(564e) Predicting Colloidal Retention in Porous Media Using Hemispheres-in-Cell Model Under Environmental Conditions

The transport and deposition of colloidal particles in saturated granular porous media is important to various aquatic systems, such as riverbank filtration, colloid-facilitated contaminant transport, and pathogen removal in water treatment facilities. The deposition of suspended colloids onto granular surfaces during transport is governed by the physiochemical (and/or biological) interactions of particles, suspending fluid, and porous media. The process is well understood and relatively predictable for the case when no repulsion exists between colloids and medium surfaces (favorable conditions to deposition). However, for the case when colloid-surface repulsion exists, a condition that is typical in environmental contexts, predicting colloidal retention in porous media remains a major challenge, since no mechanistic, easily-accessed models yet exist. Mechanistic prediction of colloid transport and deposition in saturated porous media under favorable conditions (absent repulsive energy barriers) is made possible by idealizing the porous media as being comprised of unit bed elements (UBE) wherein the probability of colloid retention in a UBE is determined through particle trajectory (or flux) simulations. The trajectory (or flux) simulations are based on a mechanistic force and torque balance on the colloid within the flow field of the UBE. Among the various types of UBEs, the Happel sphere-in-cell has been widely used. The Happel sphere-in-cell consists of a solid sphere encircled by a concentric spherical fluid shell, where the thickness of the fluid shell is chosen such that the porosity of this unit cell (solid sphere and fluid shell) is equal to the actual porosity of a packed bed. The collector efficiency, which is the number of colloids that attach to the collector relative to the number of colloids that enter the unit cell, is determined from mechanistic simulations within the Happel sphere-in-cell. To make the power of these mechanistic simulations accessible to non-modelers, the simulations have been regressed to dimensionless parameters to provide phenomenological equations for estimation of collector efficiency. These equations serve as excellent predictive tools for colloid deposition in simple porous media when energy barriers to deposition are absent.

When energy barriers to deposition are present (unfavorable conditions), the mechanistic models operating in the context of the Happel sphere-in-cell predict zero retention; i.e., no colloids overcome the repulsive energy barrier (which is often computed from DLVO theory); whereas, experiments demonstrate that some retention does occur despite colloid-surface repulsion. To develop mechanistic predictors of retention under unfavorable conditions, the essential mechanisms of colloid retention must be identified and incorporated. Experiments indicate that the mechanisms driving retention under unfavorable conditions include: a) surface charge heterogeneity (or roughness) on the colloid or porous media grain surface, which acts to locally eliminate or reduce repulsion; b) wedging in grain to grain contacts or straining at pore throats too small to pass; c) retention without direct contact with the grain surface in zones of low fluid drag. Colloid retention in the presence of energy barriers by the above mechanisms has been demonstrated in mechanistic simulations in unit cells containing multiple grains in various packing arrangements (e.g. the dense cubic packing unit). These simulations corroborate expectations from experiments; however, to serve as a predictive framework, mechanistic simulations should provide good prediction in both the absence and presence of energy barriers. Unfortunately, the packing arrangements examined to date predict collector efficiencies in the absence of energy barriers that are far higher than those predicted by existing theory, as well as those determined from experiments. Furthermore, to serve as a predictive framework, these unit cells need to be capable of representing the spectrum of porosities encountered in environmental systems. The foundation for a general colloid filtration theory (for prediction in both the absence and presence of energy barriers) needs to meet at minimum the following three criteria: 1) ability to represent a range of porosities; 2) provide accurate prediction of collector efficiency in the absence of an energy barrier; 3) incorporate attributes to allow colloid retention in the presence of an energy barriers (e.g. grain to grain contacts). We propose a new unit cell geometry, namely the hemispheres-in-cell model, for the purpose of developing predictive capability of colloidal deposition in the presence of energy barriers. The hemispheres-in-cell model preserves the utilities provided in the Happel sphere-in-cell (e.g., capability of representing a spectrum of porosities, the outer fluid boundary shell serving as "watershed divide" between adjacent collectors in the flow field), but also incorporates geometries (e.g. grain-to-grain contact) that potentially allow colloid retention in the presence of an energy barrier. We will demonstrate that, in the absence of energy barriers to deposition, simulated collector efficiencies from the hemispheres-in-cell model agree favorably with existing Happel sphere-based model predictions, as well as experimental results, under a range of parameter conditions (colloid size, fluid flow velocity, porosity, etc.). We will also present preliminary results simulated from the hemispheres-in-cell model under conditions when repulsive energy barriers are present, by considering all the possible retention mechanisms as described above (i.e. heterogeneity, wedging in grain to grain contacts, and retention with attachment at zones of low fluid drag), and then compare with existing experimental observations.