Transient Finite Element Code: A Versatile Tool for Well Performance Analyses

Abstract

Abstract This paper describes a system of general transient finite element flow programs for analyzing complex flow problems. It emphasizes a structured system consisting of a set of mesh generators, a main program, and a post processor, allowing applications as a routine practical tool rather than a research tool for well performance analysis, completion design tool, and pressure transient analysis. Introduction During 1970, numerous papers appeared for applications of the finite element method to three-phase reservoir models. These research efforts emphasized improved accuracy with high order elements. However, the finite element model could not replace the finite difference model since reservoir heterogeneity required many low order elements rather than fewer high order elements. In addition, if parallel-piped elements are used, most low order finite element formulations give basically the same numerical form as the finite difference, although the mathematical process to convert a set of partial differential equations to numerical equations is different. The research to apply the finite element methods to reservoir models has been diminished during the 1980's and 1990's since the advantage of the high accuracy of the finite element method is not the essential requirement for reservoir models. However, there is another advantage of the finite element method: it uses many high order elements which can be adapted to any irregular boundaries. The computation time is, however, still one order of magnitude higher than the finite difference method if a three-phase reservoir model is generally made to include a variety of high order elements. Although it is still too early to be used for three-phase reservoir models, the computation time is within economically feasible range if it is used for one-phase problems. Since most well performances, pressure transient analyses, and completion design programs use one-phase flow, the finite element method is best suited to these applications. This paper emphasizes the wide applications of the finite element models to these areas as a routine analysis tool and how the system of computer programs should be structured to accomplish these applications. Well performance analyses have become increasingly complex due to the various stimulation methods for vertical and horizontal wells. Various numerical methods (infinite series, numerical Laplace inversion) have been used for analyzing well performance with complex boundary conditions. The computation time using analytical solutions becomes significant due to the infinite series solution for double and triple integrations. The comparison of these methods with the general finite element code showed that the finite element code gives competitive accuracy and computation time. In addition, its flexibility to include boundary irregularity and formation heterogeneity provides a powerful tool to analyze complex well performance problems. This paper emphasizes two objectives:shed light on the finite element code for routine field analyses and how it should be structured to achieve the objective, anda versatile software system (with 11 2-D and 3-D elements and mesh generators) which allows us to study complex well performance and pressure transient data without spending months of manpower in developing other simplified numerical solutions. P. 407^