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.