Numerical modelling of fluids mixing, heat transfer and non-equilibrium redox chemical reactions in fluid-saturated porous rocks

Non-equilibrium redox chemical reactions of high orders are ubiquitous in fluid-saturated porous rocks within the crust of the Earth. The numerical modelling of such high-order chemical reactions becomes a challenging problem because these chemical reactions are not only produced strong non-linear source/sink terms for reactive transport equations, but also often coupled with the fluids mixing, heat transfer and reactive mass transport processes. In order to solve this problem effectively and efficiently, it is desirable to reduce the total number of reactive transport equations with strong nonlinear source/sink terms to a minimum in a computational model. For this purpose, the concept of the chemical reaction rate invariant is used to develop a numerical procedure for dealing with fluids mixing, heat transfer and non-equilibrium redox chemical reactions in fluid-saturated porous rocks. Using the proposed concept and numerical procedure, only one reactive transport equation, which is used to describe the distribution of the chemical product and has a strong non-linear source/sink term, needs to be solved for each of the non-equilibrium redox chemical reactions. The original reactive transport equations of the chemical reactants with strong non-linear source/sink terms are turned into the conventional mass transport equations of the chemical reaction rate invariants without any non-linear source/sink terms. A testing example, for some aspects of which the analytical solutions are available, is used to validate the proposed numerical procedure. The related numerical solutions have demonstrated that (1) the proposed numerical procedure is useful and applicable for dealing with the coupled problem between fluids mixing, heat transfer and non-equilibrium redox chemical reactions of high orders in fluid-saturated porous rocks; (2) the interaction between the solute diffusion, solute advection and chemical kinetics is an important mechanism to control distribution patterns of chemical products in an ore-forming process; and (3) if the pore-fluid pressure gradient is lithostatic, it is difficult for the chemical equilibrium to be attained within permeable cracks and geological faults within the crust of the Earth.