SPE-171671-MS

Understanding Water Flood Response in Tight Oil Formations: A CaseStudy of the Lower Shaunavon

Adrian Thomas, Anjani Kumar, and Kenny Rodrigues, Computer Modelling Group Ltd.; Ryan Sinclair,Colin Lackie, Angela Galipeault, and Mike Blair, Crescent Point Energy Corp.

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE/CSUR Unconventional Resources Conference - Canada held in Calgary, Alberta, Canada, 30 September –2 October 2014.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

The evolution of producing resource plays in Saskatchewan Canada has gained momentum in the last 10years. Many new tight formations in Western Canada have been discovered or are now economic to bringon production due to the emergence of horizontal drilling and hydraulic fracturing technologies. One playgaining momentum over the last few years has been the Lower Shaunavon located in the south westquadrant of Saskatchewan. Through learning’s from tight oil plays, such as the Bakken, Crescent Pointhas been able to apply some of the development strategies to the Lower Shaunavon; however, there is stilla large factor of uncertainty and risk involved in these tight formation plays. Reservoir modelling can beused as a tool to reliably forecast well performance and reduce future risk and uncertainty.

An eighteen well numerical simulation model was built to represent Crescent Point Energy’s LowerShaunavon waterflood pilot area. Numerical simulation was used as a tool to obtain a better understandingof the reservoir and hydraulic fracture parameters in the area along with waterflood response in the tightoil play. A history match on the pilot area was performed. Using parameters obtained from the historymatch, a representative model was built and a sensitivity study was performed on hydraulic fracturespacing and well spacing in both primary depletion and waterflood scenarios. This paper will discuss theworkflow, challenges, and general findings related to waterflood performance on Lower Shaunavon.

While industry continues to study and optimize hydraulic fracturing decisions, the combination of thesedecisions with IOR potential, namely waterflooding tight oil plays, needs to be understood. Developinga workflow that enables optimization of both fracture completions (spacing, half lengths, etc.) and waterinjection schemes may lead to a more complete approach to maximizing asset value.

IntroductionCrescent Point Energy entered into the Shaunavon area initially by drilling a vertical strat well in township10, range 20 west of the third meridian in southwest Saskatchewan. The company further expanded intothe region with the formation of Shelter Bay Energy in which Crescent Point held a 21% working interest.The company’s interest grew even larger with the acquisitions of Wild River Resources, GibraltarExploration and Wave Energy in 2009.

Initially, only one initial horizontal well was injecting into the Lower Shaunavon during 2009 and ithad only been operational for approximately one year. Results and conclusions from the influence of theinjection scheme were premature at best. Crescent Point continued to monitor the performance of theoffset wells for signs of increased reservoir support from the water injection. Due to the infancy of welldevelopment in the Lower Shaunavon at the time, additional producer to injector conversion opportunitieswere limited. As positive influences were observed from the original injector, additional horizontalinjection was implemented in other areas of the play in 2010 as horizontal development progressed.

Waterflooding the Lower Shaunavon provided encouraging initial results and is still the most eco-nomical method of secondary recovery for oil reservoirs. Many challenges pertaining to other secondaryrecovery techniques were encountered due to geographical location, infrastructure and actual fieldapplication. Gas injection and CO2 flooding could have been promising, but would have taken many moreyears to implement in comparison to waterflooding.

Currently, Crescent Point has 24 horizontal injectors injecting into the Lower Shaunavon with plans toincrease the total injectors to approximately 40 by the end of year 2014. To date, the company is verypleased with the waterflood response in the offset producers and has observed positive results in all of itswaterflood projects and pilots. This study will focus on Crescent Points Lower Shaunavon Waterfloodpilot area consisting of 18 wells and 1 water injection well.

GeologyThe study area is within the Lower Shaunavon oil resource play in south west Saskatchewan. The middleJurassic Shaunavon formation was deposited as a result of a drop of sea level followed by a transgression.It is bounded by marine shale of the underlying Gravelbourg and capped by the Lower Vanguard seasediments.

The Shaunavon is partitioned into a Lower and Upper Member. The Lower Member is an authigeniccarbonate shelf while the Upper Member has a strong clastic influence from the west. Oil is trappedhydro-dynamically; the oil fairway crosses both stratigraphic and structural trends.

Figure 1—Type Well Geologic Intervals

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The Lower Shaunavon is divided into four inter-vals in the study area (see Figure 1).

The lowest interval is a calcareous cryptocrystal-line mudstone. It was deposited in a deep waterlow-energy environment once the carbonate com-pensation depth was achieved. It is considered to benon-reservoir. Sitting above this interval is the BMarker which is a slightly more energetic environ-ment; the mudstone is cryptocrystalline to micro-crystalline, but does contain some wackestonelenses that are likely storm deposits. The A Markermarks a regressive lag as a result of a sea level drop.It consists of wackestone to some packstone rockand is bounded above and below by mudstones. Theuppermost interval represents a high energy envi-ronment. It contains stacked shoals with texturesranging from mudstone up to grainstone. They pre-dominately contain ooids and peloids along with some fossiliferous debris. There has been somedolomitization, possible due to sub areal exposure.

The porosity types are cryptocrystalline, microcrystalline, intergranular, small vugs and some fractureporosity seen in core. All but the cryptocrystalline porosity was observed to have oil staining. Pay can be

Figure 2—Lower Shaunavon Pilot Area - Top View

Figure 3—Logarithmically Spaced Local Grid Refinement around Hy-draulic Fractures with High Permeability Blocks

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Figure 4—Cumulative Volumes for History Match Pilot Area

Figure 5—Injectivity Comparison for Hydraulic Fracture Breakthrough of Shale Barrier

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as thick as 22m; one cored section has over 16m of oil stained rock. Porosity generally ranges from14-18%. Digenesis has kept decent porosity, but constriction of pore throats means the matrix permea-bility is generally well below 1 mD. In some areas the permeability has been enhanced by localdolomitization and natural fractures.

The presence of oil within the Lower Shaunavon has been known for a long time, with some productionbeing achieved as early as 1953. There were sporadic successful wells through the years, but these weremainly found when exploring and developing the more conventional Upper Shaunavon reservoirs. Severaloperators attempted horizontal wells in the mid 90’s but the poor inflow discouraged further development.In 2006, Wave energy Ltd. drilled the first Lower Shaunavon well in the study area at location191/09-15-009-19W3 using multi-stage horizontal fracturing completion technics. Since that time the playhas been developed extensively with horizontal fracturing.

Early on, Crescent Point recognized the potential to use its knowledge of horizontal technics from itssuccess in the Bakken and elected to transfer this knowledge to the Lower Shaunavon. Through landsalesand acquisition it has built a dominant position in the Shaunavon fairway.

Modelling Workflow DescriptionA geological model was developed for the Lower Shaunavon pilot area based on well logs, petrophysicaldata, and surface maps. The model was further developed into a dynamic simulation model by incorpo-

Figure 6—Block Model Forecast Patterns - Primary Depletion

Figure 7—Block Model Forecast Patterns – Waterflood

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rating PVT data, relative permeability, well trajec-tory, well completion, and historical well produc-tion and injection information for all wells locatedwithin the pilot area.

A history match was performed on a single wellsub model to obtain improved values of reservoirhydraulic fracture properties in the surrounding re-gion. These values were applied to the full pilot areaand the model was simulated in an attempt toachieve a history match. Once the pilot area washistory matched, prediction forecast runs of an ad-ditional 50 years were performed to gauge futureproduction along with future drilling scenarios. Us-ing the properties obtained through history match-ing, a new generalized model was built and differentforecast scenarios were run to determine well spac-ing under both primary depletion and waterfloodrecovery.

Reservoir Parameter SelectionProductivity in low permeability reservoirs is ex-pected to be largely influenced by parameters re-lated to the hydraulic fracture network. The fracturespacing of the individual wells contained within thepilot area remained fixed as they were set when thewells were originally completed. However, the un-certainty lies in the hydraulic fracture conductivityand hydraulic fracture growth. Characteristics ofhydraulic fracture systems seen in tight reservoirsare difficult to measure and highly complex tomodel.

Hydraulic fracture conductivity can vary spa-tially as well as in magnitude. A range of hydraulicfracture conductivities were investigated by per-forming a sensitivity study on a one well sub modelto obtain an estimate of parameters to apply to allwells during the history match phase.

Estimated reservoir properties were provided by Crescent Point Energy as a baseline for the simulationand were based on previous studies and log analysis. The reservoir was divided into 10 discrete layers witha range of thicknesses from 0.5m to 4m. Base reservoir properties were held constant aerially, but variedper vertical layer in the model. The model was built under the assumption that the vertical permeabilityratio to horizontal permeability was 10%. Initial estimates of permeability were in the micro-Darcy range;estimates of porosity were less than 20%; initial water saturation distribution was greater than 35%. Otherreservoir properties were held constant throughout the reservoir. Estimates of the reservoir parameters canbe found in Table A-1 in Appendix A. The reservoir pressure for the model was initialized abovesaturation conditions; therefore, no free gas was present initially in the model.

Figure 8—Block Forecast Element of Symmetry Model for 4 and 8Wells per Section

Figure 9—Block Forecast Element of Symmetry Model for 16 Wells perSection

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The PVT and fluid characterization was done by matching and tuning lab data using the equation ofstate (EoS) phase behavior and fluid properties software WinProp. The lab data was summarized in aReservoir Fluid Study performed in the Lower Shaunavon.

The available experiments for matching included:

● Compositional analysis of the separator oil and gas, plus calculated reservoir fluid composition

Figure 10—Block Forecast Full Section Model for 10 Wells per Section

Figure 11—Normalized Historical Liquid Rates vs. Primary Forecast Production

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● Multistage separator test● Constant composition expansion (CCE) test● Differential liberation (DL) test

The following steps were followed to develop and characterize the reservoir fluid:

● Characterize the hydrocarbon liquid by splitting the C30� component into 5 pseudo components● Tune the Equation of State (EoS) model to predict bubble point condition, separator GOR, CCE

test, and DL test for the reservoir fluid● Generate the simulator PVT model for blackoil simulation

The final tuned EoS model was used to create the PVT component data required for the blackoilsimulation model. The PVT table values are extrapolated to the pressure above saturation conditions andare based on the linear relationship between GOR, formation volume factor, and viscosity with density.

Simulation Model SetupA geological model was created before preforming numerical simulation. A single porosity model wascreated with 10 vertical layers representing the Lower Shaunavon pilot area. Layer 1 represented a highpermeability streak above the reservoir and layer 2 was defined as a shale barrier separating the higherperm streak from the Lower Shaunavon pool. 18 producing wells in which one well later converts to waterinjection were added into the model. Crescent Point Energy provided historical oil, gas, and waterproduction rates along with water injection rates for each well. No flowing pressure data was available atthe time of this simulation study.

Figure 12—Pilot Area 50 Year Forecast Cumulative Volumes

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To model hydraulic fractures in the simulation, the logarithmically spaced, locally refined, dualpermeability (LS-LR-DK) methodology was used. Using this methodology hydraulic fractures areexplicitly modeled in the matrix blocks by assigning high permeability values for the hydraulic fracturesand low permeability values for the tight reservoir matrix. Local grid refinement is defined around thehydraulic fracture blocks to accurately account for transient effects in the region encompassing thefracture network. By logarithmic spacing of the refinement, the reservoir is discretized to a finer degreearound the hydraulic fractures and more coarsely further away from the hydraulic fractures. This enablesfor quicker simulation run times without loss of accuracy.

Grid blocks where hydraulic fractures were encountered had a 5�5�1 (referring to the I, J, and Kdirections) local grid refinement applied at the perforations. The refined blocks along the center of theparent block were set to a width of 2 ft. These center blocks represent the hydraulic fractures. Theremaining blocks in the locally refined grid were logarithmically spaced away from the center blocks. Toconserve the fracture conductivity in the 2 ft wide grid block, a new effective permeability was calculatedas follows:

Due to the increased cross sectional area from using a larger block width, the velocity in the block willbe lower than the actual velocity in the fractures. Therefore, a non-Darcy correction factor had to beapplied so that flow resistance due to non-Darcy effect will be correctly calculated.

Figure 13—Pilot Area 50 Year Forecast Oil Recovery Factor

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History Match WorkflowA single well sub model was extracted from the pilot area to get a handle of the fracture properties. Thechosen well was picked based on the distance to adjacent wells and potentially limited effects from thewater injection well. It was observed though micro seismic data from hydraulically fractured horizontalwells adjacent to the pilot area that the produced fractures appeared to be bi-wing in nature. It was alsoobserved that micro seismic activity had been detected in all 10 vertical layers (approximately 20m) themodel incorporates. Therefore, it was assumed that the hydraulic fractures break through all 10 layers andconnect all layers of the model from the top of the model to the bottom where fractures are located.

Hydraulic fracture placement was provided by the Crescent Point and bi-wing hydraulic fractures wereinput into the model. Using the automated sensitivity analysis tool CMOST a variety of fracture halflengths, fracture width, and fracture permeability combinations were tried in an attempt to achieve ahistory match for the one well model. At times the gas production was not monitored; therefore, historymatching concentrated on matching withdrawals of oil and water and the gas production profiles heldlimited weighting to the effectiveness of the history match.

Once the fracture properties were found from the sub model, the results and information wastransferred to the full pilot area. A range of the most sensitive parameters were adjusted during the historymatch to reduce the error between historical production and the simulation results.

Bi-wing fractures were added to all wells with the exception of well Prod 8 at the perforation intervalsprovided by Crescent Point Energy. Well Prod 8 was not hydraulically fractured within the timeline of thissimulation study. Numerical simulation was performed on the base case and results were compared to thehistorical production. A match was not originally achieved with the main issues listed below:

– Initial water production too high when comparing to historical production– Initial production of oil and gas (when data available) was too low in comparison with historical

data– Low water injectivity into the reservoir

Figure 14—Oil Recovery Factor for Primary Depletion Forecast per Section

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To address the issues above and achieve a history match, uncertain parameters were from the base caseand regressed upon. The final changes involved:

1. Initial water saturations in vertical layers 6, 8, and 10 were decreased from 70% to 60%

X Aid in decreasing the initial water production when the wells are initially brought on production

2. Porosity in the shale layer (vertical layer 2) was increased in the hydraulic fracture to 13.5%(average of Lower Shaunavon porosity values by vertical layer)

X Stimulation from hydraulic fractures will alter pore space in comparison to the tight matrixvalues

3. A new set of relative permeability curves were added for the hydraulic fracture – Refer to FigureA-1 – Figure A-3 in Appendix A

X Due to hydraulic fracture stimulation the relative permeability will be altered in the pore spacecreated by the fracture

4. Matrix relative permeability value of water at the irreducible oil saturation was increased

X Done to enable additional flow of water and aid with injectivity issues of the model

5. An additional area of stimulated rock volume due to the hydraulic fracture was added in the modelfor each fracture stage per well.

X Done by increasing the effective permeability in the grid blocks directly adjacent to bi-wingfracture stimulated volume - Refer to Figure A-4 in Appendix AX Done to increase initial flow into the wellbore to match the peak rates early in life of well

Figure 15—Oil Recovery Factor for Waterflood Recovery Forecast per Section

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6. Assumption was made that Prod 2 does not break though shale barrier (vertical layer 2) anddirectly connect to the high permeability streak (vertical layer 1). It is also possible that the highpermeability layer does not exist at this location due to possible compartmentalization

X Done to match oil and water withdrawal at this locationX If hydraulic fracturing connects to the high permeability streak, unable to match late timeoil/water ratio’s due to proximity of injection well INJ 1 and preferential flow of injected waterto reservoir oil

7. Assumption made that hydraulic fractures from well Prod 14 partially connect to the highpermeability layer. Similar to Prod 2, compartmentalization of the high permeability streak maybe a possibility

X 3 of 7 hydraulic fractures were modeled to connect directly to the high permeability streak(Layer 1) via fracture growth

Results of History MatchAll wells were able to achieve a match on liquid, oil, and water production within a reasonable amountof accuracy with the exception of oil production on well Prod 12. A reasonable match on the gasproduction trend was achieved; however, gas production may not have been recorded at certain timesthroughout the simulation time period. An oil match was difficult to achieve on well Prod 12 at late times.Similar to well Prod 2, due to the proximity of injector INJ 1 late time oil production was difficult to matchas injected water proved to have preferential flow over reservoir oil. Unlike Prod 2, if the well is notconnected to the high permeability streak via hydraulic fractures, water demand cannot be met. Therefore,it appears that not only is Prod 12 receiving pressure support from the neighboring injector, injection wateris most likely present in the historical liquid production data. Since the match of the late time productioncannot be achieved, it is believed there is a geological event or there is a wellbore related issue which isunknown at the time of simulation that prevents a good history match from being achieved. It is possiblethat the high permeability steak modeled in layer 1 is not as continuous as simulated.

Cumulative volumes for the entire pilot area can be seen below in Figure 4. Individual well historymatches can be found in the Appendix.

An assumption made early in the creation of the model on the basis of micro seismic data is theresulting fractures cover all 10 vertical layers of the model. To validate this assumption, a model was runwhere the hydraulic fractures from all wells only covered vertical layers 3 to 10 (Lower Shaunavonreservoir) and did not break through the shale barrier (layer 2) and connect the high permeability streak(layer 1). The majority of the wells could not sustain the required liquid withdrawals from historical dataand injectivity in the reservoir was quite poor for this model. Based on model input data, it was found thathydraulic fractures for the majority wells did indeed connect to the high permeability streak via breakingthough the 1.0 m thick shale barrier.

A comparison of the water injection rates from INJ 1 for both the final history match and a case wherethe hydraulic fractures only cover layers 3-10 (shale barrier remains intact):

Based on the simulation model and input data, it was observed that the flood front due to water floodingin the Lower Shaunavon reservoir is extremely slow and considered negligible in respect to the simulatedtimeframe. If no connection to the high permeability streak is modeled, the injectivity of well INJ 1 dropssignificantly from historical rates and injected water saturation increases are only observed locally aroundthe injection wells hydraulic fractures. Pressure maintenance is observed in surrounding wells to theinjector, but this support is not enough to supply the demand of production, especially related to waterproduction. Once there is a connection between the high permeability layers, historical injectivity isobserved. Water injection was tracked separately from reservoir water in the model and was extensively

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used in the history match process to investigate the movement of injected water throughout the reservoir.The simulation indicates that the majority of the injected water travels through hydraulic fracture networkand into the high permeability streak. A flood front is formed in this highly conductive layer and fluidsare swept towards surrounding production wells and injected water is produced via the connection fromfracturing through the shale barrier. The benefits of the waterflood are evident when comparing the fullheight fracture case to the non-connected case. While not in the conventional displacement model of waterinjection, the current oil production rates would be unattainable without this secondary scheme.

Forecast SetupUsing the history matched data; nine different forecast scenarios were simulated for 50 years.

1. Using the history matched pilot area, ran the model for an additional 50 years using well operatingconstraints provided by Crescent Point Energy. Primary liquid constraint based on last availableliquid rate in History match.

2. Primary depletion of a 4 well per section (wps) model3. Waterflooding of a 4 wps model4. Primary depletion of a 8 wps model5. Waterflooding of a 8 wps model6. Primary depletion of a 10 wps model7. Waterflooding of a 10 wps model8. Primary depletion of a 16 wps model9. Waterflooding of a 16 wps model

Scenario 1 listed below uses the history matched pilot area as a base case for prediction simulation andare forecast from the end of the history match in May 2013 to January 2065.

In scenarios 2-9, a block model was built using the history match reservoir and hydraulic fractureparameters from the pilot area. In all cases the model was forecast for 50 years beginning in January 2014.The block model consists of 10 vertical layers and each grid block has a dimension of 25m � 25m. Thewaterflood forecast scenarios require that the water injection begins after 6000m3 of oil has been producedby the converted wells. The forecast patterns covering two sections of land for both primary depletion andwaterflood recovery can be seen in Figure 6 – 7.

To save on model size and simulation run time, a repeatable element of symmetry pattern wasincorporated into all block model cases expect for 10 wells per section (wps). Since the properties of themodel vary vertically, but are homogenous in nature horizontally, an element of symmetry patternbecomes valid. To avoid modeling a full section, three simulation wells (1 full well – middle well and 2half wells – edge wells) were modeled in the 4wps and 8wps cases. The presented forecast results will begrossed up over a section. All wells were placed into the 4th layer in the model.

It should be noted that 8 wps model will be very similar to the 4 wps model. The 4 wps model willbe based on a half section of land while the 8 wps and 16 wps models will be based on a quarter sectionof land. All forecast predictions will be grossed up to a full section when presenting results. The 10 wpsmodel was modeled as a full section due to the well placement as an element of symmetry within a sectioncould not be achieved. Diagrams of the element of symmetry patterns for all cases can be found in Figure8–10.

In all waterflood cases, all wells are originally producers and after each selected conversion wellproduces 6000 m3 of oil, the well is converted to a water injector. The water injected into the block modelis also constrained by a voidage replacement ratio of 1 for the section, along with the individual wellconstraints. For the water injection scenarios, simulated full wells (the middle well) of the 4, 8, and 16 wellmodels will be converted to water injectors. The 10 wps model will have the wells on the boundary of thesection convert to water injectors after the produced oil volume. It should be noted that the 10 wps model

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includes 4 half wells (edge wells) which surround the 4 boundaries of the model and 6 full wells. Whenpresenting results these edge wells will not be grossed up, so technically speaking, the model and resultscontain 8 full wells. The edge wells were modeled as half wells as opposed to full wells due to therepetition of the pattern. If this pattern was repeated, especially in the water flood case, the adjacentsection would also have an injector at the boundary and there would be two injectors side by side. It wasassumed that the adjacent sections would share the one water injector, instead of drilling neighboringinjectors.

To validate that the forecast data represents observed historical data, the individual well liquid ratesfrom the primary depletion forecasts were plotted against historical liquid production from the historymatch; refer to Figure 11. It can be seen that the liquid rates from the forecast fall in line with the historicaldata; however, a bit on the high end of production in the early stages of production and on the low sidein the late stages of production. It should be noted that the historical production has water flood influencein the majority of the wells in the late times of production. Also, the forecast runs have 8 hydraulicfractures per well with a well length of 1300m compared to an average of 7 fractures and an average welllength of approximately 1000m in historical production.

Forecast Results

Scenario 1

Plots of cumulative volumes and total oil recovery factory for the Pilot Area forecast for Scenario 1 arepresented in Figure 12–13.

Scenarios 2-9Comparison plots of total oil recovery factory per section of the block model are presented below.

ConclusionsIn this study, a workflow is given for completing a history match on the Lower Shaunavon pilot area. Thefollowing conclusions are reached for the pilot area:

– An acceptable overall history match was achieved for the Lower Shaunavon Pilot area consistingof 18 producing wells and with one well converting to a water injector

– Full historical injectivity could not be achieved unless the hydraulic fracture stimulation brokethrough the shale layer separating the high permeability streak from the Lower Shaunavonformation

– Due to the nature of the reservoir and proximity to the high permeability layer, the primary benefitof the water flood scheme appears to be pressure maintenance

– Within the confines of this model, the majority of injected water travels through the hydraulicfractures of the injection well into the high permeability layer above the shale barrier due topreferential flow. The injected water propagates to surrounding production well hydraulic fracturesvia the high permeability layer while sweeping the layer

– With respect to the Lower Shaunavon pilot area, the extensiveness of the high permeability streakmodeled needs to be further investigated. History match results tend to show that compartmental-ization may be an issue for this high conductive layer and may not be as far reaching as modeled

– The pilot area was forecast for 50 Years after the history matched timeframe

X The simulated pilot area oil recovery factor at the end of the history match is ~1.4%X The simulated pilot area oil recovery factor after 50 additional years of production is ~ 5.1%

– A block model was built with different layouts of wells per section

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X Overlooking economics to drill additional wells, forecast scenarios show 10 wells per sectionto have the best oil recovery factor for primary depletion at ~6.4% after 50 years of simulationX Overlooking economics to drill additional wells and the costs associated with water injection,forecasts scenarios show 16 wells per section to have the best oil RF for waterflood recovery at~9.5% after 50 years of simulation

AcknowledgmentsThe authors would like to thank the team at Crescent Point Energy Corp. for their support andcontributions to this paper. Also, thanks to Crescent Point Energy for support in publication of this work.

Nomenclature

EoS Equation of StateN1g: First coefficient in the Forchheimer equation for non-Darcy flowNDARCYCOR: non-Darcy correction factorKeff: Effective permeabilityKf: Fracture permeabilityLS-LR-DK: Logarithmically spaced, logarithmic refined, dual permeabilityWf : Width of fractureWgrid: Block widthwps: Wells per section

References1. Huffaker, C., Stewart, R., and Vescarelli, L. 2013. Tight Oil. Unconventional Resource Guide-

book 2(1): 27–35.2. Novlesky, A., Kumar, A., and Merkle, S. 2011. Shale Gas Modeling Workflow: From Micro-

seismic to Simulation – A Horn River Case Study. Paper SPE 148710 presented at the CanadianUnconventional Resources Conference, Calgary, AB, November 15-17

3. Rubin, B. 2010. Accurate Simulation of Non-Darcy Flow in Stimulated Fractured Shale Reser-voirs. Paper SPE 132093 presented at SPE Western Regional Meeting, Anaheim, CA, May 27-29

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Appendix A

Table A-1—Base Values for Reservoir Parameters on a Per Layer Basis

Figure A-1—Matrix Water-Oil Relative Permeability

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Figure A-2—Matrix Liquid-Gas Relative Permeability

Figure A-3—Hydraulic Fracture Water-Oil Relative Permeability

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Figure A-4—Hydraulic Fracture Extra Stimulation

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