Page 73 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 12

Therefore, while it is obvious that one would not produce an aquifer, but rather, let the
water expand and displace the oil; so too, the gas in the gascap, although having
commercial value, is frequently kept in the reservoir and allowed to play its very
significant role in contributing to the primary recovery through its expansion. The
mechanics of primary oil recovery will be considered in greater detail in Chapter 3.

1.5 VOLUMETRIC GAS RESERVOIR ENGINEERING

Volumetric gas reservoir engineering is introduced at this early stage in the book
because of the relative simplicity of the subject. lt will therefore be used to illustrate
how a recovery factor can be determined and a time scale attached to the recovery.

The reason for the simplicity is because gas is one of the few substances whose state,
as defined by pressure, volume and temperature (PVT), can be described by a simple
relation involving all three parameters. One other such substance is saturated steam,
but for oil containing dissolved gas, for instance, no such relation exists and, as shown
in Chapter 2, PVT parameters must be empirically derived which serve the purpose of
defining the state of the mixture.

The equation of state for an ideal gas, that is, one in which the inter-molecular
attractions and the volume occupied by the molecules are both negligible, is

pV = nRT (1.13)

in which, for the conventional field units used in the industry
p = pressure (psia); V = volume (cu.ft)

T = absolute temperature − degrees Rankine (°R=460+°F)
n = the number of lb. moles, where one lb. mole is the molecular weight of the
gas expressed in pounds.

and R = the universal gas constant which, for the above units, has the value
10.732 psia.cu.ft/lb. mole.°R.

This equation results from the combined efforts of Boyle, Charles, Avogadro and Gay
Lussac, and is only applicable at pressures close to atmospheric, for which it was
experimentally derived, and at which gases do behave as ideal.

Numerous attempts have been made in the past to account for the deviations of a real
gas, from the ideal gas equation of state, under extreme conditions. One of the more
celebrated of these is the equation of van der Waals which, for one Ib.mole of a gas,
can be expressed as
a
(p + ) (V b− ) RT= (1.14)
V 2

In using this equation it is argued that the pressure p, measured at the wall of a vessel
containing a real gas, is lower than it would be if the gas were ideal. This is because
the momentum of a gas molecule about to strike the wall is reduced by inter-molecular
attractions; and hence the pressure, which is proportional to the rate of change of