chap16- mbal appl
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DESCRIPTIONHW reservoir 16
MATERIAL BALANCE EQUATIONAPPLICATIONAdrian C ToddHeriot-Watt UniversityINSTITUTE OF PETROLEUM ENGINEERING
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.
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seems no longer fashionable to apply the concept of the material balance to oilfields, the belief that it is now superceded by the application of modern numerical simulation.Acceptance of this idea is a tragedy and has robbed engineers of their most powerful tool for investigating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.
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 & 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.
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.
Material Balance EquationThe material balance equation can be written as
Wp, Winj and We are sometimes not includedHavlena and Odeh simplified equation to:-Left hand side are production terms in reservoir volumes
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
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
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.
Gas Drive Reservoirs, No Water Drive and Known Gas CapPlot of F vs. (Eo + mEg) should produce a straight line slope N.
If m is not known then m can be adjusted to generate linear form at correct value for m.
Gas Drive Reservoirs, No Water Drive and N & G unknownPlot of F/Eo vs. Eo/Eg should be linear with a slope of G=mN and intercept N.
Water Drive ReservoirsCovered in Chapter 17
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
Divide by Eo +Efw
Depletion drive or other? Two unkowns, N & We. Dake suggests plot of F/(Eo+Efw) vs. Np, or time or pressure dropEnergy from oil and dissolved gas.Intercept oil in place
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.
Beware of the p/z plot.
Beware of the p/z plot.
Craft & Hawkins
MB Approach to Gas ReservoirsFluid production = gas expansion + water expansion & pore compaction and water influxHavlena and Odeh approach gives:
MB Approach to Gas ReservoirsShort hand MB equation for gas reservoirsWith gas reservoirs the pore and water compressibility can be ignored
MB Approach to Gas ReservoirsPlot F/Eg vs. Gp, time or Dp
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/z approachLong established in gas reservoir engineering to determine gas in placeGas produced = gas initially in place gas remaining in reservoir
We is the net water influx (includes Wp)Compressibility terms small for water & pores
p/z approachReplacing gas formation factor with z/p gives
WeBw/GBgi water invaded volumeHigher this term the higher the pressure and vice versaWith no water drive becomesWell known p/z plot
p/z approachThe equation enables gas in place to be determined when p/z=0
If any pressure support curve will deviate from linear.In early time periods pressure support may not be felt.
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/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.
Material Balance Equation Applied to Oil Reservoirs Depletion DriveSolution gas drive has two stages of depletion
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
Solution gas drive above bubble point.MB equation above bubble point simplifies to:-
No gas capAquifer small in volume We = Wp =0Rs=Rsi=Rp all gas at surface dissolved in oil in reservoir
Solution gas drive above bubble point.Oil compressibility -
Replacing oil term in MB equation gives
So + Swc = 1
Solution gas drive above bubble point.
ce is the effective saturation weighted compressibility of the reservoir systemRecovery at bubble point
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.
Instantaneous producing gas-oil ratio equation.Saturation equation
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:
Gas production comes from gas in solution in reservoir and from free gas in reservoir which has come out of solution.
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
Instantaneous Gas- Oil Ratio
Instantaneous Gas- Oil Ratio
Therefore in previous equation:Instantaneous Gas- Oil Ratio Equation
- 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
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.
Oil Saturation EquationOil saturation equation provides an average oil saturation for a reservoir at any time.
Equation can be rearranged as:The Oil Saturation Equation
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.
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
Solution Gas Drive CharacteristicsRapid pressure declineWater free productionRapidly increasing gas-oil ratioLow ultimate oil recoveryPrediction methods
Schilthuis, Tarner and Tracy & Tarner
Solution Gas Drive-Tarners MethodSimilar approach to Schilthuis procedureAbove Pb use effective compressibility equation
Below bubble point pressure use MB, Instantaneous GOR and Oil Saturation equations
Solution Gas Drive-Tarners MethodAssemble dataProduction dataField data and rockField data
Formation volume factorsGas solubilityGas compressibilityGas and oil viscositiesRock dataLaboratory relative permeabil