Page 307 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 243

which is the real gas equivalent of equ. (7.10) in field units. This equation was also
found to compare favourably with the numerical simulation results, providing the
viscosity-compressibility product was evaluated as (µc) i, at the initial pressure p i,
(ref. sec. 8.8).

2
One obvious practical disadvantage in using the p formulation can be appreciated by
considering a frequently occurring problem in gas inflow calculations, namely, the
calculation of p wf if both p and Q are known using, in this case, the semi-steady state
inflow equation. A schematic of the calculation procedure is shown in fig. 8.2. If it is
assumed that p has been determined in the drainage volume of the well from material
balance considerations then, for a fixed offtake rate, it will be necessary to solve the
inflow equation by iteration to determine p wf since both µ and Z must be evaluated at
k
the pressure defined in equ. (8.4). In any iteration cycle p is calculated using values
wf
k k k1
−
of µ and Z evaluated at the pressure (p p+ wf )/ 2 , where k is the iteration counter. For
1
1
k = 1, both µ and Z can be evaluated at some convenient starting pressure, which in
this case has been selected as p. When the difference between successive values of
k
p is less than some tolerance value (TOL) the iteration is terminated. Other
wf
2
disadvantages in using the p formulation for inflow equations will be discussed in
section 8.5.
8.4 THE AL-HUSSAINY, RAMEY, CRAWFORD SOLUTION TECHNIQUE

In their approach the authors attempted to linearize the basic flow equation, (5.1), using
the following version of the Kirchhoff integral transformation

p pdp
mp 2 (8.7)
() =
p b µ Z

which was given the name, in this present context, of "the real gas pseudo pressure".