SPESociety of PetroIet.rn Engineers

SPE 21657

Evaluation of Underbalanced Through-Tubing Pe!rforatingand Closed Chamber Test Interpretation TechniquesM.M. Manohar and C.W. Morris, Schlumberger; S.R. Brunner, Chevron U.S.A. Inc.;and D.O. Hill, Schlumberger

SPE Members

Copyright 1991, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the Production Operations Symposium held in Oklahoma City, Oklahoma, April 7-9,1991.

This paper was selected for presentation by an SPE Program Committee following review of information .:ontained in an abstract sUb~itted by the author(s). Contents of t~e paper,. as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correctio~ by the aut~or(s). The.ma!enal, ~ presen!ed: does no! necessarily reflect

any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE '"!1eellngs are subJee.t to publication review by Edl~onalCommittees of the Societyof Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. lIIustratio~s may not be COPied. The abstract should contaIn conspicuous acknowledgmentof where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Rlc1ardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL.

ABSTRACT

Underbalanced, through-tubing perforatingoperations represent a compromise between the pressuredifferential needed for effective perforation cleanup and thedifferential that causes sand production or tends to the thegun and cable. This paper explores the dynamic variablesinvolved in through-tubing perforating and describes a newmodel developed to evaluate the underbalance perforatingconditions and predict the effects on the wireline gunsystem. Using this model, formations can be aggressivelyperforated with the optimum safe underbalance pressure, andcompletion operations can also be combined with closedchamber test techniques to accurately evaluate the completionefficiency and initial reservoir parameters.

Utilizing new wireline technology to measuredownhole pressure and temperature during perforating,operational data were obtained from numerous field tests tovalidate the dynamic model. The results indicate that themodel reliably predicts the maximum underbalance to avoidsanding, the change in gas cushion pressure, the volume ofreservoir fluid influx and the gun/cable movement Examplesfrom Louisiana Gulf Coast wells are used to illustrate theapplication of the design model and the associated closedchamber test technique.

The transient pressure data from the closed chambertest are used to accurately evaluate reservoir parameters andcompletion efficiency. The data are analyzed by assumingthe formation is subjected to an impulse rate created bybriefly flowing the well. In addition, by measuring thesurface and bottomhole pressure during the perforatingoperation, the approximate fillup rate can be determined aswell as the cumulative volume of fluid entry. In the fieldexamples presented, these data are utilized in otherinterpretation techniques, such as rate convolved pressureanalysis, and the derived formation parameters are comparedwith conventional well test results.

References and figures at end of paper

255

mmODUCTION

Underbalance perforating operations ensure a surgeof resc:rvoir fluid such that gun debris and crushed rock inthe pelforation tunnel are swept into the borehole, providingbetter flow performance for subsequent production. Formaximum cleaning effect, it is desirable to perforate with themaximum possible amount of underbalance pressure. Thedegree of perforation tunnel cleaning is directly proportionalto the amount of underbalance and fluid influx. In general,the larger the underbalance and fluid influx, the better thecleaning effect. The pressure differential required forperforation cleanup ranges from 200 psi to more than 5000psi and has usually been established by trial and error in eachfield.1•2,3

However, practical experience dictates that problems(sand production, casing collapse, etc.) will develop if toohigh an underbalance pressure is used. In unconsolidated orpoorly consolidated formations, the mechanical strength: ofthe fOlmation must be considered to avoid sand producttonand/oI the movement of the fine particles that could causeplugging of the matrix. Excessive underbalance pressureduring the perforating operation can lead to significant sandprodul:tion and to the sticking of wireline tools being in thewell.

In the case of through-tubing perforating, agas/liquid cushion is commonly used to obtain the desiredunderbalance pressure. The drag force exerted on the gun­cable nystem when the fluid accelerates upward must also beconsidered when perforating underbalanced. The pressurediffen:ntial must be designed to avoid blowing the wirelinegun and cable up the hole during the initial fluid surge. Ingeneral, the larger the underbalance and fluid influx, thelarger the drag force exerted on the gun-cable system.

Thus, the optimum through-tubing perforatingoperation is a balance between the pressure differential thatwill cause sand production and that needed for effectiveclean-up of the perforations, which avoids lifting the gun

Eval~a!:ion l?f _pnd~'rba1anced Through-Tubing Perforating ?" , __2 an" clo"'e" Chamh,>r .,."",t I ...... " 'I h ... I

and cable excessively. In the past little real guidanc:e has column height, gas column height and pressure, the effect ofbeen avaibalbe to the production engineer who wants to movement on liquid and gas columns, the amount ofselect a liquid column height and surface prc:ssure underbalance and fluid influx. Fluid column height, gunoptimalfor perforating. This paper explores the dynamic weight and the amount of underbalance can be adjusted untilvariables involved in through-tubing perforating and a safe, effective solution is predicted. Practicalformulates a model such that formations can be aggressively considerations, such as the lubricator length and maximumperforated with the optimum, safe underbalance. allowable total tool length, often limit the weight that can be

added to the tool to stop movement.When the well is perforated underbalanced,

formation fluid begins to flow into the wellbore immediatelyafter the guns fIre. This initial flow provides an opportunityto conduct a pressure transient test based on themeasurement of downhole flowing pressure. This test isanalogous to a "slug test" using conventional drillstem test(DST) techniques, where the flow is induced by opening aproduction valve in the DST string. Many variations arepossible during the test period; e.g., a well can be open orshut-in at the surface, the well mayor may not flow to thesurface, and the test could be complemented by one or moreflow and shut~in periods.

A number of variables, including damage fromdrilling fluids or cementing operations, chemicalincompatibilities between completion and formation l1uids,and formation heterogeneity, affect the completion pr,:x:ess.Each completion should be evaluated to confirm floweffIciency and to determine, if any, remedial actions areneeded. If performed, the evaluation of completions hastraditionally been an expensive and time consuming processinvolving hours of conventional well testing and productionlogging.

This paper describes the combination of perforatingand testing operations designed to evaluate the completioneffIciency. Measuring the downhole pressure, temperatureand, optionally, the flow rate throughout the perforating andtesting sequence allows quick analysis of fomlationparameters such as permeability, skin factor and initialreservoir pressure.

BACKGROUND

Delermjnjn2 the Underbalance Pressure and.Eyaluatjn2 the Dynamjc WeJlbore/Wjreliu

Conditions

Little fIeld data is normally available to the engineerto assist in predicting the well flow performance as afunction of underbalance pressure or to confIdently esdmatethe maximum safe underbalance that can be used withoutblowing the gun-cable system up the hole. However, :recentpublications1,2.3,4.5 have begun to address the uncertainty ofestimating the optimum underbalance pressure usc:d forperforating.

Field experience indicates that suggested ranges forunderbalance pressure, derived from empirical models, maybe unsafe for many through-tubing perforating open.tions.High velocity movement of the completion fluid slugimmediately after perforating may cause entanglement of thewireline cable. In addition, these empirical models do notconsider other important factors, such as reservoir fluidinflux volume, liquid column height, surface pressure orproviding for a closed chamber test of the rest~rvoir

characteristics.

An analytic model has been developed to predlct thedynamic forces acting on a gun-cable system whenperforating underbalanced (Figure 1). The model considerswellbore and gun-cable geometry, tool weight, :liquid

256

The driving force behind the upward movement ofthe liquid column after perforating is the pressure differencebetween the top and bottom of the column. Clearly,formation permeability can have a signifIcant effect on theflow after perforating. A low permeability reservoir resultsin a much slower pressure buildup downhole than a highpermeability reservoir. This pressure buildup for the case ofclosed chamber testing is complicated by the fact that thewell initially starts to flow because of the pressure difference(underbalanced backsurge), but then is rapidly restrained bythe pressure buildup in the confIned wellbore. The shoot­and-test interpretation is a combination of multirate pressuredrawdown and buildup in a very short time period.6,7

For the evaluation of the dynamic forces acting onthe gun-cable system, it was found empirically that, if theformation permeability was more than about 25 md, it couldbe assumed that the bottomhole pressure surgesinstantaneously from the underbalance pressure level to thestatic reservoir pressure when the guns are shot. Thebottomhole pressure change caused by the flow of verysmall volumes of fluid and the unique nature of the transientdrawdown-buildup conditions in the wellbore made thesmall pressure changes insignifIcant with regard to thereaction of the gun-cable system to the dynamic forces. Onlyin relatively low permeability formations would reservoirpressure drawdown affect the results. In those cases, thereservoir pressure is determined from a modifIed constant­pressure flow solution proposed by Jacob and Lohman.8

The basic model is a balance of the forces acting onthe fluid column. Once the acceleration of the liquid columnis calculated, then a simple integration over time yields thevelocity, which in turn is integrated to give the position ofthe liquid column. Knowing the velocity and positioninformation, the magnitude of fluid-imposed forces on thewireline gun-cable system can be determined. The averagefriction coeffIcients have been empirically determined for thecasing or tubing wall surface and for the electric line cable,Cfw and Ctc, respectively. The following equations are thenused to calculate the drag forces on the tubing/casing andcable:

F!::.p - Fgravity - Fed - Fwd = rna (1)

2Fed = 0.5 pi} (CodHCje) (2)

2Fwd = 0.5 pi} (CidHCjw) (3)

It has been found empirically that 0.22-in-diameterelectric line cable becomes unstable (i.e., coils up) whencable tension is reduced to about 100 lb. This is consideredthe critical cable tension, and it is important to keep thedownhole cable tension above this critical value. Theminimum tension point occurs at the top of the liquidcolumn, and the tool movement criteria is applied at thisdepth.

SPE 21657 M. Manohar, C. Morris,

The resulting model·of the wellborelwireline systemdynamics is solved using the discrete time-step method. Theassumption must be made that for very small time intervals,uniformly accelerated rectilinear motion adequately describes!he fluid column movement. Using very small timelI~crements, the values for acceleration, velocity anddisplacement are calculated. The cable tension is determinedand compared with the critical value. The liquid columnvolume is then appropriately increased, all necessaryparameters are recalculated, and the cycle is repeated until theliquid slug velocity decreases to zero or the cable tensiondrops below the critical value for tool movement. Finally,the total formation fluid influx per perforation is calculated.A schematic flowchart of the model is shown in Table 1.

It is possible to achieve a particular bottomholepressure several different ways. A long, lightweight liquidcolumn gives the same bottomhole pressure as a short,heavyweight liquid column. In each case the amount ofunderbalance pressure is the same; however, the short liquidcolumn results in better perforating performance because itmoves substantially farther uphole after perforating before!he compression of the gas cap above the liquid slug slowsits movement. This means more reservoir fluid influx perperforation and, therefore, more cleaning effect However, arelatively short liquid column moving a long distance up thewellbore could exert sufficient drag on the tool and cable tolift the tool and cause problems. Therefore, a clearrequirement exists to design the cushion for the bestperforating cleanup conditions without tool movement.

AnalYsis of Transient Pressure Data AfterPerforatjng

Other recent technological advances have been thedevelopment of downhole pressure and temperature tools(Le., the Measurements-While-Perforating Tool [MWPT])that allow real-time measurement of downhole conditionsduring through-tubing perforating and the new well testinterpretation methods6.7 for closed chamber tests. Bymeasuring downhole pressure during the fluid surge andsubsequent pressure buildup, the transient pressure data canbe utilized to provide accurate estimates of the reservoirparameters (Le., permeability and skin factor) as well as tosupply direct measurements of the actual underbalancepressure and initial reservoir pressure.

Several approaches can be taken to analyze thepressure data acquired after perforating a well. The test maybe analyzed as a compressive Impulse* test or, since thewellbore fill-up constitutes a variable rate test, rateconvolution methods may be used. Ayoub et a1.6 havedeveloped the Impulse interpretation technique depends uponan initial short production period approaching instantaneousflow. The Impulse pressure response would match directlyon the derivative type curve. In practice, however, the flowperiod is not instantaneous. As pointed out by Ayoub et al.,6the shut-in pressure data follows the derivative type curvewhen the time of the flow period becomes short compared tothe duration of the shut-in period. Pressure data during theflowing period matches the drawdown type curve. Thepermeability-thickness product can be calculated from thepressure match, and the wellbore storage coefficient and skinfactor are calculated from the time match.

* Mark of Schlumberger

S. Brunner, D. Hill 3

Tariq et al.9 discuss the case where the surface valveis closed during perforating and the test becomes analogousto the closed chamber testing technique of a drillstem test.The compression of the gas column on top of the liquidcushion introduces a variable storage phenomenon that mustbe taken into account with the bohomhole and surfacepressure data. If the well is closed at the surface, pressurebuildup during the flow period is slower and the final staticpressure is reached after a longer period of time. Usingbottomhole. an~ surface pressure data, with the knowledge ofgas properties m the gas column, the flow rate history duringthe fill-up period can be estimated. These estimated flowrates can then be used for variable rate pressure analysis.

Since the fill-up period after perforating involvescontinuously changing flow rates, some type of variable rateapproach is necessary for analysis.9 One method representsthe continuously varying flow rates as a series of straightline chords. lO The response of the variable flow rates is thencontinuously superposed using the superposition theorem.This approach is called sandface rate convolution. For theconvolution method, a plot (on cartesian scales) of rate­normalized pressure versus rate convolved time yields astraight line in the radial flow regime. The slope of thatstraight line yields the permeability-thickness product, andthe associated intercept of the line gives the skin factor.

RESULTS AND EXAMPLES

Results from numerous field test wells wereexamined using the underbalance design model describedabove. All the jobs utilized the MWPT so that appropriatedownhole data were available. These through-tubingperforating jobs (where a gas/water cushion was used)include six cases where the tool was, in fact, lifted up thewellbore. The model accurately predicted this result in allcases. In general, the cause of tool movement was a shortliquid column combined with a large underbalance pressure.Tool movement, if it occurs, takes place within the first fewseconds after perforating.

Each job was compared with the model prediction interms of the surface pressure increase (when available) andcable tension change. The comparison, shown in Table 2,indicates that the model reliably indicates thewellbore/wireline response to the perforating operation. Fourof the documented jobs with surface pressure data show thatthe pressure change predicted by the model is within 20percent of the measured value.

The surface cable tension comparison (measured atthe winch unit) is a less reliable indication of model accuracysince the tension measurement can be distorted by theamount of pressure applied at the lubricator to preventleaking. This is especially true when surface pressure isapplied to the gas cushion. Additional error is introduced bythe variable gun material loss for different size jobs.However, even the cable tension loss predictions are withinan order of magnitude of the actual measured data in mostcases.

Consider the following specific example of a wellperforated using the MWPT. The model was used tosimulate the underbalance conditions and cushion volumesfor completion in this high permeability formation. Onreaching bottom and filling the well to the proper fluidcolumn height, surface pressure was brought up to the levelexpected to yield the correct bottomhole pressure. Figure 2

257

Figure 6 is an Impulse analysis plot. On this graph,the Impulse pressure group (in psi-hrs) is plotted as afunction of elapsed time (delta t). A representative type curvewas then overlaid on the Impulse data, and for a given set ofreservoir rock and fluid properties, the permeability wascalculated to be 15.05 md from the pressure match, and skinfactor was calculated at -2.86 from the time match. In thiscase, a good estimate of permeability and skin appears tohave been obtained from the fill-up data since radial flowwas reached approximately 30 min into the test

Evaluation of Underbalanced Through-Tubing Perforating4 and Closed Chamber Test lnternretation Techniaues SPE 21657

illustrates the actual well log recording during the petforating pressure of 2100 psia and the subsequent buildup to a finaloperation; sutface pressure, cable tension, dowillhole reservoir pressure of 4532 psia after petforating. At thepressure and downhole temperature are plotted in real time at conclusion of the test on the way out of the hole, the fluidthe sutface. The moment of firing is indicated on the log by level was tagged at 870 feet This change in fluid level (fromthe rapid bottomhole pressure and temperature response:. The 6670 feet at the beginning of the test to 870 feet at the end ofdownhole pressure rose from 1819 psia to the full resc~rvoir the test) correlates to an influx of 22 barrels during the fill-uppressure of 2036 psia within two sec from the moment of period.petforating, indicating a rapid surge of fluids into thewellbore. The sutface pressure increased much moregradually from 400 psia to 520 psia. The slow increase insutface pressure indicates that the top of the fluid columnmoved upward, compressing the air column above it. Therate of sutface pressure rise can be used to determine theposition of the top of the fluid column as a function of time.Calculations indicate that the column moved upward 61 ft in14 sec. The pressure change measured within the gascolumn was 120 psi and is in close agreement with thepredicted pressure increase of 103 psi.

Example 2

The downhole flow rate profile (Figure 9) wasderived using an algorithm that calculates a downhole gasrate assuming gas bubbling through a standing liquidcolumn. Specific inputs are bottomhole and surfacepressure, tubing/casing configuration, cushion fluid lengthand density, and sutface temperature.

Figure 10 is a sandface rate convolution plot with asemilog straight line drawn through the data at late time(radial flow). Based on the slope and intercept of the line,permeability and skin were calculated to 0.012 and -0.1,respectively. These answers compare very well with theImpulse answers.

Figure 8 is an Impulse plot of the downhole transientpressure data. Based on the type-curve match parameters,the reservoir permeability was calculated to be 0.017 mdwith a skin factor of +3. It can also be seen that the data hasnot yet reached radial flow (Le., flattening of the Impulsedata).

Figure 7 presents the bottomhole pressure, sutfacepressure and bottomhole temperature data acquired during apetforating job in Beauregard Parish, Louisiana. This wellwas perforated at four shots per ft from 13,072 ft to 13,090feet using a 1-11/16-in Enerjet* gun. In order to achieve thedesired underbalance, the operator filled the well withcompletion fluid and applied an additional 500 psi ofnitrogen gas pressure at the sutface. After petforating, thewell remained shut in for approximately 3.6 hrs. Figure 7shows that the bottomhole pressure continued to build at asteady rate during this time period, indicating that thereservoir could be of low permeability.

This example shows that when uncertainty existsduring type-curve matching procedures (i.e., nonuniqueness), sandface rate convolution methods may beused to calculate reservoir parameters. It is important,however, that the pressure data acquired be of good qualitysince any errors associated with such measurements reflectdirectly on the calculated flow rates. Uncertainties associatedwith deduced flow rates may be eliminated by measuringpressure and flow rate (with a flowmeter) simultaneouslyduring a petforating operation.

Example 3

Example 1

The measured sutface cable tension curve shows a200-lb drop over 6 sec (Le., changing from 1420 Ib to 1220Ib). This drop is caused by the loss of the petforating gunmaterial and the upward-moving liquid column imparting anupward drag force on the cable. The tension drop is not dueto significant upward tool movement at the momtmt ofpetforating, since this should have resulted in a suddenrather than a relatively gradual drop in cable tension.Excluding the petforating gun weight loss from themeasured data, the predicted cable tension decrease of 37 Ibis in reasonable agreement with the measured results.

Well Test Interpretation

Figure 3 shows the MWPT measured response inanother well of relatively lower formation permeability(about 38 md). The underbalanced bottomhole pre:ssure(3210 psia) increased to about 90 percent of the finalrecorded downhole pressure of 4742 psia in 3 min butcontinued to build up slowly over the next 88 min. Thesurface pressure increased from 14.7 psia to 1572 psiaduring the test, compared to the predicted increase of 1251psia. The temperature increases rapidly about l3°F(probably caused by the gun gases) and then drops off tostabilize at 218°F after about 3 minutes. The measured cabletension loss was small (Le., decreasing only 45-lb from theinitial 885-lb value). Although the tool was not in danger ofbeing moved uphole in this case, the predicted cable tensionchange was 25 percent ,or 330 Ib after 3 sec.

These examples partially illustrate the influence of thereservoir permeability and fluid parameters on the systemresponse to the petforating operation. As the fonnationbecomes less permeable, the initial backsurge of resc~rvoir

fluids decreases in volume and velocity so there i:, lesschance of moving the tool uphole.

The following examples are actual MWPT tests runin South Louisiana wells. Common petforating practice inthe Gulf Coast dictates that wells be closed at the surfaceduring the perforating operation. This being the case, mostdata sets can be analyzed as compressive Impulse tests.

This well was petforated six shots per ft with a 1­11/16-inch Enerjet* gun system from 11,851 feetto 11,877feet. Figure 4 shows that the fluid level was tagged at 6770 This well was petforated with a 1-1l/16-inchfeet while running into the hole with the MWPT. Figure 5 isCartesian plot of the pressure data showi,!g.:an::..:.irn~·~ti~al~c:::.:IJl~'~s~h~io~n:'-'_...J-__E_n_efJ_·_et_*_g_u_n_a_t_s_ix_s_ho_t_s_p_e_r_ft_fr_om__ll_,_909__fe_e_t_to_l_l_,9_1_4_---J

258

SPE 21657 M. Manohar, C. Morris,feet. From the MWPT down log, the fluid level was taggedat 4680 ft prior to perforating. Figure 11 shows the completepre- and post-perforating pressure and temperature record.The change in pressure profile (and corresponding change intemperature) from 0.10 hr to 0.30 hr indicates where thesurface production valve was inadvertently opened byoperations personnel.

Figure 12 is the associated Impulse analysis plot.Based on the match point parameters, the permeability andskin factor were calculated to be 39 md and -1.4,respectively. Total fluid recovery during the 1.6-hr test was18 bbl.

Two days later, after the well was allowed to cleanup and stabilize at a constant rate of 1573 MscflD, aconventional buildup test was performed. Figure 13 is atype-curve match of that buildup data. The welVreservoirsystem was modeled as a homogeneous reservoir withwellbore storage and skin effects between two intersectingfaults. The intersection angle between the faults is 45degrees with the well on the bisector, 470 ft away from theintersection of the faults. Based on the match pointparameters, the permeability and skin factor were calculatedto be 38 md and +3, respectively. These answers are in goodagreement with those obtained from the Impulseinterpretation method.

CQNCI.USIONS

Many interrelated conditions must be consideredwhen designing an efective, safe through-tubing perforatingjob. Systematic underbalance design techniques have beendeveloped to allow the engineer to optimize the through­tubing perforating procedure for maximum cleanup,whilemaintaining a safe operation. The results include:

(1) Maximum underbalance pressure to avoid sanding.

(2) Minimum underbalance pressure for formation cleanup.

(3) Fluid cushion (gaslliquid column) design (Le., height,fluid density, etc.) to minimize tool movement.

(4) Maximum reservoir fluid influx per perforation.

Combined with real-time downhole pressure andtemperature measurements, which allow accurate control ofthe well conditions prior to perforating, the underbalancedesign procedure significantly increases the chances for asuccessful completion operation.

After reviewing the recording and interpretation ofdownhole pressure data acquired in conjunction withunderbalanced perforating, the following concludingstatements can be made:

(1) Pressures acquired during the fill-up period can beanalyzed for fonnation parameters.

(2) The Impulse method offers a quick and relatively easyway to analyze post-perforating data for penneability, skinfactor and formation pressure.

(3) Answers obtained from the Impulse analysis techniquewere shown to compare favorably to answers obtained fromconventional buildup tests.

(4) If an accurate record of surface pressures is obtained, therate offill-up (downhole flow rate) may be deduced and

259

s. Brunner, D. °Hill

used in a variable rate analysis technique to estimatereservoir parameters.

REEERENCES

1. Bj~ll, W.T.: "Perforating Underbalance - EvolvingTechniques," Distinguished Author Series, IPT (October1984): 1653-1662.

2. Krueger, R.E: "An Overview of Fonnation Damage andWell Productivity in Oilfield Operations," DistinguishedAuthor Series, IPT (February 1986): 131-152.

3. Kiing, G.E., Anderson, A., and Bingham, M.D.: "AField Study of Underbalance Pressures Necessary to ObtainClean Perforations Using Tubing-Conveyed Perforating,"IPT (June 1986): 662-664.

4. Morris, C.W. and Ayoub, lA.: "Engineered PerforatingDesign and Evaluation," paper SPE 18840, presented at theSPE Production Operations Symposium, Oklahoma City,March 13-14, 1989.

5. Crawford, H.R.: "Underbalanced Perforating Design,"paper SPE 19749, presented at the 64th Annual TechnicalConft~rence and Exhibition of SPE, San Antonio, October 8­11, 1989.

6. Ayoub, J.A., Bourdet, D.P., and Chauvel, Y.L.:"Impulse Testing," SPEFE (September 1988): 534-546.

7. Simmons, J.E: "Convolution Analysis of Surge PressureData," IPT (January 1990): 74-83.

8. Jacob, C.E. and Lohman, S.W.: "Nonsteady Flow to aWell of Constant Drawdown in an Extensive Aquifer,"Tran~;., AGU (August 1952): 559-569.

9. Tariq, S.M. and Ayesteran, L.: "Analysis andApplications of Pressure, Flowrate, and TemperatureMeasurements During a Perforating Run," paper SPE15475, presented at the 61st Annual Technical Conferenceand Exhibition of SPE, New Orleans, October 5-8, 1986.

10. Meunier, D., Wittman, M.J., and Stewart, G.:"Interpretation of Pressure Buildup Test Using In-SituMeasurement of Afterflow," JPT (January 1985): 143-152.

~1ENCLATURE

a = acceleration, ft/sec2

Cod = cable outside diameter, in

Ctc = cable drag coefficient, dimensionless

Cid = casing or tubing inside diameter, in

Cfw = wall drag coefficient, dimensionless

Fcd = drag force on cable, Ibf

Fwd = drag force on wall, Ibf

Fdp = force due to pressure difference, Ibf

Fgravity = force due to gravity, Ibf

5

6Evaluation of Underbalanced Through-Tubing Perforating

and Closed ChambElr Test Internretation Techniaues SPE 21657

H = liquid column height, ft

h = formation thickness, ft

k = permeability, md

mn(P) = gas pseudo-pressure function, psi

P =p~ssure,p~a

$ = skin factor, dimensionless

P = density, Iblft3

'6 =liquid column velocity, ft/sec

260

TABLE 1 - UNDERBALANC! D!SIGN PROGR,~M FLOW CHART

I • O. a • 01 Y • 0, x • 0

TABLE 2COMPARISON OF ACTUAL AND PREDICTED RESULTS FOlil WELLS SHOT UNDERBALANCED

UNOER8AU\NCE ACTUAL CABlE PREDICTED CABlE CHANGEWELL PRESSURE IDSiI TENSION lOSS Ilbl TENSION lOSS Ilbl IN WHP In-oil CCMo1ENTS

1 230 N/A 37 120 measured103 predicted

2 1404 45 330 1572 measured1251 predicted

3 322 25 67 150 measured120 predicted

4 286 10 44 30 measured27 predicted

5 700 170 205 900 measured1040 predicted

6 346 20 77 N/A Res. Pres. not stabilized,

7 2434 460 > critical level N/A Tool blown uphole.

8 2341 190 > critical level N/A ToOl blown uphole.

9 1306 240 360 N/A

10 64 45 39 N/A

11 2268 550 " critical level N/A Tool blown uphole.

12 57 10 121 N/A

13 1000 N/A " critical level N/A Tool blown uphole.

14 240 195 170 N/A

15 2191 700 950 N/A

16 600 N/A " critical level N/A Tool blown uphole.

17 1000 large " critical level N/A Tool blown uphole.

18 508 N/A 38 NIA lOW permeability.

19 250 N/A 12 N/A20 490 85 50 N/A lOw permeability.21 717 32 169 N/A

261

SPE 21651

,216;1

FIGURE 1 - W!LL80RE/WIRELJNE RESPONSE TO UPWARCFLOW IMMEDIATELY AFTER PERFORATING

CABLE §~S'ONf

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FIGURE 3 - MWPT RECORDED RESPONSE liNLOW PERMEABILITY FORMATION

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FIGURE 2 - MWPT RECORDED RESPONSEIN HIGH PERMEABILITY FORMATION

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262

SPE 21657

:0

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Example 1: IM'U.SE Analysis Plot

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Example 2: M'U.SE Analysis Plot

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Example 1: Pre- and Post Perforating Data

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Figure 7

Example 2: Post Per10rating Pressll'e and Temperatll'e Data

r.rrri:rr~''l:J'r=:cm'''' ",I" ="=

0.4

0.2

I.................,."............................... I

666666666666

6666A6666...... f,.666A

'1&.6 6 .9

r~w"~-""""'''''''''''''''''''''''L''''L'''''''L''LL'''L••

f..

O-'L::::;:(7)wll>,-0

0­IUI:;:G

0­CJUI(/)0.

27240

269102600.00

860000 F I I I I i I I I I00

40000I.OGOOE 104

4BOO

4500

42000], 3900

..5 3600'"'"...t 3300

":g 3000IE.2 2700(;lD

2400

2100

lBOO0.0

'"g:

SPE 21651

~

~.,

c:

:!lCl

'"'"'"~

,- '"III~~

..--.:.~~oO~oO

E:'"~

Cl'"'"~:3

Figure 10

Example 2: Sandlace Rate Convolution Plot

"

,,////'" '"'"

rJCJo [J CJ

'"

k =kh ""5 =

.10FI OQ~12 0010:5 00\83 00377 00798 GIAOI 04446 1126 2~ Ilit, lir

72 " 001233 md I ,1../ I022186 rrld It

-0 IOI'JI66

I'" / I -0.6 iii iii I i I 1-1

-3.2 -2.B -24 -2.0 -16 -1.2 -08 -0,4 0.0 0·1 O,B

Role-Convolved Time Funclion

60

:154

C:l: 4,B,

E 42<1

~ 36

"6 30

~Jl 2,4

IB

1.2

"

o 105 ."'"'"

"o 120

"

o 135 J"

o 150 I I

'"'"'"

o 045 i'~0030J~

0015 1 ~,,~Tr!'!" II I i III'iiilll'l'lTCi I

0,000 Iii I i I I i I I00 0.4 08 1.2 1.6 2.0 2.4 2,B 32 3.b

Time, hr

Figure 9

Example 2: Computed DoNnhoIe FloNrates

"U

~:-: 0090U

:;; 0075

VJ<{(J (J 060a

~

234,00

o

0- LL:;;(JIcJ W1-0

217,50·IBOO,OO

0- .­(Jill(f1~

ooo

l"m.~ ",,,, ..,,.=,,,,,,--~(~_m ~~,,,_.

'"~

J 150.00 I eJ f r iii I I i I ~000 0.15 0,30 0.45 0.60 0,75 0,90 105 120 135 150 1.65

Time, hr

Figure 11

Example 3: Post Perforating PreSSlJ'e and TemperatlJ'e Data

seE 21657

~--=D-er~iv-at~rv-~e-­Curve

Type Curve[I[I

[I

[I

[I Impul5e" Data[I

D

kh .. 117 rrd-fts= -1.4P" = 4747 psia

100

10~

De~aTime, hr

Figure 12

MWPT Analysis Plot

kh = 114 rrd·ftI!l. s=3:::I P" = 4613 p5iaeeJ~ 10 1

:::I

'"~a.

il~-iij 10 0

~Q

-

aa

o PreSlSure Dataa Derivatrv-e Data

101

102

DimensionleSlS TimEl, TO/CD

Figure 13

Conventional Buildup Analysis Plot

265