An analytical model for desorption area in coal-bed methane production wells

Production forecasting, well spacing, and well pattern optimization are key tasks in coal-bed methane field development plan. Desorption area around a production well is an important factor in well performance and reserve estimation. Analytical models are found to be simple and practical tools for drainage area calculation and well deliverability in conventional reservoirs. However, up to now, we have found no such analytical model for coal-bed methane wells with two-phase flow in which the gas desorption in coal is the controlling mechanism while the water is flowing in the cleat system. In this paper, we present a mathematical model to predict how the size of desorption area is changing with pressure propagation during gas and water production. The pressure profiles at different production stages are determined using diffusivity equation which is solved using the known method of "continuous succession of steady states". For the case of two-phase flow of gas-water system, the pressure squared concept is used for linearization in middle and late times, while the pressure concept is used in early times when water flow is dominated. We have combined pressure from the solution of diffusivity equation with the material balance equation in order to develop our predictive model which is applicable for vertical wells for both cases of with or without hydraulic fractures. This model is verified by numerical simulation and is in excellent agreement with the numerical solutions. Furthermore, the developed model is applied in one coal-bed methane well group in Hancheng field in China. It is found that desorption area is expanded outward in elliptical shape and the area can be calculated by the gas production data. The results show that two sample wells in the group have interfered with each other after producing for 525 days. (c) 2013 Elsevier Ltd. All rights reserved.