Page 306 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 242

Mstb / d stb / d s.cc / sec 1
Q Mscf / d = q r.cc / sec
Mscf / d Mstb / d stb / d E

1 ZT
] [1.84
Q Mscf / d × [1000 × ] = q r.cc / sec

5.615 35.37p
QZT
9.265 Mscf / d = q r.cc / sec
p

Including the remaining conversion factors in equ. (8.1 ) yields

711 Qµ ZT r 3
pp wf = ln e − + S (8.2)
−

khp r w 4
Russell and Goodrich, comparing equ. (8.2) with the numerical simulation, found that
for the same reservoir and flow conditions the two were in close agreement providing
that the pressure p , at which the gas expansion factor was evaluated, was set equal to
the average of the current, average reservoir pressure and the bottom hole flowing
pressure i.e.

pp
+

p = wf (8.3)
2
Furthermore, both µ and Z should also be evaluated at this same pressure so that

pp
pp
+ +
µ = µ wf and Z = Z wf (8.4)
2 2

and substituting these values of p, µ and Z in equ. (8.2) gives
1422 Q ZT r 3
µ
2
p − p 2 wf = ln e − + S (8.5)
kh r w 4
2
Equ. (8.5) is the familiar p formulation of the well inflow equation, under semi-steady
state conditions, which was tested by Russell and Goodrich and found to be applicable
over a wide range of reservoir conditions and flow rates.

Similarly, the transient line source solution for the same initial and boundary conditions
detailed in chapter 7, sec. 2, is

711 Q ZT 4 .000264kt
µ
2
p − p 2 wf = ln + 2S (8.6)
i
kh γ φ ( ) c rµ i w 2

p p
pp
+ +
µ = µ wf and Z = Z wf (8.4)
2 2