Abstract
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.
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