Numerical investigation of pore and continuum scale formulations of bimolecular reactive transport in porous media

• Bimolecular reactive transport is simulated in 2D disaggregated porous media.
• Pore scale mixing of reactants is studied as in terms of Pe, Da, porosity, and time.
• Reaction-based closure leads to robust characterization of incomplete mixing.
• Upscaled continuum model for incomplete mixing is effective for large Pe, Da.

Focus of this study is a numerical investigation of a reactive transport problem involving an irreversible bimolecular reaction. The advection dispersion reaction equation (ADRE) is typically adopted to model and interpret these types of reactive transport scenarios in porous media at the continuum (Darcy) scale. It is well documented that the theoretical derivation of the ADRE from pore scale system dynamics requires a set of assumptions which are not always met in the context of laboratory and/or field scale applications. We start by recounting the various upscaled formulations which can be obtained through the volume averaging method in the space defined by the Damköhler (Da) and Péclet (Pe) numbers characterizing the phenomenon. The transport problem is then simulated numerically at the pore scale considering different models of disaggregated porous media. Simulation results provide a framework to discuss the key features and appropriateness of continuum scale formulations which can be employed to describe the target geochemical systems for these settings. The impact of Pe, Da and pore space configuration on the parameters embedded in the upscaled formulations is analyzed. Conditions under which such formulations hold are discussed, with emphasis on the critical and widely studied advection dominated scenarios associated with fast reactions (i.e., large values of Pe and Da). Main results include the quantitative assessment of the ability of recently proposed (Porta et al., 2012 [1]) and standard (e.g., ADRE) continuum formulations to quantify the effect of pore scale incomplete solute mixing on upscaled reaction rates.