Page 137 - Hydrocarbon Exploration and Production Second Edition

124 Reservoir Fluids

where

Field Units SI Units
P ¼ absolute pressure Psia Bara
V ¼ volume ft 3 m 3
n ¼ number of moles of gas – –
T ¼ absolute temperature 1Rankine 1Rankine
R ¼ universal gas constant 10.73 psia ft 3 8314.3 kJ/kmol K

The above equation is valid at low pressures where the assumptions hold.
However, at typical reservoir temperatures and pressures, the assumptions are no
longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the
ideal gas law. In practice, it is convenient to represent the behaviour of these ‘real’
gases by introducing a correction factor known as the gas deviation factor (also called
the dimensionless compressibility factor, or z-factor) into the ideal gas law:

PV ¼ znRT The real gas law
The z-factor must be determined empirically (i.e. by experiment), but this has
been done for many hydrocarbon gases, and correlation charts exist for the
approximate determination of the z-factor at various conditions of pressure and
temperature (Standing, M. B. and Katz, D. L. 1942. Density of natural gases. Trans.
AIME).

6.2.4.1. Relationship between subsurface and surface gas volumes
The most important use of the real gas law is to calculate the volume which a
subsurface quantity of gas will occupy at surface conditions, since when gas sales
contracts are negotiated and gas is subsequently sold it is referred to in volumes at
standard conditions of temperature (T sc ) and pressure (P sc ).
The relationship required is the gas expansion factor (E ), and is defined for a
given quantity (mass or number of moles) of gas as
Volume of gas at standard conditions 3 3
E ¼ ðscf=rcfÞ or ðsm =rm Þ
Volume of gas at reservoir conditions
It can be shown using the real gas law, and the knowledge that at standard
conditions z ¼ 1.0, that for a reservoir pressure (P) and temperature (T ):
1 T sc P
E ¼ ðvol=volÞ
z T P sc
The previous equation is only valid as long as there is no compositional change of
the gas between the subsurface and the surface. The value of E is typically in the
order of 200, in other words the gas expands by a factor of around 200 from
subsurface to surface conditions. The actual value of course depends upon both the
gas composition and the reservoir temperature and pressure. STP are commonly