Fuzzy Mathematical Model And Solution Of Cbm Transport Based On Structured Element

Consider the pores, cracks dual media, analysis of the development of gas, water phase and solid skeleton. Establish the mathematical model of methane transport, assumption the steady flow, establishment the model of CBM steady-state transport by simplification, and obtained the steady-state analytical solution.Consider the pores, cracks dual media, analysis of the development of gas, water phase and solid skeleton. Establish the mathematical model of methane transport, assumption the steady flow, establishment the model of CBM steady-state transport by simplification, and obtained the steady-state analytical solution.Numerical treatment the steady-state analytical solution and got the pressure distribution, the chart shows that under the steady state conditions, as the radius increases, gas pressure changes into the arithmetic progression, this rule similar to the existing research results at home and abroad. Also shows the reliability of the analytical solution. The important parameters of coal bed methane production which including flow, flow speed, etc. are directly related with the pressure. Explain the importance of the pressure obtained.As the unpredictable qualitative of actual penetration, take the permeability as a fuzzy number, establishing coal bed methane, water, transport steady-state two-phase mathematical model of fuzzy. Base on the fuzzy structure element method. The solution of fuzzy constraint differential equations can be expressed. Obtain the fuzzy analytical solution, and take calculated distribution of membership.In study of non-steady seepage of water phase, two cases considered, one is the infinite ground, the second is a well closed circular. Establish the coal bed methane formation infinite and closed circle formation mathematical model of steady flow. Get the analytical solution of non-steady state transport of water-phase pressure and produce in coal based on Boltzmann transformation and power integrator. Furthermore, establish the coal bed methane formation infinite and closed circle formation fuzzy mathematical model of steady flow. And get the analytical solutions and the fuzzy analytic solution. Take into the actual parameter, can calculated the permeability range consistent with the scope of membership according to each membership. Otherwise, give a penetration to know that it's membership, and get the membership of pressure, that the implementation of value. Based on Laplace transform and inversion, the analytical solution and asymptotic solution were found by studying on the unsteady state percolation mathematical model of double-medium CBM at infinity stratum. The analytical solutions show the quasi-pressure increases along the time pass when radius is definite. The pressure gradient become large what mean the pressure fall down fast nearby the gas well. Gas flowing rapidly and pressure variation slowly in the distance, so the effect on the coal seams by CBM is less. Quasi-pressure appears three sections when time is certain. First, because of the sudden pressure relief, airflow makes haste, quasi-pressure decrease and pressure increase. Then, there will be a transition moment, pore gas diffuse to crack, pressure become less. Finally, pressure becomes constant. At the same time, in-situ rock stress change slowly in the distance. There is straight effect on the pressure byωfactor. Pressure becomes large along the smallω. It decides the quasi-pressure and achieves bigger differential pressure.The asymptotic solutions show that at the beginning of vertical shaft construction, the pseudo pressure to be increased as the time increased. The press gradient decreased significantly. At a fixed time, the pseudo pressure decreased by logarithmic curve with the radius increases. As the time longer, gas pressure is stable at a fixed position, but the pressure has little effect formation by far away. Basically does not change.Established the coal bed methane formation infinite fuzzy mathematical model of steady flow, obtained the solution of short-time asymptotic solutions and the long-time asymptotic solutions. Through fuzzy analysis evaluated we can got the range of permeability under different membership degrees in different times and different radius. And get the range of pseudo pressure, further push the range of pressure. The data provide a favorable reference to the actual project.Study on the unsteady flow process of coal bed gas in double-porosity media. Found mathematical model, got the analytical solution and the asymptotic solution.This study provided a reliable theoretical study for the transport of coal bed methane. The obtained of analytical solutions has great practical value for the commercial development of CBM.