Vertical Permeability From Limited Entry Flow Tests in Thick Formations

Abstract

Abstract This paper examines the applicability of the spherical flow equations to a well producing from a limited section of a thick anisotropic formation. Though the method of analysis was suggested by Moran and Finklea several years ago, the applicability of these equations is yet to be demonstrated. Methods of determining the horizontal and vertical permeability of the formation from drawdown and buildup data are described. The effect of producing time on the determination of these parameters is discussed. Time estimates are provided parameters is discussed. Time estimates are provided to obtain the proper straight line. Introduction Transient pressure analysis of early time data of limited entry tests precludes the use of conventional semilog techniques. This is principally due to the nonradial flow regime developed in the vicinity of the wellbore at early times Moran and Finklea suggested that early-time pressure behavior from such tests can be adequately described by assuming the limited entry section to be a spherical source rather than a cylindrical source, as in the case of a well completely penetrating the formation of interest. More recently Culham has examined the applicability of the spherical flow equations to well tests wherein the producing interval is a small fraction of the total pay thickness. He developed guidelines for analyzing pay thickness. He developed guidelines for analyzing the pressure buildup data based on the assumption of spherical flow. Culham was principally interested in homogeneous thick formations. The primary objective of this paper, however, is to demonstrate that information may be obtained regarding reservoir heterogeneity specifically permeability anisotropy. This type of information is crucial to predict the performance of zones of interest under a variety of performance of zones of interest under a variety of conditions such as the presence of barriers, and the movement of fluid interfaces. MATHEMATICAL MODEL A cross-section of the idealized limited entry model is shown in Fig. 1. The following assumptions are made:The reservoir is horizontal with uniform thickness, h, porosity, phi, and infinite radial extent. It has anisotropic radial and vertical permeabilities, kr and kz, respectively. The well, which may or may not fully penetrate the formation, has an infinitely small radius, rw.A single-phase, slightly compressible liquid flows from the reservoir into the open section at a constant rate, q.The single, horizontal, open section has a radius rw, thickness hf, and is assumed to be located near the center of the producing interval. The midpoint of the open interval is located at a distance zf from the bottom of the pay. Fluid is withdrawn uniformly along the section open to flow.There is no flow across the upper and lower boundaries of the reservoir; and the pressure remains unchanged and equal to the initial pressure as radial distance approaches infinity. One point regarding the model discussed above requires clarification. SPEJ P. 65