Journal
TRANSPORT IN POROUS MEDIA
Volume 95, Issue 3, Pages 669-696Publisher
SPRINGER
DOI: 10.1007/s11242-012-0068-z
Keywords
Periodic homogenization; Evolving microstructure; Level set function; Colloidal transport; Pore scale modeling; Particle-surface interaction; Pore clogging; Porosity changes; Multiscale coefficients; Mixed finite elements
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Funding
- Deutsche Telekom Stiftung
- office of gender and diversity, University of Erlangen-Nuremberg
- German Research Foundation (DFG) [To 184/7-1, To 184/7-2]
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We consider colloidal dynamics and single-phase fluid flow within a saturated porous medium in two space dimensions. A new approach in modeling pore clogging and porosity changes on the macroscopic scale is presented. Starting from the pore scale, transport of colloids is modeled by the Nernst-Planck equations. Here, interaction with the porous matrix due to (non-)DLVO forces is included as an additional transport mechanism. Fluid flow is described by incompressible Stokes equations with interaction energy as forcing term. Attachment and detachment processes are modeled by a surface reaction rate. The evolution of the underlying microstructure is captured by a level set function. The crucial point in completing this model is to set up appropriate boundary conditions on the evolving solid-liquid interface. Their derivation is based on mass conservation. As a result of an averaging procedure by periodic homogenization in a level set framework, on the macroscale we obtain Darcy's law and a modified averaged convection-diffusion equation with effective coefficients due to the evolving microstructure. These equations are supplemented by microscopic cell problems. Time- and space-dependent averaged coefficient functions explicitly contain information of the underlying geometry and also information of the interaction potential. The theoretical results are complemented by numerical computations of the averaged coefficients and simulations of a heterogeneous multiscale scenario. Here, we consider a radially symmetric setting, i.e., in particular we assume a locally periodic geometry consisting of circular grains. We focus on the interplay between attachment and detachment reaction, colloidal interaction forces, and the evolving microstructure. Our model contributes to the understanding of the effects and processes leading to porosity changes and pore clogging from a theoretical point of view.
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