Fast image processing method for coal particle cluster box dimension measurement and its application in diffusion coefficient testing

The diffusion coefficient is the key parameter used to characterize methane diffusion behavior in coal. The commonly used analytical solutions for diffusion coefficients require simplifying the particle shape to regular shapes, which greatly deviates from the actual shape of coal particles. The influence of coal particle shape on the diffusion coefficient is currently not well understood. Based on image processing techniques and inverse problem-based numerical simulation, a new method is proposed in this paper to determine the diffusion coefficients of irregular coal particles, and a feasible solution for quantitatively assessing the influence of particle shapes on the diffusion coefficient is provided. The implementation of this method is based on two aspects: the fast quantitative characterization of the shape features of coal particle clusters and inverse problem-based numerical simulation to solve the diffusion coefficient of irregularly shaped coal particles. First, image processing technology is used to quickly and accurately extract the 2D projection contour of batch particles, and an algorithm based on fractal theory is designed to obtain the box dimension of batch contours, which achieves the quantitative characterization for the shape features of coal particle clusters. At the same time, a comparison with Fraclab is conducted to validate the scientific effectiveness of the box dimension algorithm. Then, 3 coal particles with representative fractal dimensions are selected and their diffusion coefficients are obtained using the inverse problem numerical method. The results indicate that the desorption curves obtained through inverse problem optimization for the 3 particles are excellently consistent with the experimental data, with fitting degrees R2 all exceeding 99%. Therefore, the diffusion coefficients can be effectively obtained. Meanwhile, the influence of shape on the diffusion coefficient is analyzed quantitatively. The results show that the diffusion coefficient increases with the box dimension of the contour, and the particle shape has a considerable impact on determining the gas diffusion coefficient.