Page 278 - Fundamentals of Reservoir Engineering

OILWELL TESTING 215

The reason for this disparity lies in the nature of the analysis technique itself. In plotting
the results according to equ. (7.71) the evaluation of the abscissa,
n ∆ q
t
i p D ( D − t D ) , automatically involves the boundary condition in the analysis,
j1 q n n j 1
−
=
since use of the p D function implies a knowledge of the geometrical configuration.
Therefore, unlike the buildup analysis, for which a unique plot of the observed data is
obtained, the multi-rate test analysis can yield a different plot for each assumed
boundary condition, as shown in fig. 7.28, and all the plots appear to be approximately
linear. The only time when a straight line is obtained, which has no dependence on the
boundary condition, is for the infinite reservoir case. Then the Odeh-Jones plot is
n ∆ q
applicable which has as its abscissa, j log t − t j 1 ) equ. (7.72). The problem is, of
( n
j1 q n −
=
course, how can one be sure that transient analysis is valid without a knowledge of
several of the basic reservoir parameters, some of which may have to be determined
as results of the test analysis.

As clearly shown in the MBH charts, figs. 7.11-15, the crucial parameter for deciding
the flow condition is
kt
t DA = 0.000264 (7.49)
φµ cA

If t DA is extremely small when evaluated for the maximum value of t (i.e. t = total test
duration) then it is probably safe to use the transient analysis technique. It is not
obvious, however, just how small this limiting value of t DA should be because this too
depends on the geometrical configuration. For a well positioned at the centre of a circle
or square the minimum value of t DA is 0.1, at which point there is a fairly well defined
change from pure transient to semi-steady state flow. For a well asymmetrically
positioned within a 2:1 rectangle, e.g. curve IV of the MBH chart, fig. 7.12 (which is the
correct geometrical configuration for exercise 7.8) the departure from purely transient
flow, in this case to late transient flow, occurs for t DA < 0.015. Similarly for the 4:1
geometrical configuration included in the exercise the departure occurs for t DA < 0.01.

In exercise 7.8, the relationship between t DA and the real time has a large coefficient of
0.01 (i.e. t DA = 0.01 t) . Th is results from the fact that the permeability is large and the
area relatively small and have been deliberately chosen so to illustrate the hidden
dangers in applying transient analysis techniques to multi-rate test results. After the
first 3-hour flow period the corresponding value of t DA is 0.03 and therefore there is
already a departure from transient flow for the 2:1 and the 4:1 geometries used in the
exercise. If it is assumed that the well is at the centre of a circle, however, transient
analysis can be applied throughout since the value of t DA corresponding to the entire
test duration of 12-hours is t DA = 0.12 and, as already noted, the departure from
transient flow for this geometry occurs for t DA = 0.1. The above points are clearly
illustrated in fig. 7.28 and in tables 7.11-14.

The majority of examples of multi-rate test analysis in the literature have, quite
correctly, been subjected to transient analysis. For instance, there is an example of a