Analyzing Diffusion by Analogy with Consolidation

Abstract

The analogy between Terzaghi’s governing equation for consolidation and Fick’s governing equation for diffusion (i.e., Fick’s second law) is used as the basis for analyzing diffusion of aqueous miscible solutes (e.g., contaminants) in saturated porous media. Based on this analogy, one-dimensional analytical (closed-form) solutions to the consolidation equation can be transformed into one-dimensional analytical solutions to Fick’s second law. The general methodology for transforming the analytical solutions in terms of solute concentration, solute mass flux, and cumulative solute mass is presented, and the concepts of degree of diffusion and average degree of diffusion are introduced. Analytical solutions are presented for a variety of initial and boundary conditions. Application of the methodology is illustrated through an example analysis for a problem involving matrix diffusion associated with pump-and-treat remediation. The example analysis illustrates the ability to analyze relatively complex problems involving diffusive solute transport based on the analogy between consolidation and diffusion.