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MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
Adrian C ToddAdrian C Todd
Heriot-Watt UniversityHeriot-Watt University
DEPARTMENT OF PETROLEUM ENGINEERING
Heriot-Watt UniversityHeriot-Watt University
DEPARTMENT OF PETROLEUM ENGINEERING
Reservoir Engineering TasksReservoir Engineering Tasks
Be able to make dependable estimates of Be able to make dependable estimates of initial hydrocarbons in place.initial hydrocarbons in place.
Predict the future reservoir performance.Predict the future reservoir performance.
Ultimate hydrocarbon recovery.Ultimate hydrocarbon recovery.
Material Balance EquationMaterial Balance Equation
Basic tool in reservoir engineering.Basic tool in reservoir engineering.
Many reservoir engineering techniques involve Many reservoir engineering techniques involve some application of the material balance.some application of the material balance.
Principle of conservation of mass underlies the Principle of conservation of mass underlies the MB equationMB equation
It is however written on a volumetric basis.It is however written on a volumetric basis.
Mass of fluids originally in place = fluids produced Mass of fluids originally in place = fluids produced + remaining reserves+ remaining reserves
Material Balance EquationMaterial Balance Equation
First presented by Schilthuis 1936First presented by Schilthuis 1936
Relates volumes to pressuresRelates volumes to pressures
Limited in application since no time dependant Limited in application since no time dependant terms.terms.
Provides relationship with reservoir cumulative Provides relationship with reservoir cumulative production and its average pressureproduction and its average pressure
Material Balance EquationMaterial Balance Equation Scope of the analysis depends on the Reservoir Scope of the analysis depends on the Reservoir
simulators apply material balance approach within simulators apply material balance approach within each ‘cell’each ‘cell’
MB equation enables one to get a ‘feel’ of the MB equation enables one to get a ‘feel’ of the reservoir and the contribution of various processes.reservoir and the contribution of various processes.
A danger of the blind use of the reservoir simulator A danger of the blind use of the reservoir simulator is one might not be aware of the various is one might not be aware of the various contributions to fluid production.contributions to fluid production.
Material Balance EquationMaterial Balance Equation
Basic ‘material balance’ equationBasic ‘material balance’ equation
The reservoir volume of original fluids in place = reservoir
volume of fluids produced + volume of remaining reserves
Material Balance EquationMaterial Balance EquationAs a consequence of pressure depletion in a reservoir a As a consequence of pressure depletion in a reservoir a
number of things will happen.number of things will happen.
The pore volume of reservoir will decreaseThe pore volume of reservoir will decrease
Connate water will expandConnate water will expand
Undersaturated oil will expandUndersaturated oil will expand
Saturated oil will shrink as gas comes out of Saturated oil will shrink as gas comes out of solution.solution.
Free gas will expand.Free gas will expand.
Water may start flowing into reservoir.Water may start flowing into reservoir.
MB for GAS RESERVOIRSMB for GAS RESERVOIRS Simplest MB equation is applied to gas Simplest MB equation is applied to gas
reservoirsreservoirs
Gas compressibility is very significant. Gas compressibility is very significant. Compared to reservoir volume Compared to reservoir volume compressibility.compressibility.
If no water drive and pore volume changes If no water drive and pore volume changes insignificant.insignificant.
Dry Gas Reservoir with Water DriveDry Gas Reservoir with Water Drive If gas reservoir supported by water then as gas If gas reservoir supported by water then as gas
produced water encroaches into pore space, some produced water encroaches into pore space, some MAY BE also producedMAY BE also produced
However because of very high mobility of gas However because of very high mobility of gas compared to water. Water production delayed. compared to water. Water production delayed.
Water support evidenced by pressure supportWater support evidenced by pressure support
gi p g e pGB G G B W W
Gas Reservoirs Graphical MBGas Reservoirs Graphical MB
gi p gGB G G B
From equation in gas properties
g
czTB
p
ip
i
z zG G G
p p i
pi
z zG G G
p p
ip
i
p GzG G
z P
Hence a plot of Gp vs. p/z will give a straight line.
Gas Reservoirs Graphical MBGas Reservoirs Graphical MB
If gas ideal then Gp vs. p would be a straight line
-when p/z = 0. Then Gp = G the original gas in place-When Gp = Then p/z =pi/zi
Often used in predicting gas reserves.Often water drive neglected.
Often used as a history matching tool to compare reserves based on production data with those from exploration methods.
Gas Reservoirs Graphical MBGas Reservoirs Graphical MB Great caution to be taken when using this methodGreat caution to be taken when using this method
Water drive is considered to be zero.Water drive is considered to be zero.
Gas compressibility is only pressure support.Gas compressibility is only pressure support.
If the plot deviates from straight line then this If the plot deviates from straight line then this gives evidence of other pressure supportgives evidence of other pressure support
Wet Gas ReservoirsWet Gas Reservoirs
These reservoirs produce liquids as well as gas.These reservoirs produce liquids as well as gas.
Important to convert liquids to gas equivalent figures Important to convert liquids to gas equivalent figures to add to the gas production.to add to the gas production.
For condensate systems Gp produced should include For condensate systems Gp produced should include produced condensate and produced water (originally produced condensate and produced water (originally dissolved in gas ).dissolved in gas ).
Wet Gas ReservoirsWet Gas Reservoirs
Volume of 1STB of condensate of molecular weight Mo and specific gravity o.
znRTV
P
z=0 at p= 14.7 psia and T= 520 oR
o
ooo
psia.SCF 520 R lb.mole lb cu.ft.V / STB 10.73 x x x62.4 x5.615
lb.mol. R 14.7psia M lb cu.ft. STB
o
o
SCFv 133,000
M STB
Development of General MB Eqn.Development of General MB Eqn.Gas cap ExpansionGas cap Expansion
Gas cap attached to an oil reservoir
OilOil
GBgi (G-Gpc)Bg
Gas cap exp.
Pi
Gpc
P
Change in gas cap volume due to gas production from gas cap is:
pc g giG G B GB
pc g giG G B GB
MB for Oil Reservoirs Above Bubble PointMB for Oil Reservoirs Above Bubble Point
Above the bubble point, the undersaturated condition, Above the bubble point, the undersaturated condition, production is due to expansion of liquids, oil and production is due to expansion of liquids, oil and water and reduction in pore volume.water and reduction in pore volume.
Assuming oil production only due to oil expansion. Assuming oil production only due to oil expansion. Then:Then: oi p oNB N N B
Np
NBoiNBoi (N-Np)Bo(N-Np)Bo
Pi P
MB for Oil Reservoirs Below Bubble PointMB for Oil Reservoirs Below Bubble Point
Below bubble point gas liberated in the Below bubble point gas liberated in the reservoir. The mechanism of Solution Gas reservoir. The mechanism of Solution Gas DriveDrive
Produced fluids: oil plus its dissolved gas, gas Produced fluids: oil plus its dissolved gas, gas which has come out of solution in reservoir which has come out of solution in reservoir and produced and free gas which has come and produced and free gas which has come out of solution in reservoir and remains there.out of solution in reservoir and remains there.
MB for Oil Reservoirs Below Bubble PointMB for Oil Reservoirs Below Bubble Point
Free gas in reservoir = original gas in solution – remaining gas in solution – produced gas Gps
oi p si p s ps gNB N N NR N N R G B rbbl
si p s psNR N N R G SCF
si p s ps gNR N N R G B rbbl
Original volume oil = remaining oil volume + volume of free gas
oi p si p s ps gNB N N NR N N R G B rbbl
MB for Oil Reservoirs Below Bubble PointMB for Oil Reservoirs Below Bubble Point
Equation in terms of original stock-tank volume in reservoir
Pi
NBoi
Oil (N-Np)Bo
P
Free gas(NRsi-(N-Np)Rs-
Gps)Bg
Np Gps
p o ps p s g
o oi si s g
N B G N R BN
B B R R B
MB with gas cap and water driveMB with gas cap and water drive
So far no volume change in reservoir considered.If gas cap expands or water encroaches there will be a
loss to reservoir volume
Change in volume due to gas cap expansion:
pc g giG G B GB
Change in volume due to water encroachment:
e pW W
Total change in volume = original oil volume – (remaining oil volume + free solution gas)
MB with gas cap and water driveMB with gas cap and water drive
e p pc g gi
oi p o si p s ps g
W W G G B GB
NB N N B NR N N R G B
NBoi
Pi P
Np GpsGpc Wp
We
MB with gas cap and water driveMB with gas cap and water drive
Gp = Gpc+Gps
p o p p s g g gi e p
o oi si s g
N B G N R B G B B W WN
B B R R B
p o ps p s g pc g gi e p
o oi si s g
N B G N R B G G B GB W WN
B B R R B
NBoi
Pi P
Np GpsGpc Wp
We
Effect of Pore Volume ChangesEffect of Pore Volume Changes Water and rock pore compressibility although low can contribute to overall pore Water and rock pore compressibility although low can contribute to overall pore
volume changes.volume changes.
Impact of pore volume changes due to rock.
As pressure falls bulk volume reduces ( increased nett overburden stress )
and increase in volume of grains.
Nett effect reduction in porosity
Compressibility of rock cf
prf
p
V1c
V p
pr f pV c pV
Effect of Pore Volume ChangesEffect of Pore Volume Changes
Impact of pore volume changes due to connate water.
Expansion of water can contribute to reduction in pore volume for the hydrocarbons.
Compressibility of water:pw
wpw
V1c
V p
pw p wcV V Spw w wc pV c pS V
Total Pore Volume Change due to rock & water:
p pr pwV V V
p f w wc pV c c S pV
Effect of Pore Volume ChangesEffect of Pore Volume ChangesThis term can be added to MB equation and expressed in terms of oil (and gas) in place.
If we neglect a gas cap then the pore volume = oip
wc
NBV
1 S
Compressibility of water and rock
If we also include gas cap then
oip wc f
wc
NBV c S c p
1 S
oip wc f
wc
NBV 1 m c S c p
1 S
M is ratio of gas
to oil in place
If free gas present then errors in gas compressibility effects greater than absolute pore compressibility effects, so M ignored.
General Material Balance EquationGeneral Material Balance Equation
Net water influx + gas cap expansion + pore volume reduction =
Original oil volume – volume of remaining oil and free solution gas.
f w wce p w pc g gi oi
wc
oi p o si p s ps g
c c SW W B G G B GB pNB
1 S
NB N N B NR N N R G B
General Material Balance EquationGeneral Material Balance Equation
Other forms of the MB EquationOther forms of the MB EquationEquation sometimes presented using total formation volume
factor.Bt.
t o si s gB B R R B
Using m, where gi
oi
GBm
NB Using Gp where
p p pG N R
p t p s g e p
g gi
t ti ti f w wc ti wcgi
N B R R B W WN
B BB B mB c c S pB / 1 S
B
Modifications to the General MB Eqn.Modifications to the General MB Eqn. All of the parameters not significant over the life of a reservoir.All of the parameters not significant over the life of a reservoir.
Above bubble point some terms go to zero.Above bubble point some terms go to zero.
Above Pb, Rs is constant. Gp-NpRs =0. Only solution gas Above Pb, Rs is constant. Gp-NpRs =0. Only solution gas produced.produced.
Above Pb no gas cap, G or m = 0Above Pb no gas cap, G or m = 0
Below Pb, gas related terms have significance. Some Below Pb, gas related terms have significance. Some consider pore & water compressibility terms can be neglected consider pore & water compressibility terms can be neglected when compared to the errors associated with the free gas when compared to the errors associated with the free gas terms.terms.
As well as water influx, WAs well as water influx, We, the equation can be used for , the equation can be used for artificial drive, e.g. gas injection, Gartificial drive, e.g. gas injection, Gi and water injection, Wand water injection, Wii..
Alternative Alternative method for method for deriving MB eqn.deriving MB eqn.
According to Dake, Underground withdrawal = expansion of the system +
cumulative water influx.
Reservoir volume at pressure P of the produced fluids= expansion of primary gas cap+ expansion of oil plus originally dissolved gas + expansion of connate water + water influx+reduction of total pore volume
Assumptions in MB EquationAssumptions in MB Equation Pressure Pressure
– the MB equation is tank model. Pressure constant throughout the the MB equation is tank model. Pressure constant throughout the reservoir at any time. An average pressure has to be selected to be reservoir at any time. An average pressure has to be selected to be represent fluid properties.represent fluid properties.
TemperatureTemperature
– Changes in a reservoir take place at constant temperature, isothermal.Changes in a reservoir take place at constant temperature, isothermal.
Production rateProduction rate
– Time has no part within MBE.Time has no part within MBE.
Representative PVT dataRepresentative PVT data
– PVT measurements should be made or calculated to reflect behaviour in PVT measurements should be made or calculated to reflect behaviour in the reservoirthe reservoir
Good production data essentialGood production data essential
Significance and use of MBESignificance and use of MBE MBE is a relation between;MBE is a relation between;
– Oil & gas in place, N & GOil & gas in place, N & G
– Production,NProduction,Npp,G,Gpp, & W, & Wpp
– Water influx, WWater influx, Wee
– Average reservoir pressure, PVT parameters and in Average reservoir pressure, PVT parameters and in compressibility termscompressibility terms
If three of these are known the fourth can be calculated.If three of these are known the fourth can be calculated.
– If production and pressure data available and oil & gas in If production and pressure data available and oil & gas in place known, then water influx can be determined.place known, then water influx can be determined.
– If no water drive then can history match reserves.If no water drive then can history match reserves.
– For a known oil in place, the pressure at future dates can be For a known oil in place, the pressure at future dates can be determined for a proposed production plandetermined for a proposed production plan
Significance and use of MBSignificance and use of MB(Dake)(Dake)
Should be knownShould be known NNpp
RRpp
WWpp
CCww
SSwcwc
BBww
Potential unknownPotential unknown NN WWee
PP BBoo,B,Bgg,R,Rss
MM ccff
6 known and 8 unknowns – need more independent equations
Significance and use of MBSignificance and use of MB(Dake)(Dake)
6 known and 8 unknowns – need more independent equations
In reservoir simulation more unknowns re. Reservoir description, porosity, relative permeabilities etc.
Np & Rp generally best known except when good productions records not available.
Petrophysical data is generally good.
Significance and use of MBSignificance and use of MB
UnknownsUnknowns
Once production starts MB provides useful route to Once production starts MB provides useful route to upgrade STOIIP estimate, N.upgrade STOIIP estimate, N.
MB provides opportunity to determine water drive, MB provides opportunity to determine water drive, We.We.
Size of gas cap if not drilled may be difficult to Size of gas cap if not drilled may be difficult to determine.determine.
Important to determine rock & water compressibility.Important to determine rock & water compressibility.
MB zero dimensional. Requires average pressure. MB zero dimensional. Requires average pressure. Can be obtained from range of pressures from wells Can be obtained from range of pressures from wells in drainage area.in drainage area.
Sources of Data for use in MBESources of Data for use in MBE
PVT dataPVT data
– From PVT reportsFrom PVT reports
Production dataProduction data
– Well and reservoir Well and reservoir recordsrecords
Oil & Gas in PlaceOil & Gas in Place
– From volumetric From volumetric estimatesestimates
Connate Water SaturationConnate Water Saturation
– From petrophysicsFrom petrophysics
Water CompressibilityWater Compressibility
– Should be measuredShould be measured
Pore Compressibility Pore Compressibility
– Should be measuredShould be measured
Reservoir PressuresReservoir Pressures
– From pressure surveysFrom pressure surveys
Water InfluxWater Influx
– Calculation or history Calculation or history matchmatch
Limitations of MBELimitations of MBE
Zero dimensional Zero dimensional
– fluid properties averaged over entire reservoir.fluid properties averaged over entire reservoir.
Saturations distributions cannot be Saturations distributions cannot be determined.determined.
No time parameter.No time parameter.
– It will calculate what will happen but not when.It will calculate what will happen but not when.
MB Quotation – Muskatt 1947MB Quotation – Muskatt 1947The material balance equation method is by no means a universal tool for estimating reserves. In some cases it is excellent. In others it may be grossly misleading. It is always instructive to try it, if only to find out that it does not work, and why. It should be a part of the stock in trade of all reservoir engineers. It will boomerang if applied blindly as a mystic hocus- pocus to evade the admission of ignorance. The algebraic symbolism may impress the old timer and help convince a Corporation Commission, BUT it will not fool the reservoir. Reservoirs pay little heed to either wishful thinking or libellous misinterpretation. Reservoirs always do what they aught to do. They continually unfold a past which inevitably defies all man-made laws. To predict this past while it is still the futures is the business of the reservoir Zhengmengengineer. But whether the engineer is clever or stupid, honest or dishonest, right or wrong, the reservoir is always right.