Traditionally, physicochemical processes whose result is the release of methane from a coal sample-often referred to as desorption-are discussed in relation to two phenomena, i.e., the transportation of gas inward (or outward) the porous substance, and the desorption (or sorption) proper of gas from the coal surface. The complex pore structure of coal necessitated the adoption of an arbitrary division of the gas transportation into: the diffusion of gas within the pore network in grains (understood as a molecular phenomenon) and the filtration of gas through the system of fissures and large pores (understood as a phenomenon related to the fluid mechanics). The filtration-type transportation of gas through a porous medium is most typically discussed in the context of the flow of gas through coal beds, or other porous rocks. In laboratory analyses carried out on granular samples obtained from the porous material, the filtrational flow of gas among the sorbent grains and within the fissure system is so fast (as compared to the diffusion occurring inside the grains) that the decisive factor influencing the kinetics of gas release is, most often, diffusion. In the case of such observations, it is assumed that the process of the sorption proper is almost instantaneous in its nature. There are no theoretical premises that would challenge an assumption thus formed, however, it would be very interesting to carry out an experiment confirming their existence. The present paper discusses an attempt to estimate, under laboratory conditions, the kinetics of the sorption proper. It provides a description of the specially built measuring equipment, as well as the results of the performed experiments, together with their analysis. In the performed experiments, the obtained time constants of sorption were smaller than 50 ms. The lowest values did not exceed 10 ms. Since the obtained time constant values are very low-in spite of the fact that it was impossible to completely eliminate the delays connected with the transportation of molecules to the sorption sites-the authors are of the opinion that the process of sorption proper shall be assumed to be instantaneous.

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The authors derived the analytical solution to diffusion equations. The solution requires linearization of diffusion equations, as well as developing the obtained expression into a series. In particular, the result of the first procedure is highly deviated from the exact solution. The authors conducted a sorption experiment and then, in relation to the registered kinetics of the diffusion of CO2 inside hard coal grains, approximated the linear solution and the numerical nonlinear solution by means of the least squares method. As confirmed by the lower value of the sum of deviation squares, it can be clearly demonstrated that the nonlinear equation represents the actual measurement more accurately.