Page 137 - Geology and Geochemistry of Oil and Gas

108 NATURAL GASES AND CONDENSATES

In practice, however, the Clapeyron equation with the compressibility factor Z
(due to intermolecular attraction) is used:
pV ¼ ZmRT (6.7)
where m is the mass of gas, R ¼ the gas constant, T ¼ the absolute temperature, and
Z ¼ the compressibility of the natural gas (which is a function of pressure, temper-
ature, and gas composition). For ideal gases, Z ¼ 1. The compressibility of a gas
mixture may be computed as a weighted average of compressibility of all components.

6.3.4. Deviation of pressure at bottom of gas column

If point 2 (in a gas column) lies at distance DL below point 1 ( p 1 in psi), the
pressure at point 2 ( p 2 in psi) is equal to
p ¼ p þ ðg DLÞ=144 (6.8)
2 1
where g is the specific weight of gas in lb/cu ft.
On using the equation of state and considering 1 lb of gas,
pv ¼ ZNRT (6.9)
where p is the absolute pressure in lb/sq ft, v ¼ the specific volume in cu ft/lb,
Z ¼ the compressibility factor, N ¼ the number of moles of gas, R ¼ the universal
gas constant, and T ¼ the absolute temperature in 1R.
Thus,
v ¼ ZNRT=p (6.10)
In as much as
v ¼ 1=g (6.11)
and
g ¼ p=ZNRT (6.12)
On substituting Eq. 6.12 into Eq. 6.8,
p ¼ p þ ð p=144ZNRTÞDL (6.13)
2 1
Rearranging,
p p ¼ ð p=144ZNRTÞDL (6.14)
2 1
and
dp=p ¼ dL=144ZNRT (6.15)
In integral form, Eq. 6.15 becomes
L
Z Z
p bc
dp=p ¼ ð1=144ZNRTÞ dL (6.16)
0
p s
Thus,
lnð p =p Þ ¼ L=144Z av NRT av (6.17)
bc
s