Page 320 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 255

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Because of the latter assumption the FQ term can be included in equs. (8.15) and
(8.16) in very much the same way as the mechanical skin factor, only in this case it is
interpreted as being a rate dependent skin. Thus equ. (8.15), for instance, including the
non-Darcy flow component, becomes

1422 TQ r 3
() m
mp − (p wf ) = ln e − + S + FQ 2 (8.25)
kh r w 4

1422 TQ r 3
= ln e − + S + DQ (8.26)
kh r w 4

where in the latter expression, which is commonly used in the literature, DQ is
interpreted as the rate dependent skin factor and

Fkh
D = (8.27)
1422T

Either F or D is used in the remainder of this chapter, to allow for non-Darcy flow,
depending on which is the more convenient for the application being considered.

8.7 DETERMINATION OF THE NON-DARCY COEFFICIENT F

Two methods are available for the determination of the non-Darcy flow coefficient,
which are

- from the analysis of well tests

- by experimentally measuring the values of the coefficient of inertial resistance,
β and using it in equ. (8.24) to calculate F.

Of these two, the well testing method will give the more reliable result just as in the
case of oil well testing in which, from the slope of the pressure buildup plot, a more
meaningful value of the kh product can be obtained than by measuring values of the
permeability on a selection of core samples and trying to average these results over
the entire formation. Furthermore, in the well test F will be measured in the presence of
any liquid saturation in the vicinity of the well. The determination of F by well testing will
be described in detail in secs. 8.10 and 8.11 and will not be discussed further at this
stage.

To determine β experimentally, the procedure is to first measure the absolute
permeability of each of the core samples and then to apply a series of increasing
pressure differentials across each sample by flowing air through the core plugs at ever
increasing rates. Knowing the flow rates and pressure differentials across the plugs,
the coefficient of inertial resistance can be directly calculated using a linear version of
the Forchheimer equation (8.19). The results are usually presented as shown in fig. 8.8
in which β is plotted as a function of the absolute permeability over the range of core
samples tested.