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

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

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 momentum, is reduced.

To correct for this the term a/V2 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 BeattieBridgeman 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

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.