Concept of Geometric Factor and Its Practical Application to Estimate Horizontal and Vertical Permeabilities

Abstract

Summary 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. Introduction A formation test is initiated when a probe from a formation tester is set and sealed against the formation. A measured volume of fluid is withdrawn from the formation through the probe. The test continues with a pressure buildup when fluid withdrawal is halted. Pressure in the tool is continuously monitored throughout the test. The flow pattern during the formation test using a probe is believed to be close to spherical flow. Because of the geometry of the wellbore and the sealing effect of mudcake, however, such spherical flow is imperfect. To account for deviations from spherical flow, several correction factors have been proposed. These correction factors include flow shape factor (Steward and Wittmann 1979; Wilkinson and Hammond 1990; Dussan and Sharma 1992; Goode and Thambynayagam 1992), geometric shape factor (Proett and Chin 1996), and geometric factor (Kasap et al. 1999). Although they have different forms or names, their physical meaning is the same. We use a general term, geometric factor, to represent these correction factors in this paper. The physical meaning of these factors is that because the actual relationship between pressure and flow rate in a probe-type test cannot be described by a spherical-flow equation, these factors are added in the spherical-flow equation to correct for the actual flow relationship. These correction factors are a function of permeability anisotropy, among other parameters. Similarly, the concept of geometric factor is applied to estimate permeability with mini-permeameters (Goggin et al. 1988; Georgi and Jones 1992; Jones 1994, 1997).