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

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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.

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.

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.

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.