Analytical Steady-State Solution of Single-Probe Tests in a Horizontal Well and Its Application to Estimate Horizontal and Vertical Permeabilities

Abstract

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.