Instantaneous Diffusion-seepage Model And Permeability Measurement Of Coal Seam By Gas Pressure Recovery Method

Permeability of coal seam is an important parameter for evaluating coal mine gas extraction conditions.Based on the theories of gas geology,diffusion theory and seepage mechanics and drawn lessons from the results of well testing in the field of oil and gas reservoir development to determine reservoir permeability,the instantaneous diffusion-seepage model and the method of measuring coal seam permeability by gas pressure recovery were developed by means of theoretical analysis,numerical calculation,laboratory test and field test.Firstly,the instantaneous diffusion model of coal gas was established and its analytical solution was obtained.On this basis,the instantaneous diffusion coefficient was introduced into the process of coal matrix gas diffusion,then an unsteady instantaneous diffusion-seepage model of coal seam gas was established.The equations were solved by COMSOL numerical software,and the permeability calculation charts were drawn accordingly.At the same time,a laboratory coal gas pressure recovery curves measurement system was built,and the gas pressure recovery curves under different conditions were measured.Moreover,permeability of the tested coals was calculated by the chart method according to the pressure recovery curves.Reliability for this method was verified via comparing with the permeability measured using the steady-state method.Finally,the borehole gas pressure recovery curves were measured on the spot,and permeability of coal seam was calculated by the chart method basing the cures.Practicability of this method is verified via comparing the permeability measured by predecessors.Through this study,we have achieved the following results:(1)Based on the similarity theory and the second law of diffusion,a calculation method of diffusion coefficient was established.And the diffusion coefficients calculated via the method mentioned above decrease with time elapse(instantaneous diffusion coefficients),which can be expressed as a power function.(2)The coal matrix is simplified as a sphere with porous pores,and it is considered that the gas in the coal matrix moves outward in the form of instantaneous diffusion.on the basis of the power function-instantaneous diffusion coefficients and the second Fick diffusion law,an instantaneous diffusion model was constructed and the solution conditions were given.Meanwhile,the infinite series solution of the power function instantaneous diffusion equation was obtained by using the separation variable method.(3)For coal permeability measurement in the laboratory and field,unsteady transient diffusion-linear seepage model and unsteady transient diffusion-radial seepage model were constructed,and the models were solved by COMSOL numerical software.Using the result of calculation,a permeability calculation chart of coal seam pressure recovery method is established.(4)A measuring system of gas pressure recovery curve of coal sample was set up,and the gas pressure recovery curves of coal sample under different gas pressure and different stress conditions were measured.At the same time,a simple and accurate permeability calculation method was established via permeability calculating chart of coal seam pressure recovery method,and the permeability values of coal sample under different conditions was calculated.Comparing with the coal permeability measured by the "steady-state method",it is proved that the pressure recovery method is reliable.(5)A small device is developed to measure borehole gas pressure recovery curves in situ.The borehole gas pressure recovery curves were measured in situ and the coal seam permeability values were calculated.It is proved that the method is feasible to compare with the coal seam permeability measured by predecessors.