This paper presents a simple, but accurate, computer method for predicting the performance of multiple gas wells in complex reservoir scenarios. Real life gas reservoir characterization and forecasting can be accomplished with the substantial reduction of effort when compared to numerical simulation and a substantial increase in accuracy when compared to traditional decline methods. Conventional analytical methods in many cases are highly unsuitable for new field development, in-fill drilling, or long-term production planning. Numerical simulation methods often require impractical pre-processing or computational time. With the method presented in this paper, production profiles can be generated for arbitrary shaped gas reservoirs with multiple wells. The model presented overcomes many limitations of traditional methods, and extends analytical modeling into multiple well scenarios with interference effects, arbitrary reservoir shapes, and perhaps even varying rock properties.

Introduction: General History & Motiviation

Modeling of petroleum reservoirs and its application to pressure and production analysis have been studied for years. Publications by Hurst (1981), Lee (1982), Streltsova (1988), Stanislav and Kabir (1990), Raghavan (1993), Mattox and Dalton (1990), and Settari and Aziz (1979) cover the important concepts of both numerical and analytical models. Others such as Muskat (1937) and Van Everdingen and Hurst (1949) outline more specific solutions for constant rate drawdown in infinite reservoirs, while Matthews, Brons, and Hazerbroek (1954) and Dietz (1965) investigated solutions for a single well in a bounded reservoir. Agarwal, Al-Hussainy and Ramey (1970) included wellbore storage and skin effects into the wellbore boundary conditions. Odeh and Jones (1965) described the pressure changes due to variable rate production. The list of contributors to the science and technology of reservoir modeling is extensive - and can generally be classified into either analytical or numerical.

With respect to analytical methods, there are only a few conventional methods for solving the diffusivity equation. These include separation of variables, eigenfunction expansion, similarity transform, Laplace Transform, Fourier Transform, and Green's functions. However, due to certain restrictions in solving such problems, analytic methods are generally only amendable to simple geometric shapes. Generally, this problem can be alleviated by superposition (assuming linear differential operators).

The shortcomings of analytical methods are also alleviated by numerical schemes such as the Finite Element Method (FEM) and Finite Difference Method (FDM) which have a greater flexibility in solving complex problems - however, this is generally at the expense of time and computational power. For example, with FEM, users must spend significant amounts of time generating appropriate grid orientation, and ensuring that accuracy is not compromised due to numerical dispersion etc. A literature review suggested that a good comparison of FDM and FEM is given by Russell and Wheeler.

Therefore, a technique which has the accuracy of the analytical methods and preserves the versatility of the numerical techniques to solve complex reservoir problems is highly desirable. As a result, the Boundary Element Method (BEM) has become popular, and has been heavily studied by Kikani,[1] Archer,[2] and Pecher[3] to name a few. Others such as Larsen attempted to improve the use of superposition to handle more complicated reservoir geometry. In all cases, significant computation effort was required for success - either in calculating image well locations or evaluating complex (and sometimes undefined) integrals. Lin,[4] Caudle,[5] Jankovic,[6] and Haitjema[7] made use of approximate forms of superposition to handle more sophisticated aspects of multi-well interaction - however, most studies were limited to steady state applications for pressure contour and streamline mapping.

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