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.

Una nueva interpretación cuantitativa de curvas de avance con mesetasy largos limbos de recesión a partir de ensayos de trazadoren el acuífero cárstico artesiano de Stuttgart, Alemania

“…The two-region non-equilibrium model (2RNE; Toride et al 1993) was initially developed for porous media, where partitioning of solutes between mobile water in the centres of the large pores and immobile water in fine pores or adsorbed to mineral surfaces can be observed. Field and Pinsky (2000) demonstrated that this model could also be applied to karst aquifers, where rapid flow velocities occur in the centres of active conduits (mobile fluid region), while flow velocities are much slower at the conduit margins, in adjacent fractured rock volumes, but also in eddies and pools, and in the pores of cave sediments (immobile fluid region).…”

“…2). Reactive processes such as retardation and degradation, can also be included (Toride et al 1993) and were already implemented for karst aquifers (Geyer et al 2007), but are not relevant in this case. In karst conduits, dispersion is often most relevant in the flow direction so that one-dimensional models represent a legitimate simplification.…”

Solutions to the One‐Dimensional ADR in Literature

“…Boundary condition 2 Genuchten and Alves (1982, p. 31 Genuchten and Alves (1982) pp. 32 Genuchten and Alves (1982, p. 63 Genuchten and Alves (1982, p. 60 Toride et al (1993) Initial condition (t = 0)…”

“…32 Genuchten and Alves (1982, p. 63 Genuchten and Alves (1982, p. 60 Toride et al (1993) Initial condition (t = 0)…”

Surface and Subsurface Solute Transport Properties at Row and Interrow Positions

“…It is directly affected by heterogeneity in flow and can, therefore, help to assess nonuniformity in surface and soil profile flow introduced by crop production practices. Solute dispersivity can be determined by fitting a solution of the onedimensional convective-dispersive equation (CDE) to observed soil solute resident concentrations established in response to controlled boundary conditions (Toride et al, 1993). The model has been successfully applied at both the column scale (Wierenga and van Genuchten, 1989) and the field scale (Biggar and Nielsen, 1976;Roth et al, 1991).…”