Gas Transport in Bidisperse Coal Particles: Investigation for an Effective Diffusion Coefficient in Coalbeds
Authors: Yi J. , Akkutlu I.Y. , Deutsch C.V. 
Published: March 2010

Abstract
Much work has been carried out on adsorption capacity of coals. Diffusive transport processes within the coal matrix blocks could be the rate-limiting step for adsorption during gas injection and production operations. Identifying these processes and determining their contributions to overall mass transport is a complex and time consuming procedure. The paper presents numerical diffusion models in varying coal particles and investigates transport mechanisms. For this purpose, the coal particle is represented as a microporous solid penetrated by a network of larger interconnected macropores. The solid adsorbs the bulk of the gas. A simple relationship between the apparent and intrinsic Fickian diffusion coefficients is derived in the case of single-component (methane) transport and Langmuir-type adsorption. Mass transport in the bidisperse coal particle is significantly influenced by the adsorption in the microporous solid. The investigation is then extended to study concentration dependence of the microporous solid diffusion for binary (methane-CO2) mixtures using the Maxwell-Stefan formulation. It is found that co-diffusion of the gas molecules enhances the gas mass transport in the solid in the presence of competitive sorption dynamics, while counter-diffusion may diminish the gas mass transport. The influence of lateral interactions among the adsorbed molecules in the solid phase is discussed. The work finds application in modelling CBM and CO2-ECBM processes.

Introduction
As an unconventional natural gas resource, coalbed methane receives worldwide attention. Deep coal seams that are not accessible for mining are suitable for in situ gas production using conventional drilling, well completion and gas recovery technologies. Hence, a vast amount of natural gas is globally available. Unlike conventional gas resources, however, the gas storage, flow and transport processes in coalbeds are quite complex mainly due to the intricate nature of coal(1–6).
Coalbeds are porous media often characterized by a bimodal pore structure: a primary structure consisting of micro- and meso-scale pores, and a secondary structure with macropores and interconnected natural fractures. The microporous coal has an extremely large internal surface area and a strong affinity for certain naturally occurring chemical species such as methane, carbon dioxide, nitrogen and water. At high coalbed pressures, therefore the majority of the natural gas-in-place, in particular, methane, exists abundantly at an adsorbed liquid-like state in the microporous solid(1).
Depressurizing the coalbed may yield a significant volume of natural gas. However, the initial stage of recovery is often dominated by water production, whereas, the latter stage is under the influence of diffusional resistances of the primary pores of the coal matrix. Treatment and disposal of the produced water is expensive and its long-term environmental impact has not been clearly understood yet. Injection of a second gas with much higher adsorption capacity, on the other hand, could possibly enhance recovery by maintaining the overall reservoir pressure, thus, keeping the water production at a minimum level. Additionally, injecting a second gas would promote methane desorption by lowering the partial pressure of the coalbed methane in the migrating gas phase.