Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media

作者：Lugo Mendez Helen D; Valdes Parada Francisco J; Porter Mark L; Wood Brian D; Ochoa Tapia J Alberto^*

来源：Transport in Porous Media, 2015, 107(3): 683-716.

DOI：10.1007/s11242-015-0462-4

• Upscaling
• Reactive transport
• Linearization
• Closure problem

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-A -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-A -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.

• 出版日期2015-4