Identification of homogeneous-heterogeneous pore-scale reaction rates in porous media

This paper presents a model of homogeneous-heterogeneous reaction in the pore scale based on Stokes equations, convection-diffusion-reaction equations with the Robin boundary condition at the inclusion boundaries. The homogeneous reaction is described as cubic autocatalysis on the whole pore space, and the kinetics of the heterogeneous reaction is described by the Langmuir isotherm. Numerical solution of the problem is carried out by the nite element method on piecewise linear elements. The Crank-Nicholson scheme is used for discretization in time. The nonlinear problem is solved using Newton’s iteration method. The mass transfer is simulated with a calculated velocity eld. In addition, a sensitivity analysis of the model to the parameters has been carried out to study their in uence on the reactive transport through the porous medium. A numerical solution for the inverse problem, namely, identi cation of key parameters characterizing the reactive transport based on two breakthrough curves of two di erent solutions is presented. Noisy measurements with di erent noise amplitudes including mixed amplitudes were considered. For approximate solution of the multidimensional inverse problem the metaheuristic Arti cial Bee Colony Algorithm was applied and showed good e ciency at rather low computational cost.