New Single-Well Test for Determining Vertical Permeability

Abstract

A short-term vertical interference test between isolated sets of perforations in the same well can be used to determine the vertical perforations in the same well can be used to determine the vertical and horizontal permeabilities of each tested interval as well as to determine the effectiveness of tight streaks as barriers to vertical flow. Introduction Vertical flow is an important mechanism in many petroleum reservoirs. Yet no adequate method has petroleum reservoirs. Yet no adequate method has heretofore been proposed for determining the in-situ vertical permeability in a reasonable length of time. Core measurements of vertical permeability do not necessarily represent effective in-situ values. Cores may be representative of only localized pockets of high or low permeability, and total reliance on cores night cause one to overlook the presence of vertical fractures altogether. Conventional single-well tests, interference tests, and pulse tests commonly are used to determine horizontal transmissibility, k(h)h/mu, but generally are not designed to measure vertical transmissibility or other groups containing vertical permeability, k(v). permeability, k(v). A new well test described here provides a measure of in-situ vertical permeability as well as the previously measurable horizontal permeability. This previously measurable horizontal permeability. This "vertical test" determines the vertical diffusivity, k(v)/phi c mu, and horizontal transmissibility, k(h)d(1)/mu (where d(1) is the length of injection or production perforations). The test is basically a production perforations). The test is basically a short-term interference or pulse test normally lasting less than a day. Conventional down-hole equipment is used between two isolated sets of perforations in the same well, as shown in Fig. 1. A "layer-cake" description of a reservoir can be obtained by running two or more vertical tests in the same well, each over different vertical intervals. Each test can be analyzed for the effective vertical and horizontal properties of the interval tested. In addition, a vertical well test can determine the effectiveness of a shale barrier or tight zone by testing across it. Field use to date of vertical testing has confirmed its utility in reservoir description. Mathematical Basis Interpretation of vertical tests for k(v) and k(h) is based on comparison of measured pressure response with computer-generated response. Pressure behavior during a vertical test in a homogeneous, anisotropic, infinite-acting reservoir (infinite in radial extent and bounded in both directions vertically) is given by the diffusion equation for slightly compressible fluids with negligible gravity effects.,.........(1) with the boundary and initial conditions = 0, ..........(2) lim,.....(3) lim, ,....(4) ,........................(5) ,........................(6) JPT P. 743