Modeling Bimolecular Reactions and Transport in Porous Media Via Particle Tracking

15 We use a particle-tracking method to simulate several one-dimensional bi16 molecular reactive transport experiments. In our numerical scheme, the 17 reactants are represented by particles: advection and dispersion dominate 18 the flow, and molecular diffusion dictates, in large part, the reactions. The 19 particle/particle reactions are determined by a combination of two proba20 bilities dictated by the physics of transport and energetics of reaction. The 21 first is that reactant particles occupy the same volume over a short time 22 interval. The second is the conditional probability that two collocated par23 ticles favorably transform into a reaction. The first probability is a direct 24 physical representation of the degree of mixing in an advancing interface be25 tween dissimilar waters, and as such lacks empirical parameters except for 26 the user-defined number of particles. This number can be determined ana27 lytically from concentration autocovariance, if this type of data is available. 28 The simulations compare favorably to two physical experiments. In one, 29 Preprint submitted to Elsevier November 10, 2012 the concentration of product, 1,2-naphthoquinoe-4-aminobenzene (NQAB) 30 from reaction between 1,2-naphthoquinone-4-sulfonic acid (NQS) and ani31 line (AN), was measured at the outflow of a column filled with glass beads 32 at different times. In the other, the concentration distribution of reactants 33 (CuSO4 and EDTA 4−) and product (CuEDTA2−) were quantified by snap34 shots of light transmitted through a column packed with cryolite sand. These 35 snapshots allow us to estimate concentration statistics and calculate the re36 quired number of particles. The experiments differ significantly due to a 37 ∼ 10 difference in thermodynamic rate coefficients, making the latter ex38 periment effectively instantaneous. When compared to the solution of the 39 advection-dispersion-reaction equation (ADRE) with the well-mixed reaction 40 coefficient, the experiments and the particle-tracking simulations showed on 41 the order of 20% to 40% less overall product, which is attributed to poor 42 mixing. The poor mixing also leads to higher product concentrations on the 43 edges of the mixing zones, which the particle model simulates more accurately 44 than the ADRE. 45