Summary
One of the common assumptions in horizontal-well interference-test analysis
is to ignore fluid flow in and out of the horizontal observation well and
represent it by a point. In some cases, the active well is also approximated by
a vertical line source. Using a semianalytical model, this paper answers three
fundamental questions:
• What is the critical distance between the wells to represent the
horizontal observation well by an observation point?
• Where should the observation point be placed along the horizontal
well?
• Under what conditions may the active well be approximated by a vertical
line source and the exponential integral solution be used to analyze
observation-well responses?
Two correlations are presented to simplify the analysis of horizontal-well
interference tests. Example applications are presented, and error bounds are
documented.
Introduction
Analysis of horizontal-well interference tests is an extremely difficult
problem because the lengths, orientations, locations, and distances between
wells need to be considered. One of the assumptions used to make the
horizontal-well interference-test analysis a tractable problem is to ignore the
flow pattern that results because of the existence of the horizontal well and
to treat the horizontal observation well as an observation point. It also has
been suggested that if the distance between the two wells were sufficiently
large, then the active horizontal well could be replaced by a vertical well. In
this case, the observation-well responses may be approximated by the
exponential integral solution, and the analysis is reduced to the conventional
interference-test analysis between vertical wells.
For the application of the approximate analytical techniques, two questions
need to be answered. The first question is whether the distance between the two
horizontal wells is large enough for the geometry of the wells to be ignored.
Malekzadeh investigated this question by considering the interference between a
horizontal active well and a vertical observation well in an isotropic
reservoir. Because anisotropy has a major effect on the pressure-transient
responses of horizontal wells, the results of Malekzadeh have limited
applicability. In addition, the influence of the geometry of the observation
well cannot be deduced from the model used by Malekzadeh.
The second question is, where should the equivalent observation point (EOP)
be placed in the reservoir if the horizontal well were to be replaced by a
vertical well? This question has yet to be addressed in the literature. The EOP
is defined as the location at which the pressure recorded at the heel of the
horizontal observation well would exist in the absence of the observation well.
Because of the lack of theoretical guidance, the physical location of the heel
or the center of the observation well is usually chosen as the observation
point.1 But such an assumption ignores the fact that fluids enter and leave the
horizontal observation well although there is no surface production. Therefore,
some disturbance of equipotential lines around the observation well should be
expected. Thus, if the horizontal well were to be removed from the system, we
may expect the pressure recorded at the heel of the horizontal well to exist at
a different location. The location of the EOP would be a function of the
variables that determine pressure at the observation well.
This work uses a semianalytical model to answer the above questions. The
model has been discussed in detail in Refs. 4 and 5 and is capable of
considering interference between two horizontal wells in a homogeneous but
anisotropic reservoir. Based on the results of the semianalytical model, two
correlations have been developed to significantly simplify the analysis of
horizontal-well interference tests without sacrificing accuracy.
The first correlation provides the location of the EOP, which has not been
available in the literature. The second correlation provides information on the
distance under which both horizontal wells may be treated as vertical wells and
the exponential integral solution may be used to analyze the interference test.
Compared with the correlation presented by Malekzadeh, the correlation
presented here is more comprehensive because it accounts for the effects of
anisotropy, location of the EOP, and relative position of the wells. To assess
the adequacy of the correlations, error bounds have been calculated and are
documented in this paper.
The correlations enable us to analyze horizontal-well interference tests by
the single-horizontal-well solutions or by the exponential integral solution.
The convenience of the single-horizontal-well models for the regression
techniques used in well-test-analysis software becomes clear if the
computational complexity of the rigorous horizontal-well interference-test
models4,5 is noted (the increase in the speed of computations is usually more
than six-fold).
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
10 May 2004
- Revised manuscript received:
13 May 2005
- Manuscript approved:
24 May 2005
- Version of record:
15 August 2005
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