Summary
During a single-probe test in a vertical well, the probe of a formation
tester is set horizontally against a sidewall of the borehole. In a horizontal
well, the probe can be set either horizontally against a sidewall or vertically
against the top or bottom wall of the borehole. When the probe is set
horizontally against a sidewall, the solution for a horizontal well is the same
as that for a vertical well, if the wellbore curvature is not considered (in
other words, the wellbore radius is considered to be much larger than the probe
radius). However, when the probe is set vertically against the top or bottom
wall, the solution for a horizontal well is not available in the literature.
This paper presents an analytical solution to the described problem.
The solution shows that the relationship between the pressure drop and flow
rate for a single-probe test in a horizontal well depends on the geometric
average of horizontal and vertical permeabilities when the probe is set
vertically against the borehole. One of the important applications of the
solution is to estimate horizontal and vertical permeabilities from two probe
tests. If two tests are conducted at the same measured depth, with the probe
set vertically in one test and horizontally in the other, two permeabilities
are obtained. Then the horizontal and vertical permeabilities at the measured
depth can be estimated by combining these two permeabilities.
The analytical solution is validated by numerical simulation, and the
solution is shown to be the same as a published analytical solution for a
vertical well in an isotropic formation. Examples to estimate horizontal and
vertical permeabilities from synthetic tests are presented.
Introduction
A single-probe test is initiated when the probe of a formation-testing tool
is set and sealed against a borehole wall and a measured volume of fluid is
withdrawn from the formation through the probe. The test continues with a
pressure buildup when fluid withdrawing is halted. The tool monitors pressure
continuously throughout the test. A schematic of probe settings in a vertical
well and in a horizontal well is shown in Fig. 1. During a single-probe test in
a vertical well, the probe is always set horizontally against a sidewall of the
borehole (Position A). The relationship (solution) between the pressure at the
probe and the rate at which fluid withdraws from an anisotropic formation has
been published (Dussan-V. and Sharma 1992). In a horizontal well, the probe can
be set either horizontally against a sidewall (Position B) or vertically
against the top (Position C) or bottom wall of the borehole. When the probe is
set horizontally against a sidewall, the solution for a horizontal well is the
same as that for a vertical well. However, when the probe is set vertically
against the top or bottom wall, the solution for a horizontal well is not
available in the literature. As more and more pretests are conducted in
horizontal wells using measurement-while-drilling tools, the solution to the
described problem becomes the timely need.
This paper presents the mathematical formulation and derivation of the
solution to the problem for a probe test in a horizontal well, when the probe
is set vertically against the top or bottom wall. The solution is validated by
numerical simulation. The paper also proposes a method to determine horizontal
and vertical permeabilities with the aid of this solution.
Mathematical Formulation
The paper’s objective is to determine the relationship between the pressure
at the probe and the rate at which fluid withdraws from an anisotropic
formation. In a vertical well when a probe is set and sealed horizontally
against the sidewall of wellbore, the relationship between pressure and rate is
first derived at steady-state flow, and we have found that the derived
relationship can be applied to unsteady-state flow (Sheng et al. 2004a). Using
a similar approach, we first derive the relationship in steady-state flow in a
horizontal well, then we apply the relationship to unsteady-state probe tests
where the probe is set vertically against the top or bottom wall of a
horizontal wellbore.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
19 June 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
18 July 2007
- Manuscript approved:
20 January 2008
- Version of record:
20 June 2008
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