Numerical Simulation and Experimental Study of Bimolecular Reactive Transport in Porous Media

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The traditional advection–dispersion–reaction equation (ADRE) often meets difficulty in simulating diffusion-controlled reactive transport, because the grid-based ADRE with a laboratory-measured reaction rate overpredicts pore-scale mixing and the product concentration. In this study, we chose bimolecular reactive transport (A++B→→AB) in porous media as an example and developed a fully implicit Galerkin finite-element method with Picard’s linearization scheme for solving the ADRE considering incomplete mixing at pore scale (IM-ADRE) based on a continuum approximation by Sanchez-Vila et al. (Water Resour Res 46:W12510, 2010). Sensitivity analysis showed that the IM-ADRE model was most sensitive to the parameter “m,” which was the power index of time used to control the decline rate of the time-dependent kinetic reaction term considering effects of incomplete mixing at pore scale. We used the IM-ADRE model to interpret the column experiment reported by Raje and Kapoor (Environ Sci Technol 34(7):1234–1239, 2000), which studied bimolecular reactive transport of aniline (AN) +1,2-naphthoquinone-4-sulfonic acid (NQS)→→1,2-naphthoquinone-4-aminobenzene (NQAB) in porous media. Previous studies found that the discrepancy between the simulated and observed peak product concentrations was as large as 55 % by the traditional ADRE, while the discrepancy was reduced to 5 % by the IM-ADRE model. We further conducted new reactive transport column experiments with NQS and AN to systematically understand the nature of bimolecular reactive transport in porous media and further check the validity of the IM-ADRE model. Our experiments differed from previous ones in two aspects. First, we used two different realistic porous media with six different flow velocities while previous experiments mostly involved artificial media such as glass beads under two similar flow velocities. Second, our experiment used a column (with the length of 100 cm) relatively longer than that (18 cm) in Raje and Kapoor (2000), and thus, the boundary effect of the column was minimized, and the time dependence of the effective reaction term could be further checked rigorously. Our study reveals that the IM-ADRE is a feasible tool in quantifying reactive transport at a travel distance up to 100 cm, further validating the effective, time-dependent rate coefficient proposed empirically by Sanchez-Vila et al. (2010).


Applied Mathematics