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United States Department of Agriculture

Agricultural Research Service

Title: Combined physical and chemical nonequilibrium transport model: Analytical solution, moments, and application to colloids

item Leij, Feike -
item Bradford, Scott

Submitted to: Journal of Contaminant Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: September 11, 2009
Publication Date: November 20, 2009
Repository URL:
Citation: Leij, F.J., Bradford, S.A. 2009. Combined physical and chemical nonequilibrium transport model: Analytical solution, moments, and application to colloids. Journal of Contaminant Hydrology. 110(3-4)87-99.

Interpretive Summary: Pathogenic microorganisms that are found in animal waste pose a risk to water and food resources. Recent experimental evidence indicates that the migration and fate of pathogenic microorganisms in soil and groundwater environments is enhanced in low velocity regions of the soil. In this work we develop a mathematical model to account for these observations. The influence of variables that are used in this model on colloid (such as microorganisms) transport and retention in soil is demonstrated. This modeling framework and findings will be of use to scientists, engineers, and regulators concerned with predicting and modeling the transport and fate of a variety of colloid and colloid-associated contaminants in the environment.

Technical Abstract: The transport of solutes and colloids in porous media is influenced by a variety of physical and chemical nonequilibrium processes. A combined physical–chemical nonequilibrium (PCNE) model was therefore used to describe general mass transport. The model partitions the pore space into “mobile” and “immobile” flow regions with first-order mass transfer between these two regions (i.e, “physical” nonequilibrium or PNE). Partitioning between the aqueous and solid phases can either proceed as an equilibrium or a first-order process (i.e, “chemical” nonequilibrium or CNE) for both the mobile and immobile regions. An analytical solution for the PCNE model is obtained using iterated Laplace transforms. This solution complements earlier semi-analytical and numerical approaches to model solute transport with the PCNE model. The impact of selected model parameters on solute breakthrough curves is illustrated. As is well known, nonequilibrium results in earlier solute breakthrough with increased tailing. The PCNE model allows greater flexibility to describe this trend; for example, a closer resemblance between solute input and effluent pulse. Expressions for moments and transfer functions are presented to facilitate the analytical use of the PCNE model. Contours of mean breakthrough time, variance, and spread of the colloid breakthrough curves as a function of PNE and CNE parameters demonstrate the utility of a model that accounts for both physical and chemical nonequilibrium processes. The model is applied to describe representative colloid breakthrough curves in Ottawa sands reported by Bradford et al. (2002). An equilibrium model provided a good description of breakthrough curves for the bromide tracer but could not adequately describe the colloid data. A considerably better description was provide by the simple CNE model but the best description, especially for the larger 3.2-µm colloids, was provided by the PCNE model.

Last Modified: 4/18/2015
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