Page 327 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 262

In conclusion, it can be stated that the use of equs. (8.39) and (8.40) to analyse gas
well tests is never quite as satisfactory as using the combination of equs. (7.31) and
(7.42) for oilwell tests. Nevertheless, the former equations do provide what is usually
described in the literature as "a reasonable engineering approximation" and their
application will now be described in detail.

8.10 MULTI-RATE TESTING OF GAS WELLS

This section will be presented in the form of a brief history of the subject of multirate
testing of gas wells in which former analysis techniques will be compared with the
method implied in the use of equ. (8.39) and (8.40).

The first and perhaps the best known equation for analysing multi-rate tests is that of
11
Schellhardt and Rawlins which was empirically established as the result of the
analysis of some 600 gas well tests during the 1930's. The equation is

n
2
Q = C p − p 2 wf ) (8.42)
( i
"back pressure equation". Using the observed pressures at the end of each flow period
2
2
a plot can be made of log (p − p ) versus log Q, the slope of which has the value 1/n.
wf
i
Having thus determined n, the value of C can be calculated using equ. (8.42).
It was originally believed that both C and n were constants that, once determined from
the test analysis, could be used for the long term prediction of gas well deliverability.
This being accomplished merely by replacing p i by the current average reservoir
12
pressure p. Carter et al. , have shown, however, that n is a variable with a range
between .5 and 1 depending on whether the value of the non-Darcy flow component
2
FQ , defined by equ. (8.24), is very large (n = .5) or negligible (n = 1). Furthermore, the
value of C can be shown to be dependent on k, A, C A and S and also on the pressure
dependent functions, µ, Z and the flowing time, and can hardly be expected to remain
constant throughout the producing life of the well. These statements will not be
substantiated in this text since it is not intended to use equ. (8.42) which may be
regarded, at best, as being a useful empirical approximation.

Nevertheless, in spite of all the drawbacks mentioned above, it was found that the back
pressure equation could be used with tolerable accuracy in analysing tests in which it
was suspected that semi-steady state flow conditions prevailed during each separate
flow period. As a result, it became, and still is, quite fashionable to test wells in such a
way that stabilized flow is achieved at each rate. Precisely when the change from
transient to semi-steady state flow occurs depends on some minimum value of
t DA = .000264 kt/φ (µc) iA, (a fact which is clearly illustrated by the MBH charts,
figs. 7.11-15), which in turn depends upon the geometry of the drainage area and well
asymmetry. As already noted in sec. 8.8, since the µc product for gas is considerably
smaller than for a liquid, there is at least some justification in attempting to analyse gas
well tests assuming stabilized flow conditions, even for a test of relatively short
duration.