A stochastic approach for describing convective‐dispersive solute transport in saturated porous media

Abstract

A stochastic approach is used to model convective‐dispersive transport of nonreactive solutes in homogeneous, isotropic, water‐saturated porous media during steady, one‐dimensional water flow at a volumetric rate Q and solute application at a rate of Mh ( t ). The expected solute concentration C ( x, t ) is shown to be C ( x, t ) = ( M / Q )∫ h ( u ) ƒ( t − u; x ) du , where t is time and ƒ( t; x ) is the probability density function (pdf) of the first‐passage time for the solute at position x . This expression yields known solutions for two cases examined (instantaneous release and continuous input) where closed form analytical solutions exist. This stochastic approach leads to statistically valid estimates and confidence intervals for the drift (velocity) and diffusion (dispersion) coefficients under the assumption that ƒ( t; x ) is the first passage time pdf for Brownian motion of solute particles with a positive drift.