Ray Mireault, P. Eng.

Lisa Dean, P. Geol.

fekete.comcspg.org

PRINCIPALAUTHORS

Nick Esho, P. Geol.

Chris Kupchenko, E.I.T.

Louis Mattar, P. Eng.

Gary Metcalfe, P. Eng.

Kamal Morad, P. Eng.

Mehran Pooladi-Darvish, P. Eng.

CONTRIBUTINGAUTHORS

RESERVOIR

for GeologistsENGINEERING

Overview...................................................................................... 03

COGEH Reserve Classifications.................................................. 07

Volumetric Estimation ..................................................................11

Production Decline Analysis.........................................................15

Material Balance Analysis.............................................................19

Material Balance for Oil Reservoirs.............................................. 23

Well Test Interpretation................................................................. 26

Rate Transient Analysis................................................................ 30

Monte Carlo Simulation/Risk Assessment - Part 1...................... 34

Monte Carlo Simulation/Risk Assessment - Part 2...................... 37

Monte Carlo Simulation/Risk Assessment - Part 3 ...................... 41

Coalbed Methane Fundamentals................................................ 46

Geological Storage of CO2........................................................... 50

Reservoir Simulation.................................................................... 54

Reservoir Engineering for Geologists was originally published as a fourteen-part series

in the CSPG Reservoir magazine between October 2007 and December 2008.

TABLE OF CONTENTS

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RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle I – Overview by Ray Mireault, P. Eng., and Lisa Dean, P. Geol., Fekete Associates Inc..

Welcome to the first article in a seriesintended to introduce geologists toreservoir engineering concepts and theirapplication in the areas of Corporate ReserveEvaluation, Production, Development, andExploration.

Topics covered in the series are:• Article 1: Overview• Article 2: COGEH Reserve

Classifications• Article 3: Volumetric Estimation• Article 4: Decline Analysis• Article 5: Material Balance Analysis• Article 6: Material Balance for Oil

Reservoirs• Article 7: Well Test Interpretation• Article 8: Rate Transient Analysis• Article 9: Monte Carlo Simulation• Article 10: Monte Carlo Simulation (cont.)• Article 11: Monte Carlo Simulation (cont.)• Article 12: Coalbed Methane

Fundamentals• Article 13: Geological Storage of CO2

• Article 14: Reservoir Simulation

The format for each article will generally be tointroduce the concept(s), discuss the theory, andillustrate its application with an example.

ARTICLE DEFINITIONS AND USESARTICLE DEFINITIONS AND USESARTICLE DEFINITIONS AND USESARTICLE DEFINITIONS AND USESARTICLE DEFINITIONS AND USESCOGEH, the Canadian Oil and Gas EvaluationHandbook, Reserve Classifications provide aCanadian standard reference methodology forestimating reserve volumes according toreserve and resource category. There havebeen many recent changes in an attempt toachieve a “global standard” in order to ensurethe public release of accurate, understandablereserve and resource estimations andclassifications.

Volumetric Techniques are used to indirectlyestimate Hydrocarbons in Place (OOIP andOGIP) from estimates of area, thickness,porosity, water saturation, and hydrocarbonfluid properties. Analogue or theoreticalestimates for hydrocarbon recovery are thenapplied to estimate recoverable hydrocarbons.These techniques are utilized prior to theacquisition of sufficient production data toallow a more rigorous determination ofreserves and resource estimates. Thesemethods are therefore primarily used forevaluating new, non-producing pools and theevaluation of new petroleum basins.

Decline analysis techniques extrapolate thehistorical performance trend to an economic

production limit or cutoff to forecast theexpected ultimate recovery (EUR). Themethod plots the production rate throughthe production history (time) and recordsthe production rate decline as cumulativeproduction increases (Figures 1.1 and 1.2).

In theory it is only applicable to individualwells, but in practice extrapolations of groupproduction trends often provide acceptableapproximations for EUR. Two keyassumptions are that past trends representthe full capability of the producing entity and

Figure 1.1. Traditional decline analysis - Rate vs. Cum. Prod.

Figure 1.2. Traditional decline analysis - Rate vs. Time.

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that the trends and operating practicescontinue into the future. Deviations fromtheoretical performance can help identifywells and areas that are underperforming.Well workovers to resolve mechanicalproblems or changes in operating practicescan enhance performance and increaserecovery. The presence of pressuremaintenance by an aquifer may make thismethod inappropriate to use. This techniqueis also more rel iable than volumetricmethods when sufficient data is available toestablish a reliable trend line.

Material balance techniques are used toestimate hydrocarbons in place (OOIP andOGIP) from measurements of f luidproduction and the resultant change inreservoir pressure caused by thatproduction. The technique requires accurateestimates of fluid properties, productionvolumes, and reservoir pressure. Estimatesfor hydrocarbon recovery, based on fluidproperties and analogue producing pools/formations, are then applied to estimaterecoverable hydrocarbons. These methodsare more reliable than volumetric methodsas long as there is sufficient data to establishthe relationship.

Well tests and the subsequent pressuretransient analyses are used to determinefluids present in the reservoir, estimate wellproductivity, current reservoir pressure,

permeability, and wellbore conditions frommathematical flow equations and dynamicpressure bui ldup measurements. The

technique requires that a well be producedfor a period of time and then shut-in for anappropriate length of time. Analysis inputs

Figure 1.3. Horizontal well model.

Figure 1.4. Flowing material balance.

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include fluid viscosity, rock properties, netpay thickness of the producing interval, andthe mechanical configuration of the wellbore.An adequate buildup provides informationon the reservoir flow pattern near thewellbore, identifies restricted reservoirs,and can sometimes infer the geometric shapeof the well’s drainage area (see Figure 1.3).

Rate transient analysis (RTA), also know asadvanced decline analysis is a relativelyrecent development that uses well flowingpressures to characterize well and reservoirproperties and estimate inplace volumes. Thistechnique has been made available by theintroduction of SCADA (SupervisoryControl and Data Acquisition) data capturesystems that generally provide the frequencyof flow and pressure information requiredfor real-life application (flowing materialbalance and type curve analysis – see Figures1.4 and 1.5). Since pressure information canbe captured without shutting the well in andwithout the loss of cash flow, the frequencyof “testing” can be significantly increased andchanges in operating performance identifiedmore quickly than is practical withconventional testing.

Monte Carlo simulation is used to deal withthe uncertainty in every input parametervalue in the volumetric equation. Instead ofa single number, it allows the geologist toprovide a value range for areal extent, paythickness, porosity, water saturation,reservoir pressure, temperature, f luidproperties, and recovery factor. Multiple(typically 10,000) iterations are run togenerate a probable range of values for in-place and recoverable hydrocarbons (Figure1.6). The simulation is especially applicableto play and resource assessments.

Numerical reservoir simulation uses materialbalance and fluid flow theory to predict fluidmovement through three-dimensional space.The inputs of geometric shape of thedeposit, the rock, and fluid properties mustbe determined from other methods to dealwith the nonuniqueness of the forecasts.However, it has the abi l ity to visual lyintegrate the geological and geophysicalinterpretation with the analytical approachto reservoir analysis (Figure 1.7).

Although different techniques are used indifferent situations, a major purpose ofreservoir engineering is to estimaterecoverable oil or gas volumes and forecastproduction rates through time. Forecasts ofproduction rate and cumulative volumes area key input for the following:

• Exploration play assessment,• Development drilling locations,

Figure 1.5. Blasingame typecurve analysis.

Figure 1.6. Visualization of results.

Figure 1.7. Pressure profile from numerical model.

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• Accelerated production from aproducing pool,

• Rank and budgeting of potentialexploration and developmentexpenditures,

• Corporate reserve evaluations.

The different techniques also have differentapplications at different times in the life of afield or prospect. For example, the initialstages of exploration may require volumetricestimates based upon analogue data due tothe lack of existing well information andestimating volumes with Monte Carlosimulation. Volumetric estimates based uponactual well data may be the next step afterexploration drilling and testing has provensuccessful. As development and productioncommence, SCADA frequency productionand pressure measurements can be obtainedfor RTA analysis . Monthly productionvolumes provide the data for material balanceand decline analysis techniques.

As production continues, the accuracy andreliability of the estimates obtained fromRTA, material balance, and decline analysisincreases. Integrating all the techniquesprovides more reliable answers than relyingsolely on any one method. In addition,integrating the techniques can lead toadditional hydrocarbon discoveries and/orincreased recovery from knownaccumulations.

Articles two through nine address the maintopics of reservoir engineering. Theremaining articles will focus on play typesthat are presently of interest to the industry.Included in this group of plays are coalbedmethane concepts and interpretation(Figures 1.8 and 1.9), tight gas, shale gas, andan overview of secondary and tertiary oilrecovery methods.

Figure 1.8. Historical rates vs. time.

Figure 1.9. Drainage area and permeability.

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RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 2 – COGEH Reserve Classifications by Gary Metcalfe, P. Eng., Vice President Evaluations

In 2004, the Royal Dutch Shell Groupreported five separate write-downs of 3,900MSTB, 250 MSTB, 200 MSTB, 100 MSTB, andone undisclosed volume. In that same year,El Paso reported a 41% write-down inreserves from 4,500 BCF to 2,600 BCF.Where did the reserves go? The answer is…nowhere! These write-downs resultedfrom misinterpretation of standards andguidelines for reserve classification. Thereported oil and gas volumes likely exist; itwas just a matter of premature classificationinto the proved reserves category.

The Canadian Securities Administrators(CSA), through National Instrument 51-101(NI 51-101), sets the standards for disclosureof oil and gas activities for companies listed

on Canadian stock exchanges. The definitionsand standards for reserve appraisals andevaluations are defined in the Canadian Oiland Gas Evaluation Handbook (COGEH).

Reserves are the estimated remainingquantities of oil and natural gas and relatedsubstances anticipated to be recoverablefrom known accumulations based on analysisof drill ing, geological, geophysical, andengineering data; established technology; andspecific economic conditions.

Under the COGEH definitions, the reportedproved reserves are those estimated with ahigh degree of certainty to be recovered,probable reserves are less certain to berecovered than proved, and possible are

those less certain to be recovered thanprobable. The degree of certainty is definedas:

Proved: 90% probability of meeting orexceeding the estimated proved volume(P90).

Proved plus probable: 50% probability ofmeeting or exceeding the sum of theestimated proved plus probable volume(P50).

Proved plus probable plus possible: 10%probability of meeting or exceeding the sumof the estimated proved plus probable pluspossible volume (P10).

Figure 2.1. COGEH reserves and resources classification.

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Each of the reserve classifications can bedivided into Developed and Undevelopedcategories, with the developed categoryfurther subdivided into Producing and Non-producing.

REQUIREMENTS FOR RESERVEREQUIREMENTS FOR RESERVEREQUIREMENTS FOR RESERVEREQUIREMENTS FOR RESERVEREQUIREMENTS FOR RESERVECLCLCLCLCLAAAAASSSSSSIFICSIFICSIFICSIFICSIFICAAAAATIONTIONTIONTIONTIONWithin COGEH, there are requirements andprocedures for classifying reserves. Theconditions that must be met to assignreserves are:

• Drilling – accumulation must have awell;

• Testing – accumulation must haveevidence of commercial productionfrom a test;

• Economics – for producing reserves,cash flow and NPV must be positive;for undeveloped reserves, areasonable return on investment mustbe demonstrated; and

• Regulatory – prohibitive governmentrestraints must be incorporated whenestimating appropriate levels of risk.

MEMEMEMEMETHODTHODTHODTHODTHODS OF ES OF ES OF ES OF ES OF ESSSSSTIMATIMATIMATIMATIMATING RETING RETING RETING RETING RESESESESESERRRRRVVVVVEEEEESSSSSReserves can be estimated usingdeterministic or probabilistic methods:

Deterministic: A single value assigned foreach input parameter of the reservescalculations is used. The appropriate valuefor each reserve category must be selected.The majority of reserves in Canada areestimated using this method.

Probabilistic: A full range of values are usedfor each input parameter into the reservecalculation. Reserve estimates can beextracted from a Monte Carlo type ofanalysis at the various confidence levels P90,P50, P10, etc. This method pertains mainly tovolumetric evaluations prior to the onset ofproduction.

Both the deterministic and probabilisticmethods will be presented in subsequentarticles.

AAAAAGGGGGGGGGGREREREREREGGGGGAAAAATION OF RETION OF RETION OF RETION OF RETION OF RESESESESESERRRRRVVVVVEEEEESSSSSUnder COGEH, the P90, P50, and P10 valuesare reported at the corporate level, not atthe entity (well/property) level. Whendeterministic methods are used, simplesummation of all individual entities within aportfolio provides the aggregate total.

With probabi l ist ic methods, reservedistributions for the individual entities mustbe combined in accordance with the laws ofprobabi l ity to determine the correctdistribution for the aggregate. The arithmeticP90 summation will be less than the P90 ofthe aggregate (i.e., too conservative) and

conversely the arithmetic summation of P10will exaggerate the upside and be optimisticcompared to the P10 from the aggregatedistribution.

For reserve reporting to an investment typeaudience, probabilistic aggregation poses aproblem as a P90 aggregate type corporatedisclosure cannot be allocated back oridentified in any individual well or propertyor prospect.

RESOURCESRESOURCESRESOURCESRESOURCESRESOURCESThe NI 51-101 regulations also allow for thedisclosure of information for propertieswith no attributed reserves. The generalreserve / resource classifications as they aredefined in COGEH (see Figure 2.1: COGEHReserves and Resources Classification, p. 30),are as follows:

Resources are l imited to discovered(known) and undiscovered accumulations.Contingent resources are discovered but notcurrently economic. Prospective resourcesare undiscovered but are technically viableand economic to recover. These resourcesare further classi f ied into Low(conservative), Best (realistic) and High(optimistic) estimates.

There are no detailed guidelines in COGEHfor resource appraisals; however, COGEHdoes recommend probabilistic evaluation. Ifresources are subitted in an NI 51-101report, disclosure must include volumes, netpay, areal extent, flow rates, land, seismic,wells, exploration / development programs,and capital expenditures. The expl icitdisclosure of risk and / or probability ofsuccess are also required. This is problematicin that a single probability estimate is notpossible to calculate.

RECENT DEVELOPMENTS IN RESERVESRECENT DEVELOPMENTS IN RESERVESRECENT DEVELOPMENTS IN RESERVESRECENT DEVELOPMENTS IN RESERVESRECENT DEVELOPMENTS IN RESERVESCLCLCLCLCLAAAAASSSSSSIFICSIFICSIFICSIFICSIFICAAAAATIONSTIONSTIONSTIONSTIONSInternational propertiesThe scrutiny of oi l and gas reservescontinues to increase, especially as more andsmaller Canadian issuers are competing inthe U.S. and international markets. Thefinancial world is attempting to create a setof global accounting standards through theInternational Accounting Standards Board(IASB). The IASB expects reserve estimatesto reflect expected values rather thanconservative (proved) estimates and believesreserve estimates should be presented as arange reflecting uncertainty.

Petroleum Resource ManagementSystem (PRMS)Establishing a rigorous, harmonized, anduniversal reserves and resourcesclassification system for all stakeholders (oilindustry, accountants, regulators, business /f inancial analysts, investors, andgovernments) is an ongoing process. Therecent 2007 SPE / AAPG / WPC / SPEE {etrp;ei,Respirce <amage,emt Suste, (PRMS) has beenproposed as the new standard for petroleumreserve and resource classi f icat ion,definition, and guidelines. This system has a“commercial ity” or “projectmaturity”subclass (see Figure 2.2: ProjectStatus Categories / Commercial Risk).

The United Nations Economic Commissionfor Europe (UNECE) and the United NationsFramework Classification for Fossil Energyand Minerals Resources (UNFC) bothrecognize project maturity (along witheconomic viability and geological knowledge)as the basic criteria for categorization andalignment of energy management and financialreporting. To this end, it appears the UNFCand the PRMS definitions are compatible.

Figure 2.2. Project status categories / commercial risk (sourced from SPE Oil and Gas Committee FinalReport - December 2005).

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Figure 2.3. Multi-well gas pool example reserves classification (sourced from Canadian Oil and GasEvaluation Handbook, Volume 2, Secion 6 - Procedures for estimation and calssification of reserves, Figure6-2B).

Figure 2.4. Aggregation (summation)issues (sourced from Kemirmen, Ferruh, Society of Petroleum EngineersPaper #103434, Figure 10).

PRMS is an ongoing, long-term process. Ifthese new standards are developed andimplemented, Canadian and U.S. regulatorsmust respond posit ively and provideregulatory enforcement in order to gain thetrust of investors and have credibility in themarketplace.

Unconventional Reserves andResourcesThe industry is investing heavi ly intechnology to improve recovery andprocesses for unconventional extra heavyoil, tight gas sands, CBM, oil shales, and gashydrates. The classification and technicalstandards for these unconventional reserves/ resources must conform to the system usedfor conventional reservoirs.

The COGEH Volume 3 “Detailed Guidelinesfor Estimation and Classification of CBMReserves and Resources” is in draft stage atthe time of writing this article. This hugeundertaking is likely the first publicationdealing specifically with classifying, defining,and quantifying unconventional reserves andresources.

Reserves Evaluator TrainingThe SPEE/WPC/AAPG and SPE have formedthe Joint Committee on Reserves EvaluatorTraining (JCORET) to investigate trainingcourses for reserve evaluators that focus, inpart, on reserves and resources definitions,classification, and applications. Discussionson qual i f icat ions and standards forprofessional reserve evaluators and auditorsare ongoing.

CONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONThe reason for NI 51-101 and COGEH is toprovide the shareholder/ investor/stakeholder with consistent and reliablereserves information using standardizedreporting guidelines in a format that can bewidely understood. While the COGEHframework al lows for def init ions andclassifications for current conventional andunconventional reserves and resources, theclassification and definition of reserves is anever-evolving process. COGEH will continueto be modified to adapt to new technologyand standardization in a global economy.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESKemirmen, Ferruh, 2007. “ReservesEstimation: The Challenge for the Industry,”Society of Petroleum Engineers Paper#103434, In Journal of Petroleum TechnologyMay 2007, P80-89.

Canadian Oil and Gas Evaluation Handbook,First Edition, November 1, 2005, Volume 2,Detailed Guidelines for Estimation andClassification of Oil and Gas Resources and

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Reserves. Section 6: Procedures forEstimation and Classification of Reserves,2005.

Oil and Gas Reserves Committee, MappingSubcommittee Final Report – December2005: Comparison of Selected Reservesand Resource Classifications andAssociated Definitions, 2005. Richardson,Texas: Society of Petroleum Engineers.http://www.spe.org/web/ogr/OGR_mapping_Final_Report_15Dec05.pdf.

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RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 3 – Volumetric Estimation by Lisa Dean, P. Geol., Fekete Associates Inc..

You have been asked to:

• Evaluate the properties that are forsale in a data room.

• Determine whether to participate in aprospect.

• Calculate the potential reservesencountered by a discovery well.

• Identify the upside potential in amature field.

In all these situations, the bottom line is“how much oil or gas exists and can beproduced, and what will be the return oninvestment?” This article addresses thisquestion.

Volumetric estimation is the only meansavailable to assess hydrocarbons in placeprior to acquiring sufficient pressure andproduction information to apply materialbalance techniques. Recoverablehydrocarbons are estimated from the inplaceestimates and a recovery factor that isestimated from analogue pool performanceand/or simulation studies.

Therefore, volumetric methods are primarilyused to evaluate the in-place hydrocarbonsin new, non-producing wells and pools andnew petroleum basins. But even afterpressure and production data exists,volumetric estimates provide a valuable checkon the estimates derived from materialbalance and decline analysis methods (to bediscussed in upcoming Reservoir issues).

VVVVVOLOLOLOLOLUMEUMEUMEUMEUMETRIC ETRIC ETRIC ETRIC ETRIC ESSSSSTIMATIMATIMATIMATIMATIONTIONTIONTIONTIONVolumetric estimation is also known as the“geologist’s method” as it is based on cores,analysis of wireline logs, and geological maps.Knowledge of the deposit ionalenvironment, the structural complexities,the trapping mechanism, and any fluidinteraction is required to:

• Estimate the volume of subsurface rockthat contains hydrocarbons. Thevolume is calculated from thethickness of the rock containing oil orgas and the areal extent of theaccumulation (Figure 3.1).

• Determine a weighted average effectiveporosity (See Figure 3.2).

• Obtain a reasonable water resistivityvalue and calculate water saturation.

With these reservoir rock properties andutilizing the hydrocarbon fluid properties,

Figure 3.1. Areal estent of rock volume accumulation.

Figure 3.2. Weighted average effective porosity.

Sand Grain

CementingMaterial

Interconnected orEffective Porosity

25%

Isolated orNoneffective

Porosity5%

Total Porosity30%

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original oil-in-place or original gas-in-placevolumes can be calculated.

For OIL RESERVOIRS the original oil-inplace (OOIP) volumetric calculation is:

Metric:OOIP (m3) =Rock Volume * Ø * (1 - Sw) * 1/Bo

Where: Rock Volume (m3) = 104 * A * hA = Drainage area, hectares (1 ha =

104m2)h = Net pay thickness, metresØ = Porosity, fraction of rock

volume available to store fluidsSw = Volume fraction of porosity

filled with interstitial waterBo = Formation volume factor (m3/

m3) (dimensionless factor forthe change in oil volumebetween reservoir conditionsand standard conditions atsurface)

1/Bo = Shrinkage (Stock Tank m3/reservoir m3) = volume changethat the oil undergoes whenbrought to the earth’s surfacedue to solution gas evolvingout of the oil.

Imperial:OOIP (STB) =Rock Volume * 7,758 * Ø * (1 - Sw) * 1/Bo

Where: Rock Volume (acre feet) = A * hA = Drainage area, acresh = Net pay thickness, feet7,758 = API Bbl per acre-feet (converts

acre-feet to stock tank barrels)Ø = Porosity, fraction of rock

volume available to store fluidsSw = Volume fraction of porosity

filled with interstitial waterBo = Formation volume factor

(Reservoir Bbl/STB)1/Bo = Shrinkage (STB/reservoir Bbl)

To calculate recoverable oil volumes theOOIP must be multiplied by the RecoveryFactor (fraction). The recovery factor is oneof the most important, yet the most difficultvariable to estimate. Fluid properties suchas formation volume factor, viscosity, density,and solution gas/oil ratio all influence therecovery factor. In addition, it is also afunction of the reservoir drive mechanismand the interaction between reservoir rockand the fluids in the reservoir. Some industrystandard oil recovery factor ranges forvarious natural drive mechanisms are listedbelow:

Solution gas drive 2 – 30%Gas cap drive 30 – 60%Water drive 2 – 50%Gravity Up to 60%

For GAS RESERVOIRS the original gas-in-place (OGIP) volumetric calculation is:

Metric:OGIP (103m3) =Rock Volume * Ø * (1-Sw) * ((Ts * Pi) / (Ps * Tf * Zi))

Where: Rock Volume (m3) = 104 * A * hA = Drainage area, hectares (1 ha =

104m2)h = Net pay thickness, metresØ = Porosity, fraction of rock volume

available to store fluidsSw = Volume fraction of porosity filled

with interstitial water

Ts = Base temperature, standardconditions, °Kelvin (273° +15°C)

Ps = Base pressure, standard conditions,(101.35 kPaa)

Tf = Formation temperature, °Kelvin(273° + °C at formation depth)

Pi = Initial Reservoir pressure, kPaaZi = Compressibility at Pi and Tf

Imperial:OGIP (MMCF) =Rock Volume * 43,560 * Ø * (1-Sw) * ((Ts * Pi)/ (Ps * Tf * Zi))

Figure 3.3. Volumetric rules: Trapezoidal, pyramidal, and cone.

Trapezoidal Volume V = h * ((A1 + A2) / 2)

Frustum of a pyramid V = (h/3) * (A1 + A2 + A1 * A2)

Frustum of a cone V = (h/3) * * (r2 + rR + R2)πππππ

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Where: Rock Volume (acre feet) = A * hA = Drainage area, acres (1 acre =

43,560 sq. ft)h = Net pay thickness, feetØ = Porosity, fraction of rock volume

available to store fluidsSw = Volume fraction of porosity filled

with interstitial waterTs = Base temperature, standard

conditions, °Rankine (460° +60°F)

Ps = Base pressure, standard conditions,14.65 psia

Tf = Formation temperature, °Rankine(460° + °F at formation depth)

Pi = Initial Reservoir pressure, psiaZi = Compressibility at Pi and Tf

To calculate recoverable gas volumes, theOGIP is multiplied by a recovery factor.Volumetric depletion of a gas reservoir withreasonable permeability at conventionaldepths in a conventional area will usuallyrecover 70 to 90% of the gas-in-place.However, a reservoir’s recovery factor canbe significantly reduced by factors such as:low permeability, low production rate ,overpressure, soft sediment compaction,fines migration, excessive formation depth,water influx, water coning and/or behind pipecross flow, and the position and number ofproducing wells. As an example, a 60%recovery factor might be appropriate for agas accumulation overlying a strong aquiferwith near perfect pressure support.

Rock Volume Calculations (A * h)Reservoir volumes can be calculated fromnet pay isopach maps by planimetering toobtain rock volume (A * h). To calculatevolumes it is necessary to find the areasbetween isopach contours. Planimetering canbe performed by hand or computergenerated. Given the areas betweencontours, volumes can be computed using;Trapezoidal rule, Pyramidal rule, and/or thePeak rule for calculating volumes (see Figure3.3).

Net payNet pay is the part of a reservoir from whichhydrocarbons can be produced at economicrates, given a specific production method.The distinction between gross and net pay ismade by applying cut-off values in thepetrophysical analysis (Figure 3.4). Net paycut-offs are used to identify values belowwhich the reservoir is effectively non-productive.

In general, the cut-off values are determinedbased on the relationship between porosity,permeability, and water saturation from coredata and capillary pressure data. If core isunavailable, estimation of a cut-off can bederived from offset well information and

comparative log signatures.

Porosity and Water SaturationPorosity values are assigned as an averageover a zone (single well pool) or as aweighted average value over the entire payinterval using all wells in a pool. Similarly,the average thickness-weighted watersaturation using all wells in the pool iscommonly assumed as the pool averagewater saturation.

Drainage AreaDrainage area assignments to wells shouldbe similar to offset analogous poolsdepending on the geological similarities andproductivity of the wells within the analog.Pressure information is useful in estimatingpool boundaries and if any potential barriersexist between wells. Seismic analysis usuallyimproves the reservoir model and providesfor more reliability in reserve or resourceestimates.

Formation Volume FactorThe volumetric calculation uses the initialoil or gas formation volume factor at theinitial reservoir pressure and temperature.Both Bo and Bg are functions of f luidcomposit ion, reservoir pressure and

temperature and consequently of reservoirdepth. The Bo and Bg values from analogousoffset pools are often used as an initialestimate for the prospect underconsideration.

VVVVVOLOLOLOLOLUMEUMEUMEUMEUMETRIC UNCETRIC UNCETRIC UNCETRIC UNCETRIC UNCERRRRRTTTTTAINAINAINAINAINTTTTTYYYYYA volumetric estimate provides a staticmeasure of oil or gas in place. The accuracyof the estimate depends on the amount ofdata available, which is very limited in theearly stages of exploration and increases aswells are drilled and the pool is developed.Article 8, entitled Monte Carlo Analysis, willpresent a methodology to quantify theuncertainty in the volumetric estimate basedon assessing the uncertainty in inputparameters such as:

• Gross rock volume – reservoirgeometry and trapping

• Pore volume and permeabilityDistribution

• Fluid contacts

The accuracy of the reserve or resourceestimates also increases once production datais obtained and performance type methodssuch as material balance and decline analysiscan be utilized. Finally, integrating all the

Figure 3.4. Gross and net pay distinction (Etris and Stewart, 2003).

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techniques provides more reliable answersthan relying solely on any one method.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESAprilia, A. W., Li, Z., McVay, D. A. and Lee, W.J., SPE Gas Tech Symposium May 15-17 2006,Calgary. SPE Paper 100575-MS

Canadian Institute of Mining, Metallurgy andPetroleum, Determination of Oil and GasReserves, Petroleum Society MonographNumber 1, 1994.

Etris, Ned and Stewart, Bruce. 2003. Net-to-gross ratio. CSPG Reservoir, v. 30, issue 4,p.24-25.

SPEE and CIM, Canadian Oil and GasEvaluation Handbook, Vol 2. Detai ledGuidelines for Estimation and Classificationof Oil and Gas Resources and Reserves,November 2005.

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RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 4 – Production Decline Analysis by Lisa Dean, P. Geol., and Ray Mireault, P. Eng., Fekete Associates Inc..

Production decline analysis is a basic toolfor forecasting production from a well orwell group once there is sufficient productionto establish a decline trend as a function oftime or cumulative production. The techniqueis more accurate than volumetric methodswhen sufficient data is available to establisha reliable trend and is applicable to both oiland gas wells.

Accordingly, production decline analysis ismost applicable to producing pools with wellestablished trends. It is most often used toestimate remaining recoverable reserves forcorporate evaluations but it is also usefulfor waterflood and enhanced oil recovery(EOR) performance assessments and inidentifying production issues/mechanicalproblems. Deviations from theoreticalperformance can help identi fyunderperforming wells and areas andhighlight where well workovers and/orchanges in operating practices could enhanceperformance and increase recovery.

To the geologist, production decline analysisof an analogous producing pool provides abasis for forecasting production and ultimaterecovery from an exploration prospect orstepout drilling location. A well’s productioncapability declines as it is produced, mainlydue to some combination of pressuredepletion, displacement of another fluid (i.e.,gas and/or water) and changes in relative fluidpermeability. Plots of production rate versusproduction history (time or cumulativeproduction) illustrate declining productionrates as cumulative production increases(Figures 4.1 - 4.4).

In theory, production decline analysis is onlyapplicable to individual wells but in practiceextrapolations of group production trendsoften provide acceptable approximations forgroup performance. The estimated ultimaterecovery (EUR) for a producing entity isobtained by extrapolating the trend to aneconomic production limit. The extrapolationis valid provided that::

• Past trend(s) were developed with thewell producing at capacity.

• Volumetric expansion was the primarydrive mechanism. The technique is notvalid when there is significantpressure support from an underlyingaquifer.

• The drive mechanism and operatingpractices continue into the future.

Production decline curves are a simple visualrepresentation of a complex productionprocess that can be quickly developed,par ticularly with today’s software andproduction databases. Curves that can beused for production forecasting include:

• production rate versus time,• production rate versus cumulative

production,• water cut percentage versus cumulative

production,• water level versus cumulative

production,• cumulative gas versus cumulative oil,

and• pressure versus cumulative

production.

Decline curves a) and b) are the most commonbecause the trend for wells producing fromconventional reservoirs under primaryproduction wil l be “exponential ,” inengineering jargon. In English, it means thatthe data will present a straight line trendwhen production rate vs. time is plotted on

a semi-logarithmic scale. The data will alsopresent a straight l ine trend whenproduction rate versus cumulativeproduction is plotted on regular Cartesiancoordinates. The well’s ultimate productionvolume can be read directly from the plot byextrapolating the straight line trend to theproduction rate economic limit.

The rate versus time plot is commonly usedto diagnose well and reservoir performance.Figure 4.1 presents a gas well with anexponential “straight line” trend for muchof its production life. But in 2004 the actualperformance is considerably below theexpected exponential decline rate, indicatinga non-reservoir problem. Wellboremodelling suggests that under the currentoperating condit ions, the well cannotproduce liquids to surface below a criticalgas rate of about 700 Mscfd, which is aboutthe rate when well performance starteddeviating from the expected exponentialdecline. Water vapour is probably condensingin the wellbore and impeding productionfrom the well. Removing the water wouldrestore the well’s production rate to theexponential trend.

Critical gas rate under current line pressure @ ~0.610 MMscf/d

Flow rate less than criticalgas rate and well loads upwith liquid

Gas

Rat

e M

Msc

f/d

Figure 4.1. Gas well example showing liquid loading in the wellbore.

16

Figure 4.2 is an example of a pumping oilwell that encountered a pump problem. Arapid decline in production rate to belowthe exponential decline rate cannot be areservoir issue and must therefore be dueto equipment failure and/or near wellboreissues such as wax plugging or sol idsdeposition in the perforations. In this case,the pump was replaced and the fluid ratereturned to the value expected forexponential decline.

Arps (1945, 1956) developed the initial seriesof decline curve equations to model wellperformance. The equations were initiallyconsidered as empirical and were classifiedas exponential, hyperbolic, or harmonic,depending on the value of the exponent ‘b’that characterizes the change in productiondecline rate with the rate of production (seeFigure 4.3 and formulas at the end of thearticle). For exponential decline, ‘b’ = 0; forhyperbolic ‘b’ is generally between 0 and 1.Harmonic decl ine is a special case ofhyperbolic decline where ‘b’ = 1.

The decline curve equations assume thatreservoir rock and fluid properties (porosity,permeabil ity, formation volume factor,viscosity, and saturation) governing the flowrate will not change with time or pressure.

While the assumption is not entirelycorrect, industry experience has proven thatdecline curves present a practical way toforecast well production in all but the mostunusual circumstances.

Figure 4.3 illustrates the difference between

exponential, hyperbolic, and harmonic declinewhen production rate vs. cumulativeproduction is plotted on Cartesian scales.The “straight” orange line extrapolates anexponential decline from the data. The greenand blue l ines present hyperbolicextrapolations of the data trend with ‘b’

Figure 4.2. Pumping oil well where pump capability is decreasing.

Figure 4.3. Production history rate versus cumulative production with associated decline formulas.

17

values of 0.3 and 0.6, respectively. Note thatthe curvature of the line increases as the ‘b’value increases.

Figure 4.3 also illustrates the main challengesin decline analysis – data scatter and the typeof extrapolation that is appropriate for thewell under consideration. Data scatter is anunavoidable consequence of dealing with realdata. In western Canada, the permanentrecord of production and injection consistsof monthly totals for gas, oil, and waterproduction; operated hours; and wellheadpressure. For oil wells at least, monthlyproduction at the battery is routinely pro-rated back to the individual wells, based onsequential 1-2 days tests of individual wellcapability. Depending on the number of wellsand test capability at each battery, it can takeup to several months to obtain a test oneach well in the group.

Factors that determine the rate of decline

and whether declines are exponential,hyperbolic, or harmonic include rock andfluid properties, reservoir geometry, drivemechanisms, completion techniques,operating practices, and wellbore type. Thesefactors must be understood prior toanalyzing the production decline trends orserious errors in the ultimate productionestimates can result (see Figure 4.4).

As stated previously, oil and gas wellsproducing conventional (>10 mD)permeabil ity reservoirs under primarydepletion (or fluid expansion) generallyexhibit exponential decline trends. But theperformance of some waterfloods andunconventional low permeabi l ity gasreservoirs are better modeled usinghyperbolic decline trends.

Figure 4.4 presents an example of wellproduction from a “tight” gas reservoir. Thesereservoirs are becoming increasingly

important to the industry but they typicallyhave permeability below 0.1 md and aregenerally not productive without some formof mechanical fracture stimulation. FromFigure 4a, a slightly hyperbolic (approximatelyexponential) extrapolation of the mostrecent production data yields an ultimaterecovery of approximately 1.8 Bcf. But thehyperbolic decl ine trend of Figure 4bprovides a good f it for the completeproduction history and indicates an ultimaterecovery of 7.6 Bcf.

The typical range of ‘b’ values isapproximately 0.3 to 0.8. A ‘b’ value of 2represents an upper limit to the volume ofgas that will ultimately be produced. Theuncertainty in the trend that should be usedto forecast well performance can bereflected in the assigned reserves as follows:

• Proven = 1.8 Bcf• Proven + Probable + Possible = 7.6 Bcf

Based on the reserve def init ions, theassignment suggests there is a 95% chancethat the actual volume recovered will begreater than 1.8 Bcf and less than 7.6 Bcf. Anestimate for the proven plus probablevolume can be developed by integrating thewell pressure history and material balancegas-in-place (OGIP) estimate with the declineanalysis trend.

ReferencesReferencesReferencesReferencesReferencesArps, J. J. 1945. Analysis of Decline Curves.Trans. AIME, v. 160, p. 228-247.

Arps, J. J. 1956. Estimation of Primary OilReserves. Trans. AIME, v. 207, p. 182-191.

Canadian Institute of Mining, Metallurgy andPetroleum. 2004. Determination of Oil andGas Reserves, Petroleum SocietyMonograph Number 1, Chapter 18.

Canadian Oil and Gas Evaluation Handbook.2005. Volume 2, Detailed Guidelines forEstimation and Classification of Oil and GasResources and Reserves. Section 6:Procedures for Estimation and Classificationof Reserves.

Stotts, W. J., Anderson, D. M., and Mattar, L.2007. Evaluating and Developing Tight GasReserves – Best Practices. SPE paper #108183 presented at the 2007 SPE RockyMountain Oil and Gas TechnologySymposium, Denver, CO, USA, 16-18 April,2007.

Formulas :Formulas :Formulas :Formulas :Formulas :The Exponential decline equation is: q = qi

exp{ -Dt }

where:

Figure 4.4. Tight gas well example illustrating minimum and maximum values for EUR depending indecline methodology.

Expotential DeclineEUR = 1.8 Bcf

Hyperbolic Decline (b = 2)EUR - 7.6 Bcf

Rate vs. Cumulative Prod.

Gas Cumulative Bcf

Gas

Rat

e M

Msc

f/d

Rate vs. Cumulative Prod.

Gas Cumulative Bcf

Gas

Rat

e M

Msc

f/d

18

qi is the initial production rate (stm3/d),q is the production rate at time t (stm3/d),t is the elapsed production time (d),D is an exponent or decline fraction (1/d).

Solving for D and t gives:

D = - ln { q/qi } / t and t = - ln { q/qi } / D

The cumulative production to time t (Np) isgiven by:

Np = q dt = qi exp{ -Dt } dt = (qi - q) / D

The Hyperbolic decline equation is:q = qi { 1 + bDit }

-1/b

where:

qi is the initial production rate (stm3/d),q is the production rate at time t (stm3/d),t is the elapsed production time (d),Di is an initial decline fraction (1/d),b is the hyperbolic exponent (from 0 to 1).

Solving for Di and t gives:Di = [ (qi /q)b - 1 ] / bt and t = [ (qi /q)b - 1 ] /Di b

The cumulative production to time t (Np) isgiven by:

Np = q dt = qi { 1 + bDit }-1/b dt

= { qib / [ (1 - b)Di ] }[ qi

1-b - q1-b ]

The Harmonic decline equation is:

q = qi / { 1 + Dit }

where:

qi is the initial production rate (stm3/d),q is the production rate at time t (stm3/d),t is the elapsed production time (d),Di is an initial decline fraction (1/d).

Solving for Di and t gives:

Di = [ (qi/q) - 1 ] / t and t = [ (qi /q)-1 ] / Di

The cumulative production to time t (Np) isgiven by:

Np = q dt = qi { 1 + Dit }-1 dt

= { qi / Di } ln { qi /q }

I I

I I

I I

19

With sufficient production, material balancetechniques offer an alternative, largelyindependent, method of estimating theoriginal hydrocarbons in-place (OOIP andOGIP) to supplement the direct volumetriccalculation. A material balance of a pool’shistory can also help to identify the drivemechanism and the expected recovery factorrange, since different drive mechanismsdisplay different pressure behaviours for thesame cumulative production. Figure 5.1presents the different P/Z curve trends thatresult from different drive mechanisms.

Material balance calculations are commonlyused to answer reservoir developmentquestions but the technique can also helpwith the interpretation of reservoirgeometry. Geological and geophysicalmapping will give an indication of a pool’sshape and orientation but typically theconfidence in the in-place volume is not highunless the well and/ or seismic control isabundant. Conversely, material balance canreveal a great deal about the volume of areservoir but nothing about its shape ororientation. The combination of the twooften greatly improves the understanding andinterpretation of the pool parameters.

Material balance uses actual reservoirperformance data and therefore is generallyaccepted as the most accurate procedure forestimating original gas in place. In general, aminimum of 10 to 20% of the in-place volumemust be produced before there is sufficientdata to identi fy a trend and rel iablyextrapolate to the original in-place volumethrough material balance. Thus materialbalance is of direct use to the developmentgeologist who is attempting to identify infilland step-out drilling locations to optimizethe depletion of a pool. To the explorationist,material balance is probably most often usedto describe the production behaviour ofanalogous producing pools.

The material balance procedure describesthe expansion of oil, gas, water, and rockover time as a pool is produced. When fluidis removed from a reservoir, reservoirpressure tends to decrease and the remainingfluids expand to fill the original space.Injection situations, such as waterfloodingor gas storage, are handled by treating theinjection volumes as negative production.

The material balance equation is simply aninventory of the mass of al l materials

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 5 – Material Balance Analysis by Ray Mireault, P. Eng., and Lisa Dean, P. Geol., Fekete Associates Inc..

entering, exiting, and accumulating in thereservoir. For the sake of convenience, thismass balance is usually expressed in termsof reservoir voidage (see CIM Monograph 1,page 143 for the general material balanceequation). In theory, the original in-placevolume can be determined knowing only:

• Oil, gas, water, and rockcompressibility.

• Oil formation volume factor (Bo) andsolution gas ratio (Rs) at thepressures considered.

• The amount of free gas in the reservoirat initial reservoir pressure.

• Connate water saturation.• Production/injection volumes and the

associated reservoir pressures.

In practice, the material balance calculationis quite complex and its application requiresseveral simplifying assumptions, including:

• A constant reservoir temperature isassumed despite changes in reservoirpressure and volume. For most casesthe approximation is acceptable, asthe relatively large mass and heatconduction capability of reservoirrock plus the relatively slow changes

in pressure create only smallvariations in reservoir temperatureover the reservoir area.

• A constant reservoir volume assumesthat changes in the pore space of therock with pressure depletion are sosmall that they can be ignored. Theassumption is valid only when there isa very large contrast betweenreservoir rock compressibility andthe compressibility of the containedfluids.

Typical compressibility ranges are:

• Rock: 0.2 to 1.5x10-6 kPa-1

• Gas: 10-3 to 10-5 kPa-1 (Variessignificantly with reservoirpressure.)

• Water: 0.2 to 0.6x10-6 kPa-1

• Oil: 0.4 to 3x10-6 kPa-1

Thus rock compressibility can be ignored innormally pressured or volumetric gasreservoirs (see Figure 5.1) and oil reservoirswith free gas saturation. Ignoring rockcompressibility in over-pressured reservoirsand in fluid systems that do not have a gasphase will overestimate the original in-place

Figure 5.1. Gas reservoir P/Z material balance diagnostics.

20

hydrocarbons (see Figure 5.2).

• Representative pressure / volume /temperature (PVT) data for the oil, gasand water in the reservoir. Usually, thechallenge is to obtain a representativeoil sample for laboratory analysis.Bottomhole sampling can inadvertentlylower the sampling pressure and causegas to come out of solution. Surfacesampling requires accuratemeasurements of oil and gas productionduring the test to correctly recombinethe produced streams. Gas reservoirsampling requires accuratemeasurement of the gas and condensateproduction and compositional analysisto determine the composition andproperties of the reservoir effluent.

• Accurate and reliable production datadirectly impacts the accuracy of the in-place estimate. Produced volumes of oil(and gas if it’s being sold) are generallyaccurate because product sales metersat the oil battery and gas plant are keptin good repair. Prorationing of themonthly sales volumes back through thegathering system(s) to the individualwells is standard industry practice. Itintroduces a level of uncertainty in thereported production values for thewells that can generally be tolerated,

provided the prorationing is performedin accordance with industry standards.

• A uniform pressure across the pool isassumed because the properties of thereservoir f luids are al l related topressure. In practice, average reservoir

pressures at discrete points in time areestimated from analyses of wellpressure build-up tests (we’ll talk aboutwell tests in another article). Althoughlocal pressure variations near wellborescan be ignored, pressure trends acrossa pool must be accounted for. Theadditional uncertainty in the pressureestimate introduces another challengeto the hydrocarbon in-place calculationsbut is generally tolerable.

A material balance can be performed for asingle well reservoir (or flux unit) or a groupof wells that are all producing from acommon reservoir / flux unit. However, wellproduction and pressure information iscommonly organized into “pools” orsubsurface accumulations of oil or gas byregulatory agencies, on the basis of theinitially available geological information. The“pool” classification does not account forinternal compartmentalization so a singlepool can contain multiple compartments/reservoirs/flux units that are not in pressurecommunication with each other. To furtherconfuse the issue, the word “reservoir”is often used interchangeably with theword “pool” and is also used to refer tothe “reservoir” rock regardless of fluidcontent. For clarification, in this series ofarticles “reservoir” means an individual,hydraulically isolated compartment withina pool.

Thus the first real world challenge to areliable material balance is identifying whichportions of the off-trend data scatter aredue to measurement uncertainty, pressuregradients across the reservoir, and different

Figure 5.2. Multi-well gas reservoir P/Z plot.

Figure 5.3. Multi-well gas reservoir pressure vs. time plot.

21

pressure trends over time due to reservoircompartmentalization. For gas reservoirs(oil reservoirs will be discussed in nextmonth’s Reservoir), a pressure vs. time plot(see Figure 5.3) greatly assists in thediagnosis as follows:

• The accuracy of electronic pressuregauges has dramatically reduced theuncertainty in the interpreted reservoirpressure due to gauge error. It can causesmall random variat ions in theinterpreted pressures but themagnitude is so small that it is seldom afactor when a pressure deviates fromthe trend line on a P/Z plot.

• Inadequate bui ld-up t imes duringpressure tests lead to interpretedreservoir pressures at the well that arealways less than true reservoirpressure.

• Pressure gradients across a reservoirare always oriented from the wells withthe greatest production to wells withlittle or no production.

• The failure to separate and correctlygroup wells into common reservoirs isthe most common reason for excessivedata scatter. Wells producing fromdif ferent reservoir compartments

within a common pool will each havetheir own pressure/time trend that canbe identified with adequate productionhistory and used to properly group thewells.

For confidence in the original-gas-in-placeestimate of Figure 5.2, Figure 5.3 comparesa computer-predicted “average” reservoirpressure, based on the combined productionhistory of the grouped wells and theinterpreted gas-in-place volume of Figure 5.2,with the interpreted reservoir pressuresfrom well pressure bui ld-up tests. Al lpressure measurements fol low thepredicted trend, which indicates that thewells have been correctly grouped into acommon reservoir.

Well pressures that fall below the trend lineof Figure 5.3 are consistent with aproductioninduced pressure gradient acrossthe reservoir (well G and I) and/or aninadequate build-up time during pressuretesting (wells D and G). For the occasionalanomalous reservoir pressure in a seriesthat otherwise follows the trend, othercircumstances may justify a detailed reviewof selected well build-up tests and theirinterpretation. The horizon(s) tested, thereservoir geometry, formation permeabilityand depth variations across the reservoir,the type of test (static gradient, wellhead,

flow, and buildup), the length of the test(shut-in time for buildups), the temperaturegradient in the reservoir, and the accuracy ofthe fluid composition all contribute to theaccuracy of the reservoir pressureinterpretation.

The classical P/Z plot for normally pressuredgas reservoirs is perhaps the simplest formof the material balance equation and so it isintroduced first. Rock and water expansioncan be ignored because of the high gascompressibility. Assuming an isothermal orconstant temperature reservoir andrearranging terms yields the equation in theform of a straight line y = b - mx as follows:

P / Z = (Pi / Zi ) – Q * ( Pi / (Gi * Zi))

Where:

P = the current reservoir pressureZ = the gas deviation from an ideal gas atcurrent reservoir pressurePi = the initial reservoir pressureZi = the gas deviation from an ideal gas atinitial reservoir pressureQ = cumulative production from thereservoirGi= the original gas-in-place

As the equation and Figures 5.1 and 5.2indicate, when there is no production,current reservoir pressure is the initialreservoir pressure. When all the gas hasbeen produced, reservoir pressure is zeroand cumulative production equals the initialgas-in-place volume.

A straight line on the P/Z plot is common inmedium and high (10 to 1,000 mD)permeability reservoirs. A strong upwardcurvature that develops into a horizontalline, as presented in Figure 5.1, demonstratespressure support in the reservoir and isusually associated with a strong water drive.Formation compaction can cause a non-linear,downward trend, as in the example of Figure5.2. However, a downward trend may alsobe caused by unaccounted-for wellproduction from the reservoir.

A slight upward curvature in the P/Z plotindicates some gas influx into the mainreservoir from adjacent t ight rock asillustrated by Figure 5.1 and the single wellreservoir of Figure 5.4. The upward curvaturei l lustrates that there is a s igni f icantpermeability difference between the mainreservoir and the adjacent rock. A limitedupward curvature on P/Z plots is beingobserved with increasing frequency in Albertaas medium and high permeability reservoirsare produced to depletion and the industrydevelops lower and lower permeability plays.

Figure 5.4. Single well gas reservoir P/Z plot.

22

ReferencesReferencesReferencesReferencesReferences

Canadian Institute of Mining, Metallurgy andPetroleum, 2004. Determination of Oil andGas Reserves. Petroleum SocietyMonograph Number 1, Chapter 7.

Canadian Institute of Mining, Metallurgy andPetroleum, 2005. Canadian Oil and GasEvaluation Handbook, Volume 2, DetailedGuidelines for Estimation and Classificationof Oil and Gas Resources and Reserves.Section 6: Procedures for Estimation andClassification of Reserves.

Cosentino, Luca, 2001. Integrated ReservoirStudies. Gulf Publishing Company. Chapters5-6.

Mattar, L. and Anderson, D, 2005. DynamicMaterial Balance (Oil or Gas-in-place withoutShut-ins). SPE paper # 2005-113, presentedat the 2005 Canadian International PetroleumConference, Calgary, AB, Canada, 7-9 June2005.

Mattar, L. and McNeil, R, 1998. The “Flowing”Gas Material Balance. Journal of CanadianPetroleum Technology, Volume 37, No. 2,Pages 52-55.

Rahman, Anisur N.M., Anderson, D., andMatter, L., 2006. New, Rigorous MaterialBalance Equation for Gas Flow in aCompressible Formation with Residual FluidSaturation. SPE Paper #100563, presented atthe 2006 SPE Gas Technology Symposium,Calgary, AB., 15-17 May 2006.

23

Material balance calculat ions for oi lreservoirs are more complex than for gasreservoirs. They must account for thereservoir volumes of the produced fluids andthe effect of pressure depletion on the oilvolume remaining in the reservoir. They mustaccount for the formation, expansion, andproduction of solution gas. The calculationsmust also account for the expansion of thereservoir rock and formation water, sincethey have similar compressibility as oil. Asnoted in last month’s ar ticle , typicalcompressibility ranges are:

• Rock: 0.2 to 1.5x10-6 kPa-1

• Gas: 10-3 to 10-5 kPa-1 (Variessignificantly with reservoirpressure.)

• Water: 0.2 to 0.6x10-6 kPa-1

• Oil: 0.4 to 3x10-6 kPa-1

Nonetheless, in theory, material balancecalculations can provide an independentestimate for the original oil-in-place for asolution gas drive reservoir with sufficientproduction history.

Havlena and Odeh (1963) developed a usefulgraphical procedure for estimating the oil-in-place volume for a solution gas drivereservoir (see Figure 6.1). By rearrangingthe material balance equation so that thetotal withdrawals from the reservoir aregrouped onto the y axis while al l theexpansion terms are grouped on the x axis,the correct oil-in-place value will generate astraight line trend on the graph. Thus the oilvolume for a solution gas drive reservoircan be determined by successively iteratinguntil a straight line is achieved. Upwardcurvature indicates that the value selectedas the OOIP is too small . Downwardcurvature indicates that the selected value islarger than the true size of the oil deposit.Various formulations of the material balanceequation can be sourced in any of thereferences cited.

Figure 6.2 presents a Havlena-Odeh plot fora solution gas drive reservoir with an OOIPof 49 MMSTB. The four points calculated fromreservoir pressure measurements are ingood agreement with the predicted trendbased on the OOIP value. Inadequatepressure buildup time may be the reasonthat the third pressure measurement comesin slightly below the predicted trend line.

When an oil deposit has a gas cap, the

material balance calculations must alsoaccount for gas cap expansion andproduction. However, there are now toomany unknowns to develop a unique solutionby material balance alone. Estimating the oil-in-place in the presence of a gas cap firstrequires a volumetric estimate for the size

of the gas cap. Then the size of the oil depositcan be estimated via material balancecalculations.

Though it cannot independently determinethe oil-in-place volume when a gas cap ispresent, the Havlena-Odeh plot can assist in

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 6 – Material Balance for Oil Reservoirs by Ray Mireault, P. Eng.; Chris Kupchenko, E.I.T.; and Lisa Dean, P. Geol., Fekete Associates Inc.

Figure 6.1. Gas reservoir P/Z material balance diagnostics.

Figure 6.2. Multi-well gas reservoir P/Z plot.

24

confirming the consistency of the proposedsolution. For every gas cap volume, therewill be a corresponding oilin- place volumethat together result in a straight l inepressure trend on the Havlena- Odeh plot.As before, upward curvature on the plotindicates that the OOIP value is too small;downward curvature that it is too large(Figure 6.3).

In practice, a table of values for OOIP is oftenset up and iteration performed on the ratioof the reservoir volume of the gas caprelative to the oil-inplace (referred to as“m”). Now upward curvature on theHavelena-Odeh plot indicates that the “m”value (size of the gas cap) is too small relativeto the selected oil volume. Downwardcurvature indicates that “m” (size of the gascap) is too large (Figure 6.3).

Due to the fact the solution is non-uniquemany combinations of OOIP and “m” can befound that will mathematically match thereservoir production and pressure history.Mathematically successful solutions can rangefrom:

• A large oil volume with a relativelysmall gas cap.

• A small oil volume with a relativelylarge gas cap.

• Multiple intermediate oil and gas capvolume combinations.

The dilemma can usually be resolved by using

geological knowledge to identify the materialbalance solution(s) consistent with thereservoir’s physical geometry. Thisconsistency check provides the best chanceof determining the correct magnitude ofOOIP and OGIP.

Geologic knowledge of the reservoirgeometry is also essential when attemptingto assess fluid influx into a reservoir. Forexample, water influx into a D-3 reef withan underlying aquifer could be assessed byperiodically logging selected wellbores todetermine and relate a rising oil-waterinterface to a water influx volume. Once theinflux volume is estimated, in theory amaterial balance estimate for the original oil-in-place volume can be calculated. However,internal compartmentalization of the reefinto multiple reservoirs may make the tasksignificantly more challenging than might beconcluded from this article.

The Havlena-Odeh plot is also useful whenfluid influx is suspected, as in possible inflowacross a fault. In theory, measured reservoirpressures on a Havlena-Odeh plot willexhibit (Figure 6.4):

• A straight line for a volumetric (solutiongas or gas cap) expansion reservoirprovided the OOIP and OGIP values arecorrect.

• An upward curvature when there ispressure support due to fluid influx.

• A downward curvature when there is apressure deficit.

The Havlena-Odeh plot cannot however,identify the reason for pressure support orthe pressure deficit. Potential reasons forpressure support include:

• An unaccounted-for water injection/disposal scheme.

• Flow from a deeper interval via a fault oracross a fault from an adjacent reservoircompartment. Note that the fluid canbe any combination of oil, gas, and water.

• “U tube” displacement of the producingreservoir’s water leg by a connectedreservoir. The connected reservoir isusual ly gas-bearing and may beundiscovered.

• Expansion of water. Due to the limitedcompressibility of water (0.2 to 0.6x10-6

kPa-1) the water volume must be at least10 times the reservoir oil volume forwater expansion to provide pressuresupport. Thus the Cooking Lake aquiferunderlying Alberta D-3 oil pools has thepotential but water legs in clasticreservoirs are too small.

Potential reasons for a pressure deficit ordownward curvature include:

• Later time interference fromunaccounted-for producing wells.

• Rock compressibility in anoverpressured reservoir.

• An inflow that gradually decreases overtime, perhaps because of depletion orbecause flow across the fault decreases/ceases below a certain pressurethreshold.

In cases where fluid inflow is suspected,knowledge of the reservoir geometry is anabsolute requirement to limit the possiblereasons for either an upward or downwardcurving trend.

Thus far, the discussion has been on thetheoretical challenges to material balanceanalysis. In addition, a real world challengeis the scatter that is present in the pressuredata. As with gas systems, oil well pressuredata must first be correctly grouped intocommon reservoirs to generate reliabletrends. But oil pressure data generallyexhibits greater scatter because:

• Longer build-up times are required to

Figure 6.3. Multi-well gas reservoir pressure vs. time plot.

25

extrapolate the pressure data to areliable estimate of reservoir pressure,due to the increased viscosity of oil

• Pressure gradients across the reservoirare more pronounced, due to the oilviscosity.

• Pressure differences in an oil column,due to the density of the oil , aresufficient to require careful correctionto a common datum.

• Multiple perforation intervals andinadvertent commingling of intervalsthat were isolated by nature creates thepotential for crossflow and furtherconfuses the pressure datainterpretation.

Other potential sources of error include:

• Thermodynamic equil ibrium is notattained.

• PVT data that does not representreservoir conditions.

• U ncertainty in the “m” ratio.

• Inaccurate production allocation.

Yet despite the foregoing theoretical andpractical challenges, material balance analysishas proven its worth, with the accuracy ofthe analysis generally increasing as thereservoir is produced. In Fekete’sexperience, the most reliable analyses areobtained by integrating the reservoirgeology; fluid properties; and the wellproduction, pressure, and completionhistories into a consistent explanation.

ReferencesReferencesReferencesReferencesReferencesCanadian Institute of Mining, Metallurgy andPetroleum, 2004. Determination of Oil andGas Reserves. Petroleum SocietyMonograph Number 1, Chapter 7.

Havlenah, D., and Odeh, A.S. 1963. TheMaterial Balance as an Equation of a StraightLine. Trans., AIME, Vol. 228, p. 896.

Canadian Oil and Gas Evaluation Handbook,2005. Procedures for Estimation andClassification of Reserves, Vol 2, Section 6.

Craft, B.C., and Hawkins, M.F., 1964. AppliedPetroleum Reservoir Engineering. PrenticeHall Inc., Englewood Cliffs, NJ.

Canadian Institute of Mining, Metallurgy andPetroleum, 2004. Determination of Oil andGas Reserves. Petroleum SocietyMonograph Number 1, Chapter 7.

Figure 6.4. Single well gas reservoir P/Z plot.

Canadian Institute of Mining, Metallurgy andPetroleum, 2005. Canadian Oil and GasEvaluation Handbook, Volume 2, DetailedGuidelines for Estimation and Classificationof Oil and Gas Resources and Reserves.Section 6: Procedures for Estimation andClassification of Reserves.

Cosentino, Luca, 2001. Integrated ReservoirStudies. Gulf Publishing Company. Chapters5-6. Mattar, L. and Anderson, D, 2005. DynamicMaterial Balance (Oil or Gas-in-place withoutShut-ins). SPE paper # 2005-113, presentedat the 2005 Canadian International PetroleumConference, Calgary, AB, Canada, 7-9 June2005.

Mattar, L. and McNeil, R, 1998. The “Flowing”Gas Material Balance. Journal of CanadianPetroleum Technology, Volume 37, No. 2,Pages 52-55.

Rahman, Anisur N.M., Anderson, D., andMatter, L., 2006. New, Rigorous MaterialBalance Equation for Gas Flow in aCompressible Formation with Residual FluidSaturation. SPE Paper #100563, presented atthe 2006 SPE Gas Technology Symposium,Calgary, AB., 15-17 May 2006.

Aprilia, A.W., Li, Z., McVay, D.A. & Lee, W.J.,SPE Gas Tech Symposium May 15-17 2006,Calgary. SPE Paper 100575-MS

Canadian Institute of Mining, Metallurgy andPetroleum, Determination of Oil and Gas

Reserves, Petroleum Society MonographNumber 1, 1994.

SPEE and CIM, Canadian Oil and GasEvaluation Handbook, Vol 2. Detai ledGuidelines for Estimation and Classificationof Oil and Gas Resources and Reserves,November 2005.

26

Let’s start off with a simple situation:

• Well A produces at 100 bopd from areservoir that contains 1 millionsbarrels of oil.

• Well B also produces at 100 bopd froma reservoir that also contains 1millions barrels of oil.

Are these two wells worth the same?

The answer is NO. This is because Well A isin a high permeability reservoir, but has azone of reduced permeability around thewellbore (damage caused by drilling mudfiltrate invasion or clay swelling). If this wellwere to be stimulated its rate would increasesignificantly. On the other hand, Well B is ina low permeability reservoir, which is thefactor that limits its production rate.

How can we identify the differences betweenthese two wells? The answer is well testing.

Well testing, often called pressure transientanalysis (PTA), is a powerful tool forreservoir characterization. The followinginformation can be extracted from well tests:

• Permeability – The value obtained from awell test is much more useful than thatfrom core analysis , because itrepresents the in-situ, ef fectivepermeability averaged over a largedistance (tens or hundreds of metres).

• Skin (damage or stimulation) – Most wellsare either damaged or stimulated, andthis has a direct effect on thedeliverability of the well. The skin is ameasure of the completion effectivenessof a well. A positive skin (typically +1 to+20) represents damage, while anegative skin (typical ly -1 to -6)represents improvement.

• Average reservoir pressure – Thisparameter, which is either measureddirectly or extrapolated from well testdata, is used in material balancecalculat ions for determininghydrocarbons-inplace.

• Deliverability potential – The IPR (inflowperformance relationship) or the AOF(absolute open f low) is used inforecasting a well’s production.

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering Fering Fering Fering Fering For Gor Gor Gor Gor GeeeeeolooloolooloologggggistsistsistsistsistsArticle 7 – Well Test Interpretation by Louis Mattar, P. Eng. and Lisa Dean, P. Geol., Fekete Associates Inc.

• Reservoir description – Reservoir shape,continuity, and heterogeneity can bedetermined from pressure transienttests

• Fluid samples – The reservoir fluidcomposition and its PVT (pressure-volume-temperature) properties canhave a signi f icant effect on theeconomics and production operations.

Well testing is also an integral part of goodreservoir management and ful f i l lsgovernment regulations.

FUNDAMENTALS:::::• A well test is a measurement of flow

rate, pressure, and t ime, undercontrolled conditions. While the well

is flowing, the quality of the data is oftenpoor, thus the data during a shut-in isusually analyzed.

• Opening or closing a well creates apressure pulse. This “transient” expandswith time, and the radius investigatedduring a test increases as thesquareroot of time. The longer the flowtest, the further into the reservoir weinvestigate.

• Because of the diffusive nature ofpressure transients, any valuesdetermined from a well test representarea averages and not localized pointvalues.

• The analysis of oil well tests is similar

Figure 7.1. Drawdown and build-up test.

Figure 7.2. Semi-log (Horner) plot of build-up data.

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Figure 7.4. Modeling comparison of synthetic and measured pressures.

to that of gas well tests. The theory isderived in terms of liquid flow, and isadapted for use with gas by convertingpressure to “pseudo-pressure ( )” andtime to “pseudo-time(ta).”

• The practice of testing a flowing oil welland a gas well is similar – measure thebottom-hole pressure. However, for apumping oil well, it is often not easy tomeasure the bottom-hole pressuredirectly, so it is usually calculated fromsurface data and Acoustic Well Sounders,thereby having a greater potential forerror. This article will concentrate onthe analysis of the two most commonwell test types in Alberta, namely “build-up” and “deliverability” tests.

• Build-up test*: To conduct a build-up test, simply shut

the well in. It is obvious that a build-uptest must be preceded by one or moreflow periods. Figure 1 shows thesimplest possible build-up, a shut-in thatfol lows a single constant rate. Inpractice, the period preceding thebuildup will often consist of variablerates, and even multiple flows and shut-ins. These non-constant flow periodscannot be ignored, but must beaccounted for during the analysis. Thisis done through a mathematical processcalled superposition, which convertsthese variable flow periods into anequivalent constant rate.

• Deliverability tests: The purpose of these tests is to

determine the long term deliverabilityof a well, rather than defining thepermeability and skin (as in build-uptests). There is one overriding factor inthese tests; it is that at least one of theflow durations must be long enough toinvestigate the whole reservoir. Thiscondition is known as “stabilized” flow.Sometimes it is impractical to flow awell for that long. In that case, thestabilized condition is calculated fromthe reservoir characteristics obtainedin a build-up test.

INTERPRETATION:::::Interpretation of well test data is oftenconducted in two stages. The first is adiagnostic analysis of the data to reveal thereservoir model and the second is modelingof the test.

DDDDDAAAAATTTTTA PREA PREA PREA PREA PREPPPPPARAARAARAARAARATION:TION:TION:TION:TION:To analyze the build-up data, it is transformedinto various coordinate systems in order toaccentuate different characteristics. The most

useful transformation is the “derivative” plot,obtained as follows:

1. Plot the shut-in pressure, p (for gas*,_ ) versus log {(t+ t)/ t}, where t isthe duration of the flow period (orthe corresponding superposition time,when the flow period has not beenconstant) and t is the shut-in time. Asemi-log plot of this is called aHorner plot and is shown in Figure7.2.

2. Determine the slope of the Hornerplot at each t. This slope is called thederivative.

3. Plot the derivative versus t on log-log graph paper (Figure 7.3).

4. Calculate p (for gas*, ), thedifference between the build-up andthe last flowing pressure.

5. On the same log-log graph as thederivative, plot p (for gas, )versus _ t (Figure 7.3).

DIADIADIADIADIAGGGGGNONONONONOSSSSSTIC ANTIC ANTIC ANTIC ANTIC ANALALALALALYYYYYSIS:SIS:SIS:SIS:SIS:The buildup is divided into three timeregions – early, middle, and late time. Themiddle time represents radial flow, and it isnot until middle time is reached that thepermeability can be determined. In Figure7.2, the permeability is calculated from theslope of the semi-log straight line, and inFigure 7.3, from the vertical location of theflat portion of the derivative. These twoanswers should be the same.

The skin is calculated from the p curve. InFigure 7.3, the larger the separation betweenthe curves in the middle time region, themore positive is the skin.

Early time represents the wellbore and thenearwellbore properties (effects of damage,acidizing, or hydraulic fracture). It is oftenassociated with a (log-log) straight line offixed slope. A slope equal to “one” means

Figure 7.3. Derivative plot of build-up data.

*Injection and fall-off tests are analyzed the same way as a build-up– simply replace the production rate by the injection rate, and thepressure rise by the pressure fall.

*In well testing the corrections caused by pseudo-time are usuallynegligible. For simplicity this article will use “t” rather than “ta”.

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“wellbore storage,” and during that period,nothing can be learned about the reservoirbecause the wellbore is still filling up. Aslope of “half” typically means linear flow asa result of a hydraulic fracture. From thisstraight line, the fracture length or fractureeffectiveness can be calculated i f thepermeability is known.

The period after middle time is known aslate time, and it reflects the effect of thereservoir boundaries and heterogeneities.It is from this region that the reservoir shapecan be determined. A straight line of slopeapproximately “half” would indicate a long,narrow reservoir. A straight line slopeapproximately “one” could imply a lowpermeability reservoir surrounding theregion investigated during middle time. If thederivative trends downward during the latetime period, it could indicate an improvementin permeability (actually mobility) away fromthe well. If this downward curvature is

severe, it might be indicative of a depletingreservoir.

The average reservoir pressure (pR) isobtained by extrapolating the semi-logstraight line to infinite shut-in time (=1 onthe Horner plot). This extrapolation is calledp* and it is used, along with an assumedreservoir shape and size, to calculate theaverage reservoir pressure. For short flowdurations, for example in a DST or in theinitial test of a well, the correction from p*to pR is negligible, and p* does equal pR.

MODELING:::::Once the analysis has been completed andan approximate reservoir descriptiondeduced, a mathematical model of thereservoir is constructed. This model utilizesthe production history of the test (all theflow and shut-in data) to generate “synthetic”pressures which are then compared with thepressures that were actually measured during

the test (Figure 7.4). The values of theparameters in the model (permeability, skin,distances to boundaries, etc.) are varied untilan acceptable match is obtained between thesynthetic and measured pressures.

This process, called modeling or historymatching, is a powerful mathematical tool,but must be used with caution, as it can resultin mathematically correct, but physicallymeaningless answers. Some very complexreservoirs (multi-layers, heterogeneous,etc.) can be modeled using sophisticatedmathematical models, but for theseinterpretations to be meaningful, they mustbe consistent with known geologicaldescriptions and realistic physical wellcompletions.

TYPES OF WELL TESTS:TYPES OF WELL TESTS:TYPES OF WELL TESTS:TYPES OF WELL TESTS:TYPES OF WELL TESTS:• RFT*, WFT*, MDT*, RCI*, FRT* – These

are tests of very short duration(minutes) conducted on a wireline,usually while the well is drilling. Thepopular use is for determining thereservoir pressure at various depths.

• DST (drill stem test) – conducted duringdri l l ing of exploratory wells , todetermine reservoir fluids, reservoirpressure and permeability. OnshoreDSTs are usually open hole, whereasoffshore DSTs are cased hole. An open-hole DST typically consists of a 5-minutepre-flow and a 30-minute build-up. It isanalyzed exactly like the build-up testdescribed above. Because of the shortflow durations, p* does equal pR. Itshould be noted that on most “scouttickets” what is reported is not p* orpR, but the ISI (initial shut-in pressure)and the FSI (final shut-in pressure). Inlow permeability reservoirs, the FSI isusually less than the ISI, and sometimesthis difference is misconstrued as beingcaused by depletion occurring duringthe test (which implies a small reservoirand could lead to abandonment of thatzone).

• Build-up – The well is shut-in, followingone or more f low periods. Thepressure is measured and analyzed togive permeability, skin, average reservoirpressure, and reservoir description.This is the most commonly analyzed testbecause it is often quite long (severaldays of flow and several days of shut-in)and the data quality is usually good.

• Interference or pulse – These testsinvolve flowing one well (active) butmeasuring the pressure at another well

Figure 7.5. Modified isochronal test.

Figure 7.6. AOF plot.

*Trade Marks: RFT=Repeat Formation Tester, WFT=WirelineFormation Tester, MDT=Modular Dynamic Tester, RCI= ReservoirCharacterization Instrument, FRT=Flow Rate Tester

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(observation), and are used todetermine interwell connectivity.

• IPR – These tests are designed to yieldthe long-term deliverability of the well,and are not concerned with determiningthe reservoir characterist ics Thedeliverability test for an oil well is calledIPR (inflow performance relationship).It describes the inf low into thewellbore at various bottom-holepressures. The test consists of a singleflw until stabilization is reached, atwhich time the oil and water flow ratesand the flowing pressure are measured.An IPR is plotted according to knownrelationships such as the Vogel IPRequation.

• AOF (absolute open flow) – An AOF testis the gas well equivalent to a liquid IPRtest. It too must have at least one flowrate to stabilization. It differs from aliquid IPR in several ways:

• Often more than one flow rate isrequired. This is because gas flow in thereservoir can be turbulent (liquid flowis laminar) and the degree of turbulencecan be assessed only by uti l iz ingmultiple flow rates.

The governing equation is not Vogel’s buta “Back-Pressure Equation” of the formq = C ( p2)n, where q is the flow rate, C aconstant that depends on the well ’scharactereistics (permeability, skin, etc.) andn is a measure of turbulence. Values of nrange from 1 to 0.5, where n = 1 meanslaminar flow and n = 0.5 means fully turbulentflow.

• P2 is used instead of pseudo-pressure asa simplification.

• Typically four different flow rates areselected (e.g., four hours each) with a4-hour intervening shut-in. These arecalled the isochronal points. If the timeto stabilization is too long, then the“stabi l ized” rte is replaced by an“extended” flow (3 to 5 days). Theresults of the build-up analysis are usedto calculate what the stabilized flow rateand pressure would have been.

A best-fit straight line is drawn through theisochronal data on a log-log plot of ˜p2

versus q. A line parallel to that is drawnthrough the stabilized point (NOT theextended point) (Figure 7.6). This is thestabilized deliverability line and is used fordetermining the flow rate that correspondsto any specified back-pressure. Extrapolatingthis l ine to pR

2 gives the maximumdeliverability potential of the well (when the

back-pressure is zero, ˜p2 = pR2) . This

maximum is called the AOF (absolute openflow) and is one of the most commonly usedindicators of the well ’s del iverabi l itypotential.

• PITA (perforation inflow test analysis) –In these tests, sometimes referred toas PID (perforation inflow diagnostic),the well is perforated and the pressurerise in the closed wellbore is recorded,and interpreted to yield an estimate ofpermeability and reservoir pressure.These tests are useful for “tight gas”where most other tests would take toolong because of the very lowpermeability.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESEnergy Resources Conservation Board.1979. Gas Well Testing – Theory and Practice.ERCB, Guide G3 (Directive 034), 547 p.

Lee, J., Rollins, J.B., and Spivey, J.P. 2003.Pressure Transient Testing. Society ofPetroleum Engineers, v. 9, 376 p.

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RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 8 – Rate Transient Analysis by Louis Mattar, P. Eng., Ray Mireault, P. Eng., and Lisa Dean, P. Geol., Fekete Associates Inc..

While a well is producing, a lot ofinformation can be deduced about the wellor the reservoir without having to shut it infor a well test. Analysis of production datacan give us significant information in severalareas:

1. Reserves – This is an estimate of therecoverable hydrocarbons, and isusual ly determined by tradit ionalproduction decline analysis methods, asdescribed in Article #4 in this series(Dean, L. and Mireault, R., 2008).

2.Reservoir Characteristics –Permeability, well completion efficiency(skin), and some reservoircharacteristics can be obtained fromproduction data by methods of analysisthat are extensions of well testing(Mattar, L. and Dean, L., 2008)

3. Oil- or Gas-In-Place – The modernmethods of production data analysis

(Rate Transient Analysis) can give theOriginal- Oil- In-Place (OOIP) orOriginal-Gas-In- Place (OGIP), if theflowing pressure is known in additionto the flow rate.

The principles and methods discussed in thisarticle are equally applicable to oil and gasreservoirs, but – for brevity – will only bepresented in terms of gas.

TRADITIONAL METHODS : RESERVESTRADITIONAL METHODS : RESERVESTRADITIONAL METHODS : RESERVESTRADITIONAL METHODS : RESERVESTRADITIONAL METHODS : RESERVESFrom an economic perspective, it is not whatis in the reservoir that is important, butrather what is recoverable. The industry termfor this recoverable gas is “Reserves.” Thereare several ways of predicting reserves. Oneof these methods, traditional decline analysis(exponential, hyperbolic, harmonic) hasalready been discussed in Article #4. Themethod is used dai ly for forecastingproduction and for economic evaluations.Generally, the results are meaningful, but theycan sometimes be unrealistic (optimistic or

Figure 8.1. Traditional decline - example 1.

pessimistic), as will be illustrated by thefollowing examples.

Example 1, shown in Figure 8.1, clearlyexhibits an exponential decline. It is obviousfrom this Figure that the recoverablereserves are 2.9 Bcf. Typically this type of gaswell has a recovery factor of 80% (0.8), andone can thereby conclude that theoriginalgas- in-place (OGIP) = 2.9/0.8 = 3.6Bcf. By using the modern rate transientanalysis described later in this article, it willbe shown that this value of OGIP is grosslypessimistic.

Example 2, (Figure 8.2, page 30), also exhibitsan exponential decline. It can be seen fromthis Figure that the recoverable reserves are10 Bcf. Assuming a recovery factor of 80%(0.8), the OGIP = 10/0.8 = 12.5 Bcf. By usingthe modern rate transient analysis describedlater in this article, it will be shown that thisvalue of OGIP is optimistic.

Example 3, (Figure 8.3, page 30) is a tight gas

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Figure 8.2. Traditional decline - example 2.

Figure 8.3. Traditional decline - example 3.

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Figure 8.5. Rate transient analysis - type curve match - example 2.

Figure 8.4. Rate transient analysis - type curve match - example 1.

well and has been analyzed using hyperbolicdecline. The reserves are 5.0 Bcf which (usinga recovery factor of 50% for tight gas)translates to an OGIP equal to 10 Bcf. Byusing the modern rate transient analysisdescribed later in this article, it will beshown that this value of OGIP is overlyoptimistic.

Typical ly, the tradit ional methods ofdetermining reserves do not work wellwhen the operating conditions are variable,or in the case of tight gas. The above threeexamples fall into these categories, and whilethe results appear to be reasonable, it willbe shown using the modern methodsdescribed below, that they are in error;sometimes by a significant amount.

MODERN METHODS :MODERN METHODS :MODERN METHODS :MODERN METHODS :MODERN METHODS :HYDROCARBONS-IN-PLACE ANDHYDROCARBONS-IN-PLACE ANDHYDROCARBONS-IN-PLACE ANDHYDROCARBONS-IN-PLACE ANDHYDROCARBONS-IN-PLACE ANDRESERVOIR CHARACTERISTICSRESERVOIR CHARACTERISTICSRESERVOIR CHARACTERISTICSRESERVOIR CHARACTERISTICSRESERVOIR CHARACTERISTICSThere are two signif icant di f ferencesbetween the traditional methods and themodern methods:

a. The traditional methods are empirical,whereas the modern methods aremechanistic, in that they are derivedfrom reservoir engineeringfundamentals.

b. The traditional methods only analyzethe flow rate, whereas the modernmethods utilize both the flow ratesand the flowing pressures.

The modern methods are known as ratetransient analysis. They are an extension ofwell testing (Mattar, L. and Dean, L., 2008).They combine Darcy’s law with the equationof state and material balance to obtain adifferential equation, which is then solvedanalytically (Anderson, D. 2004; Mattar, L.2004). The solution is usually presented as a“dimensionless type curve,” one curve foreach of the different boundary conditions,such as: vertical well , horizontal well,hydraulically fractured well, stimulated ordamaged well, bounded reservoir, etc.

To analyze production data using ratetransient analysis, the instantaneous flowrate (q) and the corresponding flowingpressure (pwf) are combined into a singlevariable called the normalized rate (= q/( p))and this is graphed against a time functioncalled material-balance time. As in welltesting (Mattar, L. and Dean, L., 2008), aderivative is also calculated. The resulting dataset is plotted on a log-log plot of the samescale as the type curve, and the data movedvertically and horizontally until a match isobtained with one set of curves. Figure 8.4shows the type curve match for the data ofExample 1. This procedure is known as typeFigure 8.6. Rate transient analysis - type curve match - example 3.

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curve matching, and the match point is usedto calculate reservoir characteristics suchas permeabil ity, completion (fracture)effectiveness, and original-gas-in-place.

The data sets of Examples 2 and 3 have beenanalyzed in the same way, and the type curvematches are shown in Figures 8.5 and 8.6.Note that the type curves for each of theseexamples have different shapes because theyrepresent di f ferent well /reservoirconfigurations. Figures 8.4 and 8.5 representa damaged or acidized well in radial flow,whereas Figure 8.6 represents a hydraulicallyfractured well in linear flow.

In addition to the type curve matchingprocedure described above, another usefulmethod of analysis is known as the flowingmaterial balance (Mattar, L. and Anderson, D.M., 2005). The flow rates and the flowingpressures are manipulated in such a way thatthe flowing pressure at any time (while thewell is producing) is convertedmathematically into the average reservoirpressure that exists at that time. Thiscalculated reservoir pressure is thenanalyzed by material balance methods(Mireault, R. and Dean, L., 2008), and theoriginal-gas-in-place determined. The flowingmaterial balance plot for the data set ofExample 1 is shown in Figure 8.6, and theresults are consistent with those of the typecurve matching of Figure 8.4.

SSSSSUMMARUMMARUMMARUMMARUMMARY OF REY OF REY OF REY OF REY OF RESSSSSULULULULULTTTTTS :S :S :S :S :When Examples 1, 2, and 3 are analyzed usingmodern Rate Transient Analysis, and theresults compared to those from thetraditional methods, the following volumesare obtained:

Example#: OGI P (Traditional) OGI P (Modern)

#1 3.6 Bcf 24 Bcf#2 12.5 Bcf 6.9 Bcf#3 10.0 Bcf 1.3 Bcf

The reasons for the discrepancies aredifferent in each case. In Example 1, thef lowing pressure was continuouslyincreasing due to infill wells being added intothe gathering systems, which caused anexcessive production rate decl ine. InExample 2, the flow rate and flowing pressurewere declining simultaneously. The declinein flow rate would have been more severewith a constant flowing pressure. In Example3, the permeability is so small that the datais dominated by linear flow into the fracture(traditional methods are NOT valid in thisflow regime).

In rate transient analysis, once the reservoircharacteristics have been determined, areservoir model is constructed tohistorymatch the measured data. The modelis then used to forecast future productionscenarios, such as dif ferent operatingpressures, different completions, or welldrilling density.

A word of caution is warranted. Data qualitycan range from good to bad. Multiphase flow,liquid loading in the wellbore, wellhead tobottomhole pressure conversions,interference from infill wells, multiwellpools, rate allocations, re-completions, andmultilayer effects can all compromise dataqual ity and complicate the analysis .Notwithstanding these potentialcomplications, it has been our experiencethat significant knowledge has been gainedby analyzing production data using themodern methods of rate transient analysis.

REFERENCES :REFERENCES :REFERENCES :REFERENCES :REFERENCES :Anderson, D. 2004. Modern ProductionDecline Analysis, Getting the Most Out ofYour Production Data. Technical Video 2. http://www. fekete.com/aboutus/techlibrary.asp.

Dean, L. and Mireault, R. 2008. ReservoirEngineering For Geologists, Part 4:Production Decline Analysis. CanadianSociety of Petroleum Geologists Reservoir,Vol. 35, Issue 1. p. 20-22.

Mattar, L. 2004. Evaluating Gas-In-Place, CaseStudies Using Flowing and Shut-In Data.Technical Video 4. http://www.fekete.com/aboutus/techlibrary.asp.

Mattar, L. and Anderson, D. M. 2005. DynamicMaterial Balance (Oil or Gas-In-PlaceWithout Shut-Ins). CIPC.

Mattar, L. and Dean, L. 2008. ReservoirEngineering For Geologists, Part 6: Well TestInterpretation. Canadian Society ofPetroleum Geologists Reservoir, Vol. 35,Issue 3. p. 22-26.

Mireault, R. and Dean, L. 2008. ReservoirEngineering For Geologists, Part 5: MaterialBalance. Canadian Society of PetroleumGeologists Reservoir, Vol. 35, Issue 2. p. 24-26.

Figure 8.7. Flowing material balance - example 1.

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RERERERERESESESESESERRRRRVVVVVOIR EOIR EOIR EOIR EOIR ENGNGNGNGNGINEINEINEINEINEEEEEERING FRING FRING FRING FRING FOR GOR GOR GOR GOR GEEEEEOLOOLOOLOOLOOLOGGGGGISISISISISTTTTTSSSSSArticle 9 – Monte Carlo Simulation/Risk Assessment by: Ray Mireault P. Eng. and Lisa Dean P. Geol., Fekete Associates Inc.

Geologist A is presenting a developmentprospect. Geologist B is presenting anexploration play. Which should you investin?

This is a daily question in oil companies. Adevelopment prospect is general lyconsidered a “safer” investment but thevolume of hydrocarbons and its economicvalue is limited (Figure 9.1). The explorationprospect may carry more “dry hole” risk buta company has to make some explorationdiscoveries or it eventually runs out ofdevelopment opportunities (Figure 9.2).

However, simply estimating the size of thedeposit is not sufficient. Although GeologistA’s development prospect has a P10 to P90recoverable gas range of between 258 and1,219 106 m3 (10 to 43 BCF), it may or maynot be a good investment. For example:

• Low permeability reservoir rock mayrestrict production rates so that eachwell recovers very little gas over time.The low rate/long life profile mayactually have very little economic value.

• The combination of royalty rates,operating costs, processing fees, andtransportation tariffs may mean thatvery little of the sales revenue is retainedby the company, despite an apparentlyattractive commodity sale price outlook.

• Capital costs may simply be too great. Ifthe prospect is located offshore (or ata remote onshore) location, theprospect may contain insufficient gas tooffset the required investment capital.

Management needs to know the followingabout any exploration or developmentopportunity:

• What are the chances that at least thevalue of the capital investment will berecovered if we proceed?

• How much capital could be lost if eventsdo not turn out as expected?

• What is the potential gain in economicvalue if events do unfold as expected?

• What is the total capital commitmentrequired to realize production?

Figure 9.1. Probability chart, gas development prospect.

Answering the financial questions would be(relatively) easy if we knew exactly howmuch oil/gas is in place, the fraction that willbe recovered, its sale price when produced,and the associated capital and operatingcosts. But prior to producing a deposit, wedon’t know any of the foregoing with anydegree of precision. We need to assess andbalance the uncertainty in our technicalknowledge against the impact that theuncertainty has on the expected financialperformance (and capital exposure) of theinvestment.

When consistently applied, Monte Carlosimulation provides a tool to systematicallyassess the impact of technical uncertaintyon financial performance . A consistent

approach also enables comparison andranking of development and explorationopportunities, so a company can identify andpursue its better prospects.

In Fekete’s experience , the fol lowingassessment procedure provides a consistentapproach to prospect evaluation:

1. Estimate the probable range in OOIP/OGIP from 3-point estimates for theinput parameters in the volumetricequation.

2. Estimate the probable range in recoveryfactor from reservoir engineeringprinciples, analogue performance, and/or reservoir simulation.

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3. Estimate the total field/pool dailyproduction rate range from therecoverable hydrocarbon range basedon a seven year rate-of-take (depletethe field in about 15 years).

4. Estimate the number of wells requiredto achieve the projected dai lyproduction rate from reservoir rockcharacterist ics and test wel lperformance.

5. Estimate the type and size of pipelines,wellsite, and plant facilities required toproduce at the forecasted productionrates.

6. Estimate operating costs and assess thepresent day value of production fromeconomic runs. This is the discountedpresent day value of the sales price lessroyalties, operating costs, processingfees, and transportation tariffs.

7. Estimate well and facility capital costs.

8. Compare the probable range ineconomic value to the required capitalinvestment range. Quantify the chancesof recovering the capital investment, theexpected return on investment, thecapital exposure, and the total capitalcommitment.

The job of the earth sciences (geology,geophysics, reservoir engineering) in a MonteCarlo evaluation is to develop inputparameter ranges that reflect the currentstate of knowledge for the prospect. Therecommended approach is an integratedapproach that first develops minimum andmaximum values that are consistent with theknown facts. The end point values mustencompass the true value with a high (90 to95%) degree of certainty. The most likelyvalue is estimated only after establishing thepossible range in the parameter values.

Geologist A’s development prospect is astructural trap with 4-way closure thatcontains a series of stacked fluvial sands at adepth of about 400 m. The sands were initiallydeposited in a broad valley and are cappedwith a thick shale sequence. Subsequentbasement uplift created the present drapestructure. Drilling results to date set theminimum area of the deposit at 600 ha. Basedon the seismic interpretation, the arealextent is most likely about 1000 ha but itcould be as large as 1,600 ha (the maximumclosure area with the existing data).

The structure is estimated to contain about46 m of gross sand thickness within a 60 mgross interval. Due to fluvial deposition, theareal extent of an individual sand body is

expected to be limited and so not all sandsare expected to be gas charged. Accordingly,the average net pay is estimated to bebetween 12 and 46 m but will most likely beabout 21 m.

The geological model and limited cuttingsanalysis suggest that sand porosity alsovaries. I f the deposit is dominated byargillaceous, highly cemented sands, thenaverage porosity could be as low as 8%.However, porosity will be either betterdeveloped or better preserved when fluvialrock is saturated with hydrocarbons, so alarge percentage of ultra-clean sands couldpush the average porosity value to as muchas 18%. Assuming average quality sands,porosity will most likely be about 12%.

Currently, there is no good basis from whichto estimate the residual water saturation inthe gas-bearing sands. The best value forgood-quality sands would be 15% Sw. Anaverage water saturation value for the “dirty”fine-grained sands might be about 40% butcould be as high as 60% (the maximum value

for fine-grained sand).

Well test data indicates that the depositcontains a sweet, 0.7 gravity gas. Two pressurebuildup tests indicate a reservoir pressureof 3,448 and 4,138 kPa(abs) for an arithmeticaverage of 3,793 kPa(abs). Reservoirtemperature is estimated at 38°C. The gasdeviation factor (Z) at initial reservoirconditions is estimated to be about 0.9.

Sand permeabil ity is expected to varyconsiderably between individual sands witha range of 3 to 30 mD. Based on experienceand reservoir engineering principles, gasrecovery from volumetric expansion of areservoir at shallow depth is generally inthe order of 70 to 85%. Due to the limitedareal extent of the sands, the most likelyvalue is estimated at 75%

The following table summarizes the inputparameters that were used to develop thevolumetric estimates of gas-in-place andrecoverable gas for the developmentprospect:

Figure 9.2 Probability chart, oil exploration prospect.

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OGIP=A*h* *(1-Sw)* ((Ts* Pi) / ( Ps*Tf*Z))

Once 3-point estimates have been developed,Monte Carlo simulation can be used tocalculate the gas-in-place and recoverable gasvolumes. Monte Carlo simulation consistsof randomly selecting values for each inputparameter and calculating a gas-in-place andrecoverable gas volume. Many iterations (inthis case 10,000) creates gas-in-place andrecoverable gas distributions.

From the simulation, Geologist A’s gasdevelopment prospect has an 80% probabilityof containing between 380 and 1,624 106m3

of gas-in-place. Based on the technical input,there is an 80% chance that the recoverablegas volume is between 285 and 1,219 106m3

of gas. The mathematical significance of theP50 value is that it is the number that splitsthe distribution into 2 equal halves.

An obvious question is why can’t we simplymultiply all the minimum input parametervalues to determine the minimum gas volumeand all the maximum values for the maximumvolume? Doing so yields the following values:

As can be seen, the minimum values are muchless than the P90 values calculated previouslyand the maximum values are much greater.Even a calculation using the most likely valuesdoesn’t match the P50 values very well. Frominspection of the probability graph (Figure9.1) the chances of recovering more than120 106m3 of gas are greater than 98% (100-2%). At the other end of the scale, there isless than a 2% chance of producing 3,880106m3 from the prospect (the probabilityvalue corresponding to 3,880 106m3 is welloff the scale).

The reason for the large discrepancies isbecause the error in the product ofmultiplication successively increases witheach multiplication, unlike addition. Toillustrate, if the estimated value for eachinput parameter is out by 17%, the sum ofaddition will also be out by 17%. Not so withmultiplication:

Even alternating from a conservative to anoptimistic estimate doesn’t completely cancelout the errors when multiplying.

N

37

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 10 – Monte Carlo Simulation/Risk Assessment (cont.) by: Ray Mireault, P. Eng. and Lisa Dean, P. Geol., Fekete Associates Inc.

In the introductory article (Article 9),recoverable gas from Geologist A’sdevelopment prospect was estimated to bebetween 285 and 1,219 106m3 of gas.

Figure 10.1. Probability chart, gas development prospect.

What is this gas worth? The first factor toconsider is the time value of production. Thefollowing chart presents the present dayvalue of $100 of future year’s production ata 12% discount rate.

While $100 received today is worth $100,next year’s production is only worth 88% oftoday’s value. In year five it is only worth52.77%; in year ten, 27.85% and in year 20,7.76%. Clearly, we would like to producethe gas as quickly as possible to maximize itsvalue but there is a limit. Each incrementalincrease in production rate requires morewells and larger, more costly facilities so thateventually the incremental value of furtheracceleration cannot offset the increasedcapital requirement.

What should we assume for a depletion rate?In Fekete’s experience, a seven-year rate-of-take provides a starting point for aproduction profile with good economic value.Note that the calculation provides anestimate of the annual produced volumeduring the initial one-to-three years ofproduction. Since well productivity declinesover time, it will take between 10 and 15years to produce the prospect to depletionbut about half the gas will be recoveredduring the initial five years.

Dividing Geologist A’s recoverable gas rangeby seven yields an initial annual productionvolume of between 41 and 176 106m3/yr(Figure 10.1). A daily production rate of

between 118 and 502 103m3/day (also Figure10.1) was obtained by dividing the annualvolume range by 350 producing days per year.

With an es t imated da i l y ra te andknowledge of the gas composition, thetype and size of the central facilities canbe determined. Since the gas containsmostly methane and ethane with no H2Sand a low concentra t ion o f othernonhydrocarbon gases, only dehydrationand compression will be required to treatthe raw gas to sales gas specifications. Ifthe design capacity of the facilities is setat 236 103m3/day of raw gas, a plant with a(typical) 2:1 turndown ratio will be ableto operate down to about 118 103m3/day.

By inspection of Figure 1, 118 103m3/daycorresponds to the 10th percentile of thedaily production rate curve and 236 103m3/day is about the 47th percentile. The plant isthe correct size for the lower 37% of therange and thus capital and operating costsfor the central facilities can be estimated. Ifdevelopment drilling ultimately proves thatlarger facilities are required, increased gasrevenues wil l more than offset theincremental cost of larger facilities.

Geologist A’s prospect also requires a 70km sales gas pipeline to connect to thenearest sales point. The central facility designrate can similarly be used to estimate thesize and associated capital and operating

38

costs of the sales gas pipeline. Accountingfor processing shrinkage and fuel gasconsumption, the 236 103m3/day raw gasproduction rate equates to 217 103m3/day ofsales gas.

The next issue is the number of wellsrequired to produce at the desired rate.From the available test information, a well’s1st year average production rate, based onthe year’s production volume, could rangefrom 3 to 21 103m3/day but most likely willbe about 8.5 103m3/day. Multiplying the rangefor an individual well by the number of wellsyields deliverability curves for the selectednumbers of wells. From inspection of Figure2, about 22 wells will most likely be requiredto provide the required deliverability for theprospect but as few as 15 or as many as 30wells may be needed.

Knowing the number of wells, a scoping levellayout of the well locations and theproduction gathering system can beundertaken. The scoping plan addressesissues such as the timing and sequencing ofwell drilling, drilling and completion design,

Figure 10.2. Probability chart, gas development prospect number of wells required.

surface access, the required wellsite facilities,and wellsite layouts. The level of effortexpended is just sufficient to develop three-point estimates for the capital and operatingcosts of system components.

Contractual terms are obtained from thel icence/lease agreement while a priceforecast(s) for the production period maybe obtained from a variety of sources. Atthis point, estimate ranges have been

developed for all the inputs necessary toevaluate the economics of the prospect. Thegeneral calculation sequence is:

• Calculate the net cash flow for eachyear’s production, NCF = (SalesVolume*Sales Price) - Royalties -Operating Costs - Taxes - Capital

• Discount each year’s net cash flow toits present day value

• Sum each year’s discounted value toarrive at the prospect net presentvalue NPV = {Yearly NCF*YearlyDiscount Factor} (See table 10.1.)

The calculat ions are amenable tospreadsheet analysis (Table 10.1) and MonteCarlo simulation. Since no two prospectsare exactly alike, the calculations and theirpresentation can and should be modified tofit the details of each particular situation.

Although the final goal of Monte Carlo is togenerate the expected NPV range forGeologist A’s prospect, Fekete has found ituseful to calculate some intermediate valuesas follows:

• Calculate the cash flow for each year’sproduction before capital investment,CF = (Sales Volume*Sales Price) -Royalties - Operating Costs - Taxes

• Discount each year’s cash flow to itspresent day value (PV)

• Sum each year’s discounted value toarrive at the prospect present dayvalue PVCF = {Yearly CF*YearlyDiscount Factor}

• Categorize each year’s capitalinvestment and discount it to itspresent day value

PVcapital = Sales line*DF + Plant*DF +Gathering System*DF + Dev. Wells*DF

PVcapital = {PVsales lines + PVplant+ PVgathering system + PVdev. wells}

• Calculate the net present value NPV =PVCF-PVcapital

The mathematical manipulation generatesthe same NPV range for a prospect. But

Table 10.1. Example input spreadsheet, in any given year. Net present value @ 12% = annual net cashflow * 12% discount factor. Net present value @ 12% = PV before investment @ 12% - PV of capitalinvestment.

E

E

E

39

additionally, the present day value of a unitof production can be estimated by dividingthe prospect’s present day value beforecapital (highlighted in blue) by the projectedtotal gas sales volume (in pink).

In Fekete’s experience, the uncertainty rangeon the present day value of a unit ofproduction is relatively small compared tothe uncertainty range of the inputparameters. The reason is because increasedsales revenue, due to higher productionvolumes and/or gas prices tends to be offsetby increased royalties, operating costs, andtaxes. Conversely, lower revenue scenarioshave reduced royalties, operating costs, andtaxes.

At the time that Geologist A’s prospect wasevaluated, its unit of production PV wasestimated to be between $35.50 and $71per 103m3 ($1 to $2/Mcf). Using Monte Carlosimulation to multiply the unit PV by therecoverable gas estimate yields the presentday value of the prospect before capitalinvestment. As shown in Figure 10.3, thereis an 80% probability (P10 to P90 values)

that Geologist A’s prospect has a presentday value before capital of between $12 and$66 Million.

While the PV before investment range lookspromising, it must be compared with therequired capital investment to know if theprospect has economic potential . Thepresent value capital costs for the prospectwere estimated for each category as follows:

Figure 10.3. Probability chart, gas development prospect present value (PV).

Monte Carlo simulation can be used tosuccessively add the cost range for each

category and estimate the total capital costrange for the project. Cost estimates forwell costs and wellsite facilities that wereprovided on a per well basis were addedtogether and then mult ipl ied by thedistribution for the expected number ofdevelopment wells to determine the totalcost range for the development well category.

The development well category should alsoinclude the cost of the dry holes that will beencountered. The number of dry holes canbe estimated by dividing the number of wellsrequired by the drilling success rate to yieldthe total number of drilling attempts thatmust be undertaken. Multiplying by the chanceof a dry hole (between 15 and 30%) yieldsthe number of dry holes that are likely to beencountered. Multiplying by the cost per dryhole yields an estimated range of values fortotal dry hole cost. The updated capital costtable follows:

As can be observed, the sales pipeline andthe wells are the two largest capital costcategories. Monte Carlo simulation is oncemore used to add the separate costdistributions and estimate the range of totalcosts for the project. In Fekete’s experienceit is useful to track the effect of eachsuccessive cost category on the total costprofile as follows:

From Figure 10.4 (p. 40), the P10 (blue line)and P90 (upper red line) values of the capitalcost range intersect the PV before capitalinvestment curve at about the 43rd and 63rdpercentiles. Thus the prospect has betweena 37 and 57% chance of achieving a positiveNPV. The graph also illustrates that even atthe upper end of the reserve range we

40

cannot do any better than double the valueof the capital invested and that the salespipeline and well costs have the greatestimpact on financial performance.

Should a prospect with these financialcharacteristics be developed? One companymay choose to develop the prospect becausethis is the best investment opportunityavailable at the time. Another may determinethat its time has not yet come and choose towait until the price of gas rises sufficientlyand/or other developments in the areareduce the distance and cost of the salespipeline. Either way, a consistent MonteCarlo evaluation methodology helpsmanagement make informed decisions.

Can Monte Carlo simulation also evaluateGeologist B’s exploration prospect? We’llshow you how in the next issue of theReservoir.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESMackay, Virginia (ed.). 1994. Determinationof Oil and Gas Reserves. Petroleum SocietyMonograph No. 1, p. 106-119.

Otis, Robert M. and Schneidermann, Nahum1997. A Process for Evaluating ExplorationProspects, AAPG Bulletin, v. 81 p. 1087- 1109.

Pal l isade @ Risk Guide . Version 4.5November, 2005

Figure 10.4. Probability chart, gas development prospect PV vs. Capital.

41

RERERERERESESESESESERRRRRVVVVVOIR EOIR EOIR EOIR EOIR ENGNGNGNGNGINEINEINEINEINEEEEEERING FRING FRING FRING FRING FOR GOR GOR GOR GOR GEEEEEOLOOLOOLOOLOOLOGGGGGISISISISISTTTTTSSSSSArticle 11 – Monte Carlo Simulation/Risk Assessment (cont.) by Ray Mireault, P. Eng. and Lisa Dean, P. Geol., Fekete Associates Inc.

The second article (Mireault and Dean, 2008)in the series on Monte Carlo simulationpresented an evaluation methodology forGeologist A’s development prospect. Thislast article extends the methodology toaddress Geologist B’s exploration prospect.

Geologist B interprets a hydrocarbonbearingreef at approximately 1,500 m depth fromthe available seismic data. Wrench tectonicsand strike-slip faults influence the structuralaspects of the play. Underlying shalerepresents a potential local hydrocarbonsource while overlying lime mudstones andcalcareous shales form the prospective caprock.

Core samples and outcrops show up to 30%porosity and are considered to reflect an insitu combination of intra-crystalline and vuggy(moldic) porosity. In situ primary porositymay / may not have been altered over time.

Organic geochemistry suggests a Type IImarine algal source charged the reservoirtarget with light (35-40° API) sweet oil.Reservoir reef and trap geometry areinterpreted to have been in place at the timeof oil generation.

Carbonate reef deposits tend to be oilwetsystems and this particular prospect isinterpreted to sit on basinal material thatprecludes the existence of a mobile aquiferunderlying the reef. Accordingly, watersaturation should approach residual values.Solution gas drive is anticipated with primaryrecovery in the range of 10 to 20%.

From the viewpoint of a Monte Carlosimulation, after an exploration prospect hasbeen discovered it will require developmentcapital to achieve production, just like anyother development prospect. Thus anexploration prospect is no more than adevelopment prospect with an additionalstep. Accordingly, the financial questions tobe answered become:

• Does the prospect present sufficienteconomic potential to proceed withdevelopment (assuming it contains thepostulated volume of hydrocarbons)?If so,

• How much additional (“risk”) capital isrequired to create a high (70%)probability of locating a hydrocarbon-

Figure 11.1. Oil exploration prospect.

bearing deposit (i.e., how manyexploratory wells need to be drilled)?

• Are the prospect economicssufficiently attractive to accommodateboth the development and explorationcosts?

DEVDEVDEVDEVDEVEEEEELOPMELOPMELOPMELOPMELOPMENNNNNT EVT EVT EVT EVT EVALALALALALUUUUUAAAAATIONTIONTIONTIONTIONCOMPONENTCOMPONENTCOMPONENTCOMPONENTCOMPONENTAs with Geologist A’s development prospect,Monte Carlo simulation was used tovolumetrically estimate the potential oil-in-place and recoverable oil volumes. GeologistB’s input parameter ranges are in Table 1.

As presented in the Volumetric Estimationarticle (Dean, 2008), the equations for oilare:

OOIP = A * h * * (1 - Sw) * 1/Bo

Recoverable Oil = OOIP * Recovery Factor

Figure 11.1 graphically presents the prospectpotential based on the foregoing inputparameters. Dividing the recoverable oil

Table 11.1. Geologist B’s input parameter ranges.

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42

Figure 11.2. Oil exploration prospect number of wells required.

range by a seven-year rate-of-take providesthe initial annual production volume. Theinitial daily production rate assumes 350producing days per year.

Theoretical estimates of well productioncapability range between 80 and 320 m3/day.From the graphical comparison of Figure11.2, between 6 and 20 wells will probablybe required to achieve the initial targetproduction rate, with 12 wells as a most likelyvalue.

prospect from the individual capital costranges (Table 11.5).

At the time Geologist B’s prospect wasevaluated, the present-day (PV) value of acubic metre of production was estimated tobe between $25 and $38/m3. Based on theestimate, the expected PV before capital forthe prospect is between $62 MM and $798MM (Figure 11.3).

The development capital items and theirassociated capital costs at the time of theevaluation are summarized in Table 11.3.

Based on the estimate of between 6 and 20development wells and the cost estimatesfor an individual well (and dry hole) MonteCarlo simulation was used to generate therequired range of development drillingcapital (Table 11.4).

Table 11.2. Estimated volumes.

Table 11.3. Capital Cost Estimates (all values inmillions of dollars).

Table 11.4. Development Drilling Costs (all valuesin millions of dollars).

Table 11.5. Cumulative Development Costs (allvalues in millions of dollars).

Simulation was also used to generate thecumulative development cost profile for the

By inspection of Figure 11.3, the P90 limit oftotal development costs ($44.9 MM)intersects the PV before Capital Curve atabout the 6th percentile. Thus, there is inexcess of a 94% chance that the prospect, aspostulated to exist, would achieve a positiveNPV on the development capital. With thischance of success, most companies wouldgive the prospect further consideration.

EEEEEXXXXXPLORAPLORAPLORAPLORAPLORATION “RISK” CTION “RISK” CTION “RISK” CTION “RISK” CTION “RISK” CAPITAPITAPITAPITAPITALALALALALEEEEESSSSSTIMATIMATIMATIMATIMATETETETETESSSSSUnlike development capital, which alwaysgenerates some cash flow from subsequentproduction, exploration “risk” capital isspent without any potential for immediaterevenue generation. The majority of anexploration prospect’s risk capital consistsof:

• The up-front (land) cost for the right toexplore for hydrocarbons on specifiedacreage.

• Data acquisition (largely seismic) coststo infer the presence of prospect(s).

• Exploration drilling to locate ahydrocarbonbearing deposit.

• For offshore exploration, follow-updelineation drilling to confirm theminimum size of deposit needed fordevelopment.

Estimating “land” and seismic acquisition

43

Figure 11.3. Oil exploration prospect present value (PV) potential.

costs is generally straight forward. However,the exploration drilling cost estimate isessentially the number of consecutive dryholes that will be drilled prior to making adiscovery times the cost per dry hole.Exploration dri l l ing is evaluated as acomponent of the total “risk” capital because80 to 97% of the time, the outcome of anindividual drilling attempt is a dry hole.Fur ther, offshore exploration (anddelineation) wells are abandoned aftertesting, irrespective of what they encounter.For onshore evaluations, the successfuldiscovery well can be treated as the firstdevelopment well, as was done for GeologistB’s prospect, or as a “salvaged” explorationattempt.

Otis and Schneidermann (1997) present theconcept of geological success for anexploration well as “having a sustainedstabilized flow of hydrocarbons on test.” Theyestimate the probability of geologic success(Pg) as the product of the individualprobabilities of occurrence for four factorsas follows:

Pg = Psource * Preservoir * Ptrap * Pdynamics

where:Psource is the probability of mature

source rockPreservoir is the probability that reservoir

quality rock existsPtrap is the probability that a trap

existsPdynamics is the probability of appropriate

timing for migration andtrapping

A neutral assessment is assigned a value of0.5. Indirect supportive data increases theassigned probability of occurrence whilenon-supportive data reduces the estimatedvalue. The approach has the advantage that aneutral (50% probability) assignment for all4 factors yields a 6.25% probability ofgeologic success. The value compares withthe industry perception of about a 5% chanceof success on an exploration well.

Fekete has also successful ly used afiveparameter system to estimate the

Table 11.6. Five-factor system parameters.

probability of geologic success as follows:

Pg = Psource * Preservoir * Pstructure * Pseal * Pmigration

Note that the individual subscripts can becustomized to suit each evaluation. A neutral(50%) assignment for all 5 factors yields anoverall chance of geologic success of 3.125%.

In Fekete’s experience, either a four- or fiveparameter system can be used to evaluate aprospect. Which to use often comes downto which the earth science team that is doingthe evaluation is most comfortable with.Fekete has also evaluated prospects with aseven-parameter system (CCOP, July 2000)but when all seven parameters have a neutral(0.5) rating, the chance of geologic successis 0.8%. This does not mean that a seven-parameter system should not be used, butwhen it is, the evaluators must be aware ofthe consequence of additional multiplicationand adjust the input values relative to thevalues that would have been used in a four-or five-factor evaluation.

A five-factor system was used for GeologistB’s prospect and values estimated as shownin Table 11.6.

A 12% chance of success means there is an88% chance of a dry hole on the first drillingattempt. If the drilling sequence is a randomseries of events, as the number ofconsecutive drilling attempts increases, thechance that they wil l al l be dry holesdecreases. Table 11.7 shows the profile,assuming random events.

Table 11.7. Chance of Failure / Success.

44

In reality, we should learn something aboutthe prospect and play with each drillingattempt, so we may consider that less than10 wells are required for a 70% chance ofmaking at least one discovery. Or we maydecide that the drilling locations currentlyavailable to the company are not related andthe above table reasonably presents thechance with each successive attempt.

The consensus for Geologist B was that evenwith luck, a minimum of three dry holeswould be incurred before making a discovery.The more likely value was six (53% chanceof a discovery) but up to ten attempts couldbe required to tip the odds in the company’sfavour. An additional $10 MM was alsorecommended for addit ional seismicacquisition (Table 11.8).

The chance of realizing a positive NPV onthe capital investment can be read from thegraph. From Figure 11.4, upper and lowerlimits of the NPV curve have a value of zeroat about the 43rd and 63rd percentiles. Thechance of achieving a positive NPV on thecapital investment with Geologist A’sdevelopment prospect is between 37 and57%.

In Figure 11.5, the NPV = 0 axis is intersectedat about the 6th and 9th percentiles. IfGeologist B’s exploration interpretation iscorrect, there is between a 91 and 94% chanceof achieving a positive NPV on the capitalinvestment.

For any prospect, management needs toknow:

• The chances that at least the value ofthe capital investment will berecovered if the project proceeds.

• How much capital could be lost ifevents do not turn out as expected.

Figure 11.4. Gas development prospect NPV.

Table 11.8. Exploration Costs (all values in millionsof dollars).

Table 11.9. Cumulative Prospect Capital CostRanges.

From Monte Carlo simulation, total dry holecosts, total exploration costs, and cumulative

prospect capital cost ranges were estimatedas shown in Table 11.9:

With a total exploration and developmentcost of $60.7 MM and a PV before investmentvalue of $62 MM at the 90th percentile(Figure 11.3), the prospect has better than a90% chance of achieving a positive NPV (ifthe deposit really exists). When presentedwith this level of economic attractiveness,most companies would seriously considerpursuing Geologist B’s prospect.

PROSPECT FINANCIAL COMPARISONSFigure 4 summarizes the financial “picture”for Geologist A’s development prospect.Figure 5 presents Geologist B’s explorationprospect. The Max NPV curve is generatedby subtracting the P10 total cost value fromthe NPV before capital curve. The Min NPVcurve is similarly created from the NPVbefore capital curve less the P90 value fortotal capital costs.

• The potential gain in economic value ifevents do unfold as expected.

• total capital commitment required torealize production.

Which prospect would you invest in?

REFERENCESCanadian Institute of Mining, Metallurgy andPetroleum. 1994. Determination of Oil andGas Reserves, Petroleum SocietyMonograph Number 1, Chapter 6.

Canadian Institute of Mining, Metallurgy andPetroleum. 2004. Determination of Oil andGas Reserves, Petroleum SocietyMonograph Number 1, Chapter 6.

Coordinating Committee for Coastal andOffshore Geoscience Programmes in Eastand Southeast Asia (CCOP). 2000. The CCOPGuidelines for Risk Assessment of PetroleumProspects. July, 2000. 35 p.

45

Figure 11.5. Oil exploration prospect NPV potential.

Dean, L. 2008. Reservoir Engineering ForGeologists, Part 3: Volumetric Estimation.Canadian Society of Petroleum GeologistsReservoir, v. 34, no. 11, p. 20-23.

Mireault, R. and Dean, L. 2008. ReservoirEngineering For Geologists, Part 8b: MonteCarlo Simulation / Risk Assessment. CanadianSociety of Petroleum Geologists Reservoir,v. 35, no. 7, p. 14-19.

Otis, Robert M. and Schneidermann, Nahum.1997. A Process for Evaluating ExplorationProspects. AAPG Bulletin, vol. 81 no. 7. p.1087-1109

46

Matrix

Fracture

Matrix

Butt Cleats

Face Cleats

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 12 - Coalbed Methane Fundamentals by Kamal Morad, P. Eng., Ray Mireault, P. Eng., and Lisa Dean, P. Geol., Fekete Associates Inc.

Historically, gas emissions from coal havebeen a nuisance and a safety hazard duringcoal mining operations, causing numerousexplosions and deaths. But today, coalbedmethane (CBM) is an increasingly importantsource of the world’s natural gas productionwith many countries, including Canada,actively developing this unconventionalenergy source.

Currently, CBM accounts for 10% of U.S.natural gas production with the size of theresource (OGIP) estimated at 700 TCF. Themost active areas of production are the SanJuan Basin in New Mexico, the Powder RiverBasin in northeast Wyoming / southeastMontana, and the Black Warrior Basin inAlabama.

In Canada, CBM is still in the early stages ofdevelopment, yet it already accounts forabout 1% of total gas production. The WesternCanada Sedimentary Basin contains themajority of Canada’s estimated 600 TCF ofCBM resource potential. Formations ofgreatest interest are the Mannville, whichtends to produce water as well as gas (a“wet” coal) and the Horseshoe Canyon,which usually produces gas with virtually nowater (a “dry” coal).

In general, coal is classified into four maintypes depending on the quantity and types ofcarbon it contains as well as the amount ofheat energy it can produce. These are:

1. Lignite (brown coal) – the lowest rankof coal; used as fuel for electric powergeneration.

2. Sub-bituminous coal – properties rangebetween lignite and bituminous coal.

3. Bituminous coal – a dark brown to black,dense mineral; used primarily as fuel insteam-electric power generation.

4. Anthracite – the highest rank; a harder,glossy, black coal used primarily forresidential and commercial spaceheating; it may be divided further intopetrified oil, as from the deposits inPennsylvania.

Note that graphite, which is metamorphicallyaltered bituminous coal, is technically thehighest rank of coal. However, it is notcommonly used as fuel because it is difficultto ignite.

COAL CHARACTERISTICSCOAL CHARACTERISTICSCOAL CHARACTERISTICSCOAL CHARACTERISTICSCOAL CHARACTERISTICSCoals are recognized on geophysical logs

because of several unique physicalproperties. The coals typically have very lowgamma, low density, and high resistivityvalues.

Similar to conventional naturally fracturedreservoirs, coal is generally characterizedas a dual-porosity system because it consistsof a matrix and a network of fractures (Figure12.1). For both groups, the bulk of the in-place gas is contained in the matrix. However,matrix permeability is generally too low topermit the gas to produce directly throughthe matrix to the wellbore at significantrates.

In a naturally fractured system, most of theproduced gas makes its way from the matrixto the fracture system to the wellbore. Ifthe well has been hydraulically frac’d, gas mayalso travel from the natural fracture systemto the man-made fracture system to thewellbore. With both conventional naturallyfractured reservoirs and CBM reservoirs, thenatural fracture system has high permeability,

relative to matrix permeability, but verylimited storage capacity.

In coal terminology, natural fractures arecalled “cleats”. The cleat structure consistsof two parts: face cleats and butt cleats(Figure 12.2). Face cleats are typicallycontinuous fractures that go across thereservoir. They are considered the mainpathway for gas production.

Butt cleats are discontinuous, perpendicularto the face cleats and generally act as a feedernetwork of gas into the face cleats.

The effective porosity, permeability, andwater saturation are all properties of thecoal “cleat” system. Since coal permeabilityis a property of the cleat space, it is affectedby the structure and characteristics of thecleat network, e.g., the dominant fractureorientation, fracture continuity, frequency,and width.

The effective permeability of the cleat systemis also influenced by the contrast betweenface and butt cleat permeabil ity. CBMreservoirs are generally considered to beanisotropic systems, where the effectivepermeability is the geometric average of faceand butt cleat permeability. Permeabilityanisotropy creates elliptical drainage areasand should be taken into account whenplacing wells in CBM development projects.

DIFFERENCES WITH CONVENTIONALDIFFERENCES WITH CONVENTIONALDIFFERENCES WITH CONVENTIONALDIFFERENCES WITH CONVENTIONALDIFFERENCES WITH CONVENTIONALRESERVOIRSRESERVOIRSRESERVOIRSRESERVOIRSRESERVOIRSA good starting point to understanding theproduction characterist ics of coalbedmethane reservoirs is by considering thedifferences to conventional gas production.The most significant differences are:

• In a conventional reservoir, the majorityof the gas is contained in the pore spacebut in a CBM reservoir, the majority ofthe gas is adsorbed (bonded to the coalmolecules) in the matrix.

• In a conventional reservoir, reservoirgas expands to the producing wells indirect response to any production-induced ressure gradient. But CBMreservoirs general ly require thatreservoir pressure be below somethreshold value to init iate gasdesorption.

• In a CBM reservoir, a gas molecule mustfirst desorb and diffuse through the coalmatrix to a cleat. It can then moveFigure 12.2. Example of coal cleat structure.

Figure 12.1. Coal is a dual-porosity system.

47

through the cleated fracture system andthe hydraulic frac-stimulation to thewellbore via conventional Darcy flow.

CBCBCBCBCBM GM GM GM GM GAAAAAS SS SS SS SS STTTTTORAORAORAORAORAGGGGGE CE CE CE CE CAPAPAPAPAPABABABABABILILILILILIT YIT YIT YIT YIT YThe primary storage mechanism in CBMreservoirs is adsorption of gas by the coalmatrix. Matrix surface area, reservoirpressure, and the degree to which the coalis gas saturated are the factors that determinethe in-place gas volume of a coal. Note thatthe smaller the coal particle size, the largerthe surface area.

The complete gas-in-place volumetricequation for a CBM reservoir is:

OGIP = A * h * b* GCi + (Ah i(1-Swi) / Bgi)

Where:

• A is drainage area,• h is net pay,• b is bulk density,• GCi is initial Gas Content,• i is porosity,• Swi is initial water saturation• Bgi is initial formation volume factor.

The first term represents the adsorbed gasin the matrix while the second term is thefree gas in the cleats. Since the pore volumein CBM reservoirs is in the order of 1% ofthe total volume, the free gas contributionto the total in-place gas volume is negligible.

As with all volumetric estimates, uncertaintyin the input data creates a range of possibleoutcomes for OGIP. Some common areas ofuncertainty for CBM projects include:

• The gas content of the coal,• The degree of heterogeneity and

complexity contained in CBMreservoirs,

• The impact of modell ing complexmultilayer coal/non-coal geometrieswith simple one- or two-sequencemodels.

CBM GAS DESORPTIONCBM GAS DESORPTIONCBM GAS DESORPTIONCBM GAS DESORPTIONCBM GAS DESORPTIONWhile the relationship between pressuredecline and gas production is essentially astraight line in a conventional reservoir(Figure 12.3), the depletion profile in a CBMreservoir is distinctly non-linear. For a givenpressure drop, a CBM reservoir will desorbsignificantly more gas when the startingreservoir pressure is low compared to whenreservoir pressure is high (Figure 12.4).

If the initial reservoir pressure is significantlygreater than the pressure required to initiatedesorption (the coal is under-saturated), andwater is initially present in the cleat system,then the initial production period mayproduce only water without any gas (Figure12.5). Depending on the degree of under-saturation, dewatering can last from a fewmonths to two or three years and cansignificantly affect the economics of theprospect.

If initial reservoir pressure is equal to thecritical desorption pressure (the coal is gas-saturated), then gas production will start assoon as reservoir pressure begins todecrease. This situation most often appliesto “dry” coals but can also apply to saturated“wet” coals.

The equation that is commonly used todescribe the relationship between adsorbedgas and free gas as a function of pressure isknown as the Langmuir isotherm. Theisotherm is determined experimentally andmeasures the amount of gas that can beadsorbed by a coal at various pressures. TheLangmuir isotherm is stated as:

V = VL * (P / PL + P)

Where:• VL, the Langmuir Volume, is the gas

content of the coal when reservoirpressure approaches infinity.

• PL, the Langmuir Pressure, is the pressurecorresponding to a gas content that ishalf (½) of the Langmuir volume. Thesteepness of the isotherm curve atlower pressures is determined by thevalue of PL.

CBM gas consists primarily of methane (CH4)but may also contain lesser percentages ofcarbon dioxide (CO2) and nitrogen (N2). Ascoal has the strongest affinity for nitrogen

Figure 12.3. Conventional gas P/Z plot.

Figure 12.4. Comparison of desorption volumes with changes in reservoir pressure.

D

D N

N

48

and the weakest affinity for carbon dioxide,the three gases adsorb/ desorb at differentrates from coal (Figure 12.6). Thus, it is notuncommon for the CO2 content of theproduced gas to decrease as gas is producedand reservoir pressure depletes.

CBM GAS TRANSPORT MECHANISMSCBM GAS TRANSPORT MECHANISMSCBM GAS TRANSPORT MECHANISMSCBM GAS TRANSPORT MECHANISMSCBM GAS TRANSPORT MECHANISMSAfter desorbing from the coal, gas in a CBMreservoir uses diffusion to travel throughthe coal matrix to the cleat system. The timerequired to diffuse through the matrix to acleat is controlled by the gas concentrationgradient, the gas diffusion coefficient, and the

cleat spacing. In general , greaterconcentration gradients, larger diffusioncoefficients, and tighter cleat spacing all actto reduce the required travel time. Onreaching a cleat, gas then travels the remainingdistance to the wellbore by conventionalDarcy flow. Since flow in a CBM reservoir isgenerally two-phase flow, fluid saturationchanges in the cleat system and consequentchanges in relative permeabilities becomeimportant.

As the gas is produced from a CBM reservoir,two distinct and opposing phenomena occur

that affect the absolute permeability of thecleat system:

1. As reservoir pressure decreases, itreduces the pressure in the cleats. Cleateffective stress (which is the differencebetween overburden stress and porepressure) increases and compressesthe cleats, causing cleat permeability todecrease.

2. As gas desorbs from the coal matrix,the matrix shrinks. Shrinkage causes thespace within the cleats to widen andthe permeability of the cleats increases.From the Langmuir isotherm (Figure12.4), the amount of gas desorbed for agiven pressure drop is relatively smallat high pressures. Thus in the earlystages of production, the compactioneffect is the dominant factor and cleatpermeability will tend to decreaseslightly. As production continues and gasrecovery becomes significant, matrixshrinkage will dominate and increasecleat permeability.

In “wet” coals, changes in the relativepermeability of the cleat system with changesin water and gas saturation must beconsidered in the Darcy flow equation tocorrectly predict well performance. Asi l lustrated by a typical set of relativepermeability curves (Figure 12.7), the relativepermeability to gas increases with decreasingwater saturation and vice versa.

CBM WELL PERFORMANCECBM WELL PERFORMANCECBM WELL PERFORMANCECBM WELL PERFORMANCECBM WELL PERFORMANCEThe production of CBM wells can begenerally divided into three separate phases(Figure 12.8):

• Dewatering phase (for under-saturatedreservoirs): In this phase, no gas isproduced (excepting in the transientnear wellbore region or in complexreservoirs).

• Negative decline: Water productioncontinues to decl ine while gasproduction increases.

• Production in this phase is generallydominated by the relative permeabilityof gas and water.

• Decline phase: Declining reservoirpressure is now the dominating factoralthough its impact is mitigated to someextent by a shrinking matrix andincreasing cleat permeabi l ity.Nonetheless, the gas production ratedecl ines as in conventional gasreservoirs, albeit at a slower rate ofdecline.

The water production forecast looks similarto a production forecast for a conventionalwater producing reservoir. Maximum waterproduction rates are achieved initially butdecline thereafter through a combination of

Figure 12.5. Desorption behaviour of under-saturated CBM reservoirs.

Figure 12.6. CBM gas storage capacities for N2, CH4, and CO2.

49

reservoir pressure depletion and decreasingrelative permeability to water.

The gas production profile displays both theinitial, dormant period followed by anincreasing production rate till it reaches apeak and then declines. Although reservoirpressure is monotonically declining throughthe l i fe of the simulation well , i t iscounteracted during the inclining productionperiod by increases in the relat ivepermeability to gas and in the absolutepermeability of the cleats.

As the water saturation approaches itsminimum value, declining reservoir pressuredominates and the well goes into the declinephase of its producing life. During this timeperiod, the declining production trendresembles conventional gas production.Note that a “dry” CBM reservoir exhibitsonly the declining portion of the productionpattern.

Given the scope and complexity of the inputsfor CBM reservoirs, simulation is generallyrequired to predict the deliverability and

cumulative production of CBM wells. Asimprovements in drilling, completion andproduction techniques advance, CBM willcontinue to be an increasingly importantsource of natural gas.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESGas Research Institute. 1993. GRI ReferenceNo. GRI-94/0397, “A Guide to CoalbedMethane Reservoir Engineering,” Chicago,Illinois.

Jensen, D. and Smith, L.K. 1997. A PracticalApproach to Coalbed Methane ReservePrediction Using a Modified Material BalanceTechnique. International Coalbed MethaneSymposium, The University of Alabama,Tuscaloosa, Alabama, paper 9765, p. 105-113.

Lamarre, Robert A. 2005. “Coalbed Methane– A Non-Conventional Energy Source WhatIs It And Why Is It Important,” 25th AnnualNorth American Conference of the USAEE/IAEE, Fueling the Future.

Mavor, M.J . 1996. A Guide to CoalbedMethane: Coalbed Methane ReservoirProperties. Gas Research Institute Chicago,Illinois, GRI Reference No. GRI-94/0397,Chapter 4.

Schafer, P.S. and Schraufnagel, R.A. 1996. AGuide to Coalbed Methane: The Success ofCoalbed Methane. Gas Research InstituteChicago, Illinois, GRI Reference No. GRI- 94/0397, Chapter 1.

Steidl, P.F. 1996. A Guide to Coalbed MethaneReservoir Engineering: Coal as a Reservoir.Gas Research Institute Chicago, Illinois, GRIReference No. GRI-94/0397, Chapter 2.

Zuber, M.D. 1996. A Guide to CoalbedMethane: Basic Reservoir Engineering forCoal. Gas Research Institute Chicago, Illinois,GRI Reference No. GRI-94/0397, Chapter 3.

Figure 12.7. Relative permeability to gas and water.

Figure 12.8. CBM well production profile.

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Over the past few years, the production andusage of fossil fuels has increased despiteris ing concern over the atmosphericemission of greenhouse gases (e.g., CO2). Itappears that fossil fuels will remain theenergy of choice for at least a few moredecades. Despite conservation, alternatefuels, constrained supply, and higher prices,the National Energy Board predicts that thedemand for fossil fuels in Canada willcontinue to increase . The InternationalEnergy Agency forecasts similar trends forworldwide demand at least until 2050.

This article does not debate either theoccurrence of global warming or the roleplayed by man-made CO2 emissions. Itinstead considers the similarit ies anddif ferences between hydrocarbonproduction and the geological storage ofCO2. Assuming the public is interested incapturing the CO2 waste created by burningfossil fuels, Alberta is a suitable place for itsgeological storage and the petroleumindustry has the necessary abil ities tosignificantly reduce net CO2 emissions.

COCOCOCOCO2 2 2 2 2 Emissions in Canada and AlbertaEmissions in Canada and AlbertaEmissions in Canada and AlbertaEmissions in Canada and AlbertaEmissions in Canada and AlbertaIn 2000, Canada’s CO2 emissions wereapproximately 725 megatonnes (Mt) (Figure13.1). Alberta and Ontario togetheraccounted for 430 Mt or slightly less than60% of total emissions. Quebec, BritishColumbia, and Saskatchewan togetheraccounted for 220 Mt or about 30%.

How much gas is this? In petroleum industry

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 13 - Geological Storage of C02

by Mehran Pooladi-Darvish, Ph.D., P. Eng. and R. Mireault, P. Eng., Fekete Associates Inc.

Figure 13.1. CO2 emissions (Mt / year) in Canada in 2000 (Bachu, 2008b).Figure 13.2. Large-scale CO2 storage in the Redwater Reef (Gunter andBachu, 2007).

terms, 230 Mt/yr (Alberta’s annual emissions)translates to approximately 12 bcf/d; roughlyequal to Alberta’s daily natural gas productionrate. Conversely, injecting 12 bcf/d of CO2

would require 400 wells, each operating at30 mmcf/d.

While all generated CO2 presents equalpotential in terms of the greenhouse gaseffect, the level of effort needed to collect,purify, and inject CO2 varies with the sourceof the emission. For example, CO2 from largestationary point sources, such as coal-firedpower plants and hydrocarbon processingplants, is more easily captured and storedcompared to CO2 from small, moving sourcessuch as automobiles.

Note that fossil fuels contribute to CO2

emissions both when they are produced (e.g.,oil sand production, bitumen upgrades, andgas-sweetening plants) and when they areburned. Capture refers to the process ofselectively treating or purifying the wastegas stream to “capture” just the CO2

component for injection (e.g., f lue gascontains less than 15% CO2).

While the majority of CO2 emissions inOntario are from small emitters, about halfof the total emissions in Alberta are fromlarge, point-source stationary plants. Giventhe abundance of depleting petroleumreservoirs in the Western CanadaSedimentary Basin, capture and geologicalstorage would appear to be the preferredsolution, at least for Alberta’s point sources

of CO2.

The sheer magnitude of a 6 bcf/d injectionrate raises additional considerations. Further,a multi-century time-scale for the geologicalstorage of CO2 is a fundamental departurewith the decade(s)-long operating horizonfor hydrocarbon development (Bachu,2008a). To address these differences, themodels and workflows used for hydrocarbondevelopment are being reconsidered andrevised.

Desired Storage Site CharacteristicsDesired Storage Site CharacteristicsDesired Storage Site CharacteristicsDesired Storage Site CharacteristicsDesired Storage Site CharacteristicsA desired CO2 storage site should have atleast the following characteristics:

• Ensure containment over long periodsof time (centuries).

• Enough injectivity to receive the CO2

at the desired rates.• Sufficient storage capacity.

ContainmentContainmentContainmentContainmentContainmentThe density of CO2 increases with increasingdepth / pressure, to approximately 700 kg/m3 at 2,000 to 3,000 m. But the density offormation brines is above 1,000 kg/m3. Aswith petroleum reservoirs, competent caprock is required to ensure containment. Evenwith competent cap rock, creating large,buoyant accumulations of concentrated CO2

that are in storage for centuries raisescomplex questions. Therefore, natural andman-made processes are being studied thatcould lead to permanent trapping of theinjected CO2. For example:

51

• Designs are being considered to enhancethe contact between CO2 and theformation brine, to facilitate what iscalled “solubility trapping.” Once CO2

is dissolved in the brine, the mixture isdenser than the in-situ brine and tendsto settle.

• Reacting CO2 with formation mineralscould create new stable minerals –“mineral trapping.”

• After flowing through porous rock, smallCO2 bubbles can remain trapped in the

pore space by capillary forces – “residualtrapping.”

While many of these trapping processesoccur naturally, they occur slowly overcenturies. To accelerate these trappingmechanisms, engineering solutions are beingproposed. For example:

• In a dipping aquifer, down-dip injectionof CO2 could lead to CO2 f lowunderneath the cap rock and along thelength of the aquifer, enhancingsolubility trapping. The reduced risk of

leakage as a result of enhanced solubilitytrapping will need to be balanced againstthe increased risk of leakage withdistance from the injection site, sinceour knowledge of the integrity and arealextent of the cap rock general lydecreases with distance from the well.

• Studies conducted by Hassanzadeh et al.(2008) suggest that production of theformation brine farther away from theCO2 injection site and its injection ontop of the CO2 plume at some distancefrom the CO2 injector, could lead tosolubility trapping of a significant amountof CO2 at a small energy cost.

InjectivityInjectivityInjectivityInjectivityInjectivityAlthough total injection rates can always beincreased by drilling more injection wells,the number of wells that will ultimately berequired to inject 6 bcf/day can significantlyaffect the economics of geological storage.High permeability reservoirs and formationsare obviously preferred.

Fekete’s studies have shown that the CO2

injection rate is not only controlled bypermeability in the vicinity of the wellborebut also by the permeability distributionthroughout the reservoir. The kv/khrelationship is equal ly important withrespect to overall storage capacity of theformation. For example, in simulation studiesof the Redwater reef, the allowable injectionrate is strongly affected by the degree ofcommunication / permeability between themargins of the reef, the interior of the reef,and the underlying Cooking Lake aquifer.

Evaluating the permeability distributionthroughout a reservoir is not normalpractice when injecting petroleum wastes atmodest rates. Nonetheless, it is required toassess the dissipation of the resultingpressure build-ups (below fracture gradient)at the rates required for large scale CO2

injection. Thus, addit ional geology /geophysics / drilling / testing may be requiredto develop the degree of characterizationnecessary for detailed planning of CO2

projects.

CapacityCapacityCapacityCapacityCapacityDepleted oil and gas pools are attractive asstorage sites, because of the availability ofinformation and the knowledge that the caprock is a competent seal. But large scale CO2

injection, (6 bcf/d is 2.2 tcf/year) requiresformations that can store 10’s of tcf or 1,000+megatonnes of CO2. While depletedpetroleum pools may play a part in localizedinjection of CO2, two projects that are beingconsidered for Alberta, i l lustrate thedif ferences between conventional

Figure 13.3. Readwater’s proximity to large CO2 emitters (Gunter and Bachu, 2007).

52

hydrocarbon production and large-scalegeological CO2 storage operations.

HARPHARPHARPHARPHARPThe Heartland Area Redwater Project(HARP), run by Alberta Research Council andindustrial partner ARC Resources, envisionsusing the entire Redwater reef as a CO2

storage site. The Redwater oil reservoir wasthe third-largest oil field in Alberta but itoccupied only a small fraction of the totalreef volume (Figure 13.2). The factors thatled to the selection of Redwater for largescale CO2 storage are:

• Its proximity to several large CO2

emitters: the Heartland industrial area(northeast of Edmonton) and the CO2

that may be pipelined from oil sandsproduction faci l i t ies in the FortMcMurray area (Figure 13.3).

• Established knowledge of the reef ’scontainment geometry, capacity, andinjectivity – albeit over a small portionof the reef.

One of the challenges to the project is thelack of geoscience knowledge over largeportions of the reef, which nevertheless isrequired for storage. While hundreds ofwells have been drilled in the northeasternportion of the reef (most to shallow depths)the rest of the reef has been penetrated byonly a couple of dozen wells (Figure 13.4).

The reef and its overlying and underlyingstrata are being characterized, using availablegeological , petrophysical , geophysical ,hydrogeological , and engineeringinformation. Init ia l studies have beenconducted to estimate storage capacity,number, and location of injection wells, andfate of the injected CO2 in the reservoir.These will be refined as exploratory well(s)are drilled and a pilot project is conducted,monitored, and evaluated.

WWWWWAAAAASPSPSPSPSPThe Wabamun area CO2 SequestrationProject (WASP), run by the University ofCalgary and Industrial Partners, isinvestigating aquifer disposal for four coal-fired power plants west of Edmonton thatcontribute significantly to Alberta’s CO2

emissions (Figure 13.5).

Michael et al. (2008) have reviewed the CO2

storage potential of different formations thatare in close proximity to the power plants,mapping at least three sequences of aquifers(Figures 13.6). The dolomitized Nisku aquiferis separated from the surface by at least twosequences of seals (shales) and appears topotentially meet the three requirements ofcontainment, capacity, and injectivity. Studiessimilar to those planned for HARP areunderway.

From where we are to whereFrom where we are to whereFrom where we are to whereFrom where we are to whereFrom where we are to wherewe need to bewe need to bewe need to bewe need to bewe need to beMaking a significant impact on the net volumeof CO2 emissions, even from Alberta’s 2002rate of 12 bcf/d, requires a large industry.The petroleum industry, with its earth-science and engineering knowledge, itsoperating expertise, managerial ability, andfinancial resources, is well suited to the taskof CO2 capture and geological storage. Wealready know much about the issues by virtueof our hydrocarbon production experience:

• The same formations and knowledge thathave produced hydrocarbons from theWestern Canada Sedimentary Basin arerequired for CO2 injection and storage.Further, working in concert providesthe potential for co-optimization ofhydrocarbon production and CO2

injection.

• The industry is familiar with the challengesposed by surface transport of large fluidvolumes and their undergroundinjection and monitoring.

• For more than two decades, dozens ofacid gas disposal projects, many havingCO2 as the main constituent of the gas,have been underway in Alberta. Theseprojects have much that is of directapplication to the geological storage ofCO2 (Pooladi-Darvish et al., 2008).

There are di f ferences and signi f icantchallenges ahead:

• The injection rate and volumes for theacid gas disposal projects have beenmuch smaller than the scale of CO2

storage projects that will significantlyaffect the net volume of CO2 emissions.

• Hydrocarbon sweetening operationshave been the CO2 source for acid gas

Figure 13.4. Redwater well locations (Gunter and Bachu, 2007).

Figure 13.5. Large coal-fired CO2 emitters nearEdmonton (Mitcheal et al., 2008).

53

disposal projects. But large-scalegeological storage projects will mostlycapture CO2 from the burning of fossilfuels, such as from coalfired powerplants. The dif ferent eff luent gascomposition from power plants mayrequire dif ferent technologies tocapture and purify the CO2 componentin the emissions.

• While smaller CO2 projects couldpotentially make use of depleted oil andgas pools, there is a point where onlyaquifers can provide sufficient storagecapacity. But our present knowledge ofaquifer extent, quality, and distribution– even those associated withhydrocarbon production – is likelyinsufficient for large scale CO2 storage.

Capture and geological storage of CO2

presents both challenges and opportunities.As Figure 13.7 illustrates, the industry is ona steep learning curve.

References :References :References :References :References :Bachu, S. 2008a. CO2, Storage and GeologicalMedia: Role, means, status, and barriers todeployment. Progress in Energy andCombustion Science – An InternationalReview Journal, v. 34, p. 254-273.

Bachu, S. 2008b. personal communications.

Gunter, W. and Bachu, S. 2007. The RedwaterReef in the Heartland Area: A UniqueOpportunity for Understanding andDemonstrating Safe Geological Storage ofCO2. http://www.nrcan. gc.ca/es /etb/cetc/combustion/co2network/ htmldocs/publications_e.html. 16 p.

Hassanzadeh, H., Pooladi-Darvish, M., andKeith, D.W. 2008. Accelerating CO2

Dissolution in Saline Aquifers for GeologicalStorage – Mechanistic and Sensitivity Studies.Paper submitted (June 2008) to Journal ofPetroleum Science and Engineering.

Michael, K, Bachu, S, Buschkuehle, B.E., Haug,K., and Talman, S. 2008. ComprehensiveCharacterization of a Potential Site for CO2

Geological Storage in Central Alberta,Canada. In: Carbon Dioxide Sequestration inGeological Media – State of the Art. M. Grobe,J. Pashin, and R. Dodge, (eds.). AAPG SpecialPublication, In press.

Pooladi-Darvish, M., Hong, H., Theys, S.,Stocker, R., Bachu, S., and Dashtgard S. 2008.CO2 injection for Enhanced Gas Recoveryand Geological Storage of CO2 in the LongCoulee Glauconite F Pool, Alberta. SPE115789 presented at the SPE annual TechnicalConference and Exhibit ion, Denver,September 21-24, 2008.

Figure 13.6. Wabamun area stratigraphic chart (Mitcheael et at., 2008).

Figure 13.7. Current and projected CO2 injection rates.

54

RRRRReeeeesssssererererervvvvvoir Engoir Engoir Engoir Engoir Engininininineeeeeering for Gering for Gering for Gering for Gering for GeeeeeolooloolooloologggggistsistsistsistsistsArticle 14 - Reservoir Simulation by: Ray Mireault, P. Eng.; Nick Esho; and Lisa Dean, P. Geol.; Fekete Associates Inc.

In Fekete’s experience, a well performedreservoir simulation represents the ultimateintegration of geology, geophysics,petrophysics, production data, and reservoirengineering. Through simulation, the flow ofmultiple fluids in heterogeneous rock overtime can be quantitatively estimated to gaininsights into reservoir performance notavailable by any other means.

Initially, reservoir simulation was reservedfor large reservoirs requiring large capitalinvestments that justified costly, intensivestudies such as offshore developments.However, simulation of more modest-sizedreservoirs has increased as simulationsoftware and computer capability havebecome more readily available. Oilfieldsunder primary production, waterflood, andEOR typically qualify for reservoir simulationbut its usage is not uncommon for gas fields,unconventional reservoirs, or poolsundergoing CO

2 injection.

In broad terms, the geologist / geophysicist /petrophysicist’s role in reservoir simulationis to reliably approximate the (a) stratigraphy,(b) structure, and (c) geometry of thereservoir flow unit(s) and the initial fluiddistributions throughout. The aim of theexercise is to quantify and manage thesubsurface knowledge and uncertainties. Inthe practical sense, a good model is the onethat is f it- for-purpose uti l iz ing soundgeological reasoning and at the same timesupports reservoir dynamics (e.g., fluid flow,history matching).

Geological data is often characterized bysparseness, high uncertainty, and unevendistribution, thus various methods ofstochastic s imulation of discrete andcontinuous variables are usually employed.The final product will be a combination of:

• observation of real data (deterministiccomponent),

• education, training, and experience(geology, geophysics, andpetrophysics), and

• formalized guessing (geostatistics).

The first step is the geologist’s conceptualdepositional model which (s)he must be ableto sketch and explain to the other membersof the team. The conceptual model should bebroadly compared and tested with eachdiscipline’s observations and data (e.g., core

permeability versus well-test permeability,core porosity versus log-derived values) untilthe team has a consistent explanation of thereservoir’s pre- through post-depositionalhistory. Hydrocarbon reservoirs are toocomplex to develop a completeunderstanding “in one afternoon” so theprocess should be viewed as a series ofongoing discussions.

The next step is to define, test, and prioritizethe uncertainties to be modeled and theirimpact on the overall dimensions of themodel. For example, a gridblock height thatis too large to reflect the layering in thinbeds will introduce significant errors in theflow net-to-gross pay estimates as well asflow pathways. It is essential to agree upfronton the level of resolution and details to becaptured in the model. The appropriate levelof detail can be different for each reservoirand is also dependent on the purpose of thesimulation, sometimes testing and iterationsmaybe necessary.

Next comes selecting the appropriate gridtype (regular or faulted) to model thepresent day structure of the reservoir.Components to be modeled include the topof structure, faults, internal baffles to flow,and any areal variation in thickness and rockproperties. The objective is to replicate theorientation, geometry, and effect of thestructural imprint as it affects flow withinthe model. It is imperative to validate thefault-horizon network to ensure it isgeologically feasible and to ascertain theabsence of structural distortion and otherproblems.

Facies modeling is the next step inconstruction. Where available , the bestpractice is to integrate core data and outcropanalogues to constrain and refine logderivedfacies type and property estimates.Understanding the facies distributionprovides a tool for predicting reservoirquality away from the known datapoints. Thegeometry (length, width, thickness, anddirection) of each facies body will affect theway heterogeneit ies in porosity andpermeability are modeled. Attribute analysis(inversion/QI) and geobodies extracted fromseismic data are also useful to further refinethe geological model.

It is important to quality check at each step

of development to ensure consistency in theinterpretation and reaff irm that thedeveloping model is fit-for-purpose. A verydetailed geological model may be unable toaddress the question(s) that the simulationteam is attempting to answer.

The engineer’s role in the process is toreliably simulate the performance of thegeological model for the productionscenario(s) under consideration by historymatching a producing field and / or forecastingfuture performance. While it may seem thatreservoir s imulation would bestraightforward if we only knew all theinputs, that perception is incorrect. Limitedinformation unquestionably complicates thetask but the most fundamental (andunavoidable) issue is the error introducedby approximating overwhelmingly complexphysical geometries / interactions withsimpler but manageable mathematicalrelationships.

Of necessity, simulation uses a sequence ofthree-dimensional gridblocks as a proxy forreservoir rock volume (see Figure 1). Inorder to keep the time, cost, and computingrequirements of a simulation manageable, thetotal number of gridblocks is generallylimited to less than 500,000, with a smallsimulation requiring less than 100,000gridblocks. For either large or small projects,

Figure 14.1. Typical reservoir simulation models (a)tank, (b) ID, (c) ID radial, (d) cross-sectional, (e)areal, (f) radial cross-sectional, and (g) 3D;Mattax and Dalton, 1990.

55

a gridblock may represent a “unit” rockvolume of one or more acres in areal extentand several feet thick (Figure 14.2).

While fluid saturations and / or otherproperties can vary significantly over an acreand / or several feet of reservoir (e.g., anoil-water transition zone), each gridblockhas only a single value for each property (e.g.,porosity, saturation of water, oil and gas,permeability, capillary pressure) of thegridblock. When the true variation in thereservoir is too great to be comfortablyrepresented by a single average value, thesolution may be to (iteratively) increase thedensity of the gridblocks (“fine grid”) in aspecific area of the reservoir. Alternatively,a separate, smaller simulation may be runand the results provided as input to thelarger study, as when modeling fluid andpressure behaviour at the wellbore sandface.

Similarly, simulation must approximate thecontinuous movement of fluids and theresulting changes in fluid saturations withcalculations performed at discrete timesteps.Though it does not occur in the real world,there can be abrupt changes in a gridblock’sfluid saturation(s) as fluids move into or outof the gridblock. The usual solution is to limitthe magnitude of the change to tolerablelevels through (iterative) selection of smallertimesteps.

The use of discrete timesteps and discretegridblocks with a single value for eachproperty also leads to the dilemma of whatvalues to use in modeling the f luidproperties for f low between adjacentgridblocks and adjacent timesteps. Thisartifact of numerical simulation also hasconsequences on calculated performancethat do not exist in reality. For furtherdiscussion, see Chapter 2 of the SPEMonograph Volume 13. Though there is nocompletely satisfactory answer to theproblem, workable approximations for flowacross gridblock boundaries and betweensubsequent timesteps exist. The choice ofwhich to use in a particular situation oftencomes down to experience and iteration.

Figure 14.3. Rock and fluid properties (Mattaxand Dalton, 1990).

Figure 14.2. Example of 3D gridblocks.

56

DDDDDAAAAATTTTTA REA REA REA REA REQUIREQUIREQUIREQUIREQUIREMEMEMEMEMENNNNNTTTTTSSSSSThe rock and fluid properties required forreservoir simulation are summarized inFigure 14.3. Collecting the data and puttingit into a form that can be imported in areservoir simulator can be a major effort initself.

ASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKASSIGNMENT OF GRIDBLOCKPROPERTIESPROPERTIESPROPERTIESPROPERTIESPROPERTIESChapter 4 and 5 of SPE Monograph 13provide further discussion on the challengesof assigning representative average valuesfor rock and f luid properties to eachgridblock in a simulation model and the sizeof gridblocks and timesteps to use. Thechoices are interrelated and influenced by:

• the areal and vertical variation in theobserved rock and fluid properties,

• the type of physical processes beingmodeled, and

• the solution techniques being used.

Often, the best approach is to select thesmallest gridblock size and number of layersneeded to accurately describe the changesin reservoir facies, reservoir geometry, andfluid distribution. For example, f luidsaturation changes in an oil-water transitionzone might require gridblocks with anunusually small height of one foot or less toadequately represent the change in saturationthrough the transition zone with the seriesof single values avai lable to “stacked”gridblocks. Production and injection wells

and internal no-flow boundaries such asshale deposits or non-conducting faults areother features that can be the determiningfactor in selecting gridblock size.

Porosity and permeability distribution arenearly always important and are often thekeys to reservoir performance. Sensitivitystudies generally indicate that if the faciesdistributions through the reservoir arecorrectly modeled and each facies is assignedthe correct order of magnitude forpermeability, the relatively small errors inthe absolute value of permeability assignedto each gridblock are insignificant, since theyare compensated for by the large area offlow that is available for fluid movement.

Constructing the entire reservoir modelwith a minimum size of gridblock capturesthe level of detai l needed for crit icalaspect(s) of the reservoir simulation butover-compensates in non-critical areas.Subsequent inspection of the model, keepingin mind the physical processes (i.e., thermalprocesses) and solution techniques that willbe used to model fluid flow, will identify areasof the reservoir that do not require the levelof detail that was built into the originalmodel. The process of subsequently selectingand reducing the number of gridblocks usedto model the non-critical areas is referredto as “upscaling.”

Selection of the appropriate timestep isgenerally left to last, because the pore

volume of a gridblock and rate of fluid flow(production) both influence the rate ofchange in a gridblock’s fluid saturations overtime. Limits on the rate of saturation changethat are developed from experience, aregenerally used to determine the largesttimestep size that will present apparentlysmooth results when mapped or graphed.This process is done internally by thesimulator to ensure smoothness of results.

SIMULSIMULSIMULSIMULSIMULAAAAATION OUTION OUTION OUTION OUTION OUTPTPTPTPTPUUUUUTTTTTSince it is not possible to individually inspectthe mil l ions of calculat ions that areperformed in a simulation, editing andgraphical presentation of the output iscrucial to assessing the consistency andreliability of the results. As a minimum, theoutput graphs should include:

• oil, water and gas production rates,• producing gas-oil ratio;• producing water cut or water oil ratio,

and• bottomhole flowing pressures.

Maps / movies of f luid saturation andreservoir pressure trends are alsoinvaluable to assessing the quality andconsistency of the output. For example,inconsistent pressure behaviour – relatedto negative cell volumes – may indicate thatthere is an issue with the gridding and / orassigned transmissibility of gridblocks alonga fault zone.

UUUUUSESESESESES AND LS AND LS AND LS AND LS AND LIMITIMITIMITIMITIMITAAAAATIONS OFTIONS OFTIONS OFTIONS OFTIONS OFSIMULSIMULSIMULSIMULSIMULAAAAATIONTIONTIONTIONTIONAs computing power and software capabilityhave developed, the “art” of reservoirsimulation has proven to be a valuablecomplement to other methods of reservoiranalysis. To the geologist, a threedimensionalmodel is the ultimate tool for visualizing andthen communicating the reservoirinterpretation to others (Figure 14.4). As aworking tool, it integrates the partialinterpretations provided by each disciplineand allows for an unsurpassed level ofconsistency checks.

To the reservoir engineer, modern-dayreservoir simulation software provides thecapabil ity to visualize and present themovement of f luids through rock inaccordance with physical principals. With itwe can:

• comparatively assess the hydrocarbonrecovery eff ic iency of variousproduction systems that could beconsidered for a given reservoir priorto their implementation and

• more closely monitor producingreservoir trends and more quickly

Figure 14.4. Visualization of 3D model.

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identi fy the probable causes ofdeviations from forecastedperformance, particularly during theearly life of a reservoir.

Prior to production, Monte Carlo volumetricestimates are still the best tool to quantifythe uncertainty in the gas or oil-in-placewithin a deposit. But reservoir simulational lows comparison of productionperformance over the probable volumetricrange at a level not previously available.Simulation sensitivity studies are invaluablein identifying the uncertainties that can havea significant impact on production / financialperformance and in focusing efforts toacquire additional information and / ormodify development plans to mitigatepotential impacts.

For a producing reservoir, material balancestill provides the most accurate estimatesof oil- and / or gas-in-place. Accordingly,tuning the in-place volumes in the simulatorto the material balance results improves thediagnoses of well performance and allowsfor better reservoir management.

REFERENCESREFERENCESREFERENCESREFERENCESREFERENCESMattax, C.C. and Dalton R.L. 1990. ReservoirSimulation. Society of Petroleum Engineers, HenryL. Doherty Series, Monograph Vol. 13.