## Modeling and Stochastic Analysis of Contaminant Transport in Soils and Aquifers

- Author(s): Hantush, Mohamed M
- Marino, Miguel A
- Shumway, Robert H
- et al.

## Abstract

The effort that led to this report is twofold. First, it deals with the development of fundamental transport equations and their solutions; they describe the effect of low-permeability zones on the motion and spread of contaminant plumes in high-permeability porous layers. Second, it concerns the development of an analytical multi phase-transport model that describes leaching of pesticides in soils and their fate and transport in groundwater. Using Monte Carlo simulations, the effect of stochastic precipitation, random adsorption, and random (bio )chemical reaction, on the probability distributions of the herbicide Simazine, is investigated under conditions typical to the City of Fresno in California.

The transport equations that are developed in Chapter 2 describe the capacitance of low permeability layers to store and release reactive constituents by diffusion and mechanical mixing. It is shown that under quasi-steady conditions and a mean flow parallel to the bedding, lateral solute transfer between thin layers is governed by the phenomenological first-order rate model, with a uniquely defined mass transfer rate coefficient, modified to account for reactive constituents. Two-dimensional analytical solutions are obtained in Chapter 3 for the first-order rate model in an infinite porous medium, using the methods of Fourier and Laplace transforms. and superposition. The solutions consider a rectangular area at the source with (l) an instantaneous release of a contaminant mass, and (2) an exponentially-decaying source concentration, applied at a fixed rate. Comparison of the theory with tracer chloride levels at the Borden aquifer indicates that the first-order rate model can describe adequately the dispersion process, on the basis of lateral or transverse diffusive mass transfer between layers.

In the second effort (Chapter 4), a multiphase transport model is developed with the objective of investigating the impact of soil environment, physical and (bio )chemical processes, especially, volatilization, crop uptake, and agricultural practices on long-term vulnerability of groundwater to contamination by pesticides. The soil is separated into root and intermediate vadose zones, each with uniform properties. Transport in each soil zone is modeled on the basis of complete mixing, by spatial averaging the related point multi phase-transport partial differential equation (i.e., linear-reservoir models). Transport in the aquifer, however, is modeled by a two-dimensional advection-dispersion transport equation, considering adsorption and firstorder decay rate. Vaporization in the soil is accounted for by assuming liquid-vapor phase partitioning using Henry's law, and vapor flux (volatilization) from the soil surface is modeled by diffusion through an air boundary layer. Sorption of liquid-phase solutes by crops is described by a linear relationship that is valid for first-order (passive) crop uptake. The model is applied to five pesticides (Atrazine, Brornacil, Chlordane, Heptachlor, and Lindane), and the potential for pesticides contamination of groundwater is investigated for sandy and clayey soils. Simulation results show that groundwater contamination can be substantially reduced for clayey soil environments, where bio(chemical) degradation and volatilization are most efficient as natural loss pathways for the pesticides. Also, uptake by crops can be a significant mechanism for attenuating exposure levels in groundwater, especially in a sandy soil environment and for relatively persisting pesticides. Further, simulations indicate that changing agricultural practices can have a profound effect on vulnerability of groundwater to mobile and relatively persisting pesticides.

The deterministic model is integrated with the Monte Carlo method in Chapter 5, to obtain the probability density function, mean, and standard deviation of the concentrations in groundwater, due to random adsorption and stochastic precipitation. The distribution coefficient, which is used to calculate the retardation factor for equilibrium adsorption, is assumed to be normally distributed, and the precipitation is modeled by fitting an ARIMA model to an observed time series. Consequently, the results of the analysis are also probability distribution functions for the concentration of the contaminant. which are useful representations for regulation and management purposes. The stochastic model is applied to data typical to the Fresno area in California, to assess the impact of herbicide Simazine on groundwater quality. The results show that predicted concentrations exhibit non-Gaussian probability distributions and standard deviations of the order of magnitude of the estimated means. Further, predictions made on the basis of averaged values of input parameters may substantially overestimate in transient, and later underestimate, the actual mean (ensemble) of the contaminant levels in groundwater. The results also highlight the importance of accounting for the mechanism of preferential flow.