Validity of the Local Equilibrium Assumption for Modeling Sorbing Solute Transport Through Homogeneous Soils

TLDR

Sorption during reactive solute transport in porous media is commonly modeled with equilibrium or kinetic approaches, and many models assume local chemical equilibrium for its conceptual and mathematical simplicity, despite the existence of physical and chemical nonequilibrium formulations. This paper presents quantitative criteria to assess the validity of the local equilibrium assumption for one‑dimensional, steady flow through homogeneous soils. The authors derive time‑moment formulas for breakthrough curves that can be applied to both equilibrium and various nonequilibrium models, enabling comparison of their predictions without solving the full transport equations. The resulting criteria demonstrate that key system parameters such as seepage velocity, dispersion, distribution coefficient, sorption rate, and boundary conditions strongly affect whether local equilibrium holds.

Abstract

Sorption processes that occur during reactive solute movement through porous media can be modeled using either an equilibrium or kinetic approach. Because of the resulting conceptual and mathematical simplification, many transport models assume local chemical equilibrium is valid for describing sorption reactions. This paper presents quantitative criteria to assess the validity of the local equilibrium assumption for one‐dimensional, steady flow through homogeneous soils. A method is described whereby formulas for solute breakthrough curve time moments can be determined without knowledge of the nalytical solution to the mass transport model. This method is applied to several commonly used nonequilibrium formulations as well as the standard linear equilibrium model. The formulations considered include both the physical nonequilibrium models where the sorption rate is controlled by diffusive solute transfer between mobile and stagnant fluid zones and the chemical nonequilibrium models where the overall sorption rate is governed by the rate of reaction at the soil‐solution interfaces. Criteria for local equilibrium to be valid are derived by comparing the time moment formulas for the nonequilibrium and equilibrium models. These criteria explicitly show that basic system parameters (e.g., seepage velocity, dispersion coefficient, distribution coefficient, sorption rate, boundary conditions) have a significant influence on the attainment of local equilibrium.