ANALYTICAL SOLUTIONS FOR NONEQUILIBRIUM SOLUTE TRANSPORT IN 3-DIMENSIONAL POROUS-MEDIA

The movement of water and chemicals in soils is generally better descr ibed with multidimensional nonequilibrium models than with more common ly used one-dimensional and/or equilibrium models. This paper presents analytical solutions for non-equilibrium solute transport in semi-inf inite porous media during steady unidirectional flow. The solutions ca n be used to model transport in porous media where the liquid phase co nsists of a mobile and an immobile region (physical non-equilibrium) o r where solute sorption is governed by either an equilibrium or a firs t-order rate process (chemical non-equilibrium). The transport equatio n incorporates terms accounting for advection, dispersion, zero-order production, and first-order decay. General solutions were derived for the boundary, initial, and production value problems with the help of Laplace and Fourier transforms. A comprehensive set of specific soluti ons is presented using Dirac functions for the input and initial distr ibution, and/or Heaviside or exponential functions for the input, init ial, and production profiles. A rectangular or circular inflow area wa s specified for the boundary value problem while for the initial and p roduction value problems the respective initial and production profile s were located in parallelepipedal, cylindrical, or spherical regions of the soil. Solutions are given for both the volume-averaged or resid ent concentration as well as the flux-averaged or flowing concentratio n. Examples of concentration profiles versus time and position are pre sented for selected problems. Results show that the effects of non-equ ilibrium on three-dimensional transport are very similar to those for one-dimensional transport.