. 1961) 145-152.

Fetkovich, M. J.: “The Isochronal Testing ofOil Wells,” paper SPE 4529 presented at the48th Annual Fall Meeting, Las Vegas, Nev.,Sept. 30 - October 3, 1973. (SPE ReprintSeries No. 14,265.)

Vogel, J. V.: “Inflow Performance Relation-ships for Solution Gas Drive Wells,” J. Pet.Tech. (Jan. 1968), 83.

Whitson, C. H.: “Reservoir Well Performanceand Predicting Deliverability,” Unsolicitedpaper SPE 12518, U. of Trondheim.

Craft, B. C. and Hawkins, M. F., Jr.: “&!&lPetroleum Reservoir En ineerinInc. knglewood cliff*iJrfii:ce ‘a’”

S1 METRIC CONVERSION FACTORS

acre x 4.046873bbl X 1.589873

bbl/D X 1.589873Cp x 1.0*ft X 3.048*

ft3/D X 2.831685md x 9.869233psi x 6.894757

E+I)3= M2E-01 = m3E-01 = m3/DE-03 = Pa*3E-01 = mE-02 = M3/DE-04 = pm2E-03 = MPa

*conversion factor is exact

APPENDIX

Oil Pseudo Pressure, m(p)oil For Decline CurveAnalvsis

Reference 10) introduced the concept of a pseudo-pressure m(p) for oil well drawdown tests similar tothat now commonly used for gas wells. It was pre-sented along with a general inflow performancerelationship developed from multi-point test data ofsome 40 oil well tests.

A general inflow performance equation for declineanalysis that treats flow both above and below thebubble point pressure for an undersaturated oil wellassuming no non-Darcy flow component is

qo= J* (FR - pb) + J“ (pb2 - pwf2) . . . . . . ..(A-l)

where J* =

()141.2 i~~~ -II “‘°F-“*”(A

and J* = J*

R

a2l@o)_ “ ; ........(A-3)

PRs p.b

Assuming (UOBO) is a constant value above thebubble point pressure equal to (BOB )b (the basisfor the constant PI assumption for ?1OW above thebubble point pressure, pb) then (See also Appendixof reference 10)

1%2 = ...............(A-4)

pb(l@o)Pb

‘or l/@. to go through a zero intercept on draw-iown, we are really looking at a (kro) / (B0130),

Pwfi pseudo (poB ). This then would reproduce fieldiata 10 -log !PR curves with n = 1.DO and also

i!Iogel’s 1 Figure 7, a computer generated IPR.{Figure 17 in this paper.)

I

.,.

------- .. . .. ..- ... . ....- m - .,-., ,.,.--., -— . r! “ ma, ,., ”,,

PE 14237 M. J. FklKUVICH, M. t. VltNUl, K. u. WINXJN, ana D. H. UUWI’IMII 1

ThusJ* (@o)p Jir Vogel form 12 :(;);[+:): Ill(p) oil = -

J“ = b ._ . . . . . . . . . (A-5)

2Pb(l@%) 2p R

P bb . . ...**.... . (A-n)

Substituting equation (A-5) into (A-1) we obtain thefinal form of the single phase and two phase IPRequation

[

(TR- Pb) (Pbz - Pwf2)q~ . J* + 1..0.....(A-6)

2pku

or in terms of reservoir variables, with kro = 1at start of decline analysis

kh 1

[ 1(~R-pb)+(pb2-pwf2)qo =

[()]

1 “ =). 2pb141.2 in ~ - — pR

rw’ 2

............(7)7)

or in terms of Ill(p)oil

For the case of~ SPRb

we have from equation (A-7)

kh 1 (~R2-pwf2,q. = .— .

[()]

1 (l@30)_ 2~141.2 in ~ -— R

‘R‘w‘ 2

.......(A-9)

With pR < p we can compare the Vogel and the AP2!?”inflow r=la lonship in terms of m(p)oi~. We have

The Vogel form would be extremely cumbersome ifentered into the constant wellbore pressure s lu-tions as an m(p)oil expression whereas the AP?

form results in a simple expression identical inform to the low pressure gas well backpressureequation. Oil well IPR curves, just as gas wellbackpressure curves are most applicable to the-...--+.-+,.61Ikfi--~--..,evecnlii++nn rnnfi$tinncGullaLallti w=, Iuul c pt Gaaul = ou~uv~”,s .-”, . . . . . ..”~.a. .A

comparison of the AP2 form of IPR and Vogel’s IPRequation (both these forms assume a non-Darcy flowcomponent of zero) can be seen in figure 17. Theresults shown on Vogel’s figure 7 are the only com-plete set of curves given in his paper with whichwe could make a comparison of the two methods whenusing the same match point. Vogel’s points of matchA thru H were used to develop the comparison. Notefrom the figure 17 comparison that the Ap2 formof the equation better fits his computer calculatedIPR over the entire range of depletion than his owndimensionless form of the R equation. At very lowflowing pressures approaching O flowing pressure, aregion we seldom deal with, the Ap2 form is slightlyless than the simulation run result but still closerthan using Vogel’s dimensionless equation.

Reference 2 illustrates that when the Ap~ form ofthe IPR equation is combined with a non-linear pversus N relationship for solution gas drive reser-

Evoirs, t e expected decline curve exponent b =0.333. This is practically the same value as thatfound and used in this study.

1

()

k P2

Ap2 fOf’Mro

: m(p)oil = ~ ● — ●..(A-1O)

‘“R \ @“/~R

TA8LE IS25P30L CREEK FIELD, c#P6ELL - CON2ERSE CO., UfEU1lffiflA21c RCSERVOIR OATA NKI 02CLIIIE CmV2 WATCH PWf~

T18LE 2 SC1030i 2REEK FIELD, CNQBELL - COWERSE CO,, W3511m

Channel sand PvT Data Bar Sand PVT DataFederal M-l Pw--(ph . 340+3] Hat h●m E-l PVT [Ph . 2705] Fed ●ral J-1 ( Pb 53]

P FA @ .9P @& @p P.

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3.3D0.39O.M1.261.270.030.500.282.660.31D.752.42D .690.253 .D52.071.035.350.070.D10.672.69O.lD0.140.243,05D.36D.781.710.87

:::0.190.18D.331.140.110.480.401.96

2.590.3o0.D2D.960.960.D20.350.212.110.230.581.860.670.182.471.60D.784.270.05

.000.5D2.lD0.070.100.032.460.27D.591.33D.65D .25D.070.14D,12D.240.R70.080.370.301.54

TMLE 9

EXWLE OF EFFECT OF BACKPAESSORE CHANGE ON DECLINE W RECOVERYFEOERAl A-1

. .... . .,Pam ,-”

EXMPLE OF EFFECT OF BACKPRESSURE CHANGE ON OECL INE AND RECOYEi7rFEDERAl A-1

FR _ 3500 PSi ; Pb .2705 PSi

144tch Pdnt. b = 0.30:

q(t) . 1000 BOW; qo,j . 0.220

t = 1 m; CM-0.212

r3] ,77,,,

q Total

[21+[51+r61

Mz column [31 Colmn [41w

{}

313~ x [2]

BOPH (14s4 @t.12m0— x [273701

BOPU BOP14

@t.17mo

BOPN1000 BOPN 0.212

q “ —= 4645.5 BOP?’; o,. — - 0.212 no-l0.220 lMO

ROPN

:s456

i

1:11

;:

;:1617181920

si596061

37013050254D21S51811154813321154lo&

77668761D

%43B395357324295

zi25?4

S701305025402135lB1l154813321154mo6RBl776

1000368759668591

::72o630

ql 4545.5 60PUq(t) .

[I + bc+tllfb“ c1+ 0.0636t]3-333

Fi Mt backpressure chmge 1400 pSi a to 1069 pSt# @ t - 11 wnths31s25821518115s1s11139685

ql @ t . 1 ma . 3701 BOPN (See Figure 9) 64

;46423a35

413733302725

434358296250

i76

5.’41. ‘q

.tq . q

(FR - Pb)+(Pb2 - P~12)~

3500. 2705)+(27052 - 14002)

L 2pb J 2(2705) j66

Second S+ckpres sure chang? 1069 psla to 100 pst a @ t . 16 months Cum (BO): 27,714 2.344 3,25o 2,320 3,191

P2;:213

H

10692 - IO@

.,.,*.,.,.,.., JL

[ (TR - Ph)+(F’~ - Pti~2)l -3701 ~35C0~ 2705)+(27052. 14002j- 434 ‘op”

1 “ “2P,’] 1 2(2705) J

TMLE 10

SWIARY OF SCHOOLCREEKFIELO 00IP ANO ULTIMATE RECOVERY

Can Incl tic F1 cuing Pressure ChangesInitial

PWfl

Reserves RecoveryFortcast Factor mlp

Percent STSSTR

Reserves R~yForecast

576 Percent

ReservesForecast

S76

2W3625692

10s2

4E:10B85Z1ZB7.

335739662063

240%

2!?%5662

60117

OOIP&

528560473427

104297216

111425163949. . . . . .. ..7.’,364753642B

3Y3fl152%722920399399

1M8901

92S1014223445148

253EQ5145704231%13421601B7379

7354126150

4357401303711128353416328201421%50124

kkl1A-1c-Io-2

(PAA) F-1

Jt;K.&

3371926692

1032648

634311122.,. ..”.,.5.335739262043

27536

2:Z5662

64832

1418223130

94302852713280222435723619mo137693472

440692131128751

7925735294316165

537695999s12373

10%71B1207

. . . . . .

627830

10.3

1::;17.89.4

10.2i~.~13.115.410.011.0

1!::7.9

l-w

20.822.326.015.111.812.024.217.523.316.414.619.231.228.225.727.315.4

T

13.510.023.911.810.5

-

12.9

6.45.6

1?:35.76.B8.68.7

10.46.76.9

s!:5.7

+

15.416.320.911.3

:::16.710.2lB.713.310.616.325.523.226.122.412.3

v

o-iR-1k?

Ford A-1Ford 0-1Nath B-1Nath o-1N6th E-1

Sub Totals

00-1EE-1FF-160-16&2

n-l1-1

KK-IKK-2LL-1

0-1R-4T-1T-2T-3

;:Sub Total S

13%722091

9295267191313122243544231501B137693472

S904620205~229

77B27352919B6165

......J-i (3;K-1 (B+C) %

LL-2 [B) 66875R-3 ( B+C) 10933123-1 (WC) 969646

Sub T@#) s ~

8.9 522163 70643739756 737B0

1::: 66189 1342110.0 113?724 134702

975065 102313+ ——mlUtn—-. W>, .7,.0,,-,

Grand TotalS 9621391 9..2 816S493 1049630

Total Percent Recovery Factor . Total Reserves ~ Total ml P

819464

SPE 14237

Riww..----19 I ,

OJ 1

‘WHwi~:’( \,4 J ● Mm II I I i

-1-JJ 1●

“c< / I I I i. “..-,, !

● - CHANNEL‘BAND)PVT SAMPLE :

BAR .&m PVT 3JMPLE

1

~\

+

\ 1I ●I T3 ?2 ;5 i#

.I RI &

:K2I

C~MPB~LL-CO.

/1-1

:El 801 i?Kl I CONVERSE CO. -I

/ 31G●Q2 %Gl I- CHANNELSAND)PVT SAMPLE

36

/1/

~~1Ii I /’

●b. l-SChOOI Crnkliekl wdlhuIlonnwp,

-L E-l, — Bole. 1clw9aL1am.1%7uw.*PCOCRRLJ-1. ~ lm. lba-lmn-tmsuf/.*IuTliUOII C-1. ~ le. t-l )aOn-~/otbT-alrF

:1.s

K-----------

7 I1.s

1.0 0:~:’0 moo

(

MUOOY FORMATIONTYPE LOG

‘%%7

lRNaawsNEOMR!IC! DAR

2i---E-E

>

L----NJ

‘E=EE!R5H---t+’*-t-i

1 ! I I I 1 I1 ,

1!.

? v

~ d

i $ 0 “~ -

- -

0: u u-

❑ 0

0.1 .0 0

A 1T

.1 1

I I I I I I

IPRNMILIT7.C,Mmolrnc WmnOl . O.aomRarm:c Avana . O.\*

O.O1O ~ : I1 1 10 12 j,”-Pm0cx7Y-x

Pnu9umE. mm

spE 14737

10,00(

4=

E=J

10(

TIME

.●l o-t-, ~+,V K-3d B-10’ T-6v c-10 0-1● J-10 DD-I

.

I*. ~1.m SdmdCmkfidd10g40gtype CM..

d.

0

❑ E-<A Oe- tO B-1O R-4* K-4x H-1

0 OQ-2● Q-*4 A-2O A-1

,

Y*—

b-+

b= O.300

—

—

MONTH ONE b=O.30APRIL 1982’

\o

10 i

FEDERAL O-1

MATCH POINT

q~OOOBOpM ;qDd=0.231t-l mo ; tDd=0.178

b-O.30

a.

— ———

,, 0

1-1-%

*“

:,03-.0

\b=O .301

—.

T I ME

FIs. 8—Flnal &h<ml Cr~kfleldl lW1mtywcuwe.

——

14

13

12

11

——— ——— -- —.-—————--PERMEABIUTY~—

FEDERAL A–1

200 400 600 = WOO 1200 1400 1600BOTl?WIHOLE FLOWN(; PRESSURE P9A

Fig.8—58.81tlvlly 01 cmlc.1.ted percent recovery md parrneablllty t. MWWIOI. flowing pr.wure

FIE. 7- OaelbM ●xpomm b. 0.30 ntabllslmd from rato.tl.. din..

1001o

[ {

‘q lOTAL (@t-l mo)-747 BOPM \

z c\\

~Aq *(@t-lmo)-434 BCIPM \\

$ [

$

1010

30 1 i

TIME, MONTHS “

FEDERAL A-1

MATCH POINT

l(t)4000 BOPM ; ql)d- 0.220

t-t mo ; t13d-0.212

b-O.30

lFl~.SExamph cdeffectof badQreuure changes on resoveq.

10000

.

10(

CHANNEL SANDPRODUCTION O~LY

MONTH ONEJUNE 1982

I$”

100

0’ 30

—

&

FEDERAL A-1

t+ ORIGINIAL FIT OBTAINIED BEFORE

4

BACK PRESSURE ICHANGESb=O.30

$ 4_.REINITIIALI ED AFTER SECONDBACK PRESSIJRE CHANGE AT

t=16 MONTHSb=O.40

- II100 1000

TIME. MONTHS

FEDERAL K-1

CHANNEL SAND

MATCH POINT

q .1000BOPM; qod - 0.5810

t -1 mo; tDd= 0.134

0 1(

Fh.11-Rafe-tim. dalk for a well commlnghd vdlh amthu r.wvdr.

.,

[

:

.xI

t

t

t

(el%m) Ollva-llo/sv9

k--L>dz0

I

(91s/43s) Oliw llo/svo

WJdW ‘ ‘b

200000-

180000-

160000-

140[)00-

g

$ ,20(,00.ue

SCHOOL CREEK FIELDNORTHERN WELLS

400100

200100

m

r

0- ~——

0 2 4 6 a 20 22 24 26 28REcovEw‘;A& d’

200000-

1811000-

160000-

140000-

~

c ,200008K!

SCHOC)L CREEK FIELD

SOL2THERN WELLS

o~ 100000-

;

q 80000-

20

d ‘) ~J\60000-

40000-

/

20000-

0- &z5_

0 2 4 b 8 10 12 14 N :!0 22 24 26 28RECOVERY FACTOR (%!

m. 1S-lndivldudl well Wak GOR PUWKI,IIC,, bmml m m(~) calcuhtul OOIP, Fb. ~a-ltibw..l well wk=nprb-~, -onm(p)cabmld OOIP.I

zQ

9nnntX OPREOICTEO FLOWRATE BASEDON

q. .J4R2. &z)l”o

OR

qo

[()]

,_&2— .q. MAX ~R

. \ > ~>>~mRAIGHT-LINE EXTRAPOLATION

\ \\%,

%

!. -x,\ \\, -,

\

o 20 40 SO 80 100 120 140 1S0 tio 200 22o 240 280 2S0 300 320 :#\ , A;\ ~\ AI, ,\ -\\

1 t , 1

0

PRODUCING RATS BOPD

Fig. 17-COmpwlum cd Inflow puionnmce equml.a”s.