Lattice Boltzmann study of porosity-permeability variation in different regimes of non-isothermal dissolution in porous media

Characterizing the process of dissolution in porous media by thermally energized reactants is of great importance to different aspects of the geothermal science and petroleum industry. Notably for the petroleum industry, understanding the porosity-permeability relationship in different dissolution regimes significantly helps the optimal design of wellbore acidizing processes. Thus, in this paper, reactive flow of a non-isothermal solvent in a complex porous medium is studied at pore scale and the evolution of permeability values with dissolution advancement are thoroughly investigated. Dimensional analysis of the governing transport equations is also performed and it is shown that generally 10 dimensionless numbers characterize such processes. The effects of Arrhenius number (Ar), temperature ratio (ψ), Peclet (Pe) and Damkohler (Da) on morphology is investigated in a wide range and the corresponding porosity-permeability diagrams are presented for each regime. It is also found that at high Pe and Da where initially wormhole pattern would be dominant, decrease of ψ below 1 (injection of cooler reactant), delays face dissolution and shifts the dissolution shape toward a more uniform pattern. In contrast, by letting ψ>1 (injection of warmer reactant), the pattern shifts toward a more facial dissolution whose intensity is characterized by Ar. At low Pe and high Da, it is found that face dissolution pattern would be dominant and letting ψ>1 does not considerably affect the pattern. However, if ψ is lowered below 1, the local reaction rates are decreased and dissolution pattern slightly shifts toward a more uniform dissolution. Finally, when both Pe and Da are low, a competition between face dissolution and uniform dissolution is established. In this case, letting ψ<1 reduces the local Da and leads to a more uniform dissolution and if ψ>1, the pattern shifts to a more facial one. The role of Ar is also discussed and shown to act as an amplifier for ψ effects.