Page 83 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 22

−
G = V (1 S )E i (1.26)
φ
wc
in which E i is evaluated at the initial pressure.

Other important parameters which can be conveniently expressed using the equation
of state are, the real gas density, gravity and isothermal compressibility.
Since the mass of n moles of gas is nM, where M is the molecular weight, then the
density is

nM nM Mp
ρ = = = (1.27)
V ZnRT /p ZRT

Comparing the density of a gas, at any pressure and temperature, to the density of air
at the same conditions gives

ρ gas (M/ Z) gas
=
ρ air (M/ Z) air

and, in particular, at standard conditions

ρ gas M gas M
= γ = = (1.28)
g
ρ air M air 28.97

where γ g is the gas gravity relative to air at standard conditions and is conventionally
expressed as, for instance, γ g = 0.8 (air = 1).

Therefore, if the gas gravity is known, M can be calculated using equ. (1.28) and
substituted in equ. (1.27) to give the density at any pressure and temperature.
Alternatively, if the gas composition is known M can be calculated as

M = nM i (1.29)
i
i
and again substituted in equ. (1.27). The molecular weights of the individual gas
components, M i, are listed in table 1.1. It is also useful to remember the density of air at
standard conditions (in whichever set of units the reader employs). For the stated units
this figure is

(ρ air) sc = 0.0763 ib/cu.ft

which permits the gas density at standard conditions to be evaluated as

ρ = 0.0763 g (lbs / cu.ft) (1.30)
γ
sc
The final application of the equation of state is to derive an expression for the
isothermal compressibility of a real gas. Solving equ. (1.15) for V gives

ZnRT
V =
p