Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation

We provide a quantitative interpretation of the column experiment reported by Gramling et al. [2002]. The experiment involves advection-dominated transport in porous media of three dissolved species, i.e., two reactants undergoing a fast irreversible reaction and the resulting product. The authors found that their observations could not be properly fitted with a model based on an advection-dispersion-reaction equation (ADRE) assuming the reaction was instantaneous, the actual measured total reaction product being lower than predictions for all times. Data have been recently well reproduced by Edery et al. [2009, 2010] by means of a particle tracking approach in a Continuous Time Random Walk framework. These and other authors have questioned the use of partial differential equation (PDE) approaches to quantify reactive transport, because of the difficulty in capturing local scale mixing and reaction. We take precisely this approach, and interpret the experiments mentioned by means of a continuum-scale model based on the ADRE. Our approach differs from previous modeling attempts in that we imbue effects of incomplete mixing at the pore-scale in a time-dependent kinetic reaction term and show that this model allows quantitative interpretation of the experiments in terms of both reaction product profiles and time-dependent global production rate. The time dependence of the kinetic term presented accounts for the progressive effects of incomplete mixing due to pore-scale rate-limited mass transfer, and follows a power law, which is consistent with the compilation of existing experiments reported by Haggerty et al. [2004]. Our interpretation can form the basis for further research to assess the potential use of PDE approaches for the interpretation of reactive transport problems in moderately heterogeneous media.