Diffusive Loss of Non-Aqueous Phase Organic Solvents from a Disk Source

Abstract

<p> Matrix diffusion from planar fractures was studied both mathematically and through physical model experiments. A conceptual model was developed based on previous work by Parker (1994) and Crank (1956). Mathematical models were developed to simulate diffusion from 2D and 3D instantaneous disk sources and a 3 D continuous disk source. The models were based on analytical solutions previously developed by Carslaw and Jaeger (1959). Analytical solution is not available for the total mass diffused into the porous matrix for a 3D continuous disk source, and it was therefore calculated through the summation of the iso-concentration lines, which were assumed to be a semi-spherical shape.</p> <p> The mathematical simulations indicated that the 2D scenario produces significantly different results from the 3D scenario, the time for mass disappearance is significantly larger for continuous sources than for instantaneous sources, the normalized concentration generally decreased over time for instantaneous sources while it increased over time for continuous sources, diffusion rates decrease significantly over time and space, and the normalized mass loss from the source zone never reaches 1 for continuous sources due to the semi-infinite integral. The simulations also showed that disappearance times increase exponentially with increasing source radii and matrix porosity, and decrease with increasing aqueous-phase NAPL solubilities.</p> <p> The observations from the physical model experiments were very close to the simulated data at z = 0, validating the 3D mathematical models for this elevation. A plot of the observed vs simulated data did not reveal any trends, indicating that the majority of the differences can be attributed to experimental error. The experimental concentrations were below the method detection limit at depths of 3 and 6 cm however, indicating that either the experiments should have been conducted over a longer time period or a more sensitive analytical method should have been employed, to enable model validation at these depths.</p>