Page 336 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 271

inadequate to define the B and F factors in the well inflow equation (8.44). This is
because if the permeability is small then the flowing time required to reach semi-steady
state conditions, which depends on t DA = 0.000264kt/φ(µc) iA, can become extremely
large. Then, the use of a semi-steady state inflow equation to analyse the test is
inadmissible because the pressure response at the wellbore is strongly time
dependent. To cater for this time dependence, two methods have been presented in
the literature for analysing tests under the assumption that the wellbore pressure
response could be matched by superposing transient constant terminal rate solutions
of the radial diffusivity equation. The first of these was the Odeh-Jones technique 13
(1965), in which the test analysis equation was formulated using p-squared terms. This
14
was followed in 1971 by the method of Essis and Thomas , in which the Odeh-Jones
test equation was modified by the use of real gas pseudo pressure to give

kh ( ( n Q m t t )
() m p
=
n
i
1422T mp − wf n ) ) ∆ j D ( D n − D j 1 + Q S′ n
−
j1
=
which is the general form of the superposed constant terminal rate solution,
equ. (8.39). Both Odeh and Jones and Essis and Thomas applied their analysis
techniques strictly for transient flow conditions, for which the superposed m D functions
in equ. (8.39) can each be expressed as
4t
t
m D () = 1 2 ln D (8.32)
D
γ
rather than using the general expression, equ. (8.40), which assumes a knowledge of
the area drained and geometry. If transient m D functions can be used then the analysis
is simple and should yield values of k and S which in turn can be used to calculate a
value of the Darcy flow coefficient B, equ. (8.44), for any values of the area drained and
shape factor. The analysis also directly determines F (or D), the second coefficient in
the inflow equation. The technique will be fully illustrated in exercise 8.2.

The statements made in Chapter 7, sec. 8, about the possibility of incorrectly
interpreting multi-rate test data through making an a priori judgement concerning the
prevailing flow conditions are equally, if not more, valid in gas well test analysis. This is
because the µc product for gas is several times smaller than for oil which implies that,
for the same permeability, porosity and area drained, the boundary effects will be felt
much earlier in a gas well test. To apply transient analysis techniques it is insufficient to
assume that each separate flow period should be short enough so that transient
conditions prevail. Instead, the entire test duration must be so brief that the maximum
value of the m D function in equ. (8.39), which is

m D ( D max ) = m D (total dimensionless testing time )
t′

can still be evaluated using the transient expression, equ. (8.32). The possible error
that can be made by making the flow periods too long will be illustrated in the following
exercise.