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IntroductionThe material balance method finds wide application in order to estimate the original hydrocarbonin place of a reservoir by history matching the past production performance. It can also be used

to predict the future performance of the reservoir and to understand the dynamics of the reservoir

under various mechanisms of production, including solution gas drive and water influx. In most

studies, the data requirement is limited to average reservoir pressure, cumulative production, andfluid PVT properties over various time intervals during production. A reasonable description of

the aquifer may also be needed where applicable. A number of software tools are available in theindustry to perform the necessary analyses in a relatively straight forward manner within a short

period of time.

The classical material balance method is based upon the law of conservation of mass, whichsimply means that mass is conserved, i.e., it is neither created nor destroyed. The basic

assumptions made in this technique consist of the following

The reservoir is viewed as a homogeneous tan!, i.e., roc! and fluid properties are the

same throughout the reservoir.

"luid production and in#ection occur at single production and single in#ection points.

The analysis is independent of the direction of fluid flow in the reservoir.

$owever, in reality, the reservoirs are not homogeneous, and production and in#ection wells aredistributed areally. "urthermore, the wells are activated at different times. In addition, reservoir

fluids flow in definite directions. %evertheless, the material balance method became very popular

with reservoir engineers due to its simple yet robust foundation. It has been found to be avaluable tool for analy&ing reservoir performance with reasonably acceptable results. As

discussed later, material balance studies may aid in reservoir characteri&ation when the results

are compared against others, such as those obtained from volumetric analysis and reservoir

simulation.

The material balance method is more fundamental than the decline curve technique for analy&ing

reservoir production performance. The advantage of the material balance method is that reservoir

heterogeneities need not be !nown in detail in order to perform a meaningful analysis. 'oreover, material

balance studies are not as resource intensive as multidimensional, multiphase numerical simulation.

'aterial balance techniques are used to estimate the following

(riginal oil and original gas in place )((IP, (*IP+

ltimate primary recovery

The influence of natural production mechanisms in the reservoir, such as gascap, solution gas, or

water drives.

"urthermore, the results of material balance analysis can be used as verification of the hydrocarbon inplace and recovery estimates obtained by other methods.

This chapter is devoted to learning the following

The principle of material balance as applied to petroleum reservoirs involving production,

in#ection, and influx of various fluids.

Application of the material balance method in different types of reservoirs producing under

various drive mechanisms

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'athematical equations and graphical techniques used for oil and gas reservoir performance

analysis

Prediction of reservoir performance

-ole of material balance analysis in reservoir characteri&ation

'aterial balance analysis based on flowing bottomhole pressure

or!ing example problems and class exercises

The various capabilities of the material balance method are illustrated by the following analyses in the

later part of the chapter

/stimation of recovery factor in a newly discovered reservoir with limited data

Assessment of original oil and gas in place of an oil reservoir with a gas cap

Investigation of water influx characteristics affecting oil reservoir performance

Analysis of an abnormally pressured gas reservoir under depletion drive

Aquifer modeling for a reservoir under a strong water drive

*as reservoir simulation with various aquifer models

/stimation of original gas in place of a reservoir with a small radial aquifer, and comparison of

the result with Analysis of 3-Dplots as opposed to conventional 012 plots utili&ed in material balance studies

Performance review of a wet gas reservoir

'aterial balance of a gas well based on flowing bottomhole pressure

a numerical reservoir simulation

'ost of the analyses have been performed with the aid of various software tools available in the

industry.

Material Balance of Oil ReservoirsAproducing reservoir can be considered in which the underground withdrawal of petroleum fluids and

water is determined by any or all of the following

3hanges in volume of in1situ oil, gas, and water due to apressure decline in the reservoir ater influx from the surrounding aquifer

Pore volume compressibility

/xternal water or gas in#ection for reservoir pressure maintenance, in certain instances

In this case, the general material balance equation for oil reservoir performance can be expressed as

follows

nderground withdrawal = /xpansion of oil + (riginal dissolved gas + /xpansion of gas caps

+ -eduction in hydrocarbon pore volume due to connate water expansion and decrease in the pore

volume + %atural water influx from an ad#acent aquifer.

$avlena and (deh showed that the material balance components in the equation above can be arranged as

an equation of a straight line. The equation is solved for original hydrocarbon in place and other

parameters by using relatively simple graphical techniques. The general material balance is given as

follows

" =%)/o+ m/g+ /fw+ + e

here

" 4 underground withdrawal, rb

4 %,56, 7 )-, 1 -,+6g8 7 p6w1 i6w1 *i6g

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4 %p56t 7 )-, 1 -9i+6g87 p6w 1 i6w1 *i6g

%, 4 cumulative oil production, stb,

6, 4 oil formation volume factor, rb:stb,

-, 4 gas in solution in oil, scf:stbo,

6, 4 gas formation volume factor, rb:scf,, 4 cumulative water production, stb,

i 4 cumulative water in#ection, stb,*, 4 cumulative gas in#ection, scf,

-, 4 cumulative gas:oil ratio )cumulative gas production over cumulative oil production, scf:stb+,

% 4 original oil in place, stb,

/, 4 expansion of oil and original gas in solution, rb:stb

4 6t 1 6ti ,

4 )6, 1 6oil 7 )-si 1 -s+6g 0

6t 4 Two phase formation volume factor defined in chapter ;

46, 7 )-9i 1 -,+6g, rb:stb

m 4 initial gas cap volume fraction

/g4 expansion of gascap gas, rb:stb