Page 74 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 13

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momentum, is reduced. To correct for this the term a/V must be added to the observed
pressure, where a is a constant depending on the nature of the gas. Similarly the
volume V, measured assuming the molecules occupy negligible space, must be
reduced for a real gas by the factor b which again is dependent on the nature of the
gas.

The principal drawback in attempting to use equ. (1.14) to describe the behaviour of
real gases encountered in reservoirs is that the maximum pressure for which the
equation is applicable is still far below the normal range of reservoir pressures.

More recent and more successful equations of state have been derived, - the Beattie-
Bridgeman and Benedict-Webb-Rubin equations, for instance (which have been
conveniently summarised in Chapter 3 of reference 18); but the equation most
commonly used in practice by the industry is

pV = ZnRT (1.15)

in which the units are the same as listed for equ. (1.13) and Z, which is dimensionless,
is called the Z−factor. By expressing the equation as

P
V= nRT
Z

the Z−factor can be interpreted as a term by which the pressure must be corrected to
account for the departure from the ideal gas equation.

The Z−factor is a function of both pressure and absolute temperature but, for reservoir
engineering purposes, the main interest lies in the determination of Z, as a function of
pressure, at constant reservoir temperature. The Z(p) relationship obtained is then
appropriate for the description of isothermal reservoir depletion. Three ways of
determining this relationship are described below.

a) Experimental determination

A quantity of n moles of gas are charged to a cylindrical container, the volume of which
can be altered by the movement of a piston. The container is maintained at the
reservoir temperature, T, throughout the experiment. If V o is the gas volume at
atmospheric pressure, then applying the real gas law, equ. (1.15),

14.7 V o = nRT

since Z=1 at atmospheric pressure. At any higher pressure p, for which the
corresponding volume of the gas is V, then

pV = ZnRT

and dividing these equations gives