Chan's Diagnostics

zSPE 30775

Soolstyof PstroisufnEfminaer8

Water Control Diagnostic PlotsK.S. Chan,* SchlumbergerDowelllSPE Member

Copyright 1995, Socii of Petrvhum Engirmem, Inc.

lWs paper was pmpamd for presentation at the SPE Annual Technical Confwence & ExhiMiin hold in Dallas, U.S.A., 22-25 Cktober, IW5

nisplpfwaswbctedfmpm8wMkm by m SPE Program Committee following rwkw d infcfnutiin wntahed in an abstract subrrhted by the luthor(s). Contents of the paper,= PMWIM ~ ~ ~ ~ by ~ ~ d p~fdeum EIWIWWS and ma subjad to correction by the author(s). The material, as Pmaented does not necesaarity refbdw ~ ~~s- ~ p~r*um EW~*r*, ~ dfii of ~m. Papom PM8.nted at SPE rrmoth@ are subiad to Publicatii review by Edtorid Comrnttaea of theS0ektYdPdMbumEnOin9m. pwbsiOn to capy is m@tided ban -act d not mom than 3fM ~. Illualrdii m8y not be copid, Tfm abdmd should contain conspicuousacknowlodgrrrent of wham and by whom the paper is Pma@ntod. Write Librarrnn, SPE, P, 0, Box SSSSSS, Riirdwn, TX 7S0SS-SS3S, U.S.A., fax 01.214-952-9435.

ABSTRACTA new technique to determine excessive water and gasproductionmechanisms as seen in petroleum productionwells has been developed and verified.

Based on systematic numerical simulation studies onreservoirwater coning and channeling, it was discoveredthat log-log plots of WOR (Water/Oil Ratio) vs time orGOR (Gas/Oil Ratio) vs time show differentcharacteristictrends for different mechanisms. The timederivatives of WOR and GOR were found to be capableof differentiatingwhether the well is experiencing waterand gas coning, high-permeability layer breakthrough ornear wellbore channeling.

This technique was applied on wells in several fields inTexas, Caiifomia, the Guif Coast arid Aiaska. PM usingthe actual production history data determined theproduction problem mechanisms. Together with welltests and logs, the technique was used to select welltreatment candidates and to optimize treatments toenhance the returnof investment.

References and illustrationsat end of paper.

INTRODUCTIONOver the last 30 years, technical efforts for water controlwere mainly on the development and implementation ofgels to create flow barriers for suppressing waterproduction. Various types of gels were tiippk% h.-----different types of formations and to solve different typesof problems.2 Quite often, excessive water productionmechanisms were not clearly understood or confirmed.Althoughmany successful treatments were reported, theoverall treatment success ratio remains low.3

Through these field trials, the art of treatment jobexecution was progressivelyimproved. Good practices inthe processof candidate selection,job design, gel mixingand pumpingand job qualitycontrolwere recognizedandadapted. More effective tools and placement techniques.-. -- - -- ..---1 Tb.- -1-..:.- 6.- #L.94:m-Awe.an+ k,nae -4Wertf -A5u U3W. I IIw Uuixlc Lu UUllllu UIIIVIUIIL Lypwc3 WIexcessive water productionproblemsbegan to surface.

In general, there were three basic classificationsof theproblems. Water coning, multilayerchanneling and nearwellbore problems are most noticeable among others.Field experience showed successful job design wouldnot be the same for different mechanisms. However,tFlere e~e no mfftiiwe rn=~~~~~ ~~ Aicn=m !h~~~Wllwsm. ..s-... . .differences. In reality, the problem could be ve~complex, and usually is the combination of several

755

2 WATER CONTROL DIAGNOSTIC PLOTS SPE 30775

mechanisms taking place over a period of time andcompoundingone with the other.

This paper presents a methodology which can be usedto quickfy diagnose and evaluate the mechanisms. Itmainly uses plots generated from available productionhistory data. The set of plots include (1) produtiionhistory for the entire period or waterflood period forwater, oil and gas, (2) WOR and its derivatives, (3)~l,ifiu!a%?eOi!prod~ced Orreco~e~~~ffjjinnm ad IA) nil,. ,, , -, , ,-, -..and gas rate declines. These plots provide a compositepicture of the past and current productionbehaviors andthe remaining production potential of the well. Themethodology can become an effective tool for theselection of water control treatment candidates toenhance treatment success.

CONVENTIONAL PLOTSConventionally,water cut vs time linear plots were usedto show the progress and severityof the excessive waterproductionproblems.4The correlationbetween water cutor fractional water flow and average resewoir watersaturationfor two-phase flow is well known.sHowever, itis not practical since saturation distributionsthroughoutthe reservoir are changing with time. Averaging fluidsaturationfrom material balance does not shed any lighton fluid flow behaviors in heterogeneous formations.Although these plots can also show a drastic change inthe water cut indicative of the sudden failure of wellcompletion or rapid breakthrough of a high waterconductivitychannel, the information provided by water-cut plots is limited. Regardless of multilayer channelingor coning, the shapes of the water-cut plots are vwysimilar.

Linear or semilog WOR ~~ots have been used toevaluate recovety efficiency. A special plot (known asX-plot) that uses a correlationof a modified fraction flowfunction with the recovery efficiency has also beenshown to be capable of representing normal waterfloodvolumetric sweep efficiency.egThese plots muld beuseful to evaluate production efficiency, but they do notreveal any detail on reservoirflow behaviors.

For multilayerflow, the WOR had been expressed as theratio between the sum of the product of the permeabilityand the height of the water-out layers and that of theremaining oil production layer.5 Again, this overallestimation approach in evaluating excessive waterproductionbehavior does not shed any clue on the timingof the layer breakthrough and the relationship betweenthe rate of change of the WOR with the excessive waterproductionmechanism.

DIAGNOSTIC PLOTSA set of diagnostic plots have been generated byconducting a series of systematic water-controlnumerical simulation studies using a black oil simulator.This threedimensional, three-phase simulator is capableof modeling the performance of reservoir flow underdifferent drive mechanisms and waterflood schemes.Log-log plots of the WOR (rather than water cut) vs timewere found to be more effective in identifying thep,~ducti~n ?rends and pmb!ern mechanisms, !t wasdiscovered that derivatives of the WOR vs time can beused for dtierentiating whether the excessive waterproduction problem as seen in a well is due to waterconingor multilayerchanneling.

Figure 1 shows a clear distinction between a waterinning and a multilayer channeling development usingthe same set of PVT and saturation function data,permeability and porosity distribution, and having thesame initialCondtiions.The only difference in the modelsetup is the flow geometry. For coning, a water/oilcontact (WOC) was defined and a bottomwater influxwas simulatedby constant pressurewater injectionat theedge and only into the bottomwater layer. The top 20%of the oil zone was perforated. For channeling, thebottomwater layer was eliminated. The water injectionwas modeled with constant pressure water injection intoall layersat the edge. All layers were perforated.

By inspectingFig. 1, three periods of WOR developmentcan be discerned. Duringthe earfy time period, the WORcurves remain flat showing expected initial production.The value of the initialWOR depends on the initialwatersaturationand its distributionamong all layers as well asthe relativepermeabilityfunctions.The time length of thisperiod depends on the waterdrive mechanism and itsending is marked by the departure of the WOR from aconstantvalue.

For coning, the departure time is often shorl dependingon various parameters but predominantlyon the distancebetween the WOC and the bottom of the nearestperforation intewal, vertical-to-horizontal penneabiliiratio, bottomwater infiux rate, production pressure------drawdown or rate, and relative permeabilii functions.Physically, the water coning departure time is the timewhen the bottomwatercone has approached the bottomof the perforationintewal.

For channeling, again the depatture time depends onvarious factors but mainly on the well spacing, injectionrate at the injectors, producer drawdown pressure orrate, initiil water saturation and distribution amongIayem, and relative permeabilityfunctions. Physically,thedeparture time of the WOR curve for channelingcorresponds to the water breakthrough at a layer in a

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.SPE 30775 K.S. CHAN 3

multilayer formation. This layer may not necessarily bethe layer having the largest permeability.The initialwatersaturationand its distributionin the layers may become avery dominant factor, if the permeability contrast amongthe layers is not large.

The second time period shows the WOR increasingwithtime. The rate of increase differs for a different problemmechanism, Figure 1 shows a striking differencebetween coning and channeling. For coning, the rate ofthe WOR increase is relatively slow and graduallyapproaches a constant value at the end of this period.During this period, the bottomwater mne not only growsverticallyupward to cover most of the perforationintervalbut also expands radially. The oil saturation within themne is gradually decreased to the residual oil saturationlevel.

For channeling, the water production from thebreakthrough layer increases very quickly. Acccmlngiy,the WOR increases relativelyfast. The slope of the waterchanneling WOR depends on the relative permeabifiifunctions and initial saturation conditions. At the end ofthis second penod, the WOR increase could actuallyslow down entering a transitionperiod. This correspondsto the productiondepletion of the first breakthroughlayer.The end of this transition period shows the WORincrease resumes at about the same rate. Thiscorresponds to the water breakthrough at the nexthighestwater conductivitylayer.

The transition period could be very shotl depending onthe layer permeability contrast. Typicallyj the transitionperiod could become insignificant when the layerpermeability contrast is less than 4. The change of theWOR in the transition period was found to be alsoaffected by the layer crossflow and capillary pressurefunction.

In the third period and for coning, a pseudosteady-statecone has been developed. The well mainly producesbottomwater. The water cone becomes a high waterconductivitychannel. The WOR increase becomes veryfast resembling that of a channeling case. This seconddeparture point can be regarded as the beginning of thethird period. For channeling, the WOR increase resumesthe same rate after going through the transition period.The second highest water conductivity layer is beingdepleted. All channeling WOR slopes, includingthe onein the coning situation,would be very close because theyare mainlycontrolledby relative permeabilityfunctions.

Further extensive studies repeatedly confirmed that thetime derivatives of the WOR can be used to dtierentiateconing from channeling. Figures 2 and 3 show the WORand WOR derivatives for channeling and coning,

respectively. The WOR (simple time derivative of theWOR) shows nearly a constant positive slope forchanneling and a changing negative slope for coning.The WOR trend for channeling behavior in the third

.,_+_. n ~;mfi&+i~Amm;= chri~n in F!ga 4.P&i3d d = %vawi VOI m IS SILUS.CW, .- -,.- . . . .. .Again, the WOR vs time plot shows a positiveslope.

The WOR derivative plot becomes very helpful todetermine the excessive water production mechanismwhen limited production data are available. Figure 5illustratesthis advantage. The limiteddata were obtainedfrom the results of the Second SPE ComparativeSolution Project tilch involved a case study forbottomwater coning.10The apparently increasing WORtrend shown in Fig. 5 could be easily taken as layerchanneling. However, the WOR shows a negative slope,characteristicof a coning case.

For gas coning in an oil well, water coning or channelingin a gas well, or gas and water coning in an oil well, theGOR (Gas/Oil Ratio) or WGR (Water/Gas Ratio) andtheir derivativescan be used. Again, slopes of the GORand WGR vs time curves indicate different mechanisms:positive slope for channeling and negative slope forinning. An example of the GOR and GOR plot is shownin Fig. 6.

For a strong bottomwater drive, the well spacingbecomes a key factor for the occurrence of the seconddeparture point from coning to bottomwater channeling.Figure 7 shows a series of simulationplots as a functionof weii spacing (f 0- to 150-acres) and at a vertica!=tc=horizontal permeability ratio of 0.1. For 10- to 20-acresspacing, the second departure point becomesindiscernible. Bottomwater appeared to be justchanneling up vertically to the perforations whii arelocated at the top of the productionformation. The largerthe well spacing, the further the delay of this departuretime. This phenomenon would also depend on several

-- A- ..A-. -other factors, siuchus UIUhJLAI I rate G: pressure, wa!erinfluxrate, and again the relative permeabilityfunctions.

Immediately after the beginning of the waterflood,injectionwater could very rapidlybreak through very highconductivii channels or (thief) layers. For instance, a 3-ftlayer having a lo-darcy penneabifity among the 100-mdadjacent layers could become a water recyclingconduit.Figure 8 shows such a situation in the WOR change.The WOR rapidly increases after the injection waterbreakthroughat the productionwell. Wfih a high vertical-to-horizontalpermeaMii ratio, the water could cone upat the wellbore and the water cone could rapidly expandto cover the entire zone. At this time, the waterproductionrate starts to approach the total injection rate.The WOR curve in Fig. 8 showssteep positiie slope within a ve~

this evolutkm: a veryshort time after water

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breakthrough, followed by a period of a negative slopeindicative of cone buildup and a late period of gradualpositive slope corresponding to the completion of thewater-recyclingconductivevettical channel construction.

VERIFICATIONSupport from the operating companies wasoverwhelming during the long process of the diagnosticplot verifications.The monthly average production ratesand, in a few cases, the daily rates were providedtogether with the well workover history, logs and recent.-.-it ._-* ..1.- Al.._- J--lwt311IwSl ruSuus. mUIIIeIIUUI SIII Iulauul I= WI aI I II IUIVIUkI:-, .l**:An- f-. am kAi.,iA mlwell or for a group of wells involved in a displacementpattern were also conducted for further confirmation ofcomplex problem mechanisms, which usually entailed aA:u ---- -umereru piobkm mechanism fOi Zi different :ime periodand a superpositionof these problems.

Figure 9 shows an excellent example of a good andnormal production process in a linedrive waterflooddisplacement process in a muitilayer sandstoneformationin California. Note that the firstWOR departurepoint and the slope are clearly defined. In this second-a -~ lk- I /no* d + -h-..,e m Aaarli, Iimaar aFUI nne~tm~nw, c1l= Avm ~IoLalIvwa = WIQ=I,Y,11,==1=,,= ~e,.t.=slope, characteristics of a water channeling case. Theduration of this period was about 4000 productiondaysor 11 years. This reflects consequential waterbreakthrough at several layers or intewals which have asmall permeability contrast (< 4). There occurred two tothree times, near wellbore in&ients in the late timeperiod, as shown by the spiking of the WOR andparticularlyWOR in the plots. At these points, the WORvalues exceeded well beyond 1.

Production changes could affect the appearance of thediagnostic plots. These changes could be the change indrawdown pressure at the productionwell, and changesin the injection rate and layer injection distributionat theassociated injection wells. Figure 10 is a good exampleshowing the WOR and WOR deviations from the linearslope in the second period. This well and the well shownin Fig. 9 are adjacent wells in a linedrivepattern. A nine-well linedrive model was progressively built to simulatethe continuous changes in the producers and theinjectors. The histoty match results confirmed that thecauses of the deviation were the pressure distributionchanges and the disproportional overall water and oilproduction corresponding to the changes in thedrawdown pressure in each layer. Note that the WORregains the original slope after achieving a pseudostablepressurecondition.

For some reservoirs,the initialWOR could be very high.A good example is shown in Fig. 11. It is for a typicalwellproducing from a limestone/dolomite formation in west

Texas. The initial WOR was about 4 (80Y0 water cut).The reason muld be a high initial water saturation.Waterflood started in this field at about 2000 days. Theoverall WOR trend shows a linear slope indicative of anormal displacement behavior. For this well, the WORslope is about 0.5.

In cettain parts of the formation, there could be high-permealilii streaks or fissured layers associated withthe wells in a waterflood displacement pattern. Rapidwater breakthroughcan be seen at the producers. Figure12 shows this drastic WOR increase from a wellmn+tminfi frnm a dnlnmite fnrma~~~n in fl~fihe~stern NQWpmuuuwm..~ . . . . . . w WW.v. . ...= . . . . . .Mexico. Note that the initialWOR was less than 0.1. TheWOR slope was about 4 and recently shifted vety fast tolarger than 10. The WOR drasticallychanged as well, aSymp?Orn c?rapidwater breakthrough.

For water coning, a good sandstone example from theGuif Coasi area is siiown kI F@. i 3. At zwoiurld1000days, water coning began and the WOR derivativestatted to decline and show a changing negative slope.Construction of a pseudosteady-state cone wascompleted at about 2000 days (3 years later). Since thenthe cone be~cxunea water charme! for producingbottomwater, and the WOR showed a linear positiveslope.

Quite often, a near wellbore problem could suddenlyoccur during a normal displacement and production.Figure 14 shows such a dramatic event taking placerecently in a sandstone Alaskan well. The initial WORwas constant but above 1. The WOR rapidly increasedand followed a linear slope (about 3) after theimplementation of a waterflood. Recently, the WORincrease accelerated and the slope turned almost toinfinity.The WOR trend and evolution substantiatedthisanalysis. The peak WOR was a very high value of 10.The well was then treated with a small volume of polymergel. Posttreatment results showed the water rate wasreducedby 500A.

RECOMMENDED PRACTICESThe available productionhistorydata base could be verylarge. There could be a different production mechanismfor a different period of time. The followingis a partial listof possible productionchanges and workover operationsthat couldtriggera change in the produdion history:

l reservoirpressuredeclinel productiondecline due to skin damagel imnltwnenta!icmof waterfloodor gas displacement....r._.... . ..l additionor aiterationof perforationsl choke size adjustment. gas liftvs flowing

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.SPE 30775 K.S. CHAN 5

l reservoirand well stimulationl cement squeeze.

A good practice is to plot (log-log) the entire productionki-+am~+mmnta hi- r++ Ira =nA thnn Abeam tha narinrleI 11-LUI y LU ywL u uqj pwtu,w, u, w u I-I I us-u-t I B u mu put IWUWin which the production mechanism changes. Select anyperiod of interest and plot the WOR or other variations(such as GOR and WGR) with their time derivatives toidentify the excessive water production mechanism inthat period. This should be done not only for the wellswith known water productionproblems, but also for goodwells in the same area producing from the sameformation. Some suggested procedures include thefollowing:

. lookfor the normal productionbehaviorl determine the normal WOR or GOR or WGR slopesl check the trend of their derivativesl use expanded plotsfor the period of interest.

A good example is a well in the Midland area. The entireproduction history is shown in Fig. 15.1, and itsassociated diagnostic plots are in Fig. 15.2. It shows fourdistinctiveperiods of productions.

The first period was from well production start-up toabout 1200 days (May 1961 to July 1964). In this period,the oil rate was progressively increased in three stagesby altering either one or several of the above-mentionedproduction change implementations (adding newperforations, increasing choke size, changing into biggerpump, etc.). The WOR values in the period remained flatand constant at or about 0.4, 0.2 and 0.3, respectively.

The second period was from about 1200 days to 3100days (July 1964 to October 1969). The oil rate statted todecline and the water rate started to increase. The WORplots showed an initial normal depletion followed by anaccelerated WOR change which could be induced by arapid layer depletion as hinted by the peak value of theWOR.

The third period was from 3100 days to about 7000 days(October 1969 to August 1980), which showed a veryunique condition in which all phases (oil, water and gas)of the productionrates decline simultaneously.This wasdue to gradual reservoir pressure depletion. In othercases, it could be due to the development of a skindamage but normallywithin a much shorter time period.A pressure testing could be used to discern thedifference if needed. A waterflood program wasimplementedat the end of this period.

The expanded plots for this waterflood period are shownin Figs. 15.3 and 15.4. For the first two years, the waterdisplacement process appeared to be quite normal,

although there was no oil rate response until April 1982.A bigger pump was used in July 1982. The oil rategradually increased to about 50 BOPD in December1985. The water rate increased accordingly. The WORnints in Fin. 1S84shQwed a constant value for this neriod.~---- ... . .=. _< _. .-. _ ... ---- .- . ....- ~------

A submersible pump was installed in early 1986. The oilrate began to rapidly decrease and the water rateaccelerated. The WOR plots showed a drastic change inslope when the WOR reached a vety high value of 100.The water rate was 3000 BOPD with a WOR of 3000.This is a very clear case of rapid layer breakthroughandwater recycling.

The well received a gel treatment in 1993. Since then,the well has been producing about 600 BWPD and 15BOPD with a normal decline behavior. Recently, theWOR has been around 45 (97.8Y0water cut).

CONCLUSIONSItcan be concluded that the log-log plot of productiondata and the WOR provide more insight and informationfor well performance evaluation. It can be applied eitherfor the entire well life or any chosen period, such as thewaterflood period. With a detailed workover history, theresults of the analysis improve the understanding ofresewoir flow behavior and determine the predominantmechanismsof excessive water production.

Using the WOR (time derivative of WOR), coning andchanneling can be discerned. Furthermore, the changein slope of the WOR and WOR and the value of theWOR become good indicators to differentiate normaldisplacement and production behavior, multilayer waterbreakthrough behavior, rapid layer depletion and waterrecyclingbehavior.

This technique has several advantages:

1.2.

3.

4.

5.

759

It mainlyuses available productionhistorydata.It can be used to rapidly screen a great number ofwells.It entails the best reservoir engineering principlesand practices.It could yiekf resultsto form the basis for conductinga production mechanism sutvey, comparemechanisms between adjacent wells, goodproduction wells vs problematic production wells,and by area or by well pattern.. . .... .. . ----

wnn me wu~ vs cumulative oii productionpiot and. ..the oil rate decline cutves, it would become aneffective methodology to select candidate wells forwater controltreatments.


There should be more production and reservoirengineering opportunities and benefds by using thisdiagnostic technique as one further progresses alongthis approach.

ACKNOWLEDGMENTSThe author wishes to thank ARCO Long Beachfi-----..b-~ m_JI mm Pk. A I -- n--h n=ma+m~dIlluulpululuu, I I-IUIVIQ,Ully UI hul IS Wald 1 Uupal UIml ILof Oil Properties, and ARCO Alaska for their strongsupport during the early part of this techniquedevelopment Chevron engineers in Midland, NewOrleans, Lafayette, LaHabra and Houston for their beliefand appreciation in this concept and approach, andtechnical support in this project;and Amoco engineers inHouston, Midland and Calgary for data support anduntiring technical discussions. Special thanks areextended to the management and engineers ofSchlumbergerDowell for their persistentencouragement,particularlyJoe Mach for his unswerving support duringthe development of this technique, and Sharon Jurek forher help in the preparation of this manuscflpt.

1.

2.

3.

4.

5.

R.

Sydansk, R.D. and Moore, P.E.: ProductionResponses in Wyomings Big Horn BasinResulting From Application of Acryfamide-Polymer/Cr(lll)-Catioxylate Gels, paper SPE21894,1990.

Morgan, J.C. and Stevens, D.G.: Water Shut OffWith Chemicals: Targets, Systems and FieldResults,paper presented at the 1995 InternationalSymposium on oilfield Chemicals, Geilo, Notway,March 19-22.

Seright, R.S. and Liang, J.: A Suwey of FieldApplicationsof Gel Treatments for Water Shutoff,paper SPE 26991 presented at the 1994 PermianBasin 011and Gas Recovety Conference, Midland,TX, March 16-18.

Hwan, R-N. R.: Numerical Simulation Study ofWater Shutoff Treatment Using Polyrnm, paperSPE 25854 presented at the 1993 SPE RockyMountain Regional/Low-Permeability ReservoimSymposium, Denver, CO, April 12-14.

Wilhite, G.P.: Watetfboding, Text Book Series,SPE., Richardson,TX(1986) 3, Chapter 5.u~gfg~~~,Q V ~~~ ~~@h@n, Rov.: Mdchinn. .. . . ...-.-. ... .-Calculated With Actual Waterflood PerformanceWtih Estimation of Some Reservoir Properties,paper SPE 4412 presented at the 1973 SPE

7.

8.

9.

10,

Rocky Mountain Regional Meeting, Casper, WY,May 15-16.

Mungan, N.: A Theoretical and ExperimentalConing Study,SPEJ (June 1975) 247-254.

Ershaghi, 1. and Abdassah, D.: A PredidonTechnique for Immiscible Process Using FieldD.dnmanna n=t~ ~I,DT (A+l I W] MA7nmw,,, ,,,-s,- -.-, ~ ~-r,l. . -a, v- , .

Ershaghi, 1, Handy, L.L., and Hamdi, M.:Applicationof the X-Plot Technique to the Studyof Water Influx in the Sldi E1-ltayem Resenfoir,Tunisia, JPT(1987) 1127-1136.

Nolen. J.S. and Charwelear, J.E.: SecondComparative Solution P~ject: A Three-PhaseConing Study,paper SPE 10469 presented at the1982 SPE Symposium on Resewoir Wlmulation,New Orleans, LA, Jan. 31- Feb. 3.

11 ...

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Figure 3-Bottomwater coning wOii and WOiTderivatives.

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Figure 4-Bottomwater coning with late time channelingbs-havior.

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Figure 5-WOR and WOR derivatives from the coningcase historyof the second SPE comparativesolution

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Figure &WOR and WOR derivatives for thief layerwater recycling.

project.

761

WATER CONTROL DIAGNOSTIC PLOTS.-

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Figure 9-Field Example 1: MultilayerChanneling.

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Figure 12-Field Example 4: Rapid Channeling.

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Figure l~leld Example 6 Near Wellbore WaterChanneling.

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Figure 15.1-17eld Example 7: Complete ProductionHistory.

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Figure 15.2-Field Example 7: DiagnosticPlotsforEntire Period.

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Figure 15.4-Field Example 7: Waterflood ExpendedDiagnosticPlots.

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Chan's Diagnostics