Stochastic Analysis for Movement of Fine Particles in Porous Media

Abstract

The method of characteristics is used to develop analytical expressions for the transient one-dimensional movement of fine particles at the local scale. These solutions are applicable when the porous medium is homogeneous with a uniform steady-state velocity field, and under a local capture/detachment probability law for the fine particles. These local-scale solutions are then used for field-scale averaging operations, which involve prediction of the time-space evolutions of the moments of particle concentrations. At this large scale, the porous medium is represented by vertical, noninteracting, parallel pathways. Spatial variability, in the pore-water velocities and the net deposition, is assumed to exist in the horizontal directions. Further analysis leads to the development of analytical expressions for the univariate moments (to any arbitrary order) of the concentration of fine particles as functions of space and time. The initial and boundary conditions are allowed to be fairly general. Some hypothetical examples are considered to illustrate the utility of the method.