Microscale simulation and numerical upscaling of a reactive flow in a plane channel

A bimolecular homogeneous irreversible reaction of the kind A+B→C is simulated in a plane channel as a base example of reactive transport processes taking place at the microscale within porous and/or fractured media. The numerical study explores the way microscale processes embedded in dimensionless quantities such as Péclet (Pe) and Damköhler (Da) numbers propagate to upscaled coefficients describing effective system dynamics. The microscale evolution of the reactant concentrations is obtained through a particle-based numerical method which has been specifically tailored to the considered problem. Key results include a complete documentation of the process evolution for a wide range of Pe and Da, in terms of the global reaction rate, space-time distribution of reactants, and local mixing features leading to characterization of effective reaction and dispersion coefficients governing a section-averaged upscaled model of the system. The robustness of previously presented theoretical analyses concerning closures of volume-averaged (upscaled) formulations is assessed. The work elucidates the dependence of the effective dispersion and reactive parameters on the microscale mixing and reactive species evolution. Our results identify the role played by Da and Pe on the occurrence of incomplete mixing of reactants, which affects the features of the reactive transport scenario.