Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional heterogeneous porous medium composed of randomly- sized, shaped and distributed circular and elliptical cylinders

Abstract

Several studies have demonstrated the important role played by transverse dispersion along the lateral fringe of chemical plumes in porous media. For example, the success of natural and engineered in-situ remediation relies on the transverse mixing of reactive chemicals or nutrients. Field, laboratory, and theoretical studies have also demonstrated that the length scale of transverse mixing zones can be very small, often on the order of millimeters or centimeters. In order to study dispersion, mixing and reaction at this scale, we have developed a pore-scale modeling approach that consists of the following: (a) geometric construction of a packed bed of randomly sized, shaped and randomly oriented grains; (b) solution for the steady flow field by the lattice-Boltzmann method; (c) solution for the steady- state distribution of reactive chemicals using a finite volume code. Due to the extreme computational burden of pore-scale simulation, we restrict our modeling to two space dimensions. We illustrate our approach through a steady-state system of two reactants injected side-by-side parallel to the mean flow direction; a kinetic dual-Monod reaction rate law is assumed. We first estimate the transverse dispersion coefficient through comparison of a continuum-scale model to the pore- scale simulation of the spread of a nonreactive solute. We then simulate the reactive case for a range of conditions (e.g., flow rate, rate coefficient, pore geometry) and compute the product formed by the reaction. We investigate whether use of the transverse dispersion coefficient gives the proper degree of mixing to accurately simulate the amount of product formed in the system. The results are compared with available experimental evidence and theoretical findings. The numerical simulations reveal new insights into the underlying processes of transport, mixing and reaction at the pore-scale.