A comprehensive set of analytical solutions for nonequilibrium solute transport with first‐order decay and zero‐order production

Abstract

Solute transport in the subsurface is often considered to be a nonequilibrium process. Predictive models for nonequilibrium transport may be based either on chemical considerations by assuming the presence of a kinetic sorption process, or on physical considerations by assuming two‐region (dual‐porosity) type formulations which partition the liquid phase into mobile and immobile regions. For certain simplifying conditions, including steady state flow and linear sorption, the chemical and physical nonequilibrium transport models can be cast in the same dimensionless form. This paper presents a comprehensive set of analytical solutions for one‐dimensional nonequilibrium solute transport through semi‐infinite soil systems. The models involve the one‐site, two‐site, and two‐region transport models, and include provisions for first‐order decay and zero‐order production. General solutions are derived for the volume‐averaged (or resident) solute concentration using Laplace transforms assuming both first‐ and third‐type inlet conditions, and arbitrary initial conditions, input solute concentrations, and solute production profiles. The solutions extend and generalize existing solutions for equilibrium and nonequilibrium solute transport. The general solutions are evaluated for some commonly used input and initial conditions, and zero‐order production profiles. Expressions for the flux‐averaged concentration are derived from the general and specific solutions assuming a third‐type inlet condition. Typical examples of calculated concentration distributions resulting from several sets of initial and input conditions and zero‐order production functions are also presented and briefly discussed.