Society of Petroleum EngineersI

SPE 35161Pressure Transient Data AcquisitionElectromagnetic Telemetry

and Analysis Using Real Time

by L.E. Doublet,* Texas A&M U., J.W. Nevans,* Fina Oil & Chemical Company, M.K. Fisher,* ProTechnics Company,R.L. Heine,* Real Time Diagnostics, Inc., and T.A. Blasingame,’ Texas A&M U.

“ SPE Meniws

Cqynghl1696,SOctdyd IWoIaum Engmere Inc.

Tfms paper was prepe~ for prssenfakm al the 1996 SPE Pen’mrn Beam Oil and Ga9Rs@/erj Ccolerame, Mdlend TX 27-29 Mach, 1S96.

?lvs paper was adtxtcui for pro%mta!tin by m SPE Picgram Comfiffee Idlowngrowew of IIfonnabon cnn!numd In an abdrec! eutnwlled by IJWauthot(s). Contenb ofhe per, .98 pfeemti! hew no! ken tiwd

ran ere aubpcl to cormcbon by the au fhof(a). %4’R’3%;%ZE2ZR%nacaswnty mlkct MY pwtion of ffw Sxaefy of Petmlaum Engtwers, ib ofkaz., ormembers Papers pmwnfad at, SPE meetings are aub)ect to publicabon rwe. byEdnooel Comm!heo of Ihe SOC@Y 01 Pdmbum En neon. ernusson to copy IS

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.4’2436, U A Tatax, 16324S SPEUT

ABSTRACT

This paper presents the operational procedures and the rcsuhs fortwo pressure buildup lests performed using a wireless lclcmclryacquisition system (TAS) tool at the North Robertson (Clcarfork)Unit (NRU) in Gaines, Co. Tx. Using a single pressure gaugesystem downholc, wc obtained real-time telemetry of pressure andtcmpcraturc data al the surface, as WCIIaa a Iargcr sampling of datathat were stored in the downholc memory syslcm.This ncw wireless lclcmclry acquisition systcm was dcvclopcd 10provide real-time prcs.sure and tcmpcra(urc data a~the surface byusing an clcctromagnc~ic signal to transmit these data through theformation strala, The LOOlis fully programmable so that a widerange of sampling frcqucncics can bc used, The systcm aIlowspressure and Icmperalurc data to bc slorcd downholc (as in thecase of a typical “memory” gauge), or these data can be trans-mitted LOsurface data acquisition systems. This provides real-drncpressure and temperature dala for pressure transient hws,stimulation monitoring, and Iong-term reservoir survcilkmcc.

Our obicctive is to demonstrate the usc of this technology forpressure buildup tests in low permeability reservoirs. Our g@ inutilizing this [ethnology is 10reduce tic shul-in Limercquircmcnlsfor pressure rmrrsicnt tests--which will ultimately result in a morecost-cffcctivc reservoir surveillance program as wells can bcreturned to production (or injection) as quickfy as possible.

Once tic pressure data were acquired, wc perfornrcd conventionalscmilog and log-log analysis, and wc simulated test profiles toverify the anafyses of the Lestdata. Both surface and downholcpressure data were compared for consistency, and both iypcs ofdata were analyzed in exactly the same fashion. The results ofthese analyses were csscnlially identical. This approach gaveconsistcn[ estimates of reservoir pressure, permeability, skinfactor, and fracusrc half-lcnglh for both of our case his[orics.

Rcfcrcnccs and illustrations aLend of paper

INTRODUCTIONThe accurate acquisition and analysis of pressure transient data isan in[egral part of the reservoir surveillance process. Byanalyzing the characteristic shape of the pressure-time profile wccan determine the reservoir- well model (i. e., homogeneous ordual-porosi[y reservoir conditions, hydraulically-fractured orhorizontal WC]]behavior, wellbore storage conditions, etc.).SpccificaHy, wc can usc pressure transient data to estimate thefollowing:

● average rcscrvoi r pressure,● completion cfficicncy,● reservoir quality,● WC1ldrainage radius and reservoir shape, and● flow boundaries or other reservoir heterogeneities,

Unfortunately, in the majority of opcraling environments thecritical issue for most pressure tnrtsicnt tests is the timely rehrmof a well to production or injection. This paper presents onemethodology that shows promise in minimizing test time whilefulfilling the data acquisition rtxfuircmcntsWhen performing pressure transient tests in the low pcrrncabilityreservoirs of the Pcrrnian Basin (such as the NRU), it has beenour cxpcricncc that a test of al least [WOto three weeks is requiredfor a comprchcnsivc analysis to bc possible. The issue is that thelow permeability character of these reservoirs, combined withoften severe wellbore storage effects, distorts test da[a andconventional anrdysis mchniqucs cannot be used until these effectsend. One remedy is a downhole shut-in device, but this devicecan be difficult to instafl, it requires considerable welf preparation,and is quite expensive.

Our approach was to minimim the test time by using real-time datafor anatysis. Conceptually, wc can monitor the test and terminateonce a vafid analysis is obtained--but in our cases we continueddata acquisition until the power source in lhe tool depleted. Wedid this for two reasons--firsl, wc wanted to acquire as much dataas possible; and second, wc wanted to establish the practicaloperating fimits of this data acquisition system.To estimate wcfl drainage radius and identify flow boundaries wchave found from pressure falloff teats that a total test duration ofbetween five and eight weeks is rquircd. Obviously, it is noteconomically feasible to shut-in producing wells for this period oftime. In the future wc may usc the TAS tool for long-term sur-veillance tests, but at present this task is neither operationally norcconomicafly fca.siblc,

The wireless tclcmctry tooI currcnlly provides reaf-time surfacedata a~a cost com~arablc to conventional memory Eauzc instafl-

149.-.

SPE 35161 L.E. Doublet, J.W. Nevarts, M.K. Fisher, R.L. Heine, and T.A. Blaaingame 2

ations. Our experience suggests that the telemetry system can befeasible for teats on the order of 3 weeks. In addition, the systemis self-contained and requires no monitoring other than periodicdata collection (if desired). By contras~ the usc of a wireline-conveyed, real-time pressure data acquisition system is costprohibitive for tests of more than 2 or 3 days and requirescontinuous monitoring by service company personnel to ensureequipment performance.

The results obtained using the TAS tool were very good, and weresimilar to the results we obtained from other “conventional”pressure transient tests taken at NRU (both buildup and fallofftests). In this work, we have included analyses of both thereat-time surface data and bottomhole memory gauge data in order toshow how favorably these data compare. Our analyses show theutility of transmitting data to the surface on demand so that thedata can be analyzed while the tesl is proceeding, as is done onmany short-term wireline-convcycd pressure transicnl tests.

TELEMETRY ACQUISITION SYSTEM (TAS)

The transmission of bottomhole data in real time is useful in avariety of applications. The TAS tool can be used to recordbottomhole pressure and temperature for the following reservoirtesting and monitoring procedures:

G Pressure transient testing (pressure buildups and fatloffs)● Drilt stem testing (DST)● Field monitoring (continuous, long-term measurements)● Monitoring of acid jobs and hydraulic fracturing treatments● Monitoring of conformance control treatments

To transmit pressure and Iemperamre data the TAS tool injects amodulating current into the casing at a point above the tool andreturns the same current to a point below the tool. This currentgenerates a smatl voltage dipole which propagates to the surfaceon the casing or drill pipe and returns through the Emth (Fig. 1).The downhole current injection can be accomplished in thefollowing ways

● Using two casing hanger tools:- welt stimutstions down casing- pressure transient tests

● Via a bundle carrier on tubing:- through-tubing well stimulations- pressure transient twts

● Speciat fasteners on a dedicated 1001case during drill stemtest operations

The TAS tool transmits the data to the surface using a proprietynoise-rejecting modulation scheme. The voltage arriving at thesurface is measured differentially between the wellhead and aremote electrode placed in the ground at some distance from thewellhead (=150 ft).

After the incoming signal is amplified, it is filtered and amplifiedagain before being digitized and transferred to a digitst signalprocessing (DSP) board. The DSP board further filters andprocesses the signal, eatablishcs data synchronimtion, then stripsthe pressure and temperature information from the signal for real-time display via a RS232 interface to a portable PC. The data arealso stored in downhole memory and can be downloaded througha special TAS link connector after the tool is retrieved from a well.

The tool is set downhole using a slick line, sand line, or electricwireline when casing hangers are required, or via a bundle carrieron tubing during through-tubing operations, or by means of thedrillstring during DST operations.

Tool SpecificationsThe electronics sonde is 1.5 inches in diameter and the length isbetween 11 and 15 ft, depending upon the application. For ourapplications we used casing hangers above and below the tool,which resulted in a total tool length of approximately 40 ft. Thetool sonde was modified to remove any fittings or collars thatmight fail due to long term exposure in areas with a high H2S(hydrogen sulfide) level.

The pressure transducer currently used in the TAS tool is a straingauge device that can be changed according to the expectedbottomhole pressures and the type of test being run. For ourpressure buildup tt!sts we utilized a transducer with an accuracy of+0. 15% at a full scale reading of 5000 psi% a resolution of #psi, and a temperature rating of 3000F. The temperature probehas an accuracy of @50F, and a resolution of kloF.

Although this accuracy and resolution is sufficient for our prea-surc measurement requirements, some operators may require amore accurate, higher resolution quartz pressure gauge. The ~of this paper is to present our results using the current generationof the TAS tool--not to provide a general discussion of gaugespec~lcations. Such discussions are provided in refs. 1 and 2.

The battery life of the TAS tool depends on the bottomhole-lo-surface data transmission frequency. Our procedure was totransmit data approximately once an hour for several minutm,which limited battery life to approximately 3-weeks. For longerterm applications where the data transmission mxpkements are notas severe (e.g., once a day), the batteries should last for severalmonths. Research is currently being conducted to identify analternative power source or to develop a method by which thetool’s batteries can be recharged from surface during a tat.

Pressure and temperature data were sampled downhole at amaximum rate of every 6 seconds in order to obtain a represent-ative pressure profile during the shut-in period. Data weretrunsnu”ttedto surface once per hour for a period of 7 to 8 minutesat a rate of 1 sample every 15 seconds, TWa transmission ratemay seem insufficient to capture the rapid changes in pressureduring the early shut-in period, however, separate analyaea of thereal-time surface data and the downhole memory gauge data gavevery similar results.

Prtxentty we use the real-time data more to verify that represent-ative data are being obtained and to determine when a test shouldbe terminated. We later use these data for comprehensive analy-sis, as is presented and discussed in the next section. Futuremodifications may allow data transmission at almost the samefrequenciti that data arc stored downhole.

DowmwMQ@dbA wellbore schematic of the downhole configuration for thepressure buildup tests conducted at NRU is shown in Fig. 2. Thepacker is set above the perforations and the TAS tool is set incasing below the downhole pump. The pump is set below theperforations since the rates of fluid influx in this low permeabilitydolomite reservoir are extremely small, and a sufficient fluid levelmust be maintained for the pump to operate efflcientty.

In order to obtain the best possible signal-to-noise ratio, the TAStool was set so that there was approximately 300 ft of casingbelow the sonde for current return in or&r to generate as large avoltage dipole as possible.

DATA ANALYSIS

IOorder to determine the relative merit (i.e., quality) of the real-time surface data when compared to the downhole memory gaugedata, we must perform as complete an anatysis as possible. Dueto the availability of commercial aoftwate packages for pressuretransient anatysis, atmost atl operators now perform log-logarratysis, as well as “conventional” (or traditional) semilog analy-sis.s14 In this paper, we focus primarily on log-log analysia sinceUris approach gives a complete view of all of the test data--asopposed to aemilog analysis, which can ordy be used to interpretdata speciilcatly in the radial flow regime.

In general, log-log snatysis provides abetter resolution of a well’sproducing mechanisms (producing time effects, wellbott? storage,etc.) as well as most, if not all, of the flow regimes that occur in aparticular tesl. Semilog anatysis is used for validation of

150

3 Pressure Transient Data Acquisition and Analysis Using Rcaf Tne Electromagnetic Telemetry SPE 35161

permeability and skin factor, which can also be obtained from log-log (or type curve analysis).

The primary use of scmilog analysis for pressure buildup andfalloff anatysis is to determine an estimate of the average reservoirpressure. However, rigorously estimating average reservoirpressure requires accurate knowledge of both the producinghistory of the WCIIand the affected reservoir volume--neither ofwhich typically available, including our cases. For the interestedreader, semilog analysis methodologies are given in ref. 5 andAppendix B.

Time FunctionsDue to our lack of detailed knowledge regarding the productionhistory, we chose to use the actual shut-in time, At, in both thescmilog and log-log analyses. This is in contrast to using super-position (e.g., the Homer plot), which is theoretically rigorous--but without an accurate rate history superposition can yield quitearbitrary re.suits--espmially for estimate-s of average reservoirpressure obtained using the Homer plot.

Afl producing wells at NRU are pumping wells and the issue of awell’s production history or even an “lumped” estimate ofproducing time becomes extremely complex--what actually colI-stitutes a stabilim?d rate? These wells have been on pump-offcontrollers since completion, and fluid levels are kept at a fairlyconstant level–but the rates change continuously.

After short shut-in periods for running gauges or cleaningwellbore fill, we have noted IAatthe wells “pump-off’ (return 10astable fluid level) fairly quickly--~, this does not equate toa stabilized rate, and the prior rate history still significantly affeclstest data. By experimenting with different Ming sequences, wehave found that in order to minimize producing time effectsassociated with short shut-in periods during the buildup tests, wemust produce the well for a period of time approximately six toeight times as long as its previous shut-in.We have successfully used the following procedure for conduct-ing pressure buildup tests on wells at NRU (for both memorygauge installations as well as the real-time telemetry system):

1. Wellonpump forextended period . . . . . . . . . . ..~6months2. Tagwell TDandclean outwellborc fall.., . . . 3days3. Place well on pump .... ...................... .. .. 24days4. Run packer and downhole gauge . . . . . . . . . . . . . . 8-12 hours5. Place well on pump ... ... .... .... ....... ......... 4days6. Set packer and shut in well for buildup . . . . . . . 21 days

For the cases in this paper, we cxarnined the use of both the shut-in time and effective time functions (Homerg plot for semiloganalysis, Agarwalb plot for log-log anafysis) for constant-rate andvariable-rate pressure buildup cases. We found that the constantrate buildup case (using only shut-in time, At, i.e., nosuperposition) gave the most consistent and interpretable results.For a more thorough discussion of time functions used in pressurerransienl analysis, we refer the reader to ref. 5.

Type Curve Analy.dsIn this study we have focused on the use of the type curve modelfor a well with a finite conductivity vertical fracture in an inftitc-acting homogeneous reservoir that includes wellbore storage ef-fee@.T-lq AS Wme of the tests that we have reviewed at the NRUshow only slight damage or stimulation, we have afso used thetype. cuwe solution for an unfracturcd well in an infinite-actinghomogeneous reservoir with wellbore storage and skin eff@s.lA-IT The models are quite similar in both form and function, exceptfor the solutions for lower conductivity fractures

The type curve analysis relations are provided in Appendix A forboth unfracturcd and fractured wells. As mentioned above, wewill use shut-in time, M, rather than the more rigorous effectivetime function, Ate, as we do not have a detailed productionhislory. Once the appropriate pressure drop and pressure dropintegrat functions are plotted versus At on a log-log plot, thesedata are then overlain and matched onto the appropriate type

We afso used pressrue intcgraf smoothing to “falter” the raw fieldclaw, this methodology is discussed in refs. 18 and 19. Thepressure integral provides a smcxrth data trend for data that maybeaffected by data “noise” (random errors) as well as for data whichare affected by systematic errors such as “stair steps” caused bylow gauge resolution. No such “stair steps” were noted in ourdata and our rationale for using the pressure integral was tominimi2c data fluctuations, particularly in the “surface” data.The pressure integral method gave us more consistent data trends(only 1 smoolhing “pass” was used) and improved the resolutionof both the presute drop and pressure drop derivative functions--especially for the data transmitted to surface. In short, thepressure and rate intcgraf methods have been shown to be usefultools for arrafyzing both pressure transient test datastls,lg as wellas long-term production data.zo.zl

Methodology

Data analysea were performed in the following manrtec1.

2.

3.

4.

5<

The raw pressure data (real-time surface and bottomholememory pressures versus At ) were SMOOthCdusing thepressure integral in order to reduce the noise associatedwith typical field daa

Conventional scmilog analyses (MDH methodd) wereperformed on the shut-in pressure, pws, and shut-inpressure integral, PWJi,data in order to obtain preliminaryestimates of permeability, k, and the skin factor,s.

The semilog permeability estimatm were used to “force-mateh” the pressure drop and pressure drop derivative dataon the log-log type curves for both the unfractured andfraclured well models. The “matches” were refinedslightly to yield estimates of skin factor,s, fracture half-length, L.fi and the dimensionless wellbore storagecoefficients, CD and CD}

The average reservoir pressure, ~, was estimated using themelhod proposed by Mead.zz

Finally, we simulated the pressure buildup tests using theresults of the semilog and log-log analyses. For theunfractured well model k, s, and CD were optimized, andfor the fractured well model k, L~, and C Df wereoptimized.

As a means of ensuring consistency--the pressure drop,pressure drop derivative, pressure drop integral, andpressure drop integral derivative functions were allmatched simultaneously by the optimiuuion program

Sample calculations for the type curve anafysis are provided belowfor the first example case, NRU Well 905.

FIELD CASES

North Robertaon (Clearfork) Unit, Gaines Co., TXThe North Robertson (Clearfork) Unit is located in GainesCounty on the northeast edge of the Centraf Basin Platform in thePermian Basin of Wcat Texas. The Unit produces from theGlorieta and Upper, Middte, and Lower Clcarfork reservoirs,The Clearfork is a Leonardian shatlow-shetf carbonate formationconsisting primarily of a massive dolomite section with varyingdegrees of anhydritc cement; intermittent silt stringers are presentand often act as verdcal flow barriers. The depositional sequencewas cyclic (occurred seversf timm), and this sequence, coupledwith strong diagentxis, msuttcd in a thick vertically and laterallyheterogeneous reservoir interval.

The North Robertson (Clearfork) Field was developed on anominal 40-acre well spacing beginning in 1956 and thedominant re.smoir producing mechanism was solution-gas drive.Between 1987 and 1991, 116 new welfs were drilled and existingproducers were converted to water injection as a full-fieldwaterflood program was initiated on 2&acre nominal spacing.

CUNCS for analysis.. .

151

SPE 35161 L.E. Doublet, J.W. Nevans, M.K. Fisher, R.L. Heine, and T.A. Blasingiune 4

Reservoir Propem”es:Average reservoir depth = 6flXl ftWellbore radius, rw = 0.31 ftEstimated gross pay interval = 1200ftEstimated net pay thickness, h = 200 ftAverage porosity, #(fraction) = 0.055Average iIT.water saturation, SWirr = 0.25Average absolute permeability, k = 1.5 md (core data)original nominal well spacing = 40 acresCurrent norninat well spacing = 20 acres

Fluid Propem”es:Average oil FVF, B = l.lo RB/sTBAverage oil viscosity, M = 2.00 CpAverage total compressibility, cl = 1O.OX1O-6psi-l

Proakction Parameter.nInitial reservoir pressure (LCF), pi = 2800 pSiSCurrent avg. reservoir pressure, ~ . 3000 psiaPumping bottomhole pressure,pw~ = 80-150 psia

NRU Well No. 905

NRU Well 905 was drilled in 1989 as a 20-acre infilJ producer.This weU was acidized and hydraulically fractured in two stages--the Lower md Middle Clearfork intervals followed by the UpperClearfork and Glorieta intervals. Pertinent well and productiondata are given below.

Totat dt?pth = 7350 ftPlug back depth = 7318 ftSurface casing (8-5/8”) = surface to 1808 ftProduction casing (5-1/2”) = surface to 7345 ftPerforated interval = 5931 ft to 7197 ftTotal perforations ~ 100 holes

Initial potentiat: q~ = 50 STEKYD9W = 56 STBW/Dqg = <1 MSCFID

Rates prior to test: 90 = 25 STINYDq~ = 105STBWAIqg = 2 MSCFiD

Cumulative oil production = 48.5 MSTBEaliroated ultimate recovery = 95.0 MSTB

Coupling the geologic model with the historical performance, webelieve that NRU Well 905 is in an area of moderate reservoirqualhy. We also note that this area has responded fairly well towaterftooding operations on 20-acre nominal spacing. Becausethe well is near the edge of the Unit, its five-spot pattern isincomplete--and as such, the well is only partially supported byinjection.

NRU Well 905 had been on production for several months prior10shutting-in the well for approximately three days to clean outwellbore fill. The weU was then placed back on production forapproximately one month before the downhole assembly was runthrough tubing. The well was put on production for 4 days beforebeing shut-in for the pressure buildup tea~The TAS tool and its downhole assembly were set in the casing at7076 ft. approximately 55 ft below the pump and 274 ft above thecasing shoe. A fullbore packer was set above the perforations.

Type Curve Analysis ResultsFor consistency we “forced” the pressure drop functions (verticalscale match) to correspond to the permeability edirnate obtainedfrom the semilog analysis (00647 red). The aemilog,plot and theanalysis results are shown in Fig. 3. For completeness, wematched the pressure data functions on type curves for both anunfractured well (Fig. 4) as well as a fractured well (Fig, 5).Since all of the producing wells at NRU are hydraulicallyjiactured we used ttrejiactured well model for our fitud amlysis.

Once the vertical axis “force match” was made (baaed on thepermeability from semilog analysis) we shifted the data hori-

zontally (along the time axis) untU a match was obtained with atype curve for a particular wellbore storage case. We recorded the“matched” value of the dimensionkss wellbore storage CoefficientCD~ as well as the “time” axis match point. We then computedthe fracture half-length, L~ from the “time” axis match point.

In Fig. 5 we note that both the pressure drop and pressure dropderivative trends are smooth. In matching these dam we obtainedexceUent agreement between the data and fractured well model for“early” times during the wellbore storage dominated period (i.e.,the “unit slope line”) as weU as during the wellbore storagedistortion period. However, as the test began the transition fromthe wellbore storage distortion period to the undistorted radiatflow period we note that the pressure derivative data appear tooscillate slightly and that this trend eventuaUy falls below the CD!= 1 line.There are several possible explanations for the behavior of thepressure derivative data, including the following:

●

●

●

Differential pressures in different layers causing backflowinto lower pressure zones. We know that there are wveralzonm at NRU that are probably pressure depleted and asthe fluid rises in Urewellbore, these zones take fluid.The influence of lateral heterogeneities such as changingpermcabilities (due to differential diagenesia). Comparingcore and well log data we know that such features exis~ butwe cannot resolve their influence using a simple, homo-geneous reservoir model.Random and systematic data noise in the acquisitionsystem.

The results and sample calculations for the “preliminary” typecurve matches for NRU Well 905 are shown below,

Type Curve Match Results: Economies Type Curve6--Wellwith a Finite Conductivity VerticalFracture with Wetlbore StorageEffects

Matching Parameters: CDf= 0.9, C’ = 1x103

[t~CD~MP = 1.0 [Atbp = 4.85 hra

liJWDIMP = 1.0 [Ap]Mp = 800.0 psi

Pressure Analysi~

k. = 0.0647 md

Lf = 9.14 ft

Sample Cakw!utions: Pressure Analysis (Calculations andResults am l@tti@ for pre-ssum IntegralData)

The effecti~e permeability to oil, &o, is calculated from thepressure match point using

ko=141.2 ~*.......,.,......................(l)h [(@)fi,JMP

Solving Eq. 1 for the “match po~t” pressure drop, [(Ap~&p,gives

[(Ap~~p =141.2 &~wD]MP . . . . . . . . . . . . . . . .. . . . . . ...(2)

Solving for the pressure” drop at the “match point” using thepermeability estimate from semilog analysis and a specifiedvalue of ~wDIMp= 1, we have

[(hp~~p = 141.2 ~25 STWD)(1.1O RB/sTB)(2.o c

(0.0647 md)(150 ft)P)(l.o)

or

[(Ap~UJMP= 800.2 psi

152

5 Pressure Transient Data Acquisition and Analysis Using Real Time Electromagnetic Telemetry SPE 35161

The fracture haff-length, Lj is computed from the time matchpoint using

~ J- [(’’f”~p@ocO cDf [tLJD%~MP

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

Solving for the frackrrc half-length, L:, for this particular lest,wc obtin

L,= 0.01624(0.0647 md)

(0.055) (2.0 cp) ( IOX10-6psia-l)

.&@!Z#

or

L/= 9.14 ft

Simulation and Parameter OptimizationAfter obutining estimates of kO,CD , and L\ from t.hclog-log type

dcurve analysis, wc then pcrformc simulations to optimize thesepararnctcr vatucs in a statistical sense. To ensure consistency, wcsimultaneously optimized the simulation on all of the datafunctions (pressure drop, pressure drop derivative, pressure dropintegral, and pressure drop integral derivative).

The downhole memory gauge data are considered the “standard”against which we should verify our real-time surface data. Red]that the “surface” data arc simply selected intervals of data thathave been transmitted up hole during the test, As such, we choseto plot tic computed solutions for the bottomhole pressure data(i.e., the complete data set) rdong with both the surface and bot-tomhole pressure dataThe optimization results for the unfractured well modeI arc shownin Fig. 6, and the results for the fractured welt model are shown inFig. 7. We used the fractured well optimization as our finalresults.

Optimized Final Solutionsfrom Simulation

~ (Fr~~urcdWeu ModcOInput:

cDf = 0.9k. = 0.0647 mdLf = 9.14 [t

outputCD~ = 0.902kO = 0.071 mdLj = 8.24 f[

~ (Fractured WCUModel)

InputCD~ = 0.9

= 0.0647 md$ = 9.14 f[

Oulpuu@~ = 0.795k. = 0.071 mdLj = 8.28 ft

Summary for NRU Well No. 905:We note cxcellcnt agreement irr the final solutions for permeabilityand frac[ure haIf-length for both the surface and bottomhole data.The calculated pcrmeabilities are identicaf, and the fracture half-lenglhs are within 0.5%. These comparisons indicate that thesurface data are of sufficient quafity to perform accurate, real-timeanatysis of a pressure transicm test, while the test is actually beingrun.

The estimate of the effcc[ivc permeability LOoil is 0.071 md.Using the available relative perrncabfiily data, this corresponds toan absolute permeability of approximately 1.4 md. Recall that theaverage permeability from NRU core data is 1.5 md, and whife -

such close agreement is more likely a coincidence, we do believethat this well test has given us accurate estimates of reservoirparameters.

The fracture half-length was calculated to be approximately 8 ft.It is difficult for us to make a quantitative evaluation of thehydraulic fracture treatments performed at NRU since we aretesting such a large interval (approximately 1300ft). However, itappears that there has keen very little lateral fracture growthprobably due to the manner in which these wells were fracturedin large intervals using limited-entry techniques. While theseshort computed fracture haff-lengths may be cause for concern, itis important [o realize that the near wellbore area appears to beWCI1stimulated (a skin factor of -2.40 was computed from bothscmilog and log-log method using the unfraeturcd well model).Previous limited-entry fracture treatments over extremely largeintcrwds appear to have resulted irr the initiation of scveraf shortparallel (“pancake”) hydraulic fractures.” Pressure buildup testshave also indicated that although rheac treatments did removenear-wellbore damage, such treatments do not yield substantialfracture hatf-lengths.The average reservoir pressure in the area surrounding the wellwas estimated to be 2948 psia (correded to 7000 ft datum) usingthe rectangular hyperbola method (RHM) introduced by Mead.zzThe extrapolated pressure trend is shown in Fig. 8. Given the factthat the fluid injection and withdrawal rates are about average inthis area of the Unit we expect the reservoir pressure in this area tobe close to the current estimated unit-wide average pressure ofapproximately 3030 psia.

This was the first buildup rest we performed using the TAS tool,and the battery life of the tool was only sufficient to record data upto the start of the undistorted radial flow period (4-day drawdown,12-day buildup). It should be noted, however, that the durationof tie test data was sufficient to obtain a comprehensive analysis--and the data quality was exceltent.in mosl formations we would consider a 12-day pressure builduptest to be more than sufficient to sample reservoir properties.However, due to the extremely low permeability and high degreeof heterogeneity in this formation (the Clearfork dolomite), a 12-day pressure transient test wordd not ~ long enough for most ofthe WCIISat the North Robertson Unit. For subsequent tests,additional batteries were added to the tool, and the downhole-to-surface transmission rates were optimized to prolong battery life.With these chsngea we wem able to achieve a three-week pressurebuifdup sequence.

NRU Well No. 2703

NRU Well 2703 was drilled in 1988 as a 20-acre infti producer.This wclf was acidizcd and hydraulically fractured in two stages--the Lower and Middle Clcarfork intervafs followed by the UpperClearfork and Glorieta intervals. The pertinent reservoir andproduction data are given below.

Total depth = 7350 ftPlug back depth = 73(K)ftSurface casing (8-5/8”) = surface to 1750 ftProduction casing (5-1/2”) = surface to 7350 ftPerforated interval = 6030 ftto7115ftTotal perforations - 66 holesInitiaf pola-rtial: q~ = 30 STXY-D

9W = 126 STBWfD9K = c 1 MSCF/D

Rates prior to tes~ 90 = 35 STBCM3Q. = 110 sTBw/D. ..!?8 = 10 MSCFA)

Cumulative oil production = 101.0 MSTBEstimated ultimate recovery = 200.0 MSTB

From a geologic and historical performance standpoint, NRU2703 is in an area of low to moderate reservoir qurditfi however,the productive facies are more homogeneous in this area of the

I53

SPE35161 L.E. Doublel, J.W. Nevans, M.K. Fisher, R.L. Hehw, and T.A. Blasiogarne 6

unit. While tlds area did nol perform exceptionally well during40-acre primary production, it has responded 10water injection on20-acre spacing better than almost any other part of the Unit,indicating less reservoir heterogeneity.

As was the case for the previous well (NRU 905), NRU 2703was on production for an extended period of time prior to shuttingthe well in for approximately two days to clean out wellbore fillprior to the buildup test. The well was then placed back onproduction for approximately one month before the downholeassembly was run through tubing. The well was put onproduction for 4 days before being shut-in for the pressurebuildup @tWe added additional batteries to the downhole tool for thii test andwe slightly decreased the downhole-to-surface data transmissionrate. Aa a result, we were able to add an additional 7 days to thebuildup test period (4-day drawdown, 19-day buildup). The TAStool and its downholc assembly were set in the casing at 7083 ft.approximately 65 ft below the pump, and 267 ft above the casingshoe. A fullbore packer was set above the perforations.

Type Curve Analysis Results:We again used the permeability estimate catcrdated from semiloganalysis (0.09 md) to force-match the pressure drop functions inthe type curve anrdysis. The data and results for the semiloganalysis are shown on Fig. 9.

For completeness, the pressure drop and pressure drop derivativedala are matched on type curves for both the unfractured well(Fig. 10) and fractured well (Fig. 11) models, As before, weused the fractured well model to calculate our “final” results.From this anatysis the dimensionless wellbore storage coefticien~CD~ was 0.5 and the fracture half-length, L.. was calculated to be30.81 ft.On Fig. 11 (the fractured well type curve match), we note thatboth the pressure drop and pressure drop derivative trends arevery smooth and that the data match fatls between the CD~= 0.1and 1.0 stems (~ 0.5). We again note that the test was terminatedat the beginning of the undistorted radial flow period when thedownhole batterkx depleted.Results are shown below for the preliminary type curve matchesfor NRU Well 2703.

Type Curve Match Resul&r: Economidea Type Curves--Wellwith a Fink ConductivityVctlical Fracture with WellboreStorage Effects

Matching Parameters: CD~= 0.5, Cp = 1x1(P

[tdCD~Mp = 1.0 [Ar]Mp = 22.0 hrs

k+vDIMP = 1.0 [AP]MP = 805.0 psi

Pressure Analysirk. = 0.090 md

Lj = 30.81 ft

Simulation and Parameter Optimization:After obtaining estimates of k., CD\ , and L/ , from thepreliminary log-log type curve analysis above, we againperformed simulation to optimize our estimates of permeabilityand fracture half-length in order to match the test data as closely aspossible. We again matched all of the data functions simul-taneously to ensure consistency.The optimal solutions (simulated test results) were plotted with thesurface and bouomhole data for the unfractured well model in Fig.12, and for the fractured well model in Fig. 13. Recall that theoptimization was performed on the bottomhole (memory gauge)dala as this is the complete data set. We again present thefractured well match as our final result.

(lptiw”zed Final Solutionsjkom Simulation

~ (F~t~ Weu M*UInput

CDf = 0.5k. = 0.090 mdL~ = 30.81 ft

output

CD! = 0.302&o = 0.082 mdL! = 39.0 ft

~ (FracturedWell Model)

I.npuc

CDf = 0.5kO = 0.090 mdLf = 30.81 ft

Outplm

CD! = 0.288k. = 0.082 mdLf = 39.0 ft

Summary for NRU Well No. 2703:We note the excellent agrwment calculated vahrea of permeabilityand skin factor from aemilog analysis, for both the surface andbottomhole data. The permeabilities and fracture half-lengtisobtained from optimization are identicat for both the real-time(surface) data and downhole memory data.The estimated permeability to oil for this welt is 0.082 md; usingthe available relative pem~eabtity dam this estimate correspondsto an average permeability of approximately 1.6 md over the 1200ft test interval. Again, recall that the average perrneabitity fmmNRU core data is 1.5 md.

The computed fracture half-length was approximately 30.81 ft.This well has a higher production efficiency and is betterstimulated than NRU 905, as NRU 2703 produces at a highertotat fluid rate in an area of relatively lower reservoir quality--andat a lower average reservoir pressure@ is estimated to be 2203psia as shown in Fig 14).

The quality of both the real-time data and memory gauge data wasexcetlent and we were able to perform a complete analysis withboth sets of data.SUMMARY AND CONCLUS1ONS

We have shown that real-time surface data transmitted from adownhole gauge using a telemetry acquisition system can beinterpreted and analyzed accurately. The results of these “surface”data analyses coruparcive[y well with the results from the analysisof the downhole tnemory gauge data. The importance of thiswork is that it demonstrates that pressure buildup tests in lowpermeability reservoirs can be analyzed real-time. In addition, byacquiring real-time data, teats may be terminated at any time theoperator wishes.

One recommendation would be to improve the frequency of datatransmission to the surface as current rates are leas than optimal.This issue is evident on the attached plots as some of the data aresparsely scattered--particularly at early times; the data weretransmitted at intervals of 15 seconds for 7 to 8 minutes eachhour. Analyses plots with more evenly spaced data could beobtained if the hour long “silent” period could be reduced so thatdata are transmitted at more optimal intervata, especially at earlyrimes. Another goal should be to improve battery life andIorpower management in the tool so that improved data transmissionrates and longer test periods are possible.From this work we can conclu& that

● Real-time sukface pressure buildup data can be accuratelyinterpreted and aniilyze.d. In addition, the analysis rrxultifor the “surface” data compare very well with the results

154obtained using the bottomhole memory gauge data

7

●

●

●

Pressure Transient Data Acquisition and Anafysis Using Reaf Time Electromagnetic Telemetry SPE 35161

The TAS 1001is a cost-effective and efficient reservoirsurveillance 1001. Tests can be terminated after sufficientdata to perform teat anrdyses have been obtained, or if a toolor opcrationaf problcm exists.Given the current emphasis in the industsy on automationand the associated cost bcnetl& the TAS tool could be usedfor continuous long-term pressure monitoring.In order to obtain a more complete distribution of data in thercrd-time plots displayed at the surface during testing, thedownhole-to-surface data transmission rate must be im-proved in fukrre modifications of the TAS tool.

NOMENCLATURE

Fonnatr”onand Fluid Parameters:cl = total system compressibility, psia-1co = oil compmasibilily, paidB = formation volume factor, RB/STBBO = oil volume factor, RB/STB

= porosity, fraction! = totaf formation thickness, ftk . formation permeability, mdk. = effective oil pcrmcabIMy, mdP = fluid viscosity, cp.Po = oil viscosity, cp,

PressurelRat&me Parameters:Pi =Pwj =pws =

Pwsi =

Pws,ltu =

Pwsi,lhr=

Pw$i =Ap =

Af?’ =

Api =

Apl’ =

(API,.. =

Z’=q =t =

=&n =

initial reservoir pressure, psiaflowing bottomhole preaaure, psiashut-in bottomhole pressure, psia

Jt

1. pwJr) d? shut-in bottomhole pressure integral,‘opsiashut-in bottomhole pressure taken from semilogstraight line at 1 hr. psiashut-in bottomhole pressure integral taken fromsemilog straight line at 1 hr, psiashut-in bottomhole pressure intcgraf, psiaPWJ - pWf,A&r) p~ssure drOp, pSiA,(JAp dAp

— pressure drop derivative, psi~ = d(lnAt)

/+ t Adr) d r or pW$i- pw\A@O inlegral pressure

odrop, psi

At% . d+i .mtcgral pressure drop derivative,rjAf d(lnAl)

psipressure drop functions for type curve matching, Ap,Ap’, Apj, or Ap’i, psiaverage reservoir pressure, psiaproduction rate, STB/daytime, hrshut-in time, hrtime functions for type cume matching, t, At, or Att,hr

CDJ .

Cp =

PwD =

dimensionless wetlbore storage coefficient baaed onfractusc half-length

~ dimensionless fractrue conductivitykL~* Ap, dimensionless wellbore pressure

function for the constant iniection rate case,

PwD’ =

PwDi =

pwDi’=

tfJ =

t~ =

ID* = ~, logarithmic derivative ofdt~ ~hD)

dimensiordess wellbore pressure function for theconstant flow rate case, including wellbore storageand skin effects

JtD

L‘D O

PW~rPt, dimensiode= wellbore pressure

integral function, including wellbore storage andakin effects

dpdptD-lAh=a!DL,d. rht.)

logarithmic derivative of

dimensionless ;ellbore pressure integral function,including weflborc storage and akin effects

0.0002637 ~ t, dimensionless time based on@c,r~

the wellbore radius

0.0002637 ~ t, dimensionless time based on

dWC ;the fracture h -length

ACKNOWLEDGMENTSWe acknowledge the permission to publish field data provided byFina Oil and ChemicaJ, Co. (Western Division, USA). We alsoacknowledge the technical aMistance of Mr. P.K. Pan& (Fma Oiland Chemical Co.) regarding the acquisition and interpretation ofthese field data cases. Jrraddition, we gratefully acknowledge thetechnical assistance provided by Mr. Tom Hampton ofProTechnics International regarding the design of the data acquisi-tion setup and downhole tool cofllguradon.

We also acknowledge the financiaf support of the United StatesDepartment of Energy (DOE) for funding provided through theDOE Class II ~ prO@M.

REFERENCES

1.

2.

3.

4.

5.

6.

7.

including wellbore storage and sldrr effects155

Veneruso, A.F., Ehlig-Economidca, C.A., and Petitjean, L.:“Pressure Gauge Specification Considerations in PracticalWell Testing,” paper SPE 22752 preacnted at the 1991 SPEAnnual Technicaf Conference and Exhibition, Dallas, TX,October 6-9.Kikani, J., Fair, P.S., and Hite, R.H.: “Pitfalls in PressureGauge Performance,” paper SPE 30613 prcaented at the 1995SPE Annual Technical Conference and Exhibition, Dallas,TX, October 22-25.

Homer, D.R.: “Pressure Build-Up in Wells,” Proc., ThirdWorld Pet. Cong., E.J. Brill, Leiden (195 1) II, 503.

Miller, C,C., Dyes, A. B., and Hutchison, C. A.: “TheEstimation of Permeability and Reservoir Pressure fromBottom Hole Pressure Build-Up Characteristics,” Trans.,AIME (1950) 1s9, 91-104.Banthia, B.S., Meyer, B.M., and Blaairrgame, T.A.: ‘USCofSurface Derived Pressure Measurements for the Cost-Effective Reservoir Surveillance of Waterflood Operations inthe Permian Basin,” SPE paper 27685 resented at the SPE

8Permian Basin Oil and Gas Recovery onference, Midland,TX, 16-18 March 1994.Agarwal, R.G.: “A New Method to Account for ProducingTime Effects When Drawdown Type Curves Are Used toAnafyze Pressure Buildup and Other Teat Da~” paper SPE9289 presented at the 1980 SPE Annual TechnicalConference and Exhibition, Dallas, Sept- 21-24.

Cinco-Ley, H, and Samaniego-V., F.: “Effect of WellboreStorage and Damage on the Transient Pressure Behavior ofVertically Fractured Wells,” paper SPE 6752 presented at the1977 SPE Annual Technicaf Conference and Exhibition,Denver, CO. Occ 9-12, 1977,

SPE 35161 L.E. Doublet, J.W. Ncvans, M.K. Fisher, R.L. Heine, and T.A. Blaaingarne 8

8.

9.

10.

11.

12.

13,

14.

15,

16,

17.

18,

19.

20.

21.

22.

23.

24.

Economies, M.J.: “Observations and Recommendations inthe Evaluation of Tests of Hydraulically Fractured Wells,”paper SPE 16396 presented at the 1987 SPIVDOE Lowfirrneability Reservoirs Symposium, Denver, CO, May 18-

Cinco-Ley, H. and Meng, H.Z.: “Pressure TransientAnalysis of Wells with Finite Conductivity Verlical Fracturesin Double Porosity Reservoirs,” paper SPE 18172 presentedat the 1988 SPE Annuaf Meeting, Houston, TX., Oct. 5-8.Blaaingame, T.A. and Poe, B.D.: “Semianalytic Solutionsfor a Well With a Single Finite Conductivity VerticalFracture,” paper SPE 26424 presented at the 1993 SPEAnnual Technical Conference and Exhibition, Houston, TX,Oct. 3-6, 1993.

Lee, S. T. and Brockenbrough, J.R.: “A New ApproximateAnalytic Solution for Finite Conductivity Vetical Fractures,”SPEFE (February 1986) 75-88.

Ozksn, O. and Raghavan, R.: “New Solutions for Well-Test-Analysis Problems: Part 1--Analytical Considerations,”SPEFE (September 1991) 359-368.Ozkan, O. and Raghavan, R.: “New Solutions for Well-Test-Analysis Problems: Part 2--Computational Considerations,and Applications,” SPEFE (September 1991) 369-378.

Bourdet, D.P., Ayoub, J.A., and Pirard, Y.M.: “Use ofPressure Derivative in Well Teat Interpretation,” SPEFE(June 1989) 293-302.

Earlougher, R.C. Jr. and Kersch, K.M.: “Analysis of Short-Tlme Transient Test Data by Type-Curve Matching,” JPT(July 1974) 793-800; Trons., AIME (1974) 257.Gringarten, A.C., Bourdet, D.P., Landel, P.A., Kniazeff,V.J.: “A Comparison Between Different Skin and WellboreStorage Ty Curves for Early-Time Transient Anatysis,”

rpaper SPE 205 presented at the 1979 SPE Annual TechnicatConference and Exhibition, Las Vegas, Sept. 23-26.

Clark, D,G. and Van Golf-Rach~ T.D.: “Pressure-DerivativeApproach to Transient Test Analysis: A High-PermeabilityNorth Sea Reservoir Example,” JPT (Nov. 1985) 2023-2039.

Blasingame, T.A., Johnston, J.L., and Lee, W,J.: “TypeCurve Analysis Using the Pressure Integral Method,” paperSPE 18799 resented at the 1989 SPE California Regional

alMeeting, B ersfield, CA, 5-7 April 1989.

Blasingame, T. A., Johnston, J.L., Rushing, J.A., Thrasher,T.A., Lee, W.J., and Raghavan, R.: “Pressure Integral TypeCurve Analysis-II: Applications and Field Caaes,w paperSPE 20535 prcaetttcd at the 1990 SPE Annual TechnicalConference and Exhibition, New Orleans, LA, September23-26.

Palacio, J.C. and Blasirtgame, T.A.: “Decline Curve AnalysisUsing Type Curves: AnaIysis of Gas Well Production Data:paper SPE 25909 presented at the 1993 SPE Roe@ MountsinRegional/Low Permeability Reservoirs Symposium, Denver,CO, April 12-14.Doubletj L.E., etd: “Decline Curve AnaJysis Using TypeCurves--Analysis of Oil WelJ Production Data Using MaterialBalance Time Application to Field Casea; paper SPE 28688presented at the 1994 Petroleum Conference and Exhibitionof Mexico, Veracmz, Mexico, October 10-13.Mead, H.N.: “A Practical Approach to Transient pressureBehavior,” paper SPE 9901 presented at the 1981 SPECaJifomia Regionaf Meeting, Bakersfield, CA, March 25-26.

Barb% R,E. and Linroth, M.A.: “A Discussion of ClusterPerforating vs Limited Entry Completion Techniques,”presented at the 1995 Southwestern Petroleum Short Course,Lubbock, TX, April 19-20.

Stehfest, H.: “Numerical Inversion of Laplace Transfom]s,”

Communications of Ihe ACM (January 1970), 13, No. 1,47-49. (Algorithm 368 with correction)

25. Earlougher, R.C. Jr.: Advances in Well Test Analysis, HenryL. Doherty Series, SPE, Richardson, TX (1977) S.

26. PanSystem~-Well TrW Analysis Program (Veraion 1.8),Edinburgh Petroleum Services, Ltd., Edhtbtrrgh, Scotland,UK, April 1991.

27. IgorPro-Graphing and Data Analysis Program (Version2,04), WaveMetrics, Lake Oswego, OR, USA 1992.

APPENDIX A

Type Curve for an Unfractured Well in a Homogen-eous, InfSnite-Acting Reservojr with Wellbore Storageand Skin EffectsThis solution is descrrbed in refs. 14-17. The real space solutionsare computed from the Laplace transform solutions using theprocedure given by Stehfest.zd In thiS case pwD, and pwD’, areplotted versustD/cDon the “preSSUfe”typeCtMW, ~d PWDi,~dpwDi’, ue Plotted versus tD/cD on k “Pw~ ~~gr~” Vwcurve. The family parameter for both plots is given by CDe21We typically refer to this solution as the “Radial Flow Case withWellbore Storage and Skin Effects.”

This type curve can be used to estimate the following paramelem● Formation permeability, k● Dimensionless wellbore storage coeftlcien~ CD● PseudoradisJ flow skin factor, s

For any constant rate type cuma formation permeability, k, iscalculated as

k = 141.2* ~wD]Mph [(AP)~MP ””””-”--””””””””-”-””-””””””””””

(A-1)

The relations for CD ands we

Dimensionless wetlbore storage Coefticierm CD

CD= 0.0002637 ~- ... .. .. . . .. .. . . .. ....(A-2)*F: [rdcDIMP

Pseudoradial flow skin factor, s

# ‘w]~=;~cDehCD........................................(A-3)

The “presure” and “pressure derivative” type curves for this caseare shown in Figs. 4 and 10.

Type Curves for a Fractured Well with a Finite Con-ductivity Vertical Fracture In a Homogeneous, Infhdte-Acting Reservoir with Wellbore Storage Effects

This solution is described in refs. 7-13, with the plotting formatgiven by ref. 7 and the solutions are computed using the methodsdescribed in ref. 10. Then+ space solutions are computed fromthe Laplace transform solutions using the procedure given byStehfest..zd The format of ti+ type curve is the same as that forthe “radml flow” case descrtbed above. pwD, and PB?D’,areplotted versus @/CDffOr the “plWStUI?”type curve, ~d P~Di,and pWDi’,are plotted versus @D/CD~ for the “pressure integral”type curve. The family parameter is iven by the dimensionless

/’wellbore storage coefficient based on racture htrlf4engttL C~.

lndividtud type curves are given for a particular value of thedimensionless fracture conductivity, Cp. We refer to thissolution aa the “Fractured Welt Case with Wellbore StorageEffects. “

This type curve can be used to estimate h following pammetems Formation permeability, k● Fracture half-length, L~● Dimensionless wellbore storage coefficient based on

fracture hatf-length, C~● Dimensionkw frqxttm conductivity, C~

156

9 Pressure Transient Data Acquisition and Analysis Using Real Tme Electromagnetic Telemetry SPE 35161

As with the previous case, the formation pcrmeabitity is estimatedusing Eq. A-1. The anrdysis relation for the fracture half-length,Lf is

L;= 0.0002637 ~ -1-~Wc, c~f [f~c~&p

., . . . . . . . . . . . ..(A-4)

or, solving directly for Lfwe have

~ ~ [~’)f”~p?~cf C~[[t~CD~MP

.. . . . . . . . . . . ..(A-5)

The ‘“pressure” type curves for C@= lx 103 are shown in Figs. 5and 11. These type curves are for a weif with a very high fractureconductivity. Both of the field cases considered in this study areanafyzed with these particular type curves

APPENDIX B

Semilog Analysis ReiationsIn this section we provide the analysis relations required for theanalysis of pressure and pressure integral data exhibitingundisLorled radial flow behavior (i.e., scmilog straight lines onplots of pWJand PWJIversus At ).

The fundamental pressure-time relation for undistorted radiai flowduring a pressure buildup or pressure falloff @st using At (i.e., thescmilog straight line) is given by refs. 4 and 25 as

PWS = PWS,MI + m kdAt). . . . . .. . . . . . . . . . . . . . .. . . . . . . . .. . ..(B-l)

The intercept is defined as the pressure at 1 hr. Pw$,lM from thescmilog strtighl line or its extrapolation. We also note that thisrelation requires the pressure at shut-in, Pw~,&_O.

‘w’’’b=pAeO+m[m0t$t3”2272+0868’slsl. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . . ...(B.2)

Tim S1OPCof the pwr vs. log AItrend, m, is defined as

m= 162.’ @kh

. .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .(B-3)

Rearranging Eq. B-3 for the formation permeability, k, we obtainLhcfouowing

k = 162.6% .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . ..(B.4)

Rearranging Eq. B-2 for the pseudoradiaf flow skin factor,s, weobtain

[

,r = 1,1513 @W$.Ibr - PwJA1=o)m

-’04ti)+3227’l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .(B-5)

Wc note that E.qs. B-4 and B-5 are the relations that will be usedin this work for the iuratysis of the semilog straight-line portion ofthe pwl~vs. log At piot

The definition of the pnxsure intcgraf is given as

~

t1Pwsi = ~ pwJr)d~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(B.6)

oHowever, for convenience and duc to computational issues, weusually compute the pressure integral using lhe followingequivalent mathematical form

Pwsi = Pwj,AM + Api . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(B-7)

where Api is defined as

J@i+‘Ap(r)dr ........................................(B-S)

o

and Ap is dcfmcd ss

Ap =pw~. pwf&~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(B.9)

The computational issue regarding the usc of Eq. B-9 rather thanB-6 arises when we consider that the log Ap vs. log At trend hasconsiderably more “character” than the log pw~ vs. log At trend.This feature becomes quite important when we usc the power ruleintegration formula given in ref. 18.We prefer using the pressure drop fomr because the behavior ofthe logarithmic pressure arguments am relevant to the integrand ofthe pressure intcgraf for the power law formula. Significantimprovements in integration (i.e., better representation of the data)are obtained using Ap (Eq. B-8) over p~~ (Eq. B-6) in theintegration process. Ref. 18 demonstrx the utility of power ruleintegration and we have used this formula for ail of the integrationrequired in this work.

Given the definition of the pressure integral function, the fturda-mental pressure integral-time relation for undistorted radiai flow(i.e., the wmilog straight tine) is given by

Pw.d= Pwsi,Ihr + m 10g(Ad ..............................(B-1O)

The intercept is defined as the pressure integral at 1 hr. pw$i.lhrfrom the semilog straight line or its extrapolation. As withpressure analysis, we also note that this relation requires thepressure at shut-in, pwj~~o.

[ t&)-3 ”227’+0”8’8+-$!Pwsi,lb = pwj,A~O + M 10

. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(B.ll)

The slope of the pw~lvs. log AItrend, m, is defined as

m= 162.6$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(B-l2)

Rearranging Eq. B-12 for the formation permeability, k, weobtain

k=162.6# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(B.l3)

Rearranging Eq. B-11 for tie pscudoradhl flow skin factor,s, weobtain

[s = 1.1513 @W$i,lbr- PwJAM))m -’”i*l+’’’’’l+*

. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . ...(B.l4)E.@.B-13 and B-14 are the relations that will be used in this workfor the analysis of the scmilog straight-line portion of the PW$ivs.log Atplot as shown in Figs. 3 and 9.

157

in!--’-mt

\

\\

TAS@Instrument

Pm- P08t-

AmpllflcrFIIwI Ampliflor

t

+zq] kl\

Figure 1- Telemetry Acquisition System

158

Casing -l

Tubing —

TAS Tool —

m

m

*

-----

-1~

-------

— Rods

~ Pefforatio~

Seat Nipple & Pump

\ Casing Hanger

Figure 2- Downhole Configuration for NRU Pressure Buildup Tests.

159

ld

Figure3-

I

t

----1

Samilog Plot Of Real-Time Surface Data And BottomholeMemoryGauge Dsts (Using Shut-In Tfme, Af)For NRU Well 905.

‘O’w&YG-.l~

r- .H w- -“’ Iiiiii

,& L

,(p ,=1 100 10’ 1

/. v,-.-:::::: -, ..--,’. .- ,- -: . . .: .-

:... --: . . . . ..- -..... -

. . . . . . . . . . . . . . . .

., -----

FGGiR

I

,.l

[AP’~w - EOO@ 1~HOll--

[AU(t~Qj)W m4,6S hm k = 0.0

d’=3s*.2.rs

co. 7R3.O

103 Id 10s Idtotco

Figure 4- Match of BuildupTest Data for Well NRU 905 on the Type Curve for

an Unfracturad Well in an Infinite-ActingHomogeneous Reservoir.

160

10’

1Oc

TYw Cuvefora WaSwiUIa Rnka CuxiudiivmOcsl Fmdumin M~AcUmJHmnqMWM

Reaamnl with WOSMIS Slmoa Eflecis

‘ L&mcii: %=(4Yfk4J= IQ’.1

— P. T)w Cum. -- PO’ TYPSCUIW

?-,#’z4’5&l-?x

x-=-=i”-. . . ..,---- .-

‘O-’Kz%iREl A?x=i”>:.-=k----z w’..--ii=.--i-’” 4-’-”””iE%a:

, “.2,. f-/- ..-i> ..-r- [ I :3

.,,, -,..’

. <’- ki!ynl’1o~

I;---”--’-”-’t”-”””-”-”””-1- 1 I II

k. 0.0M7 idb- 9.14 II

c.= 0.9 ’111(-)+1 I I 1 I I I I_ Q&l

““104 10-2 1o“’ 10° 10’ 102 103 104 105tin/@

Figure 5- Match of BuildupTest Data for Well NRU 905 on the Type Cuwe for a Well with aFinite ConductMty Vertical Fracture In an lnflnlte-ActingHomogeneous Reservoir.

Fiur’s 6-

-* J&.2,0cp

u

s. -2.40

R634u41 mplueS Co= 696.6

C,. l,oxldmld Sutaa Oara:

:: ;.:&.o,ceel Ird

S = -2.71

P&#%&&

co= 0s0.3

R.(AM) = 17S.3 cab

&

—

=F=l

i? ,.s

shut-kn nrna, At , half3

Data Match of BuildupTest Data on LogLog Plot for Well NRU 905. Matched Using the lnfmite-Aoting Homogeneous Reservoir Model. Comparison of Real Time Surface Data with BottomholeMemory Gauge Data.

161

I -~.2.ocpReeewlr FmpeiU#s

G= I.oxio+ Lmla”’ I,.3-/[ - r.=0.31 H I

h.lSOll

,0+ ,=1 ,.O ,.l ,.2

Shut-In mmc,At,ham

T%Ri!%-.X,- 8,24 ncm. 0.932

Figure 7- Data Match of BuildupTest Data on Log-Log Plot for Well NRU 905. Matched Using the Model for aWell with a Finite Conduotivii Veriical Fracture In an Infinite-ActingHomogeneous Reservoir Model.Comparison of Reef Time Swface Data with Bottomhole Memory Gauge Data.

At Rettweceo Datum d 7LMY I

Ave. %SWVC

.——. . . .

{

. . . . . . ..

0,I

PMSSWS . i

.. . ..-——.

o lm 2[

&

—....--__— z~..-_--__+.,...-—.-—-Est. AwPrmsum

....-....—.—.

ge Rssendr -2976 peia

. .

. . .

D 30W 4m 50WTime,hre.

Figure8- Average Reservoir Pressure Estimate using RHM Method - NRU 905.

162

102

10’

[

2000 1 I

: X2 W2am-

. s = 4.4*-2.ocp

Res6vdr PqmrUe%c,= 1.Oxlo+ Fab-’

~=o.mnh.l!Y211

2ooo- - ~~+. 0.0ss (rrdm)

~qo. sssnm

/r~At-0) - 2M.6 @a

i!~ M@u I

U-1--L

a0; 1

1f 1 1 ,

I

ld

Figure 9-

,=$ lL+ ,.l lCP lo~

shut-h nm, At , hours

semilog Ptot of Real-Time Surface Data and Bottomhole MemoryGauge Oata (Using Shut-In Time, Afi for NRU Well 2703.

--m–Id+ w*ak9 +--k

—

----

—

—i.#-.

,0.1

E/104

/..

.,- ‘“’”OsY I

/ A’- / /t- /

— ,. ,=, .=,. ,., . . ..- .

r........::..-.....----.:-

/

,. , [Lw/(t~c~~ -22 IllsK - 0.09Cs .-4.2.

cd= 1.0 CD= 49%.2

10=1

1(P lU’ 10@ 101 lo~ 10J Id 10s Id

Figure 10- Match of EkffdupTesf Data for Well NRU 2703 on the Type Curve foran Unfractured Well in an lnfiiite-Acting Homogeneous Resewoir.

163

10’

10°

10-’

104

104

.-104

Figure 12-

10“2 1o“’ 10° 10’

..,.-.,..-”2 -“’”-”’*:,.m,.. -

— HI

[Ap/pJMp - sos pd

[Al /(fm/cJ~. 22hmcm-as

(BIAIAsIAna@b-FlrilaconAuc.tkity VOnbl Fmtum)k- O.03Qird+-mm nf+ 0.5

103 104 105tmmu

Figure 11- Match of BuildupTest Data for Well NRU 2703 on the Type Curve for a Well with aFinite ConductivityVertical Fracture in an Infinite-ActingHomogeneous Resewoir.

, ~4

FOst~(~i-)Be.1.1 RiUSTS/l*- 2.0 Cp

ReSeu.lr PmpdSS

Lc, . l.mlo+ pdi’

,.3 k=o.31nh=lSOll

$42gg%#

xJAM) = 264.6 @h

,Cl ,Oa ,.l

Shut-hTim., At, hum

Data Matchof BuildupTestDataon Log-Log Plot for Well NRU 2703. Matched Using the Infinite-ActingHomogeneous Reservoir Model. Comparison of Real Time Surface Data with BottomholeMemoIYGauge Data

164

Figure 13-

LJi=mn

*. 006s (rIscrhrl)P~ P~

~=ssslam

zp#BO) = 2S4.6 psia

—* . .––__I1$&$

10’-

- open Symtisluko

v v Prmslm lnrw@ww81h cmtnI@ I 1

,@ ,.9 10’

Shut-h! Tlnu, AI, hwm

Data Match of Buildup Test Data on Log-Log Plot for Well NFIU 2703. Matched Using the Model for

a Well with a Finite ConductivityVertical Fracture in an Infinite-Acting Homogeneous ReservoirModel. Comparison of Real Time Surface Dsta with Bottomhole Memory Gauge Data.

4000

3W0

6.a

‘?20W:

100a

M. Resarvdr Pr6ssuftI = 2

;

~

W4hLmuu:(Suildup Am SIS-

‘7Fmdwti Wal in abmqenewa Reservdr

SoNmmHda Data

k=om2dx,. 39.0ncm. 0.302

cm= 1X1OJSudace 08(.34.= O052M

x,. 39,0 nco, = 0.288

co= Ixld

)

K?

I I I 1

v ReterenceDatum 01 713LW’

. . . . . . .. .. ..... . :

Est. Avekge Reservoir -

2233 @a

.

Pressure

I

. .. . . ......+

. .

I

o 1600 2tioo 3&o 4600 5000Tsne,hrs.

Figure 14- Average Reservoir Pressure Estimate using RHM Method - NRU 2703.

165