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Using an Integral-Transform Technique for Developing Analytical Solutions to Transient-Flow Problems

RAHMAN, N., Bangladesh U. of Engr. & Tech

The analytical solutions in the petroleum engineering literature have been treated as benchmarks for many complicated situations in reservoirs. However, in a pressure-transient analysis, the analytical solutions are used to identify different flow regimes and subsequently to calculate the rock and fluid properties. But the efforts to develop the analytical solutions to some transient-flow problems have been seriously deterred due to the lack of appropriate mathematical tools. No systematic attempts to take advantage of using an integral-transform technique (ITT) have been reported in the literature either.This study demonstrates that the use of the ITT results in the development of a huge number of useful solutions to transient-flow problems in different coordinate systems. New analytical solutions will be presented comprehensively in a compact, convenient form. For instance, the closed-form solutions in terms of the time and space variables can be written down for all 729 possible combinations of the conditions at the boundaries with constant-potential, no-flow and mixed ones in a Cartesian coordinate system. The generality of the solutions is greatly enhanced by considering the production rates through the wells as time-dependent. This situation is treated in a general but computationally efficient way. Thus, the use of the solutions is permissible even if there has been a production history in a system.A simple algorithm is proposed showing the computation of the dimensionless potential and its derivatives at a given dimensionless time for any possible boundary conditions. The new solutions are useful for analyzing drawdown-, buildup- and interference-test data.

AAPG Search and Discovery Article #90911©2000 AAPG Pacific Section and Western Region Society of Petroleum Engineers, Long Beach, California