Particle transport in flow through porous media: advection, longitudinal dispersion, and filtration

Abstract

A theoretical and experimental investigation of the transport parameters of particles flowing through porous media has been made. These parameters are the particle advective velocity, longitudinal dispersion coefficient, and filter coefficient. Both theoretical and experimental results are limited to flows with low Reynolds number (linear, laminar flow) and high Peclet number (advection dominates diffusion). The theoretical development used dimensionless numbers to define the transport parameters and incorporated them into an advective-dispersion equation describing particle transport. A relationship for unfavorable filtration due to repulsive double layer interactions is proposed. A solution to the complete advective-dispersion equation for particle transport was derived for the case of a constant filter coefficient. This solution when compared to a similar solution previously derived for solute transport, showed that for small filtration the solutions were identical except for the exponential decay factor due to filtration. A numerical model was developed for the case of a variable filter coefficient. Flow experiments were conducted in a 1.5 m vertical column with sand (geo. mean diameter = 381 micron), with suspensions of polystyrene latex particles (three cases, mean diameter = 0.1, 1.4 and 2.8 micron), and with NaCl as the electrolyte (0.4 mM < Ionic strength < 2.1 mM). The range of Peclet number studied was 1.26 x 10^4 to 2.00 x 10^6. The measurement of the particle concentrations during passage of a displacement front provided the necessary data to determine the particle transport parameters. The particle advective velocities for the three different sized particles was found to range approximately from 0 to 5.4% greater than the solute velocity, and these values were within a few percent of predictions based on particle and pore radii. The longitudinal dispersion coefficient for the three different sized particles was found to be a function of only the advective velocity of the particles and grain diameter of the porous bed which confirmed the dimensional analysis argument and closely matched previous solute work. A dimensional analysis argument for the relationship between the favorable and unfavorable filter coefficient was proposed to be a function of the ratio of the particle diffusion length of an advecting particle and the double layer thickness (which in turn depends on the ionic strength of the water). A wide range of filtration data (Brownian to advective particles) was empirically fitted using this dimensionless number. The effects of ionic strength on particle transport were found to be either minimal or separable from the hydraulic variables. For advection, effects of changing ionic strength were analyzed as changes in the effective particle radius and calculations made using this apparent particle radius matched experimental results. For dispersion, an increase of a factor of 6 in the ionic strength increased the longitudinal dispersion by a factor of 1.2.

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