RRReeesssererervvvoir Engoir Engoir Engininineeeering … · Material balance calculations for oil...
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Material balance calculations for oil reservoirs are more complex than for gas reservoirs. They must account for the reservoir volumes of the produced fluids and the effect of pressure depletion on the oil volume remaining in the reservoir. They must account for the formation, expansion, and production of solution gas. The calculations must also account for the expansion of the reservoir rock and formation water, since they have similar compressibility as oil. As noted in last month’s article, typical compressibility ranges are: • Rock: 0.2 to 1.5x10 -6 kPa -1 • Gas: 10 -3 to 10 -5 kPa -1 (Varies significantly with reservoir pressure.) • Water: 0.2 to 0.6x10 -6 kPa -1 • Oil: 0.4 to 3x10 -6 kPa -1 Nonetheless, in theory, material balance calculations can provide an independent estimate for the original oil-in-place for a solution gas drive reservoir with sufficient production history. Havlena and Odeh (1963) developed a useful graphical procedure for estimating the oil- in-place volume for a solution gas drive reservoir (see Figure 6.1). By rearranging the material balance equation so that the total withdrawals from the reservoir are grouped onto the y axis while all the expansion terms are grouped on the x axis, the correct oil-in-place value will generate a straight line trend on the graph. Thus the oil volume for a solution gas drive reservoir can be determined by successively iterating until a straight line is achieved. Upward curvature indicates that the value selected as the OOIP is too small. Downward curvature indicates that the selected value is larger than the true size of the oil deposit. Various formulations of the material balance equation can be sourced in any of the references cited. Figure 6.2 presents a Havlena-Odeh plot for a solution gas drive reservoir with an OOIP of 49 MMSTB.The four points calculated from reservoir pressure measurements are in good agreement with the predicted trend based on the OOIP value. Inadequate pressure buildup time may be the reason that the third pressure measurement comes in slightly below the predicted trend line. When an oil deposit has a gas cap, the material balance calculations must also account for gas cap expansion and production. However, there are now too many unknowns to develop a unique solution by material balance alone. Estimating the oil- in-place in the presence of a gas cap first requires a volumetric estimate for the size of the gas cap.Then the size of the oil deposit can be estimated via material balance calculations. Though it cannot independently determine the oil-in-place volume when a gas cap is present, the Havlena-Odeh plot can assist in Reser er er er ervoir Eng oir Eng oir Eng oir Eng oir Engin in in in ineering for G ering for G ering for G ering for G ering for Geolo olo olo olo ologists ists ists ists ists Article 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.
Transcript of RRReeesssererervvvoir Engoir Engoir Engininineeeering … · Material balance calculations for oil...
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.
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.
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.
