Nonequilibrium and equilibrium sorption with a linear sorption isotherm during mass transport through an infinite porous medium: Some analytical solutions

Analytical solutions have been developed for the problem of solute transport in a steady, three dimensional field of groundwater flow with non-equilibrium mass transfer of a radioactive species between fluid and solid phases and with anisotropic hydrodynamic dispersion. Interphase mass transport is described by a linear rate expression. Solutions are presented also for the case of equilibrium distribution of solute between fluid and solid phases. Three types of release from a point source were considered: instantaneous release of a finite mass of solute, continuous release at an exponentially decaying rate, and release for a finite period of time. Graphical displays of computational results for point-source solutions show the expected variation of sorptive retardation effects progressing from the case of no sorption, through several cases of non-equilibrium sorption, to the case of equilibrium sorption. The point-source solutions can be integrated over finite regions of a space to provide analytical solutions for regions of solute release having finite spatial extents and various geometrical shapes, thus considerably extending the utility of the point-source solutions.