Page 317 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 252

p
µ Z
∆p
∆p

Pressure

Fig. 8.7 Typical plot of p/µZ as a function of pressure

The diagram also shows that even in the non-linear part of the plot, providing the
drawdown, pp− wf = dp, is small, the two methods will always give approximately the
same answers. It is only when the drawdown is very large (i.e. for low kh reservoirs
producing at high rates) that the results using the two methods will be significantly
different. Under these circumstances the assumption implicit in the Russell Goodrich
approach, namely that pressure gradients are small, is no longer valid.

With the exception of the brief description of the history of gas well testing in sec. 8.10,
all the equations for the flow of a real gas, in the remainder of this chapter, will be
expressed in terms of real gas pseudo pressures. The reasons for adopting this
approach are:
- it is theoretically the better method and in using it one does not have to be
concerned about the pressure ranges in which it is applicable, as is the case when
2
using the p method
- with a bit of practice, it is technically the more simple method to use once the basic
relationship for m(p) as a function of p has been derived

- the necessity for iteration in solving the inflow equation for p wf is avoided

- the technique is widely used in the current literature and readers are expected to be
quite familiar with its application.

8.6 NON-DARCY FLOW

For the horizontal flow of fluids through a porous medium at low and moderate rates,
the pressure drop in the direction of flow is proportional to the fluid velocity. The
mathematical statement of this relationship is Darcy's law, which for radial flow is

dp µ
= u (8.18)
dr k

q
where u is the fluid velocity = ⋅
2 π rh