Page 326 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 261

individual constant terminal rate solutions it is assumed that the only skin factor term
remaining which influences p wf is the value Sn = S + DQn. This is because the rate
′
dependent skin factor is not, in itself, a time dependent solution of the diffusivity
equation but is merely considered to have a perturbing influence on the bottom hole
flowing pressure which re-adjusts instantaneously when the rate changes. Thus, even
though the DQ terms in the summation leading to equ. (8.39) do not algebraically
cancel, as do the mechanical skin factor components, on changing the rate from Q´ n-1
to Q n the value of p wf n is only influenced by DQ n. The components DQ n-1, DQ n-2 . . .

DQ n-j have no transient effects and die out immediately.

The main difference between oil and gas well testing arises from the fact that the total
skin factor in a gas well has two components, one of which is rate dependent. Because
of this, a gas well must be tested with a minimum of two separate flow rates to be able
to differentiate between these two skins.

Thus, at rate Q 1 the total skin

+
S′ = S DQ 1
1
can be obtained from the test analysis, while at rate Q 2

+
S′ = S DQ 2
2
can be similarly determined. The two equations for S′, and S′ can then be solved
1
2
simultaneously to provide S and D (or F).
A further complication in applying equs. (8.39) and (8.40) to gas well test analysis lies
in the fact that the superposition principle itself, which is implicit in the formulation of
equ. (8.39), is strictly only valid when applied to solutions of linear differential
equations. Since it is the constant terminal rate solution of the non-linear radial
diffusivity equation (8.11) that is being superposed, some fundamental mathematical
2
error might therefore be expected. Al-Hussainy, Ramey and Crawford have shown, by
comparing superposed m D functions for gas with the superposed p D functions for liquid
flow, that the error is very slight providing that the test is conducted with an increasing
rather than a decreasing rate sequence.

As stated in sec. 8.8, the viscosity-compressibility product used in an initial well test is
(µc) i evaluated for the initial equilibrium pressure p i. In the test analysis exercises
included in the following sections of the chapter, the initial pressure in each case is
taken as 4290 psi and the PVT data and real gas pseudo pressures of table 8.1 are
-6
common to all. The value of (µc) i under these circumstances is 3.6 × 10 cp/psi and no
allowance for its variation is made during the ensuing analyses. It is interesting to note
that, in spite of the high compressibility, the µc product for a gas reservoir (≈ µc g) is
invariably three or four times smaller than for an oil reservoir, because of the low
viscosity of the gas. This implies that, for a given drainage area, permeability and
porosity, the change from transient to either late transient or stabilized flow can be
expected to occur much more rapidly in a gas than in an oil reservoir. This has
implications which will be discussed in greater detail in secs. 8.10 and 8.11.