Unsteady-State Pressure Distribution Created by a Well with an Inclined Fracture

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract An analytical solution was derived for the unsteady flow of a slightly compressible fluid toward a fractured well with an inclined fracture in an infinite slab reservoir. This solution was evaluated to obtain the dimensionless pressure drop at the fracture. Fully and partially penetrating fractures were considered. partially penetrating fractures were considered. Tables and graphs of dimensionless fracture pressure vs dimensionless time are presented. pressure vs dimensionless time are presented Introduction Hydraulic fracturing has been an effective technique to stimulate damaged wells or wells producing from a low-permeability formation. producing from a low-permeability formation. It has been established that the orientation of a hydraulic fracture is perpendicular to the direction of the least principal stress in the formation. The direction of the least principal stress is not always parallel or perpendicular to the plane of the formation. For this reason it is possible that some hydraulically fractured wells have inclined fractures. Many authors have studied flow behavior in a reservoir produced through vertically and horizontally fractured wells. At early times in the unsteady-state behavior of a fractured well there exists a linear flow perpendicular to the plane of the fracture. This can be recognized by a one-half slope line on a log-log graph of fracture pressure drop vs time. Following this flow pressure drop vs time. Following this flow period, there is a transition flow period that period, there is a transition flow period that depends on the geometry of the fracture-reservoir system. At long times, there is a pseudo-radial flow period, if the reservoir is pseudo-radial flow period, if the reservoir is considered of finite thickness and infinite radial extent, and the fracture is of finite extent. No reference to transient pressure behavior for a reservoir producing through a well with an inclined fracture was found in the literature. The purpose of this work is to present a solution of the unsteady-state pressure distribution created by a well with an inclined fracture produced at a constant rate.