Identification of homogeneous-heterogeneous pore-scale reaction rates in porous media
https://doi.org/10.25587/SVFU.2023.74.45.008
Abstract
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 finite 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 field. In addition, a sensitivity analysis of the model to the parameters has been carried out to study their influence on the reactive transport through the porous medium. A numerical solution for the inverse problem, namely, identification of key parameters characterizing the reactive transport based on two breakthrough curves of two different solutions is presented. Noisy measurements with different noise amplitudes including mixed amplitudes were considered. For approximate solution of the multidimensional inverse problem the metaheuristic Artificial Bee Colony Algorithm was applied and showed good efficiency at rather low computational cost.
About the Author
V. V. Grigoriev
Laboratory of Computational Technologies for Modeling Multiphysical and Multiscale Permafrost Processes,
Ammosov North-Eastern Federal University; North Caucasus Centre for Mathematical Research
Russian Federation
Russian Federation
Vasiliy V. Grigoriev
42 Kulakovskii Street, Yakutsk, 677000 Russia
1 Pushkin Street, Stavropol, 355000 Russia
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Review
For citations:
Grigoriev V.V. Identification of homogeneous-heterogeneous pore-scale reaction rates in porous media. Mathematical notes of NEFU. 2023;30(2):101-122. (In Russ.) https://doi.org/10.25587/SVFU.2023.74.45.008
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