102316Well Test DesignIntroductionBackground to test designAnytreatmentofthesubjectoftransientpressureanalysiswillgenerallyconcentrateon the topic of well test interpretation. However, the proper design of well tests is crucial to the achievement of the objectives and this issue will be considered here. Paradoxically, a good design willdependonareasonableestimateofthepermeabilityoftheformationtobetested,the determination of which is the main objective of a test. In this treatment, attention will be focused on the design of exploration appraisal well tests (loosely referred to as DSTs) or the frst test on a new development well (IDT). A classifcation of well tests is shown in fgures 161 and 162, where well and fuid type categories are used to defne the nature of the system. In the case of appraisal wells, which are usually near-vertical, the main elements of the classifcation are simply the fuid type specifed as one of the following options:Black oilDry gasCondensate or volatile oiland the well attributes according to the list:Surface (wellhead) or downhole shutinMemory gauge or surface readoutRepresentative or arbitrary completion1024Well Test Design and Analysis Chapter 16 Well Test DesignFig. 161. Classifcation of appraisal well test categoriesFig. 162. Classifcation of development well test categoriesThefluidtypeshouldbeknownfromtheopen-holelogginginformationincluding pressure gradient observations from wireline formation testers (WFTs) and sampling with the new-generationWFTs(NGWFTs).Tekeypressure-volume-temperature(PVT)properties required for well test design are:Saturation pressurebubble point (oil) or dew point (gas)Gas oil ratio (GOR, oil) or condensate gas ratio (CGR, gas)Fluid viscosity at reservoir pressure and temperatureInthelatestversionsofthesetools,e.g.,WeatherfordRES,thePVTpropertiesareactually measureddownholeanditmustbesaidthatNGWFTtoolshavefacilitatedmuchbetter knowledge of PVT properties needed for well test design.Well Test Design and Analysis1025Chapter 16 Well Test DesignNearly all modern DSTs will be carried out with downhole shutin, although Unocal in the Gulf of Tailand have found it economical to dispense with this technology and use simple surface shutins to reduce cost. Tis type of testing is referred to by Unocal as TST and is also being carried out in Vietnam. Te gas reservoirs in the Gulf of Tailand are highly compartmentalized and many wells are required to maintain feld production profles. Te penalty of surface shutin is increased duration of the wellbore storage efect.ThedesignofIDTsisverysimilartothatofDSTswithsimilarobjectivesbutwithtwo main diferences. Firstly, the skin factor and the testing of the completion is always important inadevelopmentwell.NotethatdeterminingtheskinfactorSfromabuildupisrelatively straightforward; the physical implication of the origin of the efect is much more difcult to assess. Secondly, the testing valve in an IDT is usually at the wellhead and the issue of wellbore storage is more serious. Tus the additional design decision whether, or not, to run a wireline shut-in tool (SIT) has to be addressed. Te utilization of permanent downhole gauges (PDGS) in development wells will not be addressed here since this merits separate treatment and is pertinent to the topic of reservoir monitoring.Attheoutset,itmustbestressedthatawelltestdesignisaneconomicexerciseanda compromise must be reached such that the cost of the test is compatible with the value of the information obtained. Particularly in the ofshore situation, the expense associated with rig time is very high and in well testing the adage is time is money. From a purely engineering point of view, there is no doubt that long fow periods and buildups are advisable; this is driven by the nature of the semilog plot where an extra half log cycle of data can imply quite an inordinate increase in the total time of testing.Te design of a well test must, of course, pay special attention to safety requirements and this should always be an overriding consideration. In the case of high-temperature, high-pressure gas condensate reservoirs, for example, the DST testing system is kept as simple as possible to minimize the risk of equipment failure.Permeability estimateIt is certainly the case that well test design is much more difcult than test interpretation andthemostfrequentcriticismofpressuretransientanalysiscoursesisthatnotenough attention is given to test design. One of the difculties associated with the design process is the requirement for a permeability estimate. If the permeability could be estimated with some degree of confdence, one of the main reasons for carrying out a well test would have disappeared. Hence it is important to undertake sensitivity studies using software packages like Pansystem and Wellfo to simulate tests at permeability levels spanning the uncertainty range. Te main sources of information regarding permeability are:Ofset appraisal wells in the same formationPermeability transform based on log dataWireline formation tester dataIn the modern environment, it is unlikely that an appraisal well will not have extensive data from a new-generation formation tester in addition to the conventional logs. Especially in the ofshore situation, well test equipment has to be ordered and brought to location before wireline 1026Well Test Design and Analysis Chapter 16 Well Test Designinformation from the candidate well is available. Hence equipment selectionwhich will require anestimateofwelldeliverabilityandfuidtypehastobebasedondatafromneighboring wells. However, one of the main considerations in a design is the duration of the fowing and shut-in periods; these decisions can be adjusted in the light of permeability data gained in the logging program.Review of seismic dataIn the case of moderate or high permeability reservoirs, one of the main objectives for pressure transient testing is the location of boundaries using data from the late time region (LTR). It is particularly important when designing a test to have an indication whether channel reservoir efects will be present in the data. Figure 163 shows terrace faulting, where it is evident that approximately parallel boundaries will manifest themselves and test design should recognize this situation. Channel behavior also occurs in fuvial systems and therefore knowledge of the depositionalenvironmentwillalsobeafactorinthedesignprocess.Inconjunctionwitha permeability estimate, a test is designed such that the propagating pressure disturbance will be infuenced by boundaries whose distance from the well is given by the seismic map.Decision to Test or NotTe main reason for drilling appraisal wells is to delineate the extent of the reservoir and obtain an estimate of oil or gas in place from volumetric studies based on logs and seismic. A transient well test is not part of this exercise. In the modern environment, all appraisal wells will have a WFT survey which, in addition to identifying fuid contacts (part of the volumetric study)andfluidtype,willalsogiveimportantinformationwithregardtopermeability particularly the so-called mini-DST. Provided the thickness of the zones tested in this way can be identifed, often image logs are used, then the total kh of the reservoir section can be obtained by summation. Tus the new-generation WFT survey is, in fact, a layered reservoir assessment tool.Te decision then has to be made as to whether or not a pressure transient test is required. TelimitationoftheWFTsurveyisthatmini-DSTsdrivenbypumpoutwillnotbeableto detect reservoir boundaries such as sealing faults. A conventional DST will cause a much larger disturbance in terms of volume of oil or gas produced, and accordingly the depth of investigation will be much greater. Traditionally, pressure transient testing has focused on the determination of average permeability, k, and skin factor S; however, in the modern environment, the location ofboundariesandthedetectionofcompartmentalizationareimportantissues.Bookingof reserves with the U.S. Securities and Exchange Commission (SEC) has always been a key issue for operating companies.Well Test Design and Analysis1027Chapter 16 Well Test DesignFig. 163. Parallel faulting in the Heidrun feldTe decision whether or not to test can be infuenced by a value of information (VOI) study which will consider the risk to the project in terms of net present value (NPV) by not testing the well. If the cost of the test is greater than the potential downside, then a recommendation not to test will be made. It is extremely difcult to get meaningful estimates of these risks to project value, and it is not the role of a service company to carry out such studies; it is defnitely theoperatorwhoshouldundertakethetask.Tedeterminationofaveragepermeabilityis essentially concerned with prediction of the deliverability of eventual development wells and aVOIstudymayinvestigatetheefectofnothavingenoughwellslotsonaplatforminthe case where individual well deliverability is underestimated. Te issue of the degree of reservoir compartmentalization is another key factor, especially in the fuvial depositional environment, anditisonlywelltesting,perhapsinconjunctionwithseismic,whichcangiverealistic information on this topic.1028Well Test Design and Analysis Chapter 16 Well Test DesignObjectives of the TestGeneral objectivesTe general objectives of an exploration appraisal well test can be summarized as follows:Determination of the initial reservoir pressure piDetermination of the formation average permeability kMeasurement of the reservoir temperature TDetermination of the fnal reservoir pressure pfGathering of representative fuid samples for PVT analysisTe determination of the initial reservoir pressure requires an initial short fow period and an initial buildup as illustrated in fgure 164, which depicts the standard dual fow and shut-in DST. In this design, it is customary to make the fnal buildup 12 times the duration of the major draw-down period. Tis rule of thumb for DST design is long established and usually works well in practice. However, there are cases where it is desirable to have longer buildups relative to the length of the fow period. For example, in the case of the channel reservoirs, arising in fuvial depositional environments or terrace faulting, it is preferable to have longer buildups particularly if an objective of the test is to determine depletion; this aspect has been discussed at length in chapter 6, where fgure 660 was used to illustrate the problem of determining the fnal reservoir pressure pf. Te term fnal reservoir pressure pf has been used to indicate some form of extrapolation to infnite shut-in time on a semilog or tandem square root plot; the exact meaning of pf in terms of average or boundary pressure has been discussed throughout this text, especially in chapter 4. Figure 165 presents an interesting review of the reasons for well testing spread over a large number of appraisal wells in the Gulf of Mexico.Fig. 164. Standard dual-fow and shut-in DSTWell Test Design and Analysis1029Chapter 16 Well Test DesignFig. 165. Reasons for well testingTe determination of the skin factor S has deliberately been omitted from the above list of general objectives taking the view that, usually, the completion of an appraisal well will not be optimized with respect to formation damage. Te main point of carrying out a pressure transient test is that the permeabilitythickness product kh can be estimated independently of the skin. However, a high skin in an appraisal well with water-based mud indicates that a water-sensitive formation is present and that development wells will have to be drilled with oil-based mud. In this respect, the skin factor from an appraisal well test is useful. However, it must not be used to predict the deliverability of eventual producers. Te design of the frst test on a new development well (IDT) will be very similar to the design of an appraisal well test (DST) except that the determination of the skin factor will now be an important objective.Te initial fow period of a DST was sometimes referred to as the fve-minute fow period indicating that a duration of 5 min was the design rule. In practice, the initial fow period should belongenoughtodisplacethecushion,illustratedinfgure166,outofthewellboreand establish a hydrocarbon column of known pressure gradient. In one major oil company (BP), it is recommended that the initial fow period be long enough to produce a volume of oil equivalent to four times the tubing volume to the wellhead. Te original specifcation of the frst buildup was a shut-in time long enough to essentially achieve stabilization of the pressure at pi. However, modern practice will allow some degree of extrapolation to reservoir pressure on a Horner plot but it is still desirable to make the duration of the frst buildup four or fve times the duration of the initial fow period.Te major source of error in the initial pressure pi is the hydrostatic correction, illustrated in fgure 167, given by p = p = p + Di DATUM wsexGAUGEDEPTH~GDrD (161)where~ = fuid static gradient corresponding to its in situ density ,DGD = diference in true vertical depth between datum and gauge location, andpwsexGAUGEDEPTH = frst buildup extrapolated pressure on a Horner plot.1030Well Test Design and Analysis Chapter 16 Well Test Design Fig. 166. Displacement of cushion to reservoir fuid columnFig. 167. Conventional hydrostatic correctionIn an exploration appraisal well, it will usually be the case that a WFT survey has been run prior to the well test. In principle, the initial pressure, at the specifed datum level, from the WFT survey should agree exactly with the pi from the well test. Certainly, the two values should be compared and, if they are identical, the initial pressure is fxed. However, in moderate and high permeability reservoirs, where supercharging of the WFT data is negligible, most practitioners wouldrecommendtheWFTinitialpressureasbeingthemorereliable.Tisisbecauseof uncertainty in the applicable fuid gradient ~. Conversely, in tight reservoirs, with all WFT points supercharged, the well test pressure is more reliable. It is interesting to observe that the origin of the fve-minute fow period in drill stem testing (DST) was to relieve supercharging in the near-wellbore region caused by mud fltrate invasion.In tight formations, where excessive supercharging renders the usual WFT pretest data invalid, the advent of the NGWFT devices with the dual packer option and more recently the cased hole versions means that the reservoir initial pressure at datum pi will be available from formation tester information in all circumstances. Tis raises the possibility of changing the standard test design by omitting the frst buildup to obtain initial reservoir pressure. Most well test designs, however, will still include the frst buildup, and with high-quality quartz transducers employed both in the wireline tester and the well test, the two estimates of pi should agree to within a 1 psi discrepancy.If the WFT survey has allowed a fuid gradient to be determined, then a correlation of the type described by Montel (chapter 12 of Wireline Formation Testing and Well Deliverability, fg. 1235) will allow the producing gas-oil ratio (GOR) to be estimated and the proper type of separator chosen. It is emphasized here that the main problem in designing a well test is obtaining a permeability estimate. Obviously, any information on permeability from the WFT survey will always be useful in the test design process. Te estimation of permeability from NGWFTs such Well Test Design and Analysis1031Chapter 16 Well Test Designas the RES, MDT or RCI and from nuclear magnetic resonance (NMR) logs is treated in depth in chapter 12 of Wireline Formation Testing and Well Deliverability.In the case of the frst test on a new well in the producing reservoir (IDT), the WFT survey is an essential component of the well test since this will indicate the presence of diferential depletion, i.e., diferences between the initial pressures (or, more correctly, potentials) of poorly communicatinglayers.Notethatthemoderntrendtounderbalancedrillingremovesthe possibility of obtaining pressure data from WFT devices; given the importance of such data to reservoir engineering, this is a very serious limitation.Equation (161) refers to the correction of shut-in pressure when the well is not fowing. In the general case, including draw-down periods, the pressure at datum is given by p = p + D + pw wGD~GD frD D (162)wherepw = true bottom-hole pressure,pwGD = pressure measured by gauge, andpf = frictional pressure drop between datum and gauge location.Te limiting case of Eq. (162) occurs when the pressure gauge is at the wellhead and it is desired to deduce the bottom-hole pressure from surface measurements. In the case of singlephase gas wells, this procedure has been embedded in a commercial system named SPIDA. In most welltestingsituationswithdownholegauges,thefrictionaltermin(162)isnegligibleand only the hydrostatic term is required. However, if the frictional pressure drop is appreciable andtheappropriatecorrectionisnotmade,thecalculatedskinwillincludeacontribution from the wellbore friction. If the fow in the tubing is laminar (Re < 2,100), then the skin will be conventional, but at higher Reynolds number it will include a component of the rate-dependent coefcient D due to wellbore friction. In the most recent version of PANSYSTEM, it is possible to import a vertical fow performance (VFP) table from a well modeling package such as WELLFLO and correct from surface to bottom-hole conditions. Tis facility can also be used to correct from any other gauge depth and make allowance for wellbore friction in the translation.Akeyissueintheuseofwellheadpressuredatatransformedtobottom-holepressure through a well modeling program is the handling of heat transfer. It is essential that the well model be tuned to a fowing gradient and temperature survey for the transformation be valid. When the well is fowing, a wellhead temperature measurement refects the actual temperature of the fowing fuid. However, when the well is shut in and the temperature relaxes back to the geothermal gradient in the body of the well, the wellhead temperature becomes anomalous as illustrated in fgure 168. A fber optic distributed temperature survey (DTS) will overcome this problem, and knowledge of the dynamic temperature profle during the shutin, as cooling back to geothermal occurs, will allow the gas density to be computed and hence the hydrostatic pressure diference between wellhead and bottomhole.1032Well Test Design and Analysis Chapter 16 Well Test DesignFig. 168. Anomaly in wellhead temperature in buildupFigure 169 shows a completion with the pressure gauge 2,500 ft above the perforations.Fig. 169. Completion diagram where wellbore friction is appreciableSkin cleanupIn the interpretation of well test data, it is frequently the case that the fowing (drawdown) pressures are unanalyzable. Tere are two principal reasons for this:Te rate is not constant but the fuctuations are not large enough to be measured;Te well skin factor is changing as fow cleans up the near wellbore region.Well Test Design and Analysis1033Chapter 16 Well Test DesignIt is the latter phenomenon which gives rise to the largest problem, and one of the most difcult tasks in well test design is to predict how long the cleanup will take. A revised fow schedule is shown in fgure 1610, where a clean-up period and intermediate buildup (to reduce superposition efects) have been added. Te initial short period and frst buildup are still included in the design to ensure an initial pressure absolutely unafected by depletion. Typically, the clean-up period is about 8 h and hence a total of 16 h has been added to the test; for a DST, this will contribute dramatically to the cost. In this latter case, where skin determination is not an issue, then it is problematic whether the altered design is justifed. A buildup will register the skin as it exists just prior to shutting-in the well. In the case of an IDT, where the development well is diverted through the platform test separator, there is not a signifcant cost implication for the modifed design.Fig. 1610. Revised fow schedule including clean-up periodEnhanced objectivesIn a modern reservoir engineering context, the basic objectives of well testing outlined above have been augmented by the requirement to elucidate reservoir structure, i.e., heterogeneity. Te advent of electronic pressure transducers of high resolution and the development of the derivative diagnostic techniques have greatly enhanced this aspect of interpretation. However, because of the lack of uniqueness problem, the use of well test data in reservoir description must be properly integrated with information from other sources such as 3-D seismic, open- and cased-hole logs, coreanalysis,etc.Tedetectionofsealingfaults(no-fowboundaries)inhigh-permeability reservoirs in the North Sea, using software packages based on interactive graphics, marked the beginning of the modern approach to pressure transient analysis. Te well test interpretation programs all have an analytical simulation capability in which the pressure response in a well test can be predicted. A wide range of idealized models are available, some of which are listed here:Radial compositeDual porositystrata or natural fracture networkLimited entry or dual permeabilityCommingled layers1034Well Test Design and Analysis Chapter 16 Well Test DesignNonintersecting fracturePartially communicating fault and/or linear compositeTwo-cell compartmentalizedHigh-permeability lens straddling the wellbore (geoskin)Stacked channels and sand body enveloping.In the context of well test design, each of these models exhibits particular fow regimes which must be detected in the well test if a viable interpretation is to be made; the EPS poster produced by the author depicts approximately 100 such fngerprints. At the planning stage of the well test design process, the reservoir description team must assess the geophysical and geological data to determine what forms of model are likely to be applicable. For example, the current fault map from a seismic survey will give some indication of the location of sealing boundaries. An analytical simulation will show how long the draw-down and build-up periods need to be to allow the detection of faults at varying distances from the well. Te application of analytic well test simulation is considered in detail later in design criteria. Te next level of objective may accordingly include some of the following:Location of no-fow boundaries (fault detection)Detection of compartmentalization (closed system behavior)Calibration of heterogeneity modelObtaining a permeability estimateTe design of a well test requires an estimate of the likely permeability k of the formation to be investigated; the better this can be achieved, the better founded will be the design. Permeability estimates are available from various sources, the most important being listed below:Estimate obtained from earlier exploration appraisal tests in the reservoir;Application of a permeability transform to the openhole log data;Use of permeabilities obtained from WFT data.Although an exploration well may be cored, it is unlikely that the core data will be available soon enough to be used in the well test design, However well-site probe permeameter data may give some indication of permeability if this type of survey is carried out. A well test cannot be designed without preceding evaluation of the open-hole logging suite since the zones to be perforated are chosen with reference to the logs. Te methods of predicting permeability from logs use porosity as the main determinant of permeability, and the efect of grain size is introduced through the connate water saturation Sw,irr. For example, the Timur equation developed by Chevron, which is the prototype for most log permeability transforms, takes the form k= 100Sk: md2.25w,irrf (163)Well Test Design and Analysis1035Chapter 16 Well Test DesignTeauthorsexperiencewiththisapproachsuggeststhatthebasicTimurcorrelationcan predict the permeability to about a factor of three in moderate and high permeability sandstone reservoirs. Recently, renewed attention in this method has been sparked by the new generation of NMR logs which detect free water. Te subject of log permeability transforms is very large, with the problem of interstitial clay fguring heavily in the poor success of such techniques. Typically, the permeability can only be predicted a priori to within an order of magnitude which doesnotgivemuchhopeforawell-foundedtestdesign.Ofcourse,theimportanceofwell testing is largely based on the failure of methods of predicting permeability from logs. Te issue of permeability estimates is treated in detail in chapter 12 of Wireline Formation Testing and Well Deliverability, which is concerned with the decision to test, or not to test, appraisal wells.Figure 1611 shows the result of an extensive study in a moderate-permeability, sandstone environment where the prediction of permeability based on the Timur correlation was compared with average permeability from well testing. Te Timur log permeability transform uses porosity e and water saturation Swc to make a permeability prediction, and the level-by-level values can be averaged to generate a quantity comparable to that which is measured in a well test. Te data from seven wells in fgure 1611 indicates that in this case permeability can be predicted towithinaboutafactorofthree.Tisuncertaintywouldgivearealisticbasisforsensitivity studies. In fgure 1612, data from the same basin shows that the prediction is also applicable to horizontal wells where the concept of net length has replaced the familiar net pay used in vertical wells. Te petrophysical cutofs defning nonproductive intervals is an important part of the averaging process.Fig. 1611. Timur predicted permeabilityfeld A1036Well Test Design and Analysis Chapter 16 Well Test DesignFig. 1612. Assorted and horizontal well permeability analysisCompletion designTe great attraction of pressure transient analysis in the case of exploration appraisal wells is the independent determination of the kh product from the slope of the semilog straight line (MTR). Tus it is customary to reject the skin S from the intercept of the semilog graph since it is likely that the mud system in an exploration well is not optimized with respect to formation damageandtheoverbalancemaybequitelarge.Theproductivityindex(PI)ofeventual development wells is predicted from the determined kh and an estimate of the likely skin for the completion method to be employed on these wells, e.g., oil-based mud with tubing conveyed perforation at optimum underbalance. Tus the exploration appraisal well is a formation test and not a completion evaluation.Figure 1613 shows the Horner plot for the test on the 1974 discovery well in the giant Sunrise-Troubador feld in the Timur Sea. Te well fowed at only 10 MMscf/d and the feld lay undeveloped for many years because it was not thought to be commercial. Te Woodside engineers went back to the original data and made the Horner plot showing a permeability of 36 md and a skin of 500; the well had been extensively damaged due to being exposed to drillingfuidsfor13daysat900psioverbalance.TePIofthediscoverywellisirrelevant because of the high skin. However, a horizontal development well with a modern completion in a permeability of 36 md will fow in excess of 150 MMscf/d. Tis feld example dramatically showsuptheimportanceofseparatingkhandskinthroughbuild-upanalysisusingthe semilog graph.However, it is possible to set an objective to test the completion method as well as the formation. In this case, the exploration appraisal well must be completed in the manner of the development wells so that the skin obtained from the fnal buildup is representative, i.e., the exploration well completion is an analog for the future producers. It is particularly important in gas well tests to Well Test Design and Analysis1037Chapter 16 Well Test Designmake a decision regarding the objective of the testing. If the completion is not representative, there is little justifcation for a step-rate fow period since the rate-dependent coefcient D is even more sensitive to the nature of the completion than the mechanical skin S.Fig. 1613. Sunrise-troubador discovery well testIf the formation to be tested is highly unconsolidated, then it may be necessary to gravel-pack theexplorationwellpriortotestingtheformation.Suchoperationsaddconsiderablytothe cost of the DST but may be necessary to ensure a satisfactory test. For example, in deep water situations ofshore Africa this has been considered necessary. If the appraisal well is, in fact, retainedtobeaneventualproducer(akeeperwell),thentheskinfactorisimportantand should be included in the objectives.Te initial test on a new development well, conveniently termed an IDT (initial development test), will certainly have as objectives the determination of kh and skin and the detection of near boundaries.Teanalysisoflater,routinebuildupsonaproducingwell(partofthereservoir monitoring exercise) is much easier if the IDT has already located the boundaries in the well vicinity.Forecasting of development well deliverabilityHistorically, the main reason for testing appraisal wells has been to predict the deliverability of eventual producers and to allow a sound feld development plan to be formulated. In an ofshore situation, it is essential to have enough platform well slots to guarantee a plateau production of, say, 10% of recoverable reserves per annum. In situations of moderate and high permeability, deliverability is governed bya) Te semi-steady-state productivity index JSSS, andb) Te decline in average pressure due to depletion.1038Well Test Design and Analysis Chapter 16 Well Test DesignIn turn, the PI is controlled bya) Te average permeabilitythickness product kh,b) Te Dietz shape factor CA, andc) Te skin factor S.Appraisal well tests give information on the average permeability of the formation, and appraisal well logging fxes the thickness (net pay) of the formation across the feld. Te Dietz shape factor CA is diferent from the default value of 31.6 only if boundaries are present close to the well. Hence the enhanced objective of identifying fault geometry, particularly the incidence of channel reservoir features. As already mentioned, it is not usually the objective of appraisal well testing to yield information that will allow the prediction of the skin factor of eventual producers; this comes from experience of completion techniques.Te depletion of fault blocks and the decline in average pressure is just as important as the PI in determining well rates. Hence the emphasis here on the determination of volume as an objective. However, it may be the case that water injection is commenced very early in feld life to maintain the pressure and in this case depletion is not an issue; it is the changing well PI through fuid changes, i.e., increasing water cut, and attendant problems of changing skin through scaling or fnes migration, for example. Volume calculations are still important because of reserve booking requirements.Insituationsoflowpermeability,welldeliverabilitywillbegovernedforlongperiodsby transient fow. Appraisal wells are normally vertical and the average permeability determined isinthehorizontalsense.Eventualdevelopmentwellsarelikelytobeverticallyfractured, horizontal, or high slant in orientation. Again, it is the prediction of the deliverability of these eventual producers which is the objective of the appraisal well testing. Te problem is that in the case of horizontal or high slant wells the macroscopic vertical permeability kv is just as important as the horizontal permeability kr.Inchapter10onlimitedentrysituations,itisshownhowawelltestcanbedevisedto determine kv as well as kr. At the design stage, it is therefore necessary to consider whether the deliberate limited entry technique should be specifed with the objective of identifying kv. Tis method, devised by Hayes, is described in chapter 10.Estimation of accessible hydrocarbonA key decision in the well test design concerns the detection of reservoir volume through depletionasillustratedinfgure1614.Notethatthecalculationofdepletionimpliesthe subtraction of two pressures, i.e., Dp =p pMB i f (164)where it has been tacitly assumed that the extrapolated pressure of the fnal buildup, denoted pf , is synonymous with the material balance average pressure p; however, these quantities are not identical. Te relation between extrapolated pressure and average pressure is explored at length in chapters 4 and 6.Well Test Design and Analysis1039Chapter 16 Well Test DesignFig. 1614. Determination of depletion in an exploration well testReservoir compartmentalization has been recognized as a signifcant feature of many systems, and failure to detect compartmentalization when it is present is a cardinal failure of the well testing procedure. In the case of primary recovery, i.e., depletion drive, the prediction into the future of the well deliverability requires two pieces of information:Te semi-steady-state productivity index JSSS, andTe compartment (block) size as defned by the drainage area A.Te depletion, driven by the cumulative volume produced in the major fow period, is given by the canonical material balance equation Dp =p p=c QVMB i t p (165)where Q = qdt (cumulativevolumeproduced0tpduringflowperiod)V= hA (reservopf iir compartment pore volume)HCPV=(1S )wcVVc=c (1S )+c S +c (total comPt o wc w wc fppressibility)From a design point of view, the key question is concerned with the duration of the fow period tp. In an extended draw-down test, it is necessary to have tp > tSSS where tSSS is the time for the reservoir compartment containing the well to reach the semi-steady-state. However, the synthetic example considered in chapter 6 section Depletion in a Channel System shows that depletion can be detected when tp < tsia, where tsia is the time for the depth of investigation to reach the far boundary of the closed compartment. Terefore a reasonable design rule for the determination of accessible hydrocarbon is t tp sia (166)1040Well Test Design and Analysis Chapter 16 Well Test DesignOf course, this implies knowledge of the geometry of the well compartment which in an appraisal well will have to come from seismic information. For a rectangular compartment, the time to reach semi-steady-state is given by t =ktc L= 0.25DLsiasiat f2fm (167)HereLfisthedistancefromthewelltothefarboundaryofthedrainagearea.Theissue of reserves, or more correctly gas-in-place, estimation in gas wells is treated in detail in the succeeding section Estimation of Gas Reserves.In the case where the depletion estimate is based on two extrapolated buildups yielding pi and pf respectively, it is necessary to consider the error in the extrapolation process. If the compartment is approximately square in shape, with the well in a central position, the extrapolation will be straightforward to carry out and the reserve estimate may be reliable when the pressure drop pdep = pi pf is as low as 10 psi, say. However, if channel reservoirs are present, the determination of volume is much more difcult, as discussed in chapter 6, and the buildup should be four times the length of the major fow period to reduce uncertainty in the extrapolation.A second approach to determining volume is to match the whole test, i.e., drawdown and buildup, with a closed reservoir model; this was demonstrated for a North Sea gas well test in chapter 5 in the section Analysis of a Variable Surface Rate Buildup Using Drawdown Type Curve. In this case the initial interpretation was a closed reservoir model, but the semi-infnite channel reservoir model gave just as good a ft to the data. If the semi-infnite channel model gives an equally good ft, a minimum estimate of volume can be found from the width of the channel W given by the match and a length of investigation from linear fow theory, i.e., t =ktc L= 0.2DLinvDDt chanfm2 (168a) V = hWLp,min chanf(168b)It is obviously useful to consider the two estimates of pore volume, one from the closed model ft and the other from the semi-infnite acting ft, to give an appreciation of potential error bands.Tubing diameter selectionIt has already been mentioned that one of the main objectives of appraisal well testing is to allow a prediction of the deliverability of eventual development wells; hence the emphasis on average permeability k. In high-permeability reservoirs, which will have prolifc development wells, it is important to select the appropriate tubing diameter Dt, and runs of Wellfo under production conditions will allow such a design to be accomplished. A good rule of thumb for a balanced well design is to choose Dt such that the frictional component of the total tubing pressure drop is approximately equal to the formation drawdown. Tis may not be the exact optimum based on discounted cash fow (DCF) considerations but it will be quite close.Well Test Design and Analysis1041Chapter 16 Well Test DesignDesign CriteriaBased on the depth of investigationIn many situations, the design of a well test simply reduces to defning the length of the major fow period and the length of the ensuing buildup. In the selection of test duration, the concept ofradiusofinvestigationiscrucialandtheclassicaldefnition,originatingintransientheat conduction where it is termed the penetration depth, takes the form r =4ktcitfm (169a)or, in SPE feld units r =0.0002636 4ktc= 0.0325ktcit t3fm fm (169b)Tis equation applies to the constant rate drawdown period, and the corresponding form for buildup is based on the Agarwal equivalent drawdown time, i.e., r =4k tcwhere t =t tt + tieteppDfmDDD (1610a)or in feld units r = 0.0325k tcietDfm (1610b)In the early days of well testing, it was considered that the depth of investigation was limited by the duration of the preceding drawdown, i.e., tp should be used in Eq. (169b) to assess a buildup. Another way of stating this adage was that a phenomenon had to be present in the drawdown before it could be detected in the ensuing buildup. Te most recent data processing involving deconvolution suggests that the total time of drawdown plus buildup can be used in (169b). Tis is not exactly correct but it is close when deconvolution is applied. However, the original idea is still relevant to designing tests and the ratio of 12 between DD and BU is close to optimum.Ithasalreadybeenmentionedthatoneoftheobjectivesofwelltestingistopredictthe deliverability of the well into the future. In the case of primary recovery, i.e., depletion drive where drainage areas at semi-steady-state become established, the SSS PI is used in conjunction with a material balance model. In the case of a vertical or deviated well, the PI is given by an equation of the form1042Well Test Design and Analysis Chapter 16 Well Test Design J =2khB12ln4ACr+ SSSSAw2amg (1611)where CA is the Dietz shape factor. Tis quantity is only signifcantly diferent from the default value of 31.6 when no-fow boundaries are present relatively near the well. Hence the depth of investigation should be sufcient to allow detection of sealing boundaries out to some specifed distance from the well, say 1,000 ft.In many situations, the designer has a fault map which gives an indication of the estimated faultlocationsfromthe3-Dseismicsurvey.Oneoftheobjectivesofthewelltestwhether it is an appraisal well DST or the frst test on a new produceris to confrm the fault system geometry and distances. Examination of the fault system type curve presented in chapter 3 as fgure 317 indicates that over a period of time in the LTR, the behavior of a parallel fault system and a right-angle fault system are indistinguishable; it is only for dimensionless times, tD/L2D, greater than about 2 do the two responses separate. Hence this type curve can be used to design a test which will allow discrimination between fault geometries. Tus t =c LktLDESt2DD2DESfm (1612)wherek = permeability estimate from logs, say,L = estimate of nearest fault distance from seismic, andt / LD D2DES = necessary dimensionless time read from type curve, e.g., 10.Tis calculation will give the appropriate drawdown time, and the buildup will usually have to be twice as long. In low-permeability (tight) reservoirs, the design times from such calculations will be so long that economics based on value of information, especially in the case of DSTs, will preclude fault detection from the objectives.Based on the duration of the wellbore storage effectTe classical theory of ideal (liquid) wellbore storage was treated at length in chapter 3, and the well known design equation due to Ramey was introduced in the form t = C(60 + 3.5S)DSLSLD (1613)where tD|SLSL is the dimensionless time to the beginning of the semilog straight line, i.e., the start of the MTR and, in SPE feld units t = 0.0002637 ktc rC =5.6146C2c hrDt w2DSt w2fm fWell Test Design and Analysis1043Chapter 16 Well Test DesignEquation (1613) may therefore be written in the explicit form t = 3390 Ckh(60 + 3.5 S)SLSLSm (1614)Te application of this equation to well test design requires a prior estimate of the likely wellbore storagecoefcientCS,whichisjustashardtocomebyasapriorestimateoftheformation permeability k, which also enters the equation. In principle, the wellbore storage coefcient is given by the formula C=c VS eff wb(1615)whereVwb= wellbore volume beneath the testing valve, andcef= efective compressibility of the fuid mixture present.Unfortunately, wellbore storage is usually nonideal and the quantity cef is changing during the test. Once a gas cushion has formed, as illustrated in fgure 24 in chapter 2, the wellbore storage model becomes C = c + c VS o o g g wb( ) f f (1616)where o is the fraction of the wellbore flled with segregated oil and g is the fraction occupied by the gas cushion.Te problem of estimating a realistic wellbore storage coefcient on which to base a design can really only be tackled by building up a database of measured storage coefcients and trying to relate these values to more fundamental variables such as tubing diameter, producing GOR, pressure in the wellbore, etc. Unfortunately, this type of approach does not seem to have been pursued and there is a real need for the beneft of experience to be made available through an exercise of data collection and assessment. In the following introduction, the use of a nodal analysis package for estimating cef will be described.AcomputersoftwarenamedOLGAwasdevelopedforstudyingsluggingintwo-phase, undulating pipelines and it is based on solving transient, multiphase fow equations for fuid fow in pipes. Tis software is much used by production and facilities engineers. Te software has been extended to model well stability (heading) in gas lift operations and in the most recent development it can be run in conjunction withECLIPSE, which is the reservoir simulation program. Te phenomenon of phase redistribution involving countercurrent fow, i.e., nonideal wellbore storage, can be modeled using transient multiphase fow codes such as OLGA and this would be a real advance in designing well tests. Coupling a transient, numerical model of the formation (i.e., ECLIPSE) to a transient, numerical model of the wellbore (i.e., OLGA) is a powerful simulation capability since nonideal wellbore storage efects could be predicted in advance.1044Well Test Design and Analysis Chapter 16 Well Test DesignWireline shut-in tools (SITs)Themainproblemintestingdevelopmentwellswithasurfaceshut-inisthatofphase redistribution in the wellbore coupled with a changing hydrostatic correction. It was shown in chapter 2 that an efective resolution of this problem is to run a wireline SIT. Tese devices have been very much improved with respect to mechanical reliability and it is particularly necessary ingascondensatewelltesting.TefeldexampleofanIDTgascondensatewelltestdesign described later in fuvial systems uses an SIT device for the fnal buildup.Based on the removal of tidal effectsA feld example of a tidal efect in well testing from the Alba reservoir in the North Sea was presented in fgures 727 to 730 in feld examples of chapter 7. Te rise and fall of the sea level and the consequent efect on overburden pressure lead to an approximately sinusoidal distortion of the true reservoir signal. Te danger is that a late time perturbation from this source may be interpreted as a reservoir phenomenon. Te tidal efect is an issue in high-permeability reservoirs where the total pressure change in a buildup is quite small. In the North Sea, for example, the tidal efect has an amplitude of the order of 0.3 psi, whereas in the Timur Sea it is approximately 0.5 psi. Te largest tidal efect known to the author is 0.7 psi in the Morecambe Bay in England. Te test design facility in PANSYSTEM allows a tidal efect of specifed amplitude to be superposed on the true reservoir response. When designing a test in a high-permeability reservoir, where the total pressure change in the buildup is small enough that a 0.3 psi oscillation on a 12-h cycle is signifcant, it may be deemed necessary to have a long buildup simply to detect the tidal efect at late time so that it can be subtracted from the signal using a tidal flter. In the design of a deep water test ofshore Nigeria, the author recommended a 50-h buildup simply to ensure that the tidal efect could be observed and properly removed from the signal. Tis implied a very large incremental cost due to the additional rig time required, but the value of the information from interpretation of the LTR segment of the buildup was judged to warrant this expenditure. In some circumstances, it has been decided to run a testing system for appraisal wells in the initial test on a new development well to achieve the benefts of downhole shutin.Theroleoftestdesignsimulationisillustratedinfigure1615,whereatidaleffectof amplitude 0.5 psi and period 12 h has been added to the buildup response of a 10-darcy oil reservoir.Infgure1616theloglogderivativediagnosticforthemodifeddatashowsthe complicated nature of the response at late time. Note that it is only in very high permeability reservoirs that the elucidation of tidal efect needs to fgure in the test design.Well Test Design and Analysis1045Chapter 16 Well Test DesignFig. 1615. Tidal effect superposed on a cartesian graphFig. 1616. Derivative loglog diagnostic with tidal effectLow-permeability systemsIn moderate and high permeability, the detection of boundaries has been an important issue for test design. In low permeability, it is unlikely that the pressure disturbance can penetrate far enough into the reservoir for faults to show up in the response; diferent criteria dominate the test design. In tight gas, where the permeability is less than about 0.1 md, a development well will usually be stimulated with a hydraulic fracture. In this case, it is important to carry out a prefracture test to determine permeability; the test design, based on a surface valve, will then be dominated by wellbore storage considerations.In a low-permeability system, an important limitation is the pressure diferential which a packer can sustain. Te drawdown can only be continued while the packer pressure diferential is less than the maximum allowable value; once this is reached, the well must be shut in for a 1046Well Test Design and Analysis Chapter 16 Well Test Designbuildup. Hence there is a limit to how long the drawdown can be. In order to partially compensate for a relatively short drawdown, the buildup may be made much longer, say 10 times the duration of the drawdown. Tus in tight reservoir situations, the standard design rule that the buildup should be twice the drawdown simply does not apply, and tests which are more like impulse testsarecarriedout.Conventionalwelltestinterpretationisbasedonthepremisethatthe sandface rate at the end of the major drawdown has become indistinguishable from the surface rate measured at the separator. In extreme low permeability, it sometimes occurs that the storage efect is strong enough that this condition is not satisfed. It is still possible to analyze the buildup but special techniques have to be used. Tese are available in Pansystem, and interpreters should be aware of circumstances where they are necessary. Te surface and sandface rates in such a situation are illustrated in fgure 1617, and it is evident that the surface rate Q cannot be used to analyze the buildup since the formation has never fowed this rate in drawdown.Fig. 1617. Downhole rate does not attain surface rate in drawdown periodIncorporation of production loggingTere has been considerable interest in the topic of layered reservoir identifcation which istreatedindetailinchapter19(addendum)wherethedualproflebuild-uptest(DPBT)is described. Here, up and down passes of a production logging tool (PLT) are run, one at the end of the drawdown and another during the buildup to measure interlayer crossfow. It is therefore a design decision whether or not to run a PLT device as part of an appraisal well test. Secondary recovery operations, e.g., water drive, are dominated by layering phenomena and permeability contrasts between layers are more important than the arithmetic average permeability k. Te inclusion of the production logging surveys allows identifcation of permeability on a layer-by-layer basis which is precisely the description required for a valid reservoir simulation study of the waterfooding process. Te question arises, of course, as to the value of this information.Well Test Design and Analysis1047Chapter 16 Well Test DesignRole of Simulation in Test DesignApplication of a nodal analysis packageIn addition to the selection of test period duration, the other key variable in test design is the choice of the well fow rate and, by inference, choke size. Te use of a nodal analysis package such as WELLFLO is recommended for this process. In conventional nodal analysis, the well IPR is modeled at semi-steady-state for a specifed average pressure for the well drainage area through an equation of the form q = J p pS SSS wf( ) (1617)where J =2khB ln rr34+ SSSSewmHowever,inthecontextofanexplorationwelltestitis(hopefully)unlikelythattheflow regime attains the state of semi-steady-state depletion. It is more likely that the well will fow in transient conditions throughout the test and the higher rates, typical of fush production, may be encountered or designed for. In this case, the infow performance is modeled by the concept of transient productivity index where q = J (p p )S t i wf(1618)where J =2khB12ln4ktc r+ Stpt w2mgfm HerethetransientPIhasbeencalculatedusingtheFetkovichapproximationandatimetp corresponding to the duration of the major fow period. Note that the initial pressure pi is used in this form and this quantity will be available at the design stage from the WFT survey. However, in order to use Eq. (1618), again a reasonable estimate of formation permeability is required. In the nodal analysis program, the PI is set to the value given by (1618) and the reservoir pressure is set to pi. Te fow diagram for nodal analysis is shown in fgure 1618, with a choke located at the wellhead. In general, the well fow rate under test will be controlled by the separator capacity, typically 10,000 bbl/day in an oil well test. Tus, initially the rate is set at a trial value and the nodal analysis will fnd the choke setting necessary to control the rate at this value presuming the potential is there to fow at much higher rate. If the choke is in critical fow at the operating point then the rate is satisfactory. At this stage, diferent tubing sizes may be examined to fnd the smallest one which will allow the well to be tested. If the choke is subcritical, good control of the rate will not be achieved and a lower rate or larger tubing should be investigated until a rate and tubing diameter that yield critical fow are obtained. It is also useful to run nodal 1048Well Test Design and Analysis Chapter 16 Well Test Designanalysis calculations without a choke to obtain estimates of maximum attainable well fow rates at diferent tubing sizes. Obviously, these calculations are very dependent on the estimate of formation permeability k used to compute the well transient PI, denoted Jt.Fig. 1618. Flow diagram for nodal analysisItisusefultoexaminehowaconventionalnodalanalysispackagecanbeusedtorun snap-shot calculations of well deliverability inwell test design. Suppose an equivalentSSS radius, denoted riae, is defned by the correspondence p = 12ln4t= lnrr34DpD eiawg (1619)i.e., 2 lnrr= 1.5 + ln 4t= ln 4.481eiawpD g77 4t1.781= ln(10.07tpDpD3)or r =10.07ktceiaptfm (1620)Tis is the radius that must be entered into the SSS formulation in order to predict transient production at time tp. Equation (1620) can also be written in the convenient form r = 1.586r = 1.5864ktceiaiptfm (1621)where ri is the classical depth of investigation. Note that it is the initial reservoir pressure pi that must be entered into the nodal analysis program along with riae in order to defne the transient fow rate.Well Test Design and Analysis1049Chapter 16 Well Test DesignIn the test design procedure the nodal analysis package is run in operating point mode for a selected tubing diameter using an riae value corresponding to the estimated formation permeability and the chosen production time tp. In addition to the tubing run, it is advisable to include a choke in critical fow as part of the nodal analysis. Te top node pressure becomes synonymous with the operating pressure for the separator, and the simulation will indicate the pressure drop over the choke. Sensitivity runs will indicate the appropriate choke diameter that will ensure critical fow at the design fow rates. Te nodal analysis simulations will indicate the maximum achievable rate at the end of the fow period of duration tp; the design test rate may be cut back (by reducing the choke diameter) until the rate is compatible with the available test separator. For example, many test separators have an upper limit on oil rate of 10,000 bbl/day. In remote locations, where equipment is brought in by helicopter, a smaller capacity separator may be selected and the test rate correspondingly limited to lower fow rates.In order to demonstrate the use of a nodal analysis package in a well test design, a test case based on the following data was run in WELLFLO (table 161).Table 161. Input data for WELLFLOData for design test casemoderate permeabilityk = 100 md h = 100 ft = 0.2 = 0.42 cppi = 5,000 psia ct = 1.41 105 psi1rw = 0.354 ft tp = 4.52 hrreIA = 1,000 ft o = 35 API g = 0.65 GOR = 900 scf/bblJ = 14.2 STB/D/psi Tubing I.D. = 2.5 Choke size = 32/64 Tubing length = 5,000 ft (vertical)Tubing roughness = 0.0012 Separator pressure = 200 psia Tres = 200F Twh = 60FpBP = 4,426 psia Tubing volume = 121.4 bbl S = 1Te nodal analysis calculation for the operating point gave the following results (table 162):Table 162. Calculated results from WELLFLOOperating point resultsmoderate permeabilityqs = 5,421 STB/D pwf = 4,618 psia pwh = 2,763 psiaTeintersectionoftheIPRandVLPgaveafowrateof5,421STB/Dwiththebottom-hole fowing pressure pwf above the bubble point pBP of the oil. Te profles of pressure and oil (liquid) holdup in the tubing are plotted in fgure 1619, where it is apparent that there is not much gas in the tubing. Integrating the gas holdup along the pipe gives an average gas holdup of 0.0634. At the wellhead pressure of 2,763 psia, the compressibility of gas is 2.81 104 psi1, while the oil compressibility is 4.92 105 psi1. An estimate of the efective compressibility of the two-phase mixture in the wellbore can be obtained as c = c + c = 2.81 10 0.0634 +4.92 10 0.g g o o4 5f f 3 3 3 3 9937 = 6.39 10 psi5 13 1050Well Test Design and Analysis Chapter 16 Well Test DesignFig. 1619. Liquid holdup and pressure profle for moderate permeability caseTe wellbore storage coefcient follows as C = V c = 121.4 6.39 10 = 0.00776bb1/psiS t53 3Tehightubingbackpressureexertedbythechokehaslimitedtheamountofgasevolved and also kept its compressibility relatively low. Te fow rate obtained with the 32/64" choke is within the separator capacity and there will not be any skin contribution from gas block. Te 2" tubing is quite adequate for testing this formation since the frictional component of the pressure gradient is approximately 0.09 psi/ft whereas the gravitational component is of the order of 0.27 psi/ft, i.e., friction comprises 25% of the total. Te well rate is essentially controlled by the choke whose pressure drop is 2,763 200 = 2,563 psi. Te formation pressure drop is 382 psi and the total frictional pressure drop in the tubing is roughly 450 psi. Te dimensionless wellbore storage coefcient CD is given by C = 5.614 C2hc r= 196DSt w23fand the time to the semilog straight line, tSLSL, given by Rameys correlation t = C(60 + 3.5S)D,SLSL Di.e., t = 3390 Ckh(60 + 3.5 S)SLSLSmbecomestSLSL=0.07 hwhich is very short indeed indicating that wellbore storage is not really a problem in this test.Well Test Design and Analysis1051Chapter 16 Well Test DesignTe formation permeability is now dropped to 10 md, resulting in a 10-fold reduction in the well PI. Te nodal analysis results for a 64/64ths choke, which is the maximum size still resulting in critical fow, are as follows:Operating point resultslow permeabilityqs = 4,345 STB/D pwf = 1,941 psia pwh = 554 psiaIn order to fow this formation at a rate compatible with the separator capacity, a much larger drawdown is required and hence the pressure in the tubing is signifcantly lower with much more gas being evolved. In this case, the bottom-hole fowing pressure pwf is below the bubble point and there will be a skin component due to gas block. In fact, there is a case for reducing the choke size, and hence the well fow rate, until pwf is slightly above the bubble point. For the 64/64ths choke, the well profles of pressure and liquid (oil) holdup are shown in fgure 1620; the average gas holdup is now 0.552 and the gas compressibility at the new wellhead pressure of 554 psia is 2.02 103 psi1. Tus there is much more gas present in the wellbore and its compressibility is much greater. An approximate calculation of the wellbore storage coefcient gives c = c + c = 10 + 10 0.448g g o3 5f fo2 02 0 552 1 31 . . . 3 3 3 3= 1.121 10 psi3 13Fig. 1620. Liquid holdup and pressure profle for low permeability caseTe well bore storage coefcient follows as C = V = 10 = bbl/psiS t3c 121 4 1 121 0 136 . . . 3 31052Well Test Design and Analysis Chapter 16 Well Test DesignTus the wellbore storage coefcient is much greater than in the moderate permeability case and the dimensionless storage coefcient becomes C = 3439DTe time to the beginning of the semilog straight line now is t = 12.3hSLSLTis is more than two orders of magnitude diferent from the moderate permeability case and againshowsthatwellborestorageisparticularlyaproblemwhentestinglow-permeability formations.Thedurationofthebuildupwillneedtobearound50htogetareasonable periodofMTRstraightline.Althoughthesecalculationsofthewellborestoragecoefcient areonlyapproximate,itcanbeseenthatthenodalanalysispackageisakeyelementinthe design procedure. Tis design corresponds to a surface shutin where the whole tubing volume contributes to the storage efect. In the case of a downhole shutin, only the gas trapped beneath the location of the testing valve need be considered and its compressibility is evaluated for the pressure at the valve location rather than the wellhead.Role of analytical well test simulationIn Pansystem the test design facility allows a well test to be simulated given a value of the permeability k; the fuid and wellbore properties, viz., h, , rw, ct, CS, Bo, o; and the fow-rate schedule. In the case of a horizontal or slant well, the measured length L and the relative well position zwD are also required. As previously mentioned, the hard part of a well test design is to obtain reasonable values for the average permeability and the wellbore storage coefcient. In the analytic simulation, any model in the supplied library can be used provided the relevant parameters are also specifed. In the simulation run, it is possible to add a specifed noise level in order to assess the efect of measurement error on the proposed test design. Tere is no doubt that the analytical simulation capability in the software can be used to great efect as a learning process; however, in training courses the author uses only feld examples for interpretation since data based on simulation is too perfect and does not give insight into the problems associated with actual responses from real systems.In chapter 18 (addendum), a comprehensive review of numerical well test interpretation is given and it is demonstrated how the fault geometry can be imported directly from a seismic map. Since a Panmesh model can be selected for well test design, it is possible to base the design on the fault locations evident on the 3-D seismic. Tis adds much to the validity of the test design since the geophysics is brought into the loop. Figure 1811 in chapter 18 (addendum) showsaseismicmapoftheHeidrunfeldinNorway,whereitisevidentfromtheparallel faulting that channel reservoir behavior will be expected in the well tests.Well Test Design and Analysis1053Chapter 16 Well Test DesignGauge selection and locationTe improvement in electronic gauge technology in the last 25 years (since the introduction of the frst quartz gauge by Hewlett-Packard in 1976) has been remarkable and this has been accompanied by a steady reduction in the cost of deploying such devices. Te modern quartz gauge has both very high resolution and absolute accuracy. Te absolute accuracy is such that it is possible to envisage measuring the initial reservoir pressure pi from a WFT survey, the f inal reservoir pressure pf from a buildup, and subtracting to give the material balance depletion pMB . Tus the f irst buildup in a DST can be made redundant. Te quartz gauge has become the standard for well testing applications and most service companies ofer high-quality gauges at a reasonable price. Tis is the industry standard and it is very rare to see mechanical devices, such as the famous Amerada gauge, still being run even in high-temperature situations. In 1998, Unocal were still having problems with electronic gauges in the Gulf of Tailand because of the high reservoir temperature; by 2000 these difculties had largely been eliminated, and quartz gauges are now exclusively being used. Te resolution of the gauge is such that noise in the signal due to residual tidal efect, for example, is the limiting factor in pressure analysis. Another cause of noise, not related to the gauge itself, is changing hydrostatic correction. Since this efect is so important test design should critically examine the location of the pressure transducer in the well. When tubing conveyed perforation (TCP) is employed, this can have the adverse efect of forcing the gauge location high above the perforations; this results in severe degradation of the signal quality. Recently, both Unocal and Saudi-Aramco have reported much improved well test results by placing the gauges close to the perforations. In fact, the best place is below the perforations.SchlumbergerhavestandardizedonitsCQGgaugeforbothwelltestingandRFT-MDT application.ExalutilizeQuartzDynegaugesofcomparablequalityandMetrolofergauges capable of high temperature operation. Te single largest improvement to the quartz gauge has been the reduction of its sensitivity to temperature changes in the wellbore. A very accurate wellbore temperature measurement, necessary for the utilization of the gauge calibration, has been a spin-of from this development.In chapter 2 it was demonstrated how the depth of investigation in well testing is related to the efective resolution of the pressure measurement. It is now possible to add noise to the results of an analytic simulation and directly assess the infuence of noise on the inverse problem of parameter estimation. For example, the pressure response with the added noise can be analyzed using the nonlinear regression algorithm and the calculated parameter values compared with those input into the original simulation. In chapter 14 the bootstrapping method is proposed for the evaluation of the error range of ftted parameters; this involves repeated runs of the nonlinear regression algorithm with diferent choices of the points included in the sum of squares. Te hard part of the problem is to defne a realistic level of the noise in a test. For ofshore tests, where the tidal efect is present, an efective gauge resolution of about 0.1psi is typical; this contrasts with the laboratory resolution of the modern quartz gauge of 0.01psi. Carrying out such simulations helps the practitioner avoid the trap of placing too much reliance on the derivative in the late stages of a buildup in a high-permeability reservoir.1054Well Test Design and Analysis Chapter 16 Well Test DesignPermanent downhole gaugesManydevelopmentwellsarenowequippedwithpermanentdownholegauges(PDGS) which are used for reservoir monitoring. When wells are shut in for operational reasons, e.g., compressor trip, then these buildups are captured by the PDG and they can be analyzed for skin S and current average reservoir pressure p. Tese tests are not designed in that the length of the shutin will depend on the resolution of the operational problem. However, a buildup will be useful only if it is long enough for the pressure transient to attain the MTR as shown in fgure 415 of chapter 4. Nearly all PDG installations have surface shutin so wellbore storage is always a problem. In this case, a semilog straight line can be ftted to yield S and p*. If the IDT has been properly designed to allow detection of near-no-fow boundaries, the Dietz shape factor will have been established and the MBH correction can be made to p* yielding p. Tus successful reservoir monitoring requires that the frst test on the producing well allows CA to be identifed. Note that it is sensible to force the same permeability, i.e., corresponding semilog straight line slope m*, on the periodic monitoring buildups so that the skin factors all refer to the same permeability and evolution of the degree of damage can be watched.In the case of gas wells, a shutin for operational reasons will allow the calculation of the total skin S' from the intercept of the Horner plot. However, as part of a reservoir monitoring exercise, it would be useful to know the two components of the skin S and D. In 1984, the author initiated an M.Eng. project on using the afterfow decay to assess both skin components, and a student, A. Amin, showed that it was possible to determine both parameters by matching the early time build-up response. Tis idea was later taken up by Shell who published a paper on the topic. Abuildupwithsurfaceshutinandafterfowisessentiallyavariablerateprocess,andhence dependent on both S and D, in the period when the sandface rate is appreciably diferent from zero. In the context of high-rate gas wells with gravel packs, this technique becomes important since it is likely that the rate-dependent coefcient will exhibit the strongest deterioration with fnes migration or scaling. Te nonlinear regression facility is used to identify the parameters S and D by matching the ETR.Special Considerations for Gas WellsClassifcation of gas reservoirsTe importance of a permeability estimate has already been emphasized and this is specially the case in gas reservoir test design. It is useful to classify gas reservoirs in terms of permeability, and test objectives depend on the category involved. Te partition takes the form:Moderate and high permeabilityk > 10 mdLow permeability0.1 < k < 10 mdTight gask < 0.1 mdIn the case of moderate and high permeability, there is not a high priority to determine the exact value of average permeability since well production is likely to be tubing controlled; however, permeability will infuence the selection of appropriate tubing size and there is still a case for its Well Test Design and Analysis1055Chapter 16 Well Test Designdetermination in a test. In the low-permeability-range well, deliverability is formation controlled and average permeability (in conjunction with net pay h) will control the PI. Tight gas production wells will routinely be hydraulically fractured and their transient deliverability will be controlled by fracture half length xf and average permeability k. Hence the forecasting of eventual producer deliverability requires a good k identifcation in the appraisal wells.Step-rate test designTe standard form of a gas well test (DST orIDT) is the step-rate schedule illustrated in fgure1621,wheretherateiscontrolledconstantineachperiod;thisallowstheparallel line construction on the semilog graph and a plot of the total skin S' versus rate Q giving the mechanical skin S from the intercept and the rate-dependent coefcient D from the slope. Te design criterion for the length of the individual step-rate periods is that the storage efect on changing the rate has died out and the correct semilog straight line is seen in each period. Note that the rate is changed by altering the surface chokes and hence the storage efect is based on the total tubing plus casing volume below the wellhead. On the other hand, the build-up storage is controlled by the much smaller volume beneath the downhole testing valve. In the case of essentially dry gas wells with no wellbore phase redistribution, the storage can be calculated from the ideal storage equation, (1614), provided the appropriate gas compressibility is employed for cef. Te compressibility of the gas in the wellbore depends on pressure and therefore it is necessary to simulate the test using the best available estimate of formation permeability to determine the expected wellbore pressure levels during the fow periods. Since wellbore storage can be included in the simulation, a good design of the test can be tied down simply by inspection of the simulation results; this aspect is treated later in constant rate buildup in a closed rectangle. Notethatinthesimulationofgaswellsthevolumebeneaththetestingvalveisnotentered directly but rather the wellbore storage coefcient. Te length of the individual fow periods should be such that roughly one-third to one-half a log cycle of MTR is present as illustrated in fgure 1622. Te fnal fow period at maximum rate can be longer if material balance or depth of investigation considerations deem this necessary. In fgure 1622, the downhole, i.e., sandface fow rate, measurable with a spinner device, is also shown and the form of the special semilog plot for step-rate gas well tests is presented alongside the rate schedule.Fig. 1621. Surface step-rate schedule for a standard gas well test1056Well Test Design and Analysis Chapter 16 Well Test DesignFig. 1622. Design of step-rate periodsAlthough the rate schedule of fgure 1621 has been stated to be the standard form, this assertionmustbequestioned.Ifthecompletionoftheappraisalwellisarbitrary,thenboth themechanicalskinSandtherate-dependentcoefcientDarenotvalidasanalogsforthe development wells. Hence the justifcation for the step-rate form is decidedly suspect and a simpler design based on a single constant-rate fow period may be preferable. Te advantage of a single fow period at maximum rate is that the size of the disturbance to the reservoir, i.e., cumulative gas production, is maximized giving the best possible chance of detecting depletion when compartmentalization has occurred. In low-permeability reservoirs where the maximum well rate is less than the separator capacitywhich is typically 15 MMSCF/Dthen the well rate when tied to a production system is not going to exceed that obtained during the test and it is not really necessary to decompose the total skin S' into the components S and D. Te well can simply be tested at as high a rate as it will fow, with some choke control to keep the rate constant, and the total skin S' will not be much in error in the production prediction.Te design of a step-rate gas well test is important if good results are to be achieved and the selection of test period duration is probably the central issue. Te objectives of testing vary according to whether the test is in an exploration or appraisal well or in a development well. Te former category is, of course, loosely referred to as drill stem testing (DST) and this type of test will be considered frst. Te main aims of a gas well DST may be summarized as follows:Determine the reservoir permeabilitythickness product;Ascertain the reservoir pressure and check for any evidence of depletion;Examine the test for boundary efects (sealing or partially communicating faults) and reservoir description parameters.TedeterminationofskinbothDarcy(mechanical)andnon-Darcy(ratedependent)is given a low priority because the formation damage and perforation conditions of an exploration or appraisal well are not relevant to ultimate development wells. However, if the well is to be utilized as a producer, this objective is raised to the same priority as the items listed above. Tere is, therefore, a strong case for scheduling a straightforward main drawdown and buildup and dispensing with the step-rate periods; a single constant rate fow period followed by a buildup Well Test Design and Analysis1057Chapter 16 Well Test Designwill allow the important information to be identifed. Te length of the fow period is governed by several factors:Achieving the desired depth of investigation;Ensuring the rate is properly stabilized for a reasonable period before the shutin;Te wellbore storage efect has completely disappeared from the signal;Te well has cleaned up and the skin factor has stabilized.Te buildup should conform to the well-established rule of thumb that the shut-in time be at least 1 times greater than the duration of the fow period. In the case of channel reservoirs involving linear fow, there is a case for even longer shut-in time if extrapolation on the tandem square root graph is required. In the case of a DST with a downhole shutin, the wellbore storage efect in buildup will be almost negligible provided the testing valve is close to the formation. However, in the step-rate period the rate changes are controlled from the surface and the wellbore storage following each step is afected by the whole tubing volume.Design calculations related to wellbore storageIn gas reservoirs with single-phase conditions in the wellbore, the duration of the storage efect can be predicted theoretically using the well known Ramey correlation: t = C 60 + 3.5SDslsl D( )(1622)i.e., t =5.6140.0002637c V2kh60 + 3.5SSlSlgm( ) (1623)in feld units. Taking the typical parameter values m=0.02cp; V=100bbl; c=10 psi ; S=0g4 1this reduces to the form t =41khSlSl (1624)Tus the key factor in determining the length of the fow periods is the formation permeabilitythickness product kh; the time to the end of storage afected data for various kh values is given in table 163.1058Well Test Design and Analysis Chapter 16 Well Test DesignTable 163. Duration of wellbore storage effect under typical conditionskh (md.ft) tslsl (hr) 1 41 10 4.1 100 0.411,000 0.041Aboveakhof1,000md.ft,thelengthoftheflowperiodswillbedeterminedbyother considerationssuchasthetimetogettheratestabilizedatthenewvaluebyadjustingthe surface choke. As usual, it is in low-permeability reservoirs that long fow periods are required, remembering that it is desirable to have about half a log cycle of data after the end of wellbore storage.In very low permeability reservoirs, this table will underestimate the duration of wellbore storage since it is based on a compressibility of 104 psi1 which is typical for gas at relatively high pressure. In tight reservoirs with a large drawdown, the wellbore pressure will be driven to quite low values and the gas compressibility may be substantially larger than this value leading to longer duration of wellbore storage efects. Suppose a tight gas well buildup is terminated before the end of wellbore storage as illustrated in fgure 1623; the efect of ftting a straight line to the last available data is to give too low an estimate of the formation permeability. Tis value is very important in the analysis of a post-fracture well test and it is imperative to ensure that the prefracture test is properly conducted. If the measure of formation permeability is too low, the incremental gas deliverability as a result of fracturing will be wrongly estimated and a fracture not considered worthwhile, whereas in reality it might make good sense.Fig. 1623. Prefracture gas well test buildup terminated before the end of wellbore storageOneoftheworldexpertsinhydraulicfracturing,MichaelSmithofNSI,madeavery interesting presentation1 at the Rio de Janeiro conference on tight gas where he considered the factors that ensure a successful fracture job. Surprisingly, it was not knowledge of rock mechanics Well Test Design and Analysis1059Chapter 16 Well Test Designproperties such as minimum horizontal stress or Youngs modulus that headed the list but a good estimate of permeability! Hence the prefracture test assumes a very important role in the design of the fracture operations and it must be designed in turn to yield a good k estimate.Role of analytical simulationIn chapter 14, the real-time algorithm for adding wellbore storage and skin to any model describedbyapDfunctionwasdescribed;inparticular,theadditionofbothmechanical and rate-dependent skin efects was possible. In the case of gas wells, the algorithm has the addedadvantagethatthecompressibilityofthegasinthewellborecanbeupdatedateach timestep.Ininterpretationmodetheefectofchanginggascompressibilitycanbehandled by the Agarwal pseudo-time transformation. In simulation (quickmatch or automatch) mode, thecompressibility of the wellbore gas is simply modifed as the wellbore pressure changes. In the case of gas well simulation, the volume beneath the testing valve or choke is entered directlyrather than a wellbore storage coefcient CSand the wellbore storage calculation based on the updated compressibility; the volume will be diferent, of course, between drawdown and buildup. At the moment,PANSYSTEM does not have a temperature model for the wellbore and the compressibility will be evaluated at reservoir temperature; this lack of exactness is not a huge problem but synthetic data will not perfectly match measured data because of wellbore temperature changes. A typical analytic simulation of a gas well test is shown later in fgures 1629 to 1631, where again the estimated permeability k = 300 md is the key element in the design process. Simulation sensitivity runs will quickly demonstrate the duration of the step-rate fow periods necessary to achieve, say, one-third of a log cycle of MTR in the situation where nonideal storage is occurring.Rate controlTraditionally, the control of the rate in a gas well test was achieved using variable chokes which are less than perfect control devices since the fow rate under critical fow conditions still depends on the upstream pressure. In a dry gas well test, the orifce plate fow measurement is of reasonable quality and it is possible to replace the choke with a pressure control valve (PCV) and a feedback loop as shown in fgure 1624. Tis was frst implemented in Canada and hopefully many more well tests in the future will have the beneft of the much tighter rate control given by a PCV.1060Well Test Design and Analysis Chapter 16 Well Test DesignFig. 1624. Feedback control in gas well testingProblem of well cleanupOne of the most difcult issues in the design of gas well tests is the question of how long itwilltakeforthewelltocleanup.Tetheoryofthesemilogplotandtheparallelstraight line construction depends on both components of the total skin S and D being constant. Te mechanism of cleanup has been discussed in chapter 14, and the displacement of mud fltrate will take longer in a low-permeability reservoir. Tus both the problem of wellbore storage and the problem of time of cleanup are more severe in tight reservoirs. A key part of the design is to have an adequate clean-up period before embarking on the step-rate test. About half of all step-rate gas well tests are, in fact, uninterpretable due to continuing well cleanup during the fow periods.Theissueofclean-uptimewasaddressedbyChevroninthedesignofappraisalwell tests for the Gorgon gas feld ofshore Australia. Chevron had made the decision to test the completionmethodaswellastheformation,andthecompletionproceduretobeusedon ultimate development wells was reproduced on the appraisal wells; this involved oil-based mud and underbalanced TCP. Te methodology of appraisal well testing developed by Chevron for the Gorgon feld in Australia shows how the optimum use of testing time can be obtained; the test sequence is illustrated in fgure 1625. With modern electronic gauges exhibiting very high absolute accuracy, Chevron have confrmed that the initial pressure pi can be determined from a WFT survey, in this case the MDT. In principle, then, the frst buildup can be omitted as shown in the second design B on fgure 1626; however, no operator in the authors experience has been bold enough to adopt this strategy.Well Test Design and Analysis1061Chapter 16 Well Test DesignFig. 1625. Optimum use of time in a gas well testFig. 1626. Alternative designs for a simple gas well testTe reservoir is of high permeability and hence there is no problem with supercharging andthemeasuredgaspressuregradientisofverygoodquality.Henceinitialpressureat datum is fxed with high confdence. Te well is fowed on cleanup for a period of around 8 h to ensure that the skin has stabilized. During this whole period, the well is producing mud fltrate indicating that gas is still displacing water from the formation. Te well is fowed at high rate during this period to aid the sweeping out of water from the near-wellbore region. Since the detection and interpretation of depletion is a major objective of the test, the rate is carefully measured during this period; also the rate schedule during the clean-up period is required for interpretation of the step-rate drawdowns since the frst shutin following cleanup willbedeliberatelykeptshort.Tewellisshutinforashortperiodandthenasequence ofshortsteprateswithanincreasingratescheduleisimplemented.Inhigh-permeability 1062Well Test Design and Analysis Chapter 16 Well Test Designsituations,step-ratefowperiodsof2harequitesufcient.Tecurtailedfrstbuildupis possible because the initial pressure is known accurately from the WFT survey. Te last rate is longer than the intermediate steps and fnally the well is shut in for a fnal buildup, the duration of which is about 1 times the total length of the step-rate periods. Te analysis of the step-rate fow periods for non-Darcy skin can only be carried out if the clean-up process has stabilized, and in the high-permeability reservoir this took about 8 h. However, the wells usuallyproducedfltratethroughoutthefowingperiodsindicatingthatcleanupwasstill taking place to some extent. Te initial fow period of 8 h duration is a compromise. During the clean-up period, liquid fltrate is being displaced from the formation by gas; this is an unfavorable process in terms of mobility ratio and as high a gas rate as possible should be employed.Temudsystememployedandtheperforationsetupintheappraisalwelltest are made as close as possible to those that will be used in the eventual development wells; under these circumstances, the skin, especially the non-Darcy component, in the appraisal well will be relevant to the ultimate development wells. Te appraisal wells were perforated underbalanced with through tubing guns.Tis is really a production test with the objective of defning the deliverability of the eventual development wells, and the allocation of the total test time between fow periods and shutins is designed to optimize the usefulness of the data acquired. Te question of accessible gas in place is not neglected since the initial pressure pi is accurately determined from the WFT survey. Te fnal buildup is long enough to reduce extrapolation error to an acceptable level. Note that the well is producing fltrate during the fow periods and the wellbore hydraulics must be checked to verify that this liquid will be lifted to the surface, i.e., the gas velocity must be greater than the critical predicted Turner correlation. When the well is shut in for the fnal buildup, it is hoped that there is negligible liquid contained in the volume beneath the testing valve so that a gas hydrostatic gradient can be satisfactorily used for the correction to datum.Te classical design of a step-rate gas well test shown in fgure 1621, where an increasing rate is depicted in the fowing period. Figure 1627 illustrates an alternative strategy where adecreasingratescheduleisemployed;thisformoftesthasnotbeenfavoredbecauseof a strong superposition efect in the fnal buildup. However, if the high fow rate in the frst drawdown following the initial buildup aids the clean-up process, then this design should not be discounted. Improving the cleanup by utilizing the viscous stripping efect (i.e., the efect of producing rate on two-phase relative permeability (discussed in chapter 3 of Wireline Formation Testing and Well Deliverability) with respect to gas condensate wells) is probably more important than the efect of declining rate on superposition.AparticularproblemarisesinIranwherefracturedgasreservoirsofhighpermeability areabouttobedeveloped.Duringthedrillingprocess,largeamountsofmudlossintothe fractured system takes place and the well tests exhibit very high skin factors. In this situation, the deliverability of wells is controlled by skin rather than the average permeability of the fracture network. Tis is an extreme example where testing the completion is the most important part of the appraisal well delineation. Finding a mud system which will bridge across the fracture openings and minimize invasion of mud solids into the fractures is a key issue.Well Test Design and Analysis1063Chapter 16 Well Test DesignFig. 1627. Reverse step-rate schedule for a gas well testTurner critical velocityItisimportantingaswellteststhatthegasvelocityissufcienttoliftliquidwateror condensate to surface and the tubing diameter must be such that the Turner critical velocity is exceeded. Tis quantity is computed by nodal analysis software and any gas well test design should check on liquid loading. In the example design discussed in the next section, the Turner velocity constraint imposed a minimum fow rate of 6 MMscf/d in 4" tubing. In the case of high-pressure,high-temperaturegascondensatewells,heattransferisanimportantissue. Elastomers in wellheads have a maximum temperature rating of around 400F and the well fow rate has to be curtailed so that the fuid temperature at the wellhead is less than the maximum allowable. In this case, the overall heat transfer coefcient U, which controls heat loss from the well fuid as the environment (geothermal) temperature falls up the well path, is the important quantity. Wellfo simulations, with the appropriate U value, will predict the fowing wellhead temperature and the maximum rate can accordingly be computed.Example gas well test designIn this section the design of a step-rate gas well test will be carried out in order to illustrate some of the ideas outlined in the preceding sections. Tis is the frst test on a new producer, and it is desired to test the completion (gravel pack) as well as the formation. Te relevant fault map is shown diagrammatically in fgure 1628, and the well is set in a closed rectangle of dimensions L=1946ft L=4867ft L=7354ft L =102731 2 3 4ft1064Well Test Design and Analysis Chapter 16 Well Test DesignFig. 1628. Diagrammatic fault map extracted from seismicA closed system was chosen for the test design since a major objective of the test is to confrm the gas-in-place accessible to the well. Te rectangular geometry with the noncentral well position is a reasonable approximation of the actual fault system. Te reservoir fuid is gas condensate with the following properties: CGR=83bbl / MMscf =0.68 =50 API T =27g o resg g 33 F and the formation properties, deduced from logs and the neighboring well, are p =5650psia k =300md =0.25 S =0.5 h=19.i wcf 77ftTe well is to be tested with 4" tubing to a depth of 11,810 ft; this gives a tubing volume of 184 bbl. Te wellhead pressure during fowing conditions will be close to 4,000 psia and the gas compressibility at this pressure is cg = 1.5 104 psi1. An estimate of the likely wellbore storage coefcient, CS, is therefore C=c V =1.5 10 184 =0.0276 bbl/psiS g tub43 3Thecompletiongroupdoesnotwanttoflowthewellabovearateof10MMscf/D.Ifthe maximumperforationvelocityis10ft/s,thentheallowableflowrateperperforationis 0.6 MMscf/D assuming a 0.7" diameter tunnel. For two shots per foot over 19.7 ft, i.e. 40 efective perforations, the upper limit to rate would be 24 MMscf/dmuch higher than the completion department restriction.Ananalyticalsimulationwasrunfora300hfowperiod(12days)followedby300-h buildup,andthetestoverviewisshowninfgure1629.Inthetestdesignsimulation,the mechanical skin S was set to 10 and the rate-dependent coefcient D set to 0.3 (MMscf/D)1; these values are representative of a gravel-packed well. Te cumulative volume produced in the fow period is 125 MMscf and this produces a depletion of 15 psi, i.e.,