This paper presents a coupled thermo-hydraulic-mechanical (THM) model to study real gas flow behaviour in a deformable coal matrix. The matrix encompasses multiple pore sizes, ranges from nanometers to micrometers, and it 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 phases, 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 behaviour is investigated. In addition, the mechanical behaviour is included to consider the stress dependency of the porosity and intrinsic permeability of porous rocks. The validity of proposed model is achieved by comparing numerical solutions with published experimental data. Numerical simulations were performed to investigate the real gas transport processes in coal matrix of multiple pore sizes. The simulated results show that the times to reach pressure equilibrium and adsorption equilibrium are not same, and they depend on the pore size, pressure and surface diffusion. Time required to reach equilibrium is reduced significantly with increase of pore sizes. Diffusion coefficients in 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.