Chap16- MBal Appl

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<ul><li><p>MATERIAL BALANCE EQUATIONAPPLICATIONAdrian C ToddHeriot-Watt UniversityINSTITUTE OF PETROLEUM ENGINEERING</p></li><li><p>Material Balance ApplicationNo one universal solution to the MB equation.Recently the computing power behind modern reservoir situation has cast a shadow of confidence in the material balance approachTo quote the late Professor Laurie Dake a proponent of the MB equation.</p></li><li><p>Laurie Dake quote from the Practise of Reservoir Engineering-Elsevier.It seems no longer fashionable to apply the concept of the material balance to oilfields, the belief that it is now superceded by the application of modern numerical simulation.Acceptance of this idea is a tragedy and has robbed engineers of their most powerful tool for investigating reservoirs and understanding their performance rather than imposing their wills upon them, as is often the case when applying numerical simulation directly in history matching..There should be no competition between MB and simulation instead they must be supportive of one another: the former defining the system which is used as input to the modelMaterial balance is excellent at history matching production performance but has considerable disadvantages when it comes to prediction, which is the domain of numerical simulation.</p></li><li><p>Material Balance as an Equation of a Straight LineMaterial balance not a difficult concept.Difficult in applying it to real reservoirsThere is often inadequate understanding of drive mechanisms.Odeh &amp; Havlena (1963) rearranged MB equation into different linear forms.Their method requires the plotting of a variable group against another variable group selected depending on the drive mechanism.If linear relationship does not exist, then this deviation suggests that reservoir is not performing as anticipated and other mechanisms are involved.</p></li><li><p>Material Balance as Straight LineOnce linearity has been achieved, based on matching pressure and production data then a mathematical model has been achieved.The technique is referred to as history matching.The application of the model to the future enables predictions of the future reservoir performance.</p></li><li><p>Material Balance EquationThe material balance equation can be written as</p></li><li><p>Wp, Winj and We are sometimes not includedHavlena and Odeh simplified equation to:-Left hand side are production terms in reservoir volumes</p></li><li><p>The right hand side includes oil and its originally dissolved gas, Eo, whereThe expansion of the pores and connate water, Efw.The expansion of the free gas</p></li><li><p>The material balance in this simplified form can be writtenUsing this equation Havlena and Odeh manipulated the equation for different drive types to produce a linear equation</p></li><li><p>No Water Drive and No Gas CapA plot of F vs. Eo should produce a straight line through the origin.Slope of line gives oil in place.</p></li><li><p>Gas Drive Reservoirs, No Water Drive and Known Gas CapPlot of F vs. (Eo + mEg) should produce a straight line slope N.</p><p>If m is not known then m can be adjusted to generate linear form at correct value for m.</p></li><li><p>Gas Drive Reservoirs, No Water Drive and N &amp; G unknownPlot of F/Eo vs. Eo/Eg should be linear with a slope of G=mN and intercept N.</p></li><li><p>Water Drive ReservoirsCovered in Chapter 17</p></li><li><p>Depletion drive or other?Material Balance can be used in short hand form to get an indication of whether field is depleting volumetrically ( depletion drive ) or there is other energy support, eg. Water drive</p><p>Divide by Eo +Efw</p></li><li><p>Depletion drive or other? Two unkowns, N &amp; We. Dake suggests plot of F/(Eo+Efw) vs. Np, or time or pressure dropEnergy from oil and dissolved gas.Intercept oil in place</p></li><li><p>Gas Field Application of MB EquarionIn earlier chapter introduced p/z plot for a gas reservoir without water drive.Many have warned about the application of this approach since it neglects another possible energy support.Plots of Gp vs. p or p/z can give wrong indications of gas in place. Under estimate when Gp vs. p and over estimate when water drive ignored.</p><p>Beware of the p/z plot.</p></li><li><p>Beware of the p/z plot.</p><p>Craft &amp; Hawkins</p></li><li><p>MB Approach to Gas ReservoirsFluid production = gas expansion + water expansion &amp; pore compaction and water influxHavlena and Odeh approach gives:</p></li><li><p>MB Approach to Gas ReservoirsShort hand MB equation for gas reservoirsWith gas reservoirs the pore and water compressibility can be ignored</p></li><li><p>MB Approach to Gas ReservoirsPlot F/Eg vs. Gp, time or Dp</p></li><li><p>MB Approach to Gas ReservoirsPlot gives initial gas in placeAdvancing water only evident when gas water contact arrivesMobility ratio of water displacing gas as low as 0.1Gas moving 100 times faster than water</p></li><li><p>p/z approachLong established in gas reservoir engineering to determine gas in placeGas produced = gas initially in place gas remaining in reservoir</p><p>We is the net water influx (includes Wp)Compressibility terms small for water &amp; pores</p></li><li><p>p/z approachReplacing gas formation factor with z/p gives</p><p>WeBw/GBgi water invaded volumeHigher this term the higher the pressure and vice versaWith no water drive becomesWell known p/z plot</p></li><li><p>p/z approachThe equation enables gas in place to be determined when p/z=0</p><p>If any pressure support curve will deviate from linear.In early time periods pressure support may not be felt.</p><p>Depletion drive gas reservoirs will exhibit straight p/z plot well established. A straight line plot however does not prove existence of depletion drive.</p></li><li><p>p/z approach rate effectBecause of the high mobility of gas then if gas extracted at a high rate then pressure decline faster since water mobility cannot keep up.If however gas extraction rate low then water drive will give pressure support.This effect can distort p/z plot for water drive reservoirs.Varying rates are common in relation to winter and summer rates.</p></li><li><p>Material Balance Equation Applied to Oil Reservoirs Depletion DriveSolution gas drive has two stages of depletion</p><p>First stage above bubble point pressureSecond stage below bubble point pressureAbove the Bubble PointProduction due to compressibility of the total system.Although appears complex MB equation isDv =C x V x DpProduction = Expansion of reservoir fluids</p></li><li><p>Solution gas drive above bubble point.MB equation above bubble point simplifies to:-</p><p>No gas capAquifer small in volume We = Wp =0Rs=Rsi=Rp all gas at surface dissolved in oil in reservoir</p></li><li><p>Solution gas drive above bubble point.Oil compressibility -</p><p>Replacing oil term in MB equation gives</p><p>So + Swc = 1</p></li><li><p>Solution gas drive above bubble point.</p><p>ce is the effective saturation weighted compressibility of the reservoir systemRecovery at bubble point</p></li><li><p>Solution Gas DriveReservoir pressure drops below bubble point solution gas drive effective.More complex as gas comes out of solution.Most common reservoir drive mechanism.However also very inefficient.Often associated with other drive mechanisms.In order to use MB equation to predict production versus pressure need other independent equations.</p><p>Instantaneous producing gas-oil ratio equation.Saturation equation</p></li><li><p>Instantaneous Gas- Oil RatioInstantaneous Gas- Oil Ratio, R, is the ratio of gas production to oil production at a particular point in production time, at a particular reservoir pressure.Instantaneous producing GOR is:</p><p>Gas production comes from gas in solution in reservoir and from free gas in reservoir which has come out of solution.</p></li><li><p>Instantaneous Gas- Oil RatioWhere:qg = free gas flow rate, res.bbls/dayqo = oil producing rate, res.bbls/dayBg =gas formation volume factor, bbls/SCFBo = oil formation volume factor, bbls/STBQo = oil flow rate,STB/dayQg = total gas producing rate, SCF/dayRs = gas solubility, SCF/STB</p></li><li><p>Instantaneous Gas- Oil Ratio</p></li><li><p>Instantaneous Gas- Oil Ratio</p><p>Therefore in previous equation:Instantaneous Gas- Oil Ratio Equation</p></li><li>Instantaneous Gas- Oil Ratio1. Above Pb, no free gas. Keg is zero, R=Rs=Rsi.2. Short time when gas saturation below critical value, keg still zero but R=Rs</li><li><p>Instantaneous Gas- Oil RatioInstantaneous GOR is not the same as cumulative GOR.Instantaneous GOR,R, is ratio at particular moment in time.Cumulative GOR, Rp, is ratio of total oil and gas produced up to a particular moment.Two GORs related as follows.</p></li><li><p>Oil Saturation EquationOil saturation equation provides an average oil saturation for a reservoir at any time.</p><p>Equation can be rearranged as:The Oil Saturation Equation</p></li><li><p>History MatchingHistory matching if your model cannot predict the past its value in predicting the future is in question.Instantaneous GOR can be used to history match relative permeabilities.Rearranged takes the form.</p><p>Production data provides R and Np as a function of pressure.Rs, B and m values from PVT report.Np values provide So from oil saturation equation.Can generate therefore keg/keo vs. So</p></li><li><p>Solution Gas Drive CharacteristicsRapid pressure declineWater free productionRapidly increasing gas-oil ratioLow ultimate oil recoveryPrediction methods</p><p>Schilthuis, Tarner and Tracy &amp; Tarner</p></li><li><p>Solution Gas Drive-Tarners MethodSimilar approach to Schilthuis procedureAbove Pb use effective compressibility equation </p><p>Below bubble point pressure use MB, Instantaneous GOR and Oil Saturation equations</p></li><li><p>Solution Gas Drive-Tarners MethodAssemble dataProduction dataField data and rockField data</p><p>Formation volume factorsGas solubilityGas compressibilityGas and oil viscositiesRock dataLaboratory relative permeabilitiesPast production data</p><p>Oil productionGas productionWater productionNew water influxAll presented as a function of pressure</p></li><li><p>Solution Gas Drive-Tarners MethodTarners method uses MB equation rearranged to calculate gas production Gp.Procedure is a trial &amp; error approach using independently MB and Instantaneous GOR eqns.</p><p>Step1 1. Start at bubble point pressure2. Select a future pressure and assume a value of Np at that pressure. Sometimes express Np as a function of N.3. Solve MB eqn. For NpRp, ie. Gp.</p></li><li><p>Solution Gas Drive-Tarners Method4. Using assumed Np solve oil saturation equation for So. This enables keg/keo to be determined.</p><p>5. Calculate instantaneous GOR.</p><p>6. Calculate gas produced during pressure drop over period.</p><p>Ri = instantaneous GOR at start of periodRi+1 = instantaneous GOR at end of periodNp1= cumulative oil produced at end of periodAssumption R vs Np linearTherefore use small pressure drops</p></li><li><p>Solution Gas Drive-Tarners Method6. Total gas produced from MB eqn. and IGOR eqn. Compared and assumed value of Np adjusted and steps 2 to 6 repeated until MB and IGOR values for Gp match.Step 21 Second pressure selected and new Np assummed.2. Solve MB for Np2. This is cumulative gas at end of second pressure.</p><p>3. Calculate gas produced during 2nd step by removing from cumulative gas from step 1.4. With assumed value of Np2 from satn eqn.determine So.5. Calculate IGOR</p></li><li><p>Solution Gas Drive-Tarners Method6. Calculate gas produced during second step</p><p>7. G2 from MB compared with G2 from IGOR and new assumed value of Np2 until convergence achieved.By plotting these two values vs Np a convergence point can be determined.Further steps as for step 2.</p></li><li><p>Tracys Form of Tarners MethodTracy took MB equation and generated a shorthand version</p></li><li><p>Tracys Form of Tarners MethodFor simplicity assume no gas cap. Then:</p><p>These functions are only dependent on reservoir pressure and oil properties.</p><p>They can all be obtained from PVT data.</p></li><li><p>Tracys Form of Tarners MethodUsing this shorthand system MB equation can be written:</p><p>If we assume no water encroachment or production</p><p>Tracy considered two pressure conditions Pj &amp; Pk and the oil production DNp during this pressure interval.Tracy estimates producing GOR Rk at the lower pressure rather than DNp.For kth pressure.</p></li><li><p>Tracys Form of Tarners MethodIf N=1 then equation takes on fractional recovery form</p><p>also</p><p>and</p><p>where</p><p>rearranging</p></li><li><p>Tracys Form of Tarners MethodSolving for DNpk</p><p>Only unknown is Ravg all the rest from PVT data or calculated at previous stepRk can also be estimated from liquid saturation known using IGOR eqn.</p></li><li><p>Tracys Form of Tarners MethodSo obtained from oil saturation equation</p><p>Tracys ProcedureSet pressure step below Pb.1. Estimate RkAt bubble point = RsiFrom extrapolation of trend2. Estimate Ravg</p></li><li><p>Tracys Procedure continued.3. Determine PVT functions fn and fg.4. Determine DNpk and SDNp.</p><p>At first pressure step, pj = pb, Npj =0, Gpj =05. Using SDNp determine So using saturation eqn.and thereby keg/keo from So vs. keg/keo data.6. Calculate Rk from IGOR equation.7. Compare Rk with Rk. According to tolerance for Rk = Rk. If not repeat steps 1 to 6</p></li><li><p>Tracys Procedure continued.8. Estimate DGp and SDGp. DGp =DNp x R avgSet next pressure step and repeat steps 1 to 8.</p></li><li><p>Gas Cap Drive ReservoirsTarners method can also be used for gas cap drive reservoirs</p></li><li><p>Average Reservoir PressureMB equation sometimes considered as a tank model.If there is uniform pressure decline in all wells then this decline gives confidence in using MB eqn.Dake suggests if equilibrium is not achieved then can still use MB eqn.He suggests an average pressure.</p></li><li><p>Average Reservoir Pressure</p><p>EquilibriumNon EquilibriumWell positions and drainage boundariesIn figure wells have their own pressure declines.Dake presents a volume weighting for each drainage area.</p><p>Pj, Vj and qj are the pressure, volume and reservoir rate for the area j.The volume weighted average pressure is therefore.</p></li><li><p>Average Reservoir PressureDake suggests an alternative method based on production rate, based on the time derivative of the compressibility equation</p><p>For constant compressibility</p></li><li><p>Average Reservoir PressureMaterial balance often applied at regular intervals .Change in underground withdrawl,UWj can be used over a pressure drop Dpj.Then:</p><p>Dake suggested that the MB approach be used prior to numerical simulation approach .</p></li><li><p>Predictions as a function of timeNone of the terms in the MB equation include time.Only a pressure volume solution .Need to use another method which uses time to work alongside MB solution.Productivity of wells for example.</p></li></ul>