A New Method of Productivity Model for Coal-bed Methane under Steady-state Based on Equivalent Continuous Media Theory

Multi-stage fractured horizontal well technology is applied to develop Coal-bed methane reservoir, besides, due to the existence of adsorption, desorption and diffusion in coal pore media, the seepage mechanisms of coal-bed methane are different from conventional gas reservoirs. It can induce large errors to analyze coal-bed methane with conventional binomial production equation. Therefore, in terms of natural fracturing coal-bed methane reservoir, this paper firstly establishes the equivalent continuous medium model with consideration of adsorption, diffusion and the anisotropy of fracture permeability, matrix permeability and gas diffusion parameter using parallel-plate theory, equivalent seepage resistance principle and equivalent continuous medium principle. As a result, the dual porosity fractured coal-bed methane reservoir is equivalent to a homogeneous gas reservoirs characterized with a certain equivalent permeability. By giving special values of the relevant parameters, the new model proposed in this paper can be simplified to a variety of conventional gas reservoirs. Some inflow performance relationship (IPR) curves of multi-stage fractured horizontal well are plotted. When considering the impact of desorption and diffusion of coal-bed methane, these curves are different from conventional gas reservoirs ,the smaller the Langmuir pressure , the deeper the curve concaves and the bigger the absolute open-flow rate, moreover, the smaller the Langmuir volume , the deeper the curve concaves and the smaller the absolute open-flow rate. Through the actual comparative analysis, the error of this model is less than 15% and this model has certain practical value.