Modeling Non-isothermal Transport Behavior of Real Gas in Deformable Coal Matrix

Abstract

This work presents a coupled thermo-hydraulic−mechanical (THM) model to study real gas flow behavior in a deformable coal matrix. The matrix encompasses multiple pore sizes ranging from nanometers to micrometers, and promotes various complex, inter-related mass transport mechanisms. In this model, the adsorbed gas layer at the interface between the solid matrix and the free gas phase is considered as an independent phase. Gas adsorption/desorption and diffusion process are defined separately for individual phase, which are then interacted via mass exchange between the phases. The Knudsen number based flow regimes are adopted to describe bulk gas transport in the matrix of varying pore sizes, and the adsorbed phase transport is described by surface diffusion mechanisms. The thermal effect on gas adsorption and transport behavior is investigated. In addition, the mechanical behavior is included to consider the stress dependency of the porosity and intrinsic permeability of porous rocks. The validity of the proposed model is achieved by comparing numerical solutions with published experimental data. Numerical simulations were performed to investigate the real gas transport processes in a coal matrix of multiple pore sizes. The simulated results show that the times to reach pressure equilibrium and adsorption equilibrium are not the same, and they depend on the pore size, pressure, and surface diffusion. The time required to reach equilibrium is reduced significantly with an increase of pore sizes. Diffusion coefficients in the porous matrix are not constant but vary with pressure and pore sizes, which is important for accurate estimation of coalbed gas production or carbon sequestration.

Modeling Adsorption and Transport behavior of Gases in Moist Coal Matrix

“…On the other hand, pore size is reduced by the coverage of the adsorbed molecule on the pore surface as the pressure increases. 38 Compared to the bulk gas diffusivity in dry coals, 1.7 × 10 −11 m 2 /s, the apparent diffusivity is only 0.75 × 10 −11 m 2 /s. It is suggested that the presence of moisture in coal matrices can hinder the decrease in bulk gas diffusivity because of the reduction of gas capacity and pore space occupied by the adsorbed gas.…”

“…The difference between times required for pressure reaching equilibrium when the matrix contains an 8.0% moisture content is not as obvious as that for the lower moisture contents because an increase of moisture content leads to a drop of pore size, and further incurring a decrease in the diffusivity of free phase gas. On the other hand, the diffusivity of free gas experiences a more significant decrease with the increase in gas pressure when the pore size is smaller, 38 as a result, the required time for reaching gas pressure equilibrium will be extended slightly.…”

“…Bulk gas transport in the nanopores of a porous media includes viscous flow and Knudsen diffusion. , The mechanisms contribute either individually or simultaneously under certain temperature–pressure conditions. To calculate their contributions in the bulk gas transport, Wu et al defined the total gas flux using a Knudsen number-based weighting factor as where J f is the total gas flux in the free phase, J fK is the Knudsen diffusion flux, and J fv is the viscous flux.…”

“…In the present study, the developed model is implemented into an in-house numerical modeling code, COMPASS, developed by Thomas and co-workers. , The partial differential equations are expressed in terms of the primary model variables C , C s . The Galerkin finite element method is used to spatially discretize the equations, while an implicit mid-interval backward difference scheme is used to achieve temporal discretization of the governing partial differential equations.…”

“…The purpose of this study is to develop a predictive model for investigating gas transport processes in moist coal matrices. Previously published model of Chen et al, which predicts gas migration behavior in dry coal matrices, is extended in this work. Gas diffusion and adsorption kinetics, which are mostly ignored in existing literatures, are included in the model.…”