Mathematical Modeling of Fines Migration snd Clogging in Porous Media
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Mathematical Modeling of Fines Migration and Clogging in Porous Media Guido Kampel 87 Pages Directed by Dr. Guillermo H. Goldsztein A porous medium is a material that contains regions filled with fluid embedded in a solid matrix. These fluid filled regions are called pores or voids. Suspensions are fluids with small particles called fines. As a suspension flows through a porous material, some fines are trapped within the material while others that were trapped may be released. Filters are an example of porous media. We model filters as networks of channels. As a suspension flows across the filter, particles clog channels. We assume that there is no flow through clogged channels. In the first part of this thesis, we compute a sharp upper bound on the number of channels that can clog before fluid can no longer flow through the filter. Soil mass is another example of porous media. Fluid in porous media flows through tortuous paths. This tortuosity and inertial effects cause fines to collide with pore walls. After each collision, a particle looses momentum and needs to be accelerated again by hydrodynamic forces. As a result, the average velocity of fines is smaller than that of the fluid. This retardation of the fines with respect to the fluid may lead to an increase of the concentration of fines in certain regions which may eventually result in the plugging of the porous medium. This effect is of importance in flows near wells where the flow has circular symmetry and thus, it is not macroscopically homogeneous. In the second part of this thesis we develop and analyze a mathematical model to study the physical effect described above. In the third and last part of this thesis we study particle migration and clogging as suspension flows through filters by means of numerical simulations and elementary analysis. We explore the effect that network geometry, probability distribution of the width of the channels and probability distribution of the diameter of the particles have on the performance of filters.