Page 355 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 290

kh
7.08 10 − 3 (m (p ) m (p )) m (t ) S
=
′
+
′
×
′
−
q o i wf D D
where
4t
′
m(t ) = 2 π t DA + 1 2 ln D − 1 2 m′ D(MBH) (t ) (8.64)
D
D
DA
γ
in which k is the effective permeability to oil in the presence of the connate water.
Raghavan has shown, using numerical simulation, that the m′ (t D) functions correlate
D
very well with the p D (t D) functions for liquid flow but, as in the case of real gas flow, the
match is better for small values of t D, before the boundary effects are felt.
It should also be noted that the compressibility used in the evaluation of t DA is the total
compressibility of the system. Above the bubble point this is simply

(5.22)
c t = c oS o + c wS wc + c f
but below bubble point there must be additional components to account for the
18
presence of free gas and for the transfer of solution gas from the oil . Thus for the oil,
a pressure drop ∆p will cause a reduction in the oil volume ∆B o and an increase in the
liberated gas volume B g∆ R s, and

1 ∂ B o ∂ R
s
c =− − B g
o
B o ∂ p ∂ p
The total compressibility, below bubble point pressure is therefore

S ∂ R ∂ B S ∂ B g
g
c = o B g s − o − + c S wc + c f (8.65)
t
w
B o ∂ p ∂ p B ∂ p
g
in which, for a significant gas saturation, the last two terms can usually be neglected.
Because of the equivalence of form of the m′ functions, equ. (8.64), with the p D or m D
D
functions, it is clear that the buildup theory must follow that detailed in Chapter 7,
sec. 7, for oil, and sec. 8.11 of this chapter, for gas. A Horner plot of m´(p ws) versus log
t +∆ t *
is made and the early linear trend extrapolated to determine m´(p ). The slope of
t ∆
the linear section is

162.6 q
m =
kh

and the skin factor can be calculated using equ. (7.52), with pseudo pressures
replacing the actual pressures in the equation. Again the MBH method can be used to
determine m(p) and hence the average pressure p. Furthermore, if the flowing time
′
before the survey is very long, the correction method of Kazemi, described in the
previous section, can be applied to improve the estimate of p.