Coupling of swelling, internal stress evolution, and diffusion in coal matrix material during exposure to methane

We construct theoretical models for time-dependent swelling of coal matrix material upon adsorption of a single gas, taking into account a coupling between stress, strain, chemical potential, and diffusion. Two models are developed. The first (model A) corresponds to diffusion and hence swelling rates being controlled by the jump frequency of adsorbed molecules between closely spaced adsorption sites and the second (model B) to transport controlled by diffusion of unadsorbed molecules through diffusion paths linking distant adsorption sites. To test these models, we performed axial swelling experiments on a single 4mmsized cylindrical sample of medium volatile bituminous coal, exposed to CH4 at pressures up to 40 MPa, at 40 degrees C, using 1-D, high-pressure dilatometry. The models were calibrated to the experimental data by adjustment of a single-valued diffusion coefficient, independent of gas pressure and adsorbed concentration. The results show that the data can be accurately explained only by model B. The implication is that the gas transport, the associated adsorption, and hence time-dependent swelling are controlled by the diffusion of unadsorbed molecules and not by molecules jumping between the adjacent adsorption sites. Our model describes a full coupling between stress, strain, sorption, and diffusion in coal matrix material in terms of parameters that have clear physical meaning and are easily obtained from sorption and swelling experiments on coal of any rank exposed to any gas. It therefore offers an important tool for modeling permeability evolution with time during (enhanced) coalbed methane operations.