Determining the diffusion coefficient of gas diffusion in coal: development of numerical solution
Determining gas diffusion coefficient from experimental data is a key step of reproducing and predicting the diffusion process in coal. Previously analytical solution, including the unipore diffusion model and the bidisperse diffusion model, has been used extensively to estimate the gas diffusion coefficient(s) in coal. The utilization of analytical solution is convenient, however, there are some defects which may affect the accuracy of the results. For example, it is not suitable for fitting manometric sorption data, and the assumption of linear adsorption isotherm is not true. In this paper, we present a numerical solution to determine the gas diffusion coefficients. Three models were developed based on different assumptions of pore system and diffusion forms, i.e., unipore model assuming one kind of pore and diffusion, bidisperse model I (BM I) assuming independent macropore diffusion and micropore diffusion, bidisperse model II (BM II) assuming dependent macropore diffusion and micropore diffusion. Nitrogen diffusion experiment was conducted and the adsorption isotherm was measured. Sphere geometry was built for numerical simulation and the proposed models were used to fit the experimental data to determine the diffusion coefficients. Results show that neither the analytical unipore model nor the numerical unipore model can describe the diffusion process perfectly. By giving the same diffusion coefficient, the modelled fractional uptake ratio of numerical unipore model is smaller than the result of analytical unipore modeling at early stage while greater at later stage, which is due to the different assumptions of adsorption isotherm. Both BM I and BM II can describe the diffusion process well. The determined macropore diffusion coefficients of the two models are similar, while the micropore diffusion coefficient and the macropore adsorption ratio of BM II are greater than that of BM I. These can be explained by the different roles of the macropore diffusion in the two models. The gas pressure change at the center of the coal sphere was examined, from the modeling result of BM I, the macropore pressure increases sharply and then drops along with the external gas pressure, while the initial increasing rate of macropore pressure of BM II is much smaller and tends to be stable at later stage. No apparent impacts of initial gas pressures on diffusion coefficients can be observed, the change of diffusion coefficients and macropore adsorption ratio are actually small with increasing gas pressure. The numerical solution of determining gas diffusion coefficients can easily relax the assumptions and restrictions of the analytical solution. It can be used to test different kinds of coal samples, investigate different diffusion mechanisms and match all kinds of experimental data. The measured sorption isotherm and coal properties can also be incorporated into the modeling, which makes the determined diffusion coefficients more reliable. This paper is a preliminary attempt and we hope it can bring the researchers some new ideas about studying the gas diffusion characteristics in coal.