A fractal theory based fractional diffusion model used for the fast desorption process of methane in coal

Study on coal pulverization characteristics and gas desorption mechanism based on impact crushing experiment

The coal's particle size distribution properties after pulverization and the gas desorption behavior driven by pulverization are of profound meaning to the study of coal and gas outburst mechanism. In this paper, based on the impact crushing experiment, the tectonic coal and primary coal are crushed under different impact energy conditions. After screening the broken coal, the particle size distribution law is analyzed, and the characterization function suitable for the particle size distribution of coal particles after crushing is determined. The relationship between crushing work and new surface area and fractal dimension of coal body is discussed. The consequences indicated that the mass proportion of tectonic coal below 0.074 mm particle size is much huger than that of raw coal. G-S, R-R, and fractal distribution model describe the best particle size distribution of the two coals in the scope of 0.074∼4 mm. The new surface area added increases with the crushing work, and the tectonic coal is 1.34-1.96 times that of the raw coal. The fractal dimension diminishes first and then increases with the crushing work ratio. In addition, the gas desorption amount of coal particles with different particle sizes after coal pulverization was measured, and a dynamic model suitable for coal pulverization-driven gas desorption was established, and the experimental results were verified. The research results of this paper can provide experimental and theoretical basis for the analysis of energy dissipation in coal and gas outburst.

Effect of micro-fractures on gas flow behavior in coal for enhanced coal bed methane recovery and CO2 storage

This study investigates the impact of micro-fractures on gas flow behavior in coal formations, specifically within the context of CO2-based Enhanced Coal Bed Methane Recovery (ECBMR). Employing comparative analysis, various gas flow models, including Unipore Diffusion Model (UDM), Bidispersed Diffusion Model (BDM), Fractal Fractional Diffusion Model (FFDM), Time-Dependent Diffusivity Model (TDDM), Anomalous Sub-Diffusion Model (ASM), and Free Gas Density Gradient Model (FGDGM), are evaluated for their efficacy in capturing the complexities. The study aims to provide insights into the accuracy and applicability of these models, considering the heterogeneity of coal seams and the influence of micro-fractures on gas flow dynamics. The major findings include the categorization of different gas flow models based on their applicability to CO2-based ECBMR. For instance, the study suggests utilizing BDM and FFDM models while considering the heterogeneity of coal seams. Similarly using the TDDM model for time dynamics of ECBMR will give higher accuracy. The article contributes to a deeper understanding of gas migration processes in coal, particularly in the context of ECBMR, with implications for optimizing recovery strategies and addressing challenges associated with micro-fracture-induced variations in gas flow behavior.

Importance of the average radius of coal particles on determining the methane diffusion coefficient

The average radius of coal particles is an estimate of the diffusion path in the particle method for determining the diffusion coefficient. It is currently calculated using the arithmetic mean of coal particle sieved intervals. This calculation, however, ignores the coal particle size distribution, resulting in significant deviations when calculating the gas diffusion coefficient. An appropriate average radius calculation method should consider the particle size distribution and the physical essence of diffusion. To accomplish this, a series of methods for calculating the mean particle diameters and their physical significance were reviewed. Next, coal samples were sieved into three intervals, and gas diffusion tests and laser particle size distribution were conducted. Results show that coal particles are within the sieving interval, ranging from 42.01 to 76.18%. By solving the diffusion coefficients using four mean particle diameters based on particle size distribution and diffusive mass transfer, the difference between the arithmetic mean value and these diameters is up to 89.06%. [Formula: see text] and [Formula: see text] are preferred for the calculation of the average radius since they are compatible with coal particle shape and the physical meaning of diffusive mass transfer.

Gas Diffusion in Coal Powders is a Multi-rate Process

Gas migration in coal is strongly controlled by surface diffusion of adsorbed gas within the coal matrix. Surface diffusion coefficients are obtained by inverse modelling of transient gas desorption data from powdered coals. The diffusion coefficient is frequently considered to be dependent on time and initial pressure. In this article, it is shown that the pressure dependence can be eliminated by performing a joint inversion of both the diffusion coefficient and adsorption isotherm. A study of the log–log slope of desorbed gas production rate against time reveals that diffusion within the individual coal particles is a multi-rate process. The application of a power-law probability density function of diffusion rates enables the determination of a single gas diffusion coefficient that is constant in both time and initial pressure.

Study on the gas desorption law and indicator influencing factors of fixed-size coal samples

The prediction of dangerous hazards in working faces is an important link to prevent coal and gas outbursts. Improving the accuracy of predictive indicators is of great significance for reducing the phenomenon of being prominently below the critical value and ensuring safe production. The fixed-size desorption index K₁ is one of the important indicators for coal face and gas outburst prediction. Based on the diffusion theory and the physical meaning of fixed-size coal samples, the mathematical expression of K₁ is established by the self-developed high/low temperature pressure swing adsorption-desorption experimental system. According to the equation, the effects of gas pressure, loss time, coal particle size and diffusion coefficient on K₁ are studied. The results show that the K₁ index is logarithmically related to the gas pressure. Under the same conditions, the longer the loss time is, the smaller the measured K₁ is, and the smaller the particle sizes of the drill cuttings are, the more notable the performance is; the diffusion coefficient represents the ability of gas to bypass micropores and the coal matrix. The greater the ability to bypass the matrix is, the larger the diffusion coefficient under the same conditions is, and the larger K₁ is; the coal particle size has a greater influence on K₁, and the smaller the size is, the more likely it is that the phenomenon of being prominently below the critical value occurs. Therefore, the particle size composition of coal during on-site measurements is crucial for obtaining the true K₁ and the exact critical values.

Parameter identification for fractional fractal diffusion model based on experimental data

This paper studies the techniques of parameter estimation and their application in determining parameters of the fractional fractal diffusion model. On account of the basic structural characteristics of the porous coal matrix, the fractional fractal diffusion model is established to express the gas transport mechanism in the heterogeneous coal matrix. A L1 finite difference method in the temporal direction while spectral collocation method in the spatial direction is proposed to solve the model numerically. Then, by means of the gas adsorption and desorption experiments in coal samples, attempts have been made by the BFGS method, nonlinear conjugate gradient method, and Bayesian method to compare and contrast to obtain the physical parameters of the model. Furthermore, advantages and limitations of different estimation methods are discussed.