A kinetic model for cell density dependent bacterial transport in porous media

Abstract

A kinetic transport model with the ability to account for variations in cell density of the aqueous and solid phases was developed for bacteria in porous media. Sorption kinetics in the advective-dispersive-sorptive equation was described by assuming that adsorption was proportional to the aqueous cell density and the number of available sites on the solid phase, whereas desorption was proportional to the density of sorbed cells. A numerical solution to the model was tested against laboratory column data, and the performance was compared with that of a two-site model. The kinetic model described the column data as well as the two-site model did, but the highest efficiencies of both models were associated with experiments with the smallest sorption. Furthermore, the kinetic model accounted for cell density dependent sorption, as demonstrated by fair predictions of bacterial transport at one cell density when using parameters obtained at another cell density. 1978; Shales and Kumarasingham, 1987; Reynolds et al., 1989; Gannon et al., 1991; Fontes et al., 1991; Tan et al., 1991; Trevors et al., 1991], and some have used mathemat-Paper number 94WR01725. 0043-1397/94/94WR-01725505.00 ical models to generalize the results [Taylor and Jaffd, 1990; Lindqvist and Bengtsson, 1991; Hornberger et al., 1992; Lindqvist and Enfield, 1992b]. The models describe bacterial movement by the advective-dispersive equation modified to account for retention processes, growth, and mortality (see Corapciouglu and Haridas [1984] and Harvey [1991] for a discussion of these and additional processes). The cell velocity may be retarded compared with the water velocity by several retention processes, namely, sorption, physical straining, sedimentation, and interception. These processes lead to a distribution of cells between the solid phase of the medium and the pore water. The growth and mortality rates may be different in the solid and aqueous habitats [DeIaquis et al., 1989], and the distribution of cells is affected by organic matter content on the sand and in the water [Scholl and Harvey, 1992], nutrient concentrations [Bengtsson, 1989; Lindqvist and Bengtsson, 1991], cell density [Lindqvist and Enfield, 1992b], physiological status [Fletcher, 1977], ionic strength [Gannon et al., 1991; Fontes et al., 1991], pH [Scholl and Harvey, 1992], grain size [Fontes et al., 1991; Lindqvist and Enfield, 1992b], and oxyhydroxide coatings

Bacterial transport in porous media: New aspects of the mathematical model

“…3 at different inlet cell concentrations (C b0 ). It shows that bacterial transport is enhanced at higher cell concentration which is also found experimentally by Tan et al [14] and Lindqvist et al [37], respectively. This is because of shortage of time in saturation of finite retention sites, i.e.…”

Processes in Microbial Transport in the Natural Subsurface

“…Therefore, in unstructured models the biomass is a fully penetrable volumeless component which assumes that a linear relation exists between mass of substrate consumed and mass of biomass produced and that no diffusion limitations affect the transfer of substrate mass from solution into the biomass. This approach has been taken in model construction [25,144,159,162], in column studies that focus on bacterial transport [69,120] and in intermediate-scale flow cell studies that focus on active degradation and growth and coupled transport [130,169]. For instance, Macquarrie et al [162] used this approach in treating biomass involved in aerobic degradation as a volumeless species undergoing transport, with equilibrium partitioning of biomass between aqueous and attached phases.…”

“…Murphy et al [169] extend the linear reversible model to include non-linear dependence of the rate coefficients on ionic strength of solution, manifest in intermediate-scale experiments. Tan et al [120], Lindqvuist et al [69], and Saiers and Hornberger [105] all introduce the classical site-saturation limiting factor on the attachment rate coefficient, in order to account for potential depletion of available surface sites as attached microbe densities increase, which may occur when aqueous microbes cannot attach to attached microbes. Ginn [43] modeled non-Markovian (i.e., residence-time dependent) attachment/detachment kinetics apparent in experiments of McCaulou et al [165] using the exposure-time approach of Ginn [153], as described below.…”

Modeling the effects of systematic variation in ionic strength on the attachment kinetics of Pseudomonas fluorescens UPER‐1 in saturated sand columns

“…After finding certain distinct modes of transport and attachment of bacteria we modeled their behavior and calculated values for more than one attachment kinetics parameter. We extend the existing first-or second-order kinetic models [Tan et al, 1994;Lindqvist et al, 1994] to include an intermediate-order kinetics ("ripening," attachment rate increases with time), which is distinct from the other two.…”