Page 81 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 20

4
1−y in the denominators of the second and first terms, respectively, instead of (1−y) 3
4
and (1−y) as in equs. (1.21) and (1.23) of this text.)
14
Takacs has determined that the average difference between the Standing-Katz
correlation chart and the analytical Hall-Yarborough method is − 0.158% and the
average absolute difference 0.518%. Figure 1.8 shows an isothermal Z−factor versus
pressure relationship, obtained using the Hall-Yarborough method, for a gas with
gravity 0.85 and at a reservoir temperature of 200°F. The plot coincides, within pencil
thickness, with the similar relation obtained by the application of the method described
in b), above.

The plot shows that there is a significant deviation from the ideal gas behaviour which
is particularly noticeable in the intermediate pressure range at about 2500 psia. At this
pressure, use of the ideal gas equation, (1.13), would produce an error of almost 25%
in calculated gas volumes.

1.6 APPLICATION OF THE REAL GAS EQUATION OF STATE

The determination of the Z−factor as a function of pressure and temperature facilitates
the use of the simple equation

pV = ZnRT (1.15)

to fully define the state of a real gas. This equation is a PVT relationship and in
reservoir engineering, in general, the main use of such functions is to relate surface to
reservoir volumes of hydrocarbons. For a real gas, in particular, this relation is
expressed by the gas expansion factor E, where