Page 323 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 258

in which m D (t D) is the dimensionless real gas pseudo pressure which for transient flow
conditions is simply

4t
t
m D () = 1 2 ln D (8.32)
D
γ
and is identical in form to equ. (7.23).
Similarly, for long flowing times the semi-steady state constant terminal rate solution of
equ. (8.11), in Darcy units, is

2p qµ 4A kt
() m
mp − (p wf ) = 1 2 ln 2 + 2π + S′
i
µΖ 2kh γ Cr φ µ cA
π
Aw
which is the equivalent of equ. (7.13). In field units this becomes
1422QT 4A
() m
mp − (p wf ) = 1 2 ln + 2 t DA + S′
π
i
kh γ C r 2
Aw
and therefore the m D (t D) function for semi-steady state flow is
4A
t
m D () = 1 2 ln + 2 π t DA (8.33)
D
γ Cr 2
Aw
which is equivalent to equ. (7.27).

To generalise, the dimensionless real gas pseudo pressures are the constant terminal
rate solutions of the equation

1 ∂ r ∂ m = ∂ m D (8.34)
D
r ∂ r D D r ∂ D t ∂ D
D
and the solution which is valid for all values of the flowing time is

4t
t
m D () = 2π t DA + 1 2 ln D − 1 2 m DMBH ( DA ) (8.35)
t
D
γ ( )
which is the same as equ. (7.42), for liquid flow.

The m D(MBH) function, the Matthews, Brons and Hazebroek dimensionless pseudo
pressure, can be read directly from the MBH charts, figs. 7.11-15, for the appropriate
value of the dimensionless time argument t DA, in just the same way as the p D(MBH)
function was evaluated for use in equ. (7.42). Since field units are being used in this
chapter, the abscissa and ordinate of the MBH charts should be interpreted as

kt (hrs )
t DA = 0.000264 (8.36)
φµ cA

and