Unsteady-state diffusion modeling of gas in coal matrix for horizontal well production

In this work, an unsteady-state diffusion model was developed to describe gas transport in coal structures for horizontal well production. The model assumes unsteady-state diffusion of gas through the matrix according to Fick’s law, Darcy flow through the cleat network (natural fractures), and that gas adsorption can be described by the Langmuir equation. Then the model using Laplace integral transformation was solved. Using the new model, dimensionless-type curves for pressure-transient and rate-decline analyses were used to analyze transient transport characteristics. The differences for unsteady-state diffusion between horizontal and vertical well models and the differences for horizontal well production between unsteady-state diffusion and pseudosteady-state diffusion were specifically analyzed. Several scenarios confronting real coal beds were studied and discussed fully through simulating well production under different conditions. The research results showed that the unsteady-state diffusion model would be another choice with which to analyze well tests.