A Semianalytical Approach for Productivity Evaluation of Complex Wells in Multilayered Reservoirs

Abstract

Summary We present a new approach to solve the problem of complex wells located in layered reservoirs with crossflow. First, the well path is discretized into a carefully chosen series of source points. Second, pressure solution for each source point is obtained in the Laplace domain anywhere in a rectangular reservoir, where crossflow is permitted between layers and with possibly mixed boundary conditions (no-flow or constant pressure). We used the Fourier transforms in the space variables after removing the time variable by the Laplace transformation. The problem is reduced to a matrix product to solve in the transformed domain. The above method is validated through comparisons with known line source solutions and numerical simulations. It can be used to compute the pressure distribution within a well with complex geometry in a stratified bounded reservoir under the assumption of infinite well conductivity. The well can be located anywhere in the reservoir. Boundaries can be no-flow or constant pressure. Last, variable skins along the well path can be imposed. An application on a field located in the deep offshore of the Gulf of Guinea demonstrates the great value for well design optimization in the context of complex heterogeneous reservoirs where classical analytical approaches are typically inappropriate.