Page 172 - Fundamentals of Reservoir Engineering

DARCY'S LAW AND APPLICATIONS 110

It is also suggested that both the Darcy and milli-Darcy be retained as allowable terms.

2) For horizontal flow, the conversion from Darcy to field units of the first part of the flow
equation is

kA dp
q =− 1.127 10 − 3 (4.17)
×
µ Bdl
o
To convert the gravity term, using the conventional manner described in the text, is
rather tedious but can be easily achieved in an intuitive manner. The second term,
6
(ρg/1.0133×10 ) dz/dl, must, upon conversion to field units, have the units psi/ft. The
only variable involved in this latter term is ρ, the fluid density. If this is expressed as a
specific gravity γ, then, since pure water has a pressure gradient of 0.4335 psi/ft, the
gravity term can be expressed as

dz
0.4335γ psi/ft
dl

Furthermore, adopting the sign convention which will be used throughout this book,
that z is measured positively in the upward, vertical direction, fig. 4.2, and if θ is the dip
angle of the reservoir measured counter-clockwise from the horizontal then

dz
dl = sin θ

and the full equation, in field units, becomes

kA dp
1.127 10
q =− × − 3 + 0.4335 γ sinθ (4.18)
µ B o dl

4.5 REAL GAS POTENTIAL

The fluid potential function was defined in section 4.2, in absolute units as

p dp
Φ= + gz (4.6)
p b ρ

and for an incompressible fluid (ρ ≈ constant) as

p
Φ= + gz (4.7)
ρ

Liquids are generally considered to have a small compressibility but the same cannot
be said of a real gas and therefore, it is worthwhile investigating the application of the
potential function to the description of gas flow.

The density of a real gas can be expressed (in absolute units) as

Mp
ρ = (1.27)
ZRT