Growth of a biofilm in a porous medium reduces the total volume and the average size of the pores. The change in the pore size distributions is easily quantified when certain geometric assumptions are made. Existing models of permeability or of relative permeability can be manipulated to yield estimates of the resulting reduction in permeability as a function of biofilm thickness. The associated reductions in porosity and specific surface can be estimated as well. Based on a sphere model of the medium, the Kozeny‐Carman permeability model predicts physically realistic results for this problem. Using a cut‐and‐random‐rejoin‐type model of the medium, the permeability model of Childs and Collis‐George yields qualitatively reasonable results for this problem, as does a generalization of the relative permeability model of Mualem. Permeability models of Kozeny‐Carman and of Millington and Quirk lead to unrealistic results for a cut‐and‐random‐rejoin‐type medium. The Childs and Collis‐George and the Mualem models predict that the permeability reduction for a given volume of biomass is greatest when the porous medium has uniform pore sizes.

1481 1482 BAVEYE ET AL.: COMMENTARY biodegradation in aquifer recharge, Ground Water, 18, 236-243, 1980. Taylor, S. W., and P. R. Jail6, Biofilm growth and the related changes in the physical properties of a porous medium, 1, Experimental investigation, Water Resour. Res., 26(9), 2153-2159, 1990a. Taylor, S. W., and P. R. Jaff6, Biofilm growth and the related changes in the physical properties of a porous medium, 3, Dispersivity and model verification, Water Resour. Res., 26(9), 2171-2180, 1990b. I'aylor, S. W., P. C. D. Milly, and P. R. Jaff6, Biofilm growth and the related changes in the physical properties of a porous medium, 2, Permeability, Water Resour. Res., 26(9), 2161-2169, 1990.Vandevivere, P., and P. Bayeye, Saturated hydraulic conductivity reduction caused by aerobic bacteria in sand columns, Soil Sci. Soc. Am. J., in press, 1992a.Vandevivere, P., and P. Baveye, Effect of bacterial extracellular polymers on the saturated hydraulic conductivity of sand columns, App!. Environ. Microb., in press, 1992b.Widdowson, M. A., Comment on "An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers"

A model describing the transport of substrate and biomass in porous media is formulated which accounts for the transport, growth and decay of biomass suspended in the water phase and attached to the solid matrix as a biofilm. Interphase transport of biomass between the water phase and attached biofilm phase due to fluid mechanical shear and filtration is considered as well. Special attention is given to changes in the porosity, permeability, and dispersivity resulting from the biofilm altering the microscopic geometry of the pore space. A numerical solution to the governing equations is obtained by the finite element method. The model is calibrated and verified against experimental data. An application is presented which assesses the effects of pulsed substrate loading, flow rate, and flow duration on the clogging of porous media by biomass.

In the first part of this paper the change in dispersivity resulting from the growth of a biofilm in a porous medium is derived from an existing model of dispersivity and a cut‐and‐random‐rejoin‐type model of the pore geometry. The change in dispersivity due to a biofilm is also estimated from experimental data. Tracer experiments were conducted in biofilm column reactors and dispersion coefficients estimated by solving the inverse solute transport problem by nonlinear, least squares regression. Due to the presence of the biofilm in the porous media, solute flux into the biofilm is an important transport process and is given special attention. Both the dispersivity model and experimentally estimated dispersivities show order of magnitude increases in dispersivity as a result of significant biofilm growth. In the second part of the paper the models for the biofilm‐affected permeability, porosity, and specific surface derived in a companion paper (Taylor et al., this issue) are verified using data from biofilm column reactors. These models are used to parameterize an equation describing the transport of substrate in the experimental columns. Numerical simulations were performed and compared to observed substrate data. Results show that the models for permeability and porosity can be used to make estimates of these parameters, while the model for specific surface appears to be inadequate.

An experimental investigation was conducted to quantify the permeability reduction caused by enhanced biological growth in a porous medium. Studies were conducted using sand‐packed column reactors for which variations in piezometric head, substrate concentration, and biomass measured as organic carbon were monitored in space and time. Methanol was used as a growth substrate. Permeability reductions by factors of order 10−3 were observed. The data show that a limit on permeability reduction exists, having a magnitude of 5 × 10−4 in the present study. The limit on permeability reduction and the existence of high densities of bacteria in substrate depleted zones are explained with an open pore model. Permeability reduction was observed to correlate well with biomass density for values less than about 0.4 mg/cm3, and exhibited independence at higher densities.