Fractal Characteristics Of Multi-scale Pore Structure And Gas Diffusion In Tectonic Coal

The complex pore structure,wide pore size distribution and fractal characteristics of tectonic coal make the initial gas diffusion speed high and the diffusion speed decay fast.Because of the fractal characteristics of gas diffusion,the classical diffusion model can not accurately describe such diffusion process,and there are errors in calculating the loss of gas,resulting in inaccurate measurement of gas content in tectonic coal.Therefore,how to combine the multi-scale pore structure characteristics,fractal characteristics and gas diffusion fractal characteristics of tectonic coal based on fractal theory,deeply analyze the diffusion law of tectonic coal and gas,explore the diffusion mechanism of tectonic coal and gas,and establish the fractal diffusion model of tectonic coal and gas are urgent problems to be solved.In view of the above problems,based on the intersection of gas geology,mass transfer and fractal geometry,and by means of laboratory experiments,theoretical analysis and field verification,this paper focuses on the comprehensive characterization of multi-scale pore structure and pore fractal of tectonic coal,the diffusion law and fractal diffusion mechanism of tectonic coal and gas,and the fractal diffusion model of tectonic coal and gas.On this basis,a new method for calculating the loss of gas based on the fractal diffusion model of coal and gas is put forward,and its validation and application are carried out.This paper mainly achieves the following research results:?1?The comprehensive characterization method of multi-scale pore structure is discussed,and the characteristics of multi-scale pore structure of tectonic coal are revealed.The pore characteristics of micropore,mesoporous and macropore were obtained by low temperature CO₂ adsorption,low temperature N₂ adsorption and mercury intrusion method.The pore structure parameters of tectonic coal were synthetically characterized by mercury intrusion-adsorption method.Micropore?<2nm?is the most developed pore in tectonic coal,and pore volume and pore specific surface area account for the vast majority of the total,followed by macropore?>5nm?and mesoporous?2-5nm?.The multi-scale pore distribution of tectonic coal is affected by the damage degree of coal body.The total pore volume and stage pore volume increase with the increase of the damage degree of coal body.The pore volume of macropore and mesopore increases relatively high while that of micropore increases relatively small,which leads to the increase of macropore volume ratio and mesopore volume ratio with the increase of the damage degree of coal body,and the increase of micropore volume ratio with the increase of the damage degree of coal body.Therefore,it is inferred that the influence of coal structure damage on micropore is relatively small.?2?The fractal dimension calculation model of structural coal micropore is discussed,and a comprehensive characterization method of multi-scale pore fractal of structural coal is proposed,which reveals the fractal characteristics of multi-scale pore structure of structural coal.Based on the scaling invariance of pore size distribution of tectonic coal and the micropore filling model,the method of calculating the fractal dimension of micropore by using density function of micropore distribution and pore size data is discussed.The multi-scale comprehensive fractal dimension of tectonic coal is defined,and the method of calculating the weighted average fractal dimension of adsorption method?low-temperature CO₂ adsorption,low-temperature N₂ adsorption?and mercury intrusion method with the weight of pore volume ratio is proposed.The comprehensive fractal dimension of pore of tectonic coal increases with the increase of damage degree of tectonic coal.The fractal dimension distribution of pore of fragmented coal and mylonite coal is close,while that of fractured coal is similar to that of primary structure coal.?3?The dynamic characteristics of gas diffusion in tectonic coal under two environmental pressures?atmospheric pressure and pressure?were studied by means of atmospheric gas desorption and diffusion experiments and pressurized gas desorption and diffusion experiments.During the diffusion process of tectonic coal and gas,the diffusion coefficient decreases with time,which has the characteristics of large initial attenuation amplitude and fast attenuation speed,resulting in large gas diffusion volume,high gas diffusion speed and fast attenuation of gas diffusion speed in the initial stage of tectonic coal.The diffusion process shows tailing phenomenon in the time direction,and has the characteristics of abnormal diffusion in physics.The law of gas diffusion under two kinds of environmental pressures is basically the same:under the same adsorption equilibrium pressure and coal destruction degree,the gas diffusion amount and initial diffusion speed of anthracite are larger than that of lean coal,the diffusion speed decays faster,and the diffusion tailing phenomenon is more obvious;Under the same adsorption equilibrium pressure and metamorphic degree,the more destructive the coal body is,the higher the gas diffusion amount and initial diffusion speed,the faster the diffusion speed and diffusion coefficient decay,and the more obvious the diffusion tailing phenomenon is.?4?The attenuation law of diffusion coefficient of coal with different degree of destruction is studied,and the equation describing the attenuation process of diffusion coefficient of tectonic coal with time is put forward.Based on the experimental data,it is found that the comprehensive fractal dimension of pore in tectonic coal increases with the increase of coal failure degree,and the attenuation rate of diffusion coefficient increases with the increase of the comprehensive fractal dimension of pore.On this basis,the attenuation equation of diffusion coefficient applicable to coal with different degree of destruction is put forward:power formula is applicable to mylonite coal and granular coal,logarithm formula is applicable to fractured coal,and exponential formula is applicable to primary structural coal.?5?Based on fractal theory,the diffusion mechanism of tectonic coal and gas is discussed.The process of gas diffusion in tectonic coal is simplified as Brownian movement of methane molecules in the pore of tectonic coal.The relationship between fractal characteristics of pore structure and gas diffusion in tectonic coal is studied.The larger the pore fractal dimension is,the larger the fractal dimension of gas diffusion path is,and the faster the diffusion coefficient decays.The larger the spectral dimension,the smaller the fractal dimension of gas diffusion path and the slower the attenuation of diffusion coefficient.Diffusion coefficient is affected by pore fractal characteristics and decreases with the increase of radial distance and time of diffusion.?6?The fractal diffusion model of coal and gas is established and validated,and a loss calculation method based on the fractal diffusion model of coal and gas is proposed.Based on the physical hypothesis that coal particle spheres are formed by fractal capillaries accumulating along different radial directions,fractal time-varying diffusion coefficient and time fractional partial differential equation are introduced to establish the fractal diffusion mathematical model of coal gas.The analytical solution of the model is obtained by the method of separating variables and the Bessel series algorithm.The comparison between the experimental data of gas diffusion and the fitting curve of the model proves that the model has higher accuracy and better applicability.Based on the fractal diffusion model of gas,a method for calculating the amount of lost gas is proposed,and the accuracy of the method is verified by the measured data of gas content in the field,which can meet the needs of production.