Filtration in a Porous Granular Medium: 2. Application of Bubble Model to 1-D Column Experiments

Abstract

This paper describes the formulation of a quasi-1-D network model, referred to as the 'bubble model', and its application for simulating particle transport and filtration through a granular filter bed. The model comprises a series of homogeneous sites linked through bundles of cylindrical bonds that represent flow pathways through distributions of pores and pore throats. This model incorporates pore scale processes of particle sieving and infiltration are based on numerical simulations described in a companion paper. The modeling of infiltration is further refined based on detailed experimental observations and measurements of the filtration of a dilute suspension of acrylic particles through a column of glass beads reported by Yoon et al. (2005 Water Resour. Res., to appear). Their data distinguish (a) between the collection of particles on grain surfaces and at grain-tograin contact points, and (b) between particles that are fully entrapped and those that are hindered (temporarily collected) and can later become detached. These effects are represented by two parameters that characterize the probability of attachment and are linked to the surface roughness of the grains; one that describes the minimum particle size that can be fully entrapped, and one that describes the detachment rate. These parameters can be readily calibrated from conventional measurements of effluent concentration and effluent particle size distribution. Detailed comparisons with the data reported by Yoon et al.show that the proposed bubble model is able to achieve reliable predictions of the spatial distribution of particles within the filter bed following phases of particle injection and washing.

Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging

“…The paper also proposes simple empirical functions for the rejection efficiency based on the numerical simulations. These are used in accounting for the conservation of mass within a network model of filtration which is presented in a companion paper (Kim and Whittle, 2005a).…”

“…The Authors propose semi-empirical functions for interpreting the numerical simulations of infiltration with mono-disperse particles including the particle collection rate and effects of mounding on the pore transmissivity. A companion paper (Kim and Whittle, 2005a) applies these results in network model simulations and compares these numerical predictions with detailed experimental observations of particle transport in a granular filter bed.…”

“…These 'rejected particles' are filtered through a different mechanism, and must be accounted for in the overall network model of filtration (cf. Kim and Whittle, 2005a). The rejection efficiency for the model pore is defined as η reject = V reject /V in .…”

Filters. The Number of Channels That Can Clog in a Network

“…Donaldson, Baker, and Carrol in 1977 [8] were the first to use networks to study particle transport within porous media. The clogging of particles has been studied in networks with different geometries including bundles of parallel tubes [8], square networks [14,16,21], triangular networks [3,25], cubic networks [2,17,29], bubble models [6,20], and the so-called three-dimensional physically representative networks [1,30].…”

Clogging of Multigraphs as Toy Models of Filters

“…in networks with different geometries including bundle of parallel tubes [8], square networks [14,16,23], triangular networks [3,27], cubic networks [2,17,33], bubble models [6,22], and the so-called three-dimensional physically representative networks [1,34].…”