The deformation of coal and the two-phase now composed of coal-bed methane and water interacts during coal-bed methane extraction. Research about this interaction has long been the essential task in energy technology. In this paper, coal is assumed to have an elasto-plastic behavior. Deformation equations of coal masses are derived accordingly. The flow continuity equations are based on Darcy's law, and the coupled equation between fluid and solid adopted was derived by Louis's pumping test results. Flow equations are solved by the finite difference method, and the deformation model by finite element method. A case study is presented. The difference between coupled model and rigid model is compared. Results of this paper are of help in the numerical simulation of coal-bed methane development.
Research of coal-bed methane flowing law is the basic task in developing this kind of energy. During extraction, deformation of coal and fluid flow interact. Both the physical and mechanical characteristics of coal are affected by coal-bed methane. On the other hand, deformation of coal brings changes of its permeability and pore pressure. Up to now, much work has been carried out in the view of fluid-solid coupling theory. A large quantity of coal-bed methane has been extracted from reservoirs that are saturated by water. The coal-bed methane and water flow coexist in such reservoirs, which is a common case. It's necessary to study this two-phase flow and its interaction with coal deformation. The author takes the effects of capillary pressure, saturation and gravity on flow into consideration, and derives the fluid- solid coupling model in elasto-plastic methane reservoirs. The fluid now model is solved by finite difference method, and the deformation model by finite element method. Through numerical simulation, the author compares the differences between the coupled model and the uncoupled rigid one.
2.1 Mathematical model of coal deformation Assuming deformation of coal is small elasto-plastic, based on elasto-plastic theory, the author derives the mathematical model of deformation. They include 3 equations.
The author has developed the mathematical model for fluid solid coupling flow for elasto-plastic coal-bed methane reservoirs. Because this model contains some coupled terms, it has to be solved with numerical methods. To solve this coupling an iterative technique is needed. First, the flow field is solved with finite difference method; secondly, use the pore pressure to calculate coal deformation in order to derive stress distribution; and lastly, modify the coal permeability and its mechanical parameters by using the calculated stress with Eq.(9), Eq.(10) and Eq. (II), respectively. Go to the following time step in such a way till the end of the simulation.
With the present mathematical model, the author has compiled a software to simulate the two-phase flow interacting with geo stress. A coal-bed methane well is analyzed with the software. Fig.1 and Fig.2 are the selected relative permeability.