Waterflood performance evaluation in a chalk reservoirwith an ensemble of tools

C. Olsen a, C.S. Kabir b,n

a Hess Denmark Aps, Østergade 26B, DK-1100 Copenhagen K, Denmarkb Hess Corporation, 1501 McKinney Street, Houston, TX 77010, United States

a r t i c l e i n f o

Article history:Received 14 August 2013Accepted 30 September 2014Available online 28 October 2014

Keywords:Waterflood performance4D seismicTracer surveysCapacitance–resistance modelingRate-transient analysisNumerical flow simulations

a b s t r a c t

Good waterflood performance management requires an understanding of injector–producer connectiv-ity. In this context, chalk reservoirs present unique challenges. Reservoir compaction, flow in longhorizontal wells with transverse fractures, fracturing above the parting pressure, and water short-circuiting along the fault planes may not guarantee the expected fluid displacement. These reservoirattributes collectively contribute to flood management challenges.

Real-time surveillance data form the basis of ongoing flood monitoring. This data interpretationimproves the estimates for ultimate recovery by way of on-time well intervention. The data also helps tobetter define the future field development plan. Besides gathering real-time rate and bottomholepressure (BHP) data, this study shows how time-lapse tracer, production logs, and 4D seismic data assistsin gaining a credible history match with numerical-flow simulations.

Before numerical modeling, this study used an array of analytical tools. These computationallyinexpensive tools include both diagnosis and analysis. Amongst the diagnostic tools, the reciprocal-productivity index (RPI) provided crucial information on the degree of pressure support felt at aproducer; the water–oil ratio (WOR) plot gave the clue on fluid displacement; and the modified-Hall plothelped understand matrix injection or the lack thereof. Combined rate/pressure data analysis with thecapacitance–resistance model (CRM) provided quantitative measures of injector–producer connectivity.Where feasible, the rate-transient analysis (RTA) provided evolving reservoir pressure and the connectedpore-volume information. The traditional decline-curve analysis (DCA) showed variability of the declinetrend based upon the pressure-support and fluid-displacement scenarios.

This study underscores the importance of both real-time and time-lapse measurements in managinga waterflood in a challenging reservoir environment. The proposed workflow emphasizes learning fromdata diagnosis and analysis with analytical tools before embarking on history matching with numerical-flow simulations in the South Arne field, located in the Danish North Sea.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Real-time monitoring of pressure and rate data has paved theway to understanding a reservoir's behavior, leading to on-timemanagement by way of frequent updates to a grid-based model.Some of the technical benefits of surveillance were suggested byHorne (2007). Many authors reported integrating surveillance datawith full-field simulation studies. Some of these studies includethose of Hustedt and Snippe (2010), Langaas et al. (2007), Baharet al. (2005), and King et al. (2002), among others over the lastdecade.

In chalk reservoirs, such as the one presented here, compactionposes additional challenges. Rapid decline in pore pressure and theconsequent well failure necessitate on-time action. Early studies byCook and Jewell (1996) in the Valhall field suggested that thecompaction drive yielded over 50% of the oil recovery. More recently,Pettersen and Kristiansen (2009) reported novel coupling of the rockmechanics and flow simulation by way of a pseudomodel in order tospeed up computations significantly for the Valhall field. The benefitsof chemical tracers and pulse testing in understanding reservoirconnectivity cannot be overstated. To that end, Cheng et al. (2012)documented a comprehensive study in a surfactant field trial. Theuse of 4D seismic in reservoir-flow modeling is emphasized bystudies of King et al. (2002), Govan et al. (2006), Mikkelsen et al.(2008), and Jin et al. (2012), among many others.

Most of the studies cited above use snapshots of dynamic data,such as pressure-transient analysis (PTA) and production logs.

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Journal of Petroleum Science and Engineering

http://dx.doi.org/10.1016/j.petrol.2014.09.0310920-4105/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author.E-mail addresses: Christian.Olsen@hess.com (C. Olsen),

skabir@hess.com (C.S. Kabir).

Journal of Petroleum Science and Engineering 124 (2014) 60–71

Although useful, a time-lapse approach may be insufficient tounderstand the evolving nature of a flood with dynamic analyticaltools complementing numerical modeling. More recently, Kabirand Boundy (2011) showed the benefits of integrating variousanalytical tools to understanding the nuances of reservoir behaviorduring history matching with a grid-based model. The use of ratetransients often provides important clues about a reservoir'sperformance. In fact, the notion of reservoir management canrevolve around many elements of RTA, as discussed by Kabir et al.(2011a), among others. Stated differently, possibly the full strengthof multiple analytical tools has remained unexplored.

The ensemble of tools used in this study includes a numericalsimulation model and a number of analytical methods to complementlearning. These analytical tools include, among others, a CRM analysis(Sayarpour et al., 2009a, 2009b) for injector/producer connectivity, aRPI plot (Kumar, 1977) for assessing degree of pressure support or lackthereof, a WOR plot (Yortsos et al., 1999) for understanding displace-ment, a modified-Hall analysis (Izgec-Kabir, 2009) for discerningmatrix injection fromwaterflood-induced fracturing, a RTA to estimateconnected pore-volume, and a DCA to obtain an independent under-standing of reserves recovery. Results of these analyses were aug-mented by both 4D seismic and tracer testing. Given that even a goodhistory-matched model may forecast less than satisfactorily because ofinherent uncertainty rooted in history matching (Tavassoli et al.,2004), new approaches must be explored to improve our under-standing of physical mechanisms governing fluid flow. Fig. 1 capturesthe workflow used in this study.

2. Background

Understanding and managing waterflood performance is key tooptimizing production and maximizing reserves. Water injection intochalk has a long and successful track record; good recovery fromthis type of rock has been reported (Hallenbeck et al., 1991, Ovens etal., 1998, Austad et al., 2008). Water injection in low-permeabilitychalk generally occurs above the fracture-propagation pressure. The

challenge is to inject high-volumewater into thematrix without watershort-circuiting into the nearby producers.

The South Arne field has been in production since 1999. Waterinjection started in 2001. The field is presently developed with 25wells, 16 producers, and 9 injectors in a line-drive pattern. The fieldhas been developed with horizontal producers and injectors, eachcompleted with a number of transverse hydraulic fractures. Waterinjection occurs directly into the oil zone and the mobility ratio isfavorable for a waterflood. Fit-for-purpose tools are brought to bearto address specific issues. To focus on typical issues encountered inthis field, this study evaluates the water injection performance ofone area, as shown in Fig. 2. Two producers, SA-5 and SA-16, which

Fig. 1. Flow chart for surveillance and analysis workflow.

Fig. 2. Well locations in the study area.

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are supported by the SA-8 up-flank injector and the SA-11 down-flank injector, are identified in Fig. 2.

The following sections discuss the well performance. These sec-tions include (1) performance diagnosis of production data withanalytical tools, (2) analysis of measurements, such as tracers, produc-tion logs, and 4D seismic, and, (3) modeling with decline curves, RTA,CRM, and numerical-flow simulations. Appendix A summarizes theattributes of various analytical tools used in this study.

3. Performance diagnosis with analytical tools

The study area is being drained by the producers SA-5 and SA-16 with water-injection support from the two injectors, SA-8 andSA-11. In general, changes in well performance are controlled bythree main groups of events: changes in pressure support, scalebuildup in wells, and well interventions. However, changes in wellperformance due to changes in pressure support and near-wellbore effects are not readily apparent from production perfor-mance data alone. This is why diagnostic plots are useful and aidhistory matching with numerical models.

Fig. 3 depicts the SA-5 well's production performance. Theinitial production period is pure depletion, as evident by therapidly declining oil rate and increasing GOR, without any waterproduction. The early water injection period is characterized byincreasing oil production, rapidly declining GOR and slowlyincreasing watercut. Thereafter, the declining oil rate with increas-ing watercut is readily apparent, and the flat GOR performancesuggests good overall pressure maintenance. However, to learn theperformance subtleties, diagnoses are needed. Fig. 4 depicts theRPI plot that shows the chronological events of depletion drive atthe start (with positive slope), followed by overinjection (sharplydipping negative slope), finally leading to a gently increasingpositive slope, signifying a void replacement of less than one.Both of the injectors' performances are shown in Fig. 4 to gaininsights into the overall RPI response.

Judging by the SA-5 well's WOR response, interaction withneighboring producer SA-16 becomes readily apparent. As Fig. 5shows, when the SA-16 well starts producing, the WOR responsedrops markedly because a fraction of water begins to support thevoid created by the new producer. However, one observes anincreasing WOR trend at a steeper slope, thereby suggesting adifferent flow path in redistribution of the energy support.Reassuringly, matrix injection is suggested by a greater-than-the-unit-slope-line response in all cases. The unit-slope line is indi-cated by the magenta line in Fig. 5.

Fig. 6 shows the production history of the SA-16 well. Thewatercut development is significantly different from the SA-5 well.However, the increase in GOR is probably related more to thewrong allocation of the gas-lift gas than to the breakout of gas inthe formation around the well. Given the significant rise in thewatercut response with the precipitous decline in oil rate, waterinjection appears to be the main reason for this behavior. Theincrease in WOR could be related to a reduction in SA-8 waterinjection starting in mid-2007.

The ever-increasing slope in the RPI plot (Fig. 7) that includesboth the total liquid and the oil clearly demonstrates the lack ofpressure support. This point is further corroborated by the WORresponse, shown in Fig. 8. The unit-slope response suggests a lackof oil bank displacement by the injected water. Collectively, Fig. 5through 7 suggest that the interaction between the SA-16 andSA-5 producers and the injectors evolves dramatically when theproduction begins in the SA-16 well. To arrest the precipitousdecline in oil rate with an increasing watercut, a plug is placed atthe toe of the SA-16 well. The benefit of this action is demon-strated in the WOR response when the steep slope develops,indicating oil displacement rather than water circulation. How-ever, benefits of this successful well intervention appeared shortlived when the injection rate at the SA-8 well was reduced afterabout six months. The WOR response began to flatten and the oil-

Fig. 3. SA-5 well's production performance.

Fig. 4. SA-5 well's RPI provides an evolution of pressure support.

Fig. 5. SA-5 well's WOR response suggests a redistribution of the injectors' energysupport.

Fig. 6. SA-16 well's production performance.

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PI began to decline. These wells illustrate the complexity ofproducer-producer and producer–injector interactions, which wewill discuss in the context of CRM analysis.

We observed the oil-cut semilog graph to be a useful discrimi-nating tool. The change in the decline trend in the oil-cut plot inFig. 9 is probably related to the injection rate reduction at the SA-8well as shown in Fig. 4, and its strong connectivity with the SA-5producer. Stated differently, when injection is reduced, propor-tionally more water appears to go into the short-circuit mode,thereby reducing the amount of oil being swept. The injector/producer connectivity was learned through the CRM study, asdiscussed in the context of DCA. Fig. 4 also suggests that theinjection rate at the SA-11 well was relatively stable and, therefore,its effect is not readily apparent on the decline plot.

Fig. 10 suggests that a shift on the oil-cut plot in the exponen-tial or log-linear trend occurs when injection at the SA-8 well isreduced. In addition, another shift in the decline trend occurswhen the plug is placed at the toe of the SA-16 well, which

reduces the water short circuit. Later, when the watercut exceeds90%, the decline trend becomes hyperbolic, as discussed in thenext section. Initially, a water short circuit dominates the watercutdevelopment, meaning that water flows separately from the oil.However, at a later stage, matrix breakthrough occurs and thefractional-flow curves begin to influence the decline. Deviationfrom the exponential decline is observed.

Perhaps the modified-Hall plot of the SA-8 injector sheds someuseful perspective, as shown in Fig. 11. The initial cumulativeinjection of 15 MMSTB appears event free, as indicated by the Hall-integral derivative overlaying on the integral curve. Subsequently,the ever-increasing flow impediment is indicated by the contin-uous separation of those two curves; the attendant decliningflowing-BHP trace simply reaffirms that notion. In particular, thereduced injection around 60 MMSTB cumulative injection coin-cides with reduced performance of the producers, as shown inboth Figs. 8 and 9.

4. Analysis of tracer, production logs, and 4D seismic data

To gain further insights into the well behavior, both tracer testsand production logs were run. Tracer campaigns have beenconducted several times over the field life at a frequency of everythree to four years. In a typical operation, chemical tracers arepumped into the injectors and the response is monitored at theproducers. Historically, a wide range of responses has beenobserved in producing wells. Overall, the total recovery of traceris low because of high imbibition potential of water-wet chalk, asexpected in this type of reservoirs. Nonetheless, for this study thetracer tests added invaluable information regarding the connec-tivity of producer–injector pairs through short circuits and tosome degree its strength, as reflected in the breakthrough time.

Fig. 12 shows very early tracer breakthrough times of two to sixdays for the wells. Note that these breakthrough times are not

Fig. 7. SA-16 well's total liquid’s RPI provides evidence of the lack of pressuresupport.

Fig. 8. SA-16 well's WOR response suggests the lack of oil displacement for about1000 days.

Fig. 9. Changing decline in the SA-5 well.

Fig. 10. Changing decline in the SA-16 well.

Fig. 11. Modified-Hall plot shows increasing injection difficulty in the SA-8 well.

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intuitive given the physical distances between the wells. Forexample, tracer breakthrough from the SA-8 injector to the SA-16 producer occurred in two days, whereas tracer breakthroughfrom the SA-8 injector to the SA-5 producer occurred in five days,even though the tracers had to travel a larger distance for theformer pair.

Production logs run in the SA-16 well in March 2005 showed thatmost of the water was being produced from the toe. Fig. 13a showingthe shut-in pass indicated significant crossflow in the well, withwater influx originating from a high-pressure zone at the toe. In June2009, a production log in the SA-5 well showed that the bulk of thewater was being produced from the three toe zones closest to thefault, as shown in Fig. 13b. These PLT observations are largelysupported by those from 4D seismic, as discussed next.

Two 4D seismic surveys conducted in 2005 and 2011 providedconsiderable insights into the fluid flow directions in. As shown inFig. 14, the normalized root mean square (NRMS) maps can beconstrued as a qualitative analog for the saturation changes in thereservoir due to water injection. These surveys indicate that aconductive flow path exists between the SA-8 injector and the toearea of the SA-5 producer, and follows the fault system to the toeof the SA-16 producer. When the SA-16 well starts producing, itdeprives the SA-5 well of water in the short term by connecting tothe fault system. However, when the SA-16 well continuesproduction, fault/fracture system depressurization occurs. As aconsequence, water appears to short-circuit from the SA-8 injectorto the SA-5 producer, thereby explaining the more rapid increasein watercut than before. These observations align with thosediscussed earlier regarding the interpretation of tracer andproduction-log data.

Fig. 15 displaying the difference map shows the saturationchanges that occurred between 2005 and 2011, indicating thatwater production in the SA-16 well continued during this period atthe heel of the well. In other words, the fault system transmittedsignificant amounts of injection water from the SA-8 well to theSA-16 producer.

5. Well performance analysis

In this section, the study analyzes production and injectiondata to understand reservoir performance, leading to recoverypotential. This section discusses the traditional DCA and RTAbefore introducing the CRM and numerical-flow simulationresults. The objective is to seek consistency in solutions withdifferent tools.

5.1. Rate-transient and decline-curve analyses

Fig. 16 suggests that the SA-5 well undergoes variable-pressureand variable-rate production history. The initial primary depletion,followed by injection support and the two-phase productiondominate the performance. An approximate history matching ofthe injection period considering a closed system suggests anacceptable match. The intrinsic idea was to get a glimpse of theoverall reservoir performance. In this context, let us point out thatthe precipitous decline in both rate and pressure during the first1000 days or so signify compaction of the chalk formation. Forsimplicity we avoided this flow period to minimize modelinghurdle with analytical tools.

To get a perspective on well behavior before significant waterproduction occurred, we plotted the integral of reciprocal-productivity index and its derivative against material-balancetime, as shown in Fig. 17. Understanding the flow regimes wasimportant in that 12 stages of propped transverse fractures werecreated in this 5500-ft horizontal well. The designed half-lengthsof the propped fractures vary from 200 to 400 ft, and theestimated formation permeability along the well length rangesfrom 3 to 14 md. Given this completion scenario, we observe linearflow, followed by the unit-slope response. The duration of linearflow is governed by the fracture spacing, whereas the unit-sloperesponse signifies the stimulated-reservoir volume (SRV). Inter-estingly enough the overall response is akin to those observed inunconventional wells, as shown by Kabir et al. (2011b) and

Fig. 12. Depiction of tracer breakthrough times for the injector–producer pairs.

Fig. 13. Shut-in (a) and flowing (b) log passes show contrasting behavior ofwater flow.

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Freeman et al. (2009), among others. Note that the SRV does notimply reservoir boundary; rather, the imaginary ellipsoidal flowgeometry, which is a manifestation of fracture stimulation. Thisvolumetric-SRV response appears to suggest that the water pro-duction occurs over limited well length, thereby raising questionsabout the volumetric sweep efficiency. In fact, this volumetricresponse is in harmony with the Arps model where the b value ofzero is calculated, indicating exponential decline behavior.

By considering the first 3.5-year history, the late-time cumulativematch results in harmonic decline behavior as characterized by the

Arps exponent b of 1.0, as Fig. 18 illustrates. However, an exponentialdecline (b¼0) sets in toward the end as flood maturity occursbeyond eight years, as the right side of Fig. 18 shows. This changein performance characteristics reveals the extrapolation limits ofdecline curves due to continuous changes in saturation and pressurethat occur in most waterflood operations. However, this study didnot pursue the conventional RTA due to the complicated productionhistory with rapidly changing saturation as signified by increasingwatercut. Modeling both the saturation and pressure changes is bestdone with a numerical-flow simulator, which is discussed later. Thevalidity of the Arps model in mature waterfloods has been shownrecently by Can and Kabir (2014).

Fig. 14. Saturation changes support the notion of well connectivity and flow through conductive paths.

Fig. 15. Saturation changes demonstrate the conductive flow path between the SA-8 injector and the SA-16 producer.

Fig. 16. Approximate history matching of the SA-5 well's late-time performance.

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Unlike the SA-5 well, the SA-16 well lent itself to an improvedRTA because the water production was not tied to fluid displace-ment, but channeled along a fault plane. Fig. 19 presents RTA of theSA-16 well's production analysis, except for the very early partcontaining 1.7 year's material-balance time. The primary reasonfor neglecting the early data originated from the notion of doingDCA for the stable flowing-BHP period. That way the study couldcompare and contrast the RTA and DCA solutions. Anothermotivation for avoiding the early-time data for about 500 daysstemmed from the sharp decline of both pressure and rate inFig. 19 is attributed to compaction. This point was made earlierwhile discussing SA-5 well's response in Fig. 16. The DCA in Fig. 20indicates an exponential decline with b of 0.0 at late times.

Producer SA-16 was completed with nine transverse-fracturestages in a 2500-ft lateral. This well is in inferior section of thereservoir with an estimated formation permeability not exceeding1 md. As Fig. 21 suggests, the SA-16 well exhibits flow regimes thatare similar to that of the SA-5 well. The unit-slope responsesignifying the SRV response indicates lack of oil displacement orvolumetric behavior, a point made earlier by Fig. 8. We surmisethat severe water short-circuiting precipitated this volumetricresponse.

5.2. Capacitance–resistance modeling

The CRM captures injector–producer connectivity in a multi-wall system using flow rates and the flowing BHP, if available.Many studies have reported CRM's successful application in a widearray of reservoirs of different degrees of complexity. Some ofthese examples include horizontal wells in a naturally fracturedsandstone reservoir (Kabir and Boundy, 2011), water and CO2

floods in carbonate reservoirs (Sayarpour et al., 2009b), inter-and intra-reservoir connectivity in a complex sets of reservoirs

(Parekh and Kabir, 2013) and strong aquifer influx in a sandstonereservoir (Izgec and Kabir, 2010), among others. Here, the study'smain objective was to obtain a connectivity map or fractional flowbetween the injectors and producers and corroborate the resultswith tracer and other measurements. The secondary objective wasto obtain a general agreement of the tracer breakthrough timewith the time constant associated with each injector in the CRM.

Fig. 17. SA-5 well's flow regimes mimic those in unconventional formations.

Fig. 18. DCA of the SA-5 well.

Fig. 19. RTA of the SA-16 well suggests a decent overall match after the initialperiod.

Fig. 20. DCA of the SA-16 well.

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Fig. 22 shows a quality history match of the total reservoirliquids (oil and water) on the left and a less-than-satisfactorymatch of the oil rate profile on the right. Because the materialbalance is based upon the total fluid, a good match is expected.However, the early time oil match suffers because of the use of anempirical power-law model to split the two phases, as shown bySayarpour et al. (2009a,b). The oil-rate match improves withincreasing water-cut because the power-law model works bestwhen the water-cut exceeds 50%.

Table 1 shows the well connectivity in terms the water'sfractional flow from an injector to the relevant producers. Forexample, the SA-5 producer receives either 40% of the injectionsupport from each of SA-11 and SA-8 injectors, or 80% of thetotal. This fact implies that void replacement is less than ideal.By contrast, the SA-16 producer receives only a total of 10% ofthe injected water from the SA-8 injector. As discussed earlier,most of this water production at the SA-16 producer occurredthrough a conductive flow path. Although most of the indivi-dual injectors' total contributions were accounted for, SA-11was exception to this rule, meaning about 20% of the injectedwater went outside the control volume. While fractional-waterinjections toward each producer (or fij's) in Table 1 are useful inunderstanding flow direction, the other parameter, time con-stant τ, can shed light on the breakthrough time. The compar-ison of breakthrough time with tracer survey is generallyfavorable, but a large discrepancy surfaces for the SA-11/SA-5pair. Although the tracer was detected after 14 days, theconnection appeared weak compared to other wells. Becausethe CRM formulation is predicated upon signal analysisbetween the injector/producer pairs, the SA-11/SA-5 shortcircuit is too weak to be detected by the CRM, thereby explain-ing the large discrepancy. Our general observation is that whenthe CRM and tracer results are in agreement, the water shortcircuit is significant; otherwise, the effect of the short circuit islimited.

5.3. Reservoir-flow simulation

A full-field, numerical-flow simulation model was used tounderstand the overall field performance. The flow-simulationmodel is a black-oil, single-porosity model with approximately600,000 cells. The areal dimensions of the grid cells are25�75 m2, and the 25 m cell dimension is dominant from injectorto producer. At a typical well spacing of 300 m, this cell issufficient to trace the main waterfront moving from an injectortoward a producer. The fluid system is modeled with a single PVTtable, which appears sufficient in matching production perfor-mance. Compartmentalization is not considered an issue becauseall producers appear to be impacted by the neighboring injector.Saturations and matrix permeability are closely related to porosityand are modeled as such. The model is computationally efficientand is able to capture the overall reservoir performance quite well.However, local features with significantly different flow propertiesthan the field will, in some cases, dominate individual wellbehavior. Incorporating those features directly in the simulationgrid will make the model computationally inefficient. Besides, theproperties of these features cannot be measured directly, but canonly be inferred indirectly, for example by tracer surveys.

The reservoir was modeled as a single-porosity system becausethe fractures appear limited in areal extent and are related tospecific geological features. This strategy allowed local enhance-ment of permeability to model the fracture system, therebyfinessing the field-wide dual-porosity modeling. Overall, theindividual well performance was well matched. However, model-ing of the water short circuits presented a challenge. As Fig. 23illustrates, those short circuits were modeled by positioning acompletion from the injection well in close proximity to aproducer. This approach turned out to be computationally efficientin matching the watercut performance, but at the expense of BHPand GOR matches. The reasons for the unsatisfactory matches aretwo-fold: firstly, the injectors were in close proximity to theproducers; secondly, the pressure-drop along the fault/fracturezone, responsible for creating the water short circuits, wasneglected. The SA-16 producer experienced significant shortcircuiting and, consequently, both the BHP and GOR matchessuffered, as Fig. 24 illustrates. In contrast, Fig. 25, showing theSA-5 well match of both BHP and GOR, is significantly betterbecause of the water short circuits marginal impact.

Fig. 21. SA-16 well's flow regimes suggest volumetric behavior beyond 1000material-balance days.

Fig. 22. CRM analysis shows a good overall match and an acceptable oil-rate match at high water-cuts.

Table 1Injector–producer connectivity and breakthrough times of CRM compared withthose of tracers.

Well Pair fij Tracer 2004 days CRM 2004 days

SA8Z SA5 0.4 5 3SA11ZSA5 0.4 14 300SA8ZSA16 0.1 1 1SA11ZSA16 0.3 Not detected 180

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Fig. 23. Depicting water short-circuits near the SA-16 and SA-5 producers on a saturation map.

Fig. 24. SA-16 well performance matching with numerical-flow simulations.

Fig. 25. SA-5 well performance matching with numerical-flow simulations.

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Obtaining a good match on a well with a high degree of shortcircuiting presented a challenge. The methodology used here did notprovide a perfect representation of the physical process in thereservoir, as seen from the match of BHP and GOR in the SA-16producer. This approach worked reasonably well in the case ofmoderate water short-circuiting. However, complicated methodsare hard to develop given the lack of specific information on theflow characteristic of water short-circuits. One such possibility is theinjector–producer connectivity of high-permeable grid cells, but thatapproach did not necessarily produce a better match or more robustpredictions of development in the watercut trend and futureperformance.

6. Discussion

In traditional methods for evaluating waterflood performance,such as with the 1D Buckley–Leverett model and the 3D numerical-flow simulator, sweep efficiency and breakthrough time are mainlycontrolled by the fractional-flow curves, encompassing relativepermeability and fluid viscosities. However, in a chalk reservoirwith water injection above the fracture propagation pressure in anatural fault/fracture system, the extension and connectivity of thehydraulic and natural fractures control the initial response to waterinjection. Only when the waterflood reaches a mature state andmatrix breakthrough occurs that the fractional-flow curves begin toinfluence a flood's performance. Therefore, ongoing surveillanceand data interpretation becomes crucial to understanding wellresponse and on-time reservoir management.

As outlined in this paper, a number of methods are available forevaluating and optimizing a waterflood. Each method has itsrelative advantage; however, when used in combination, they canprovide a consistent understanding of the physical mechanismscontrolling a waterflood. All the analytical tools are computationallyinexpensive and, therefore, allow for frequent performance updates.Diagnostic plots, CRM, and DCA belong to this category. Generally,these tools are good at detecting changes in well performance.However, understanding the underlying reasons behind thoseobservations can be difficult. In this context, physical measurementssuch as tracers and production logs are expensive, but they addadditional details on what is happening in specific wells and guideappropriate well interventions. In this context, we explored thepossibility of applying some of Yang's (2012) diagnostic tools. But,they did not perform well in light of minimal displacement processthat underpins some of the wells discussed here.

Although 4D seismic and tracers have a low-sampling frequency,they illuminate the interaction betweenwells. In particular, 4D seismiccorroborates the underlying physical mechanisms for the observationsmade from the diagnostic plots and decline curves, thereby enhancingthe value of those diagnoses. Contrary to expectation, grid-basedmodels are not well suited to predict water breakthrough in thesereservoirs. Although matching the general well behavior is feasible,efficient methods for ascertaining water short circuits are needed.Overall, the combination of analytical tools and grid-based models, aswell as periodic surveillance with 4D seismic, has collectively helpedcreate an understanding of waterflood performance. In this regard, it isa new finding that faults can act as flow conduits for the injectionwater and distribute water over large distances. Geomechanics-basedflow simulations with fine grids may be needed to bridge this gap, asdemonstrated by Pettersen and Kristiansen (2009).

The insights gained will guide future development and implemen-tation of water injection in the field with regard to the positioning ofhydraulic fractures in the future injectors by keeping a safe distancefrom the faults. This step potentially minimizes the risk of connectingan injector directly with a producer, thereby mitigating the watershort-circuiting and increasing the intrinsic value of water injection.

Furthermore, interventions are being considered for the existing wellsfor improving the volumetric sweep by way of shifting the slidingside-doors based on the improved understanding of reservoirdynamics discussed in this study.

7. Conclusions

(1) The complexity of fluid flow in a chalk reservoir can bebetter understood by on-time interpretation of real-time rate/pressure surveillance data, with support derived from periodictracer tests, production logs, and 4D seismic surveys.

(2) This study underscores the importance of the use ofanalytical tools, such as RTA, CRM, and DCA for holistic analysis,with appropriate support derived from diagnostic tools, such asRPI, WOR, and modified-Hall plots.

(3) Although numerical-flow simulations provide an under-standing of the overall reservoir performance, nuances, such aswater short-circuits through the fault planes, must be learnedabout independently with surveillance data. In this regard, asatisfactory history match of watercut, GOR, and BHP remainedelusive on an individual-well basis.

Acknowledgments

The authors express their gratitude to the partners of SouthArne (DONG Energy and Danoil Exploration A/S) and the Hessmanagement for permission to publish this study.

Appendix A. Summary of various analytical tools

RPI plot. Kumar (1977) developed an analytical model to showthat the reciprocal-productivity index (RPI) plot is useful inunderstanding the degree of pressure support, either from anaquifer or from an injector. His formulation in dimensionlessvariables is given as

pD ¼ 12ln

4A1:781 CA r2w

4f� �� �

þ2π 1� fð ÞtDA ðA� 1Þ

where

pD ¼ kh141:3qBμ

pi�pwf

� �ðA� 2Þ

and

tDA ¼0:000264kt141:3qBμ

ðA� 3Þ

Eq. (A-1) with real variables suggests that a plot of (pi�pwf)/qversus producing time t yields a straight-line relationship with aslope of (1� f), where f denotes the degree of pressure support.When performances of different producers are plotted together, thistool readily provides clues about the degree of pressure supportreceived at each producer. This tool has been used with good degreeof success in understanding waterfloods, such as that discussed byParekh and Kabir (2013), among others. Given its analytical roots, itappears quite robust and no known limitations have been encoun-tered so long the bottomhole pressure is available.

WOR plot. Yortsos et al. (1999) identified four flow regimes onthe log–log plot of water–oil ratio (W) versus producing time (t), asshown in Fig. A-1. Depending on reservoir heterogeneity, the firstflow period (i) may show slow increase in the water–oil ratio, W.Following the water breakthrough, steep increase in W occursduring the second flow period (ii), exceeding the unit-slope line.Ordinarily, the unit-slope line signifies very inefficient displace-ment of oil by water, meaning a high-permeability streak conducts

C. Olsen, C.S. Kabir / Journal of Petroleum Science and Engineering 124 (2014) 60–71 69

preferential water flow. The flow behavior during the third period(iii) suggests that the slope will always be less than one becausethe slope is N/(Nþ2), where N reflects characteristic of the wellpattern or polarity. Finally, during the late-time period (iv), thefinal asymptotic behavior of a bounded system is reflected and isrepresented by a straight line, which may written as

log W � bb�1

log tþH ðA� 4Þ

where b is the exponent of the power-law method, and H is aconstant.

This tool has been used with good success in many documen-ted studies, Kabir and Young (2004), for example. In particular, thelack of frontal displacement manifests in terms of unit-sloperesponse, which allows one to search for probable cause. Despiteits semianalytical roots, no known limitation of this tool hassurfaced.

Modified-Hall plot. The modified-Hall plot helps diagnosematrix injection or lack thereof using both the Hall integral andits derivative. The expression for the Hall integral (Izgec and Kabir,2009) is given byZ

pwf �pe� �

dt ¼ 141:2WiBμkh

lnrerw

�0:5þsn� �

ðA� 5Þ

where pwf is the flowing bottomhole pressure and pe is oil/waterinterface pressure of the moving front and is written as

pe ¼ pwf �iwBμ2πkh

r2or2o�r2w� ln re

rw�12

r2e �r2w� r2o�r2w� þsn

" #ðA� 6Þ

The analytical derivative of the Hall integral is given by

DHI ¼ α1Wi ln re=rw� þsn

� ðA� 7ÞThis tool was intended for vertical wells. Therefore, the notion

of water/oil interface pressure at the moving boundary pe is invalidfor horizontal wells. Nonetheless, this diagnostic tool is quiteuseful because only the quality of injected water is being diag-nosed with indication of progressive plugging in this situation.

Decline-curve analysis. The decline-curve analysis is a corner-stone of reservoir-performance prediction tool. Rooted in Arpsrelation and shown recently about the tool's effectiveness inpredicting performance in waterfloods (Can and Kabir 2014), thehyperbolic relation is given as

qo ¼qoi

1þbDitð Þ1=bðA� 8Þ

where qo is the time-variant oil rate, qoi is the rate parameter, t istime, Di is the initial loss ratio, and b is the decline parameter,which varies between zero and one. This tool is used here to get anindication of flood's effectiveness, rather than seeking the cus-tomary expected oil recovery. To that end, the late-time exponen-tial behavior provided the necessary clues about the boundary

condition of the stimulated-reservoir volume, as observed on thelog–log plot of rate-transient analysis.

Rate-transient analysis. Rate-transient analysis (RTA) providesevolving reservoir pressure and the connected pore-volume infor-mation. The log–log diagnostic plot entails graphing rate-normalized pressure difference; that is, (pi�pwf)/q versus thematerial-balance time, Np/q. When combined with the derivativeof rate-normalized pressure difference, the two curves provide thenecessary ingredients for understanding the overall systemresponse. This formulation permits system diagnosis in terms oftransient-pressure analysis. In general terms, in this horizontalwell configuration with transverse fractures, both the half-slope(signifying linear flow) and unit-slope (suggesting stimulated-reservoir volume) responses are expected to develop, as Figs. 17and 21 suggest.

Capacitance–resistance modeling. Combined rate/pressure dataanalysis with the capacitance–resistance model (CRM) providesquantitative measures of injector–producer connectivity. Premisedin material-balance and signal analysis, the CRM has been used forabout a decade in the context of injector/producer connectivity forunderstanding waterflood performance. Yousef et al. (2006),Sayarpour et al. (2009a), and Weber et al. (2009) have providedfoundation to this CRM tool, whereas other authors have shownpractical applications in various settings for waterfloods (Kavianiet al., 2012; Izgec, 2012, Parekh and Kabir, 2013), CO2 floods(Sayarpour et al., 2009b, 2011), and beyond (Izgec and Kabir2010), among others.

For a pattern of Ni number of injectors and Np number ofproducers, the governing differential equation for this capacitancemodel is written as (Sayarpour et al., 2009a:

dqjðtÞdt

þ 1τjqjðtÞ ¼

1τj

∑Ni

i ¼ 1f ijiiðtÞ� Jj

dpwf ;j

dtðA� 9Þ

where the producer j's time constant, τj, is defined as

τj ¼ctVp

J

� j

ðA� 10Þ

If we assume linear changes between two consecutive injectionrate and BHP during time intervals Δtk (tk�1 to tk), at time tn, thetotal production rate of producer j can be written as:

qjðtnÞ ¼ qjðt0Þe�ðtn � t0

τjÞ þ ∑

Ni

i ¼ 1f ij iiðtnÞ�e

�ðtn � t0τj

Þiiðt0Þ

� � �

� ∑n

k ¼ 1τje

�ðtn � tkτj

Þ1�e

�ðΔtkτjÞ

� ∑Ni

i ¼ 1f ijΔikiΔtk

þ JjΔpkwf ;j

Δtk

" #( )

�ðj¼ 1;2; :::;NpÞ ðA� 11ÞIn Eq. (A-11), Δii

ðkÞand ΔpðkÞwf ;j represent change in injection rateof injector i and BHP of producer j during time interval tk�1 to tk,,respectively. Stated simply, the solution of Eq. (A-11) can be soughtin spreadsheets by minimizing an objective function that containserror between the model and rate data by constraining modelparameters, fij and τj.

Although many successful field cases have been reported, thesolution quality suffers when production and/or injection rates donot contain sufficient signal quality; that is, relatively flat rateswithout much variations. As expected, the uncertainty in rateallocations to individual wells may also cloud the solutionoutcome.

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