Governing Equations for Particle Transport in Porous Media: Fid-Bau Portal

Governing Equations for Particle Transport in Porous Media

Corapcioglu, M. Yavuz / Abboud, Nelly M. / Haridas, A.

Abstract The migration and capture of particles, such as colloidal materials and microorganisms, through porous media occur in fields as diverse as water and wastewater treatment, well drilling, and in various liquid-solid separation processes. In liquid waste disposal projects, suspended solids can cause the injection well to become clogged, and groundwater quality can be endangered by suspended clay and silt particles migrating to the formation adjacent to the wellbore. In addition to reducing the permeability of the soil, mobile particles can carry groundwater contaminants adsorbed onto their surfaces. Furthermore, as in the case of contamination from septic tanks, the particles themselves may be pathogens, i.e., bacteria and viruses. In this chapter, the equations governing the transport and capture of suspended solid particles have been studied in two categories. The first category includes transport and deposition of particles in an established porous medium. In this category, following the review of governing equations and various capture mechanisms in deep bed filters, the transport equation for microbial particles has been studied. For microbial particles, the governing equation for bacterial transport is coupled with a transport equation for the bacterial nutrient present in the suspension. The deposition and declogging mechanisms are incorporated into the model as a rate process for bacteria and as an equilibrium partitioning for viruses. Formation of a cake by deposition of solid particles on a filter cloth or on a previous cake constitutes the second category. Following a literature survey, a governing equation for cake thickness is obtained by averaging the conservation of mass equation for solid particles along cake thickness. Then, the resulting equation is solved with known average porosity functions. In addition to the balance equation for solid particles, the fluid flow equation has been averaged and solved simultaneously to obtain an expression for cake thickness. Furthermore, temporal and spatial variation of pore liquid pressure across filter cake is obtained with a variable total stress expression.