Similar constructive method for solving the model of coalbed methane flow through coalbed methane reservoirs

Abstract

Coalbed methane (CBM) is produced through desorption, diffusion, and seepage processes. However, pressure during CBM production, especially the seepage process, is a very complicated problem. Methods for solving the pressure models for CBM reservoirs are multidisciplinary and rather sophisticated. In this paper, an elementary and simple method for solving the CBM seepage model is proposed. First, a classical seepage model was built to study CBM seepage at a variable flow rate. After the transformation of pressure into pseudo-pressure and dimensionless treatments, a definite problem for the CBM seepage model was obtained. By Laplace transformation, the definite problem can be solved as a boundary value problem in Laplace space. Then, this boundary value problem was solved by the proposed method which is elementary and simple and its solutions have a structure similar to that of a continued fraction. This explains why this method is called the similar constructive method. With this method, solutions for the model of the pressure response of a CBM reservoir can be obtained. A corresponding program for the method was written, which can help engineers working on CBM reservoirs solve similar problems even without pre-training. In addition to the typical analysis curves for well testing such as the conventional log–log graph of the pressure and pressure differential and semi-log graph, another type of analysis curve, i.e., a log–log graph of the first-order pressure derivative was plotted. On such basis, the diagnosis of the pressure response of a CBM well is more accurate. Our results might be of great significance to the theoretical study of pressure responses of CBM reservoirs. The results of this research could provide great simplicity for software developers to create well testing analysis software and well testing interpreters to interpret CBM well test data.