A fractal Langmuir adsorption equation on coal: Principle, methodology and implication

The conventional Langmuir equation based on the homogeneous surface assumption is failed to characterize the gas adsorption in coal due to the obvious heterogeneity of the coal pore structure. Therefore, a novel fractal Langmuir adsorption equation on coal is proposed based on the fractal characteristics of pore heterogeneity in this paper. The pore heterogeneity in coal displays obvious fractal characteristic, which can be characterized by the fractal dimension for the pore tortuosity ( D T ) and the fractal dimension for the pore size ( D f ). The principles and methodology of the proposed equation are deduced and summarized in detail. The results indicate that the proposed fractal Langmuir adsorption equation displays the higher accuracy than the conventional Langmuir equation. In addition, the proposed equation is the function of the fractal dimension for the pore tortuosity ( D T ), the fractal dimension for the pore size ( D f ), and the pore structural parameters ( lambda min , lambda max , and L ), which more comprehensively reflects the influence of pore structure on adsorption. Therefore, the proposed equation achieves a breakthrough in the calculation of the methane adsorption capacity in pores with different pore diameter ranges, which can more accurately reflect the methane adsorption in coal pores compared with the conventional Langmuir equation.