Application of Convolution Theory for Solving Non-Linear Flow Problems: Gas Flow Systems

Abstract In this paper we present the development of a rigorous approach for the solution of non-linear partial differential equations by use of the Laplace transformation in particular, the convolution theorem for Laplace transforms. While the rigor of this new approach is general, our paper is devoted to the development, verification, and application of this method for the case of real gas flow in porous media. This paper focuses on verification of real gas flow solutions using the results of numerical simulation. The major results of this work are: Development of a general analytical approach in the Laplace domain for solving non-linear partial differential equations.Verification and application of this new approach for the flow of a real gas in porous media. We observe excellent agreement between the numerical and analytical results for the case of a single well produced at a constant rate in a closed reservoir. We conclude that this approach could be adopted as a method of verification for numerical simulation, as well as for analytical modelling of the gas flow case in particular, for modelling future performance directly and accurately, without numerical simulation or some weak approximation (p or p2 approximations, etc.). In addition to the specific problem considered in this work, the flow of a real gas in porous media, we believe that it may be possible to extend this work for the development of analytical solutions for multiphase flow.

Application of Convolution Theory for Solving Non-Linear Flow Problems: Gas Flow Systems Conference Paper