A Stochastic Model for Colloid Transport and Deposition

Authors: Bradford, Scott; TORIDE, NOBUO - MIE UNIVERSITY, JAPAN

Submitted to: Journal of Environmental Quality
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/1/2007
Publication Date: 7/17/2007
Citation: Bradford, S.A., Toride, N. 2007. A stochastic model for colloid transport and deposition. Journal of Environmental Quality. Vol 36:1346-1356

Interpretive Summary: A computer model was developed to simulate the transport and retention of colloids, such as disease causing microorganisms, in soil and aquifer environments. The model is specially designed to test various assumptions about colloid transport with regard to variations in colloid chemical properties, colloid size, water velocity, and soil pore space. Results indicate that variations in these properties can produce colloid transport behavior that is not consistent with conventional modeling approaches, but has been frequently observed in experimental studies. Analysis of representative colloid transport data with this model indicates that variations in colloid chemical properties and colloid size could not explain this observed behavior, but that variations in velocity and soil pore space size may provide an alternative explanation.

Technical Abstract: Profiles of retained colloids in porous media have frequently been observed to be hyper-exponential or nonmonotonic with transport depth under unfavorable attachment conditions, whereas filtration theory predicts an exponential profile. In this work we present a stochastic model for colloid transport and deposition that allows various hypotheses for such deviations to be tested. The model is based upon the conventional advective dispersion equation that accounts for first-order kinetic deposition and release of colloids. One or two stochastic parameters can be considered in this model including the deposition coefficient, the release coefficient, and the average pore water velocity. In case of one stochastic parameter, the probability density function (PDF) is characterized using log-normal, bimodal log-normal, or a simple two species/region formulation. When two stochastic parameters are considered then a joint log-normal PDF is employed. Simulation results indicated that variations in the deposition coefficient and the average pore water velocity can both produce hyper-exponential deposition profiles. Increasing the variance of the release coefficient primarily influenced the retention close to the injection point, whereas increasing the variance of the deposition coefficient primarily influenced the deposition behavior at greater transport distances. Bimodal formations for the PDF were able to produce hyper-exponential profiles with much lower variances in the deposition coefficients. The shape of the deposition profile was found to be very sensitive to the correlation of deposition and release coefficients. Application of the developed stochastic model to a particular set of colloid transport and deposition data, indicated that chemical heterogeneity of the colloid population could not fully explain the observed behavior. Alternative interpretations were therefore proposed based on variability of the colloid size distribution, the pore size distribution, and the pore velocity distribution.