Analysis of Pressure Buildup in an Infinite Two-Layered Oil Reservoir Without Crossflow

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract The purpose of this study is to obtain a set of expressions and procedures that can be used to determine the reservoir parameters from pressure buildup curves for an infinite pressure buildup curves for an infinite two-layered oil reservoir. Equations were derived that define the pressure behavior at the wellbore. Pressure drop equations were derived for the upper and lower zones using Hartsock's method. From these pressure drop equations, other equations were derived that describe theoretical buildup for this system when the well is shut in. From these equations it is possible to determine the initial pressure of one zone the other initial pressure or the difference between the two initial pressures of the respective zones are known. The effective permeabilities can also be computed under the permeabilities can also be computed under the above conditions; that is, if the initial pressure in either zone is known or if the pressure in either zone is known or if the difference in pressure between the two zones is known. Hartsock used only the pressure drop of the upper zone for these derivations and determinations, but this study shows that from the pressure drop and shut-in pressure equations, equations can be derived to determine the skin factors for the upper and lower zones. This study also shows under what conditions an infinite two-layered oil reservoir is similar to a single-layered reservoir. Hartsock and Lefkovits et al. methods have been used to show the effects of permeability and thickness ratios on pressure buildup permeability and thickness ratios on pressure buildup curves. Also studied were the effects of skin and wellbore storage using the equations derived for an infinite two-layered reservoir with boundary conditions at the wellbore outlined by Lefkovits et al. Introduction The pressure buildup analysis considered in this study is that of an infinite two-layered reservoir without crossflow. So far, equations have not been developed to obtain the pressures, permeabilities and skin factors for the permeabilities and skin factors for the individual zones of two- or more-layered reservoirs. Lefkovits et al. studied the behavior of bounded reservoirs composed of stratified layers. Their work showed that the time necessary to reach pseudo-steady state is much longer for a two-layer reservoir than for a single-layer reservoir.