Concept of geometric factor and its practical application to estimate horizontal and vertical permeabilities

In a probe-type formation test, because of the geometry of the wellbore and the sealing effect of mudcake, the flow pattern is not perfectly spherical. To account for the deviation from spherical flow, several geometric correction factors were proposed for different analysis techniques (Steward and Wittmann 1979; Wilkinson and Hammond 1990; Dussan and Sharma 1992; Goode and Thambynayagam 1992; Proett and Chin 1996). A geometric factor is used in formation rate analysis (FRA) (Kasap et al. 1999), a technique used in analyzing a probe test to estimate formation pressure and permeability. Like other geometric correction factors, the geometric factor is a strong function of permeability anisotropy that is generally unknown before a test. When analyzing the test, we would logically assume an isotropic formation and use the corresponding isotropic geometric factor. Consequently, the FRA-estimated permeability does not represent the true spherical permeability. In contrast, the spherical permeability can be estimated from buildup analysis without prior knowledge of permeability anisotropy. Therefore, there is a discrepancy between the permeability estimates from the two analysis methods. In addition, if considered separately, neither FRA nor buildup analysis can decompose the estimated permeability into its horizontal and vertical components. This paper presents the derived numerical values of several geometric factors. Using these factors, we show that the discrepancy between the permeabilities estimated from FRA and from the conventional buildup analysis is attributable to the permeability-anisotropy effect. A correct geometric-factor value must be used to estimate permeability correctly. On the basis of the permeability-anisotropy effect, we present the procedures to estimate horizontal and vertical permeabilities by combining FRA permeability and buildup permeability or by history matching. These procedures are verified with a simulated probe test. Analysis of three actual tests is presented.