Permeability is a controlling factor for gas migration in coal seam reservoirs and has invariably been the barrier to economically viable gas production in certain deposits. Cleats are the main conduits for gas flow in coal seams though cleat mineralisation is known to significantly reduce permeability. Cleat demineralisation by the use of acids may enhance the effective cleat aperture and therefore permeability. This modelling study examines how acids transport through coal subject to reactive cleat mineralisation, and develops a fundamental understanding of the mechanisms controlling permeability change from pore scale to sample scale. A novel Lattice Boltzmann Method (LBM)-based numerical model for the simulation, prediction, and visualisation of the reaction transport is proposed to numerically investigate relationships between physio-chemical changes and permeability during coal stimulation. In particular, the work studies the interaction of acidic fluids (HCl) with reactive mineral (e. g. calcite) and assumed non-reactive mineral (e. g. coal) surfaces, mineral dissolution and mass transfer, and resultant porosity change. The reaction of a calcite cemented core subplug from the Bandanna Formation of Bowen Basin (Australia), is used as a study case. LBM simulations revealed a permeability enhancement (27.15 times of the pre-flooding permeability) along the x-axis after 20 min HCl flooding of a 5.3 cm x 5.3 cm x 1.3 cm sub-section. The analysis and evaluation of the 4D permeability evolution is conducted as a contribution work for the fluid flow modelling in the subsurface petrophysical conditions, at the micron to centimetre scales. The simulation results demonstrate the proposed algorithm is capable for studies of multiple mineral reactions with disparate reaction rates.