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Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media

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Abstract
  • In this work, we revisit the upscaling process of diffusive mass transfer of a solute undergoing a homogeneous reaction in porous media using the method of volume averaging. For linear reaction rate kinetics, the upscaled model exhibits a vis-à-vis correspondence with the mass transfer governing equation at the microscale. When nonlinear reactions are present, other methods must be adopted to upscale the nonlinear term. In this work, we explore a linearization approach for the purpose of solving the associated closure problem. For large rates of nonlinear reaction relative to diffusion, the effective diffusion tensor is shown to be a function of the reaction rate, and this dependence is illustrated by both numerical and analytical means. This approach leads to a macroscale model that also has a similar structure as the microscale counterpart. The necessary conditions for the vis-à-vis correspondence are clearly identified. The validation of the macroscale model is carried out by comparison with pore-scale simulations of the microscale transport process. The predictions of both concentration profiles and effectiveness factors were found to be in acceptable agreement. In an appendix, we also briefly discuss an integral formulation of the nonlinear problem that may be useful in developing more accurate results for the upscaled transport and reaction equations; this approach requires computing the Green function corresponding to the linear transport problem.
  • Keywords: Closure problem, Upscaling, Reactive transport, Linearization
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  • Lugo-Méndez, H. D., Valdés-Parada, F. J., Porter, M. L., Wood, B. D., & Ochoa-Tapia, J. A. (2015). Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media. Transport in Porous Media, 107(3), 683-716. doi:10.1007/s11242-015-0462-4
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  • 107
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  • 3
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  • This work was benefited from Fondo Sectorial de Investigación para la educación from CONACyT (Project Number: 12511908; Arrangement Number: 112087).
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