Dimensionless Pressures and their Derivatives for a Vertical Well Completed within a Pair of Inclined Constant-Pressure Boundaries

Abstract

Abstract Dimensionless pressure and their derivatives assist tremendously in understanding the reservoir boundary types, efficient well design, completion and production scheduling for optimum recovery from the reservoir. For a reservoir boundary as inimical as constant-pressure to oil or gas production, the need to adequately anticipate its presence and approach pattern towards the wellbore cannot be overemphasized. In this paper, dimensionless pressures and their derivatives are provided for a vertical well completed within a pair of inclined constant-pressure boundary (CPB) support. The angle of inclination of the constant-pressure boundaries is varied between 0 and 360 degrees. Hence, a generalized dimensionless pressure and derivatives expressions are derived by superposition of dimensionless pressures of all image wells on one object well. Therefore, distances of every individual well from the object well and the sign of every image, taken through a counterclockwise direction from the object well, are major inputs into the dimensionless pressures and dimensionless pressure derivatives derived. Only the object wellbore skin but not its storage is considered. The solutions are plotted as type curves. Results show dependence of both dimensionless pressure and dimensionless derivatives on angle of inclination of the constant-pressure boundaries. The dimensionless pressures exhibit a unique gradient at late dimensionless times. There is a collapse of the derivatives to zero at late dimensionless times. The rapidity of the collapse depends on object well distance from the boundaries and the angle of inclination of the boundaries. Wells completed farther away from the CPBs exhibit unperturbed production for longer periods than nearer wells.