Page 259 - Fundamentals of Reservoir Engineering

OILWELL TESTING 196

duration so that semi-steady state flow conditions prevail at the time of closure, and
even if this condition is not exactly satisfied the error introduced will be rather small.
The occasion when the use of this rate-time combination may not be acceptable is for
initial tests when the well may be produced for a relatively short period of time at an
14
uneven rate. Odeh and Selig have described a method for buildup analysis under
these conditions which can improve the accuracy of the results. In the remaining
description of pressure buildup analysis the effective flowing time will be used
exclusively and denoted by t, and the final production rate by q. An example of the use
of t sss in buildup analysis for a gas well will be described in Chapter 8, sec. 11.

Having plotted the observed pressures according to the interpretation method of
Horner, the MBH method can be applied to determine p according to the following
recipe.

t +∆ t
*
1) Extrapolate the early linear buildup trend to = 0 and determine the value of p .
t ∆
From the slope of the straight line calculate k using equ. (7.50).

2) Divide the reservoir into drainage volumes so that

q i V i
q = V
TOT TOT
th
where q i is the production rate for the i well draining a reservoir bulk volume V i and
q TOT and V TOT are the total rate and bulk volume of the reservoir respectively. This
relationship has been shown in Chapter 5, sec. 5.3, to be valid for wells draining a
reservoir under semi-steady state flow conditions, however, Matthews, Brons and
Hazebroek assert that the relationship can be applied with reasonable accuracy

irrespective of the prevailing flow condition. This step leads to the determination of V i
and hence A i, the area drained by the well, can be estimated by assuming that the
average thickness within the area is equal to that observed in the well. With the aid of a
geological structural map of the reservoir, both the shape of the drainage area and
position of the well with respect to the boundary can be roughly estimated to
correspond to one of the MBH geometrical configurations shown in figs. 7.11-15.

3) Evaluate the dimensionless time

kt
t DA = 0.000264 (t hours) (7.49)
−
φµ cA

using values of k and A obtained from steps 1) and 2) respectively. For liquid flow the
µc product is small and constant but for two phase gas-oil and for single phase gas
flow this is not the case which leads to certain difficulties in interpretation which will be
described in Chapter 8.

4) Enter the appropriate MBH chart, fig. 7.11-15, and, for the curve corresponding closest
to the estimated geometrical configuration, read the value of the ordinate, p D(MBH) (t DA),

for the calculated value of the dimensionless (effective) flowing time t DA