A Mixing-Cell Model for Assessment of Contaminant Transport in the Unsaturated Zone Under Steady-State and Transient Flow Conditions

Abstract

A one-dimensional model for water flow and solute transport in the unsaturated zone under steady-state or transient flow conditions was developed from the principles of the mixing-cell model. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations (ODE) describe the material (water and solute) balance within each cell. Water flow equations are derived from the continuity equation assuming that unit-gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material-specific moisture characteristic curves. Solute transport processes included explicit treatment of advective processes, first-order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. The system of ODEs was solved using a forth-order Runge-Kutta algorithm coupled with adaptive step size control. Computer run times for transient flow and solute transport were typically several seconds on a 2-GHz Intel Pentium IV^® desktop computer. The model was benchmarked against analytical solutions and finite-element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing-cell model and the PDE models were typically less than 2%.