Coal particle gas adsorption mathematical model and numerical solution under variable pressures

In order to verify the universality of Darcy law in coal particle gas flow,the coal particle gas adsorption ex- periment in enclosed space under variable pressures was designed on the basis of the constant pressure adsorption and desorption and variable pressure desorption experiments of different coal particles shapes. And the gas accumulative adsorption amount with time variation of 42. 976,11. 600 ~ 13. 800,3. 350 ~ 4. 000 and 1. 180 ~ 1. 400 mm coal parti- cles under 0. 5,1,2 and 4 MPa initial pressures were obtained. Based on Darcy and Fick law,the gas adsorption math- ematical models were proposed separately. The use of finite difference method,combined with the computer program coded in Visual Basic,enabled to solve the equations. And the gas accumulative adsorption amount of two models at different times and different initial gas pressures were obtained. By comparing and analyzing ln1-(Qt / Q∞ )2 vs. t di- agrams from experiment and numerical simulation,it is found that the gas adsorption process of coal particles in the en- closed space also follows Darcy’s law. This conclusion is consistent with a series of previous researches,namely wheth- er the adsorption or desorption process,and the coal particle external pressure and the coal particle shape change or not,it is concluded that Darcy law is the basic rule of coal particle gas flow.