Theoretical development and analytical solutions for transport of volatile organic compounds in dual-porosity soils

Abstract

Predicting the behavior of volatile organic compounds in soils or sediments is necessary for managing their use and designing appropriate remedial systems to eliminate potential threats to the environment, particularly the air and groundwater resources. In this effort, based on continuity of mass flux, we derive a mass flux boundary condition of the third type in terms of physically based mass transfer rate coefficients, describing the resistance to mass inflow of the soil–air interface, and obtain one-dimensional analytical solutions for transport and degradation of volatile organic compounds in semi-infinite structured soils under steady, unsaturated flow conditions. The advective–dispersive mass balance formulation allows for mobile–immobile liquid phase and vapor diffusive mass transfer, with linear equilibrium adsorption and liquid–vapor phase partitioning in the dynamic and stagnant soil regions. The mass transfer rate coefficients of volatile organic chemicals across the soil–air interface are expressed in terms of solute properties and hydrodynamic characteristics of resistive soil and air-boundary layers. The solutions estimate solute vapor flux from soil surface and describe mobile-phase solute concentration as a function of depth in the soil and time. In particular, solutions were derived for: (1) zero-initial concentration in the soil profile subject to a continuous and pulsed source at the soil surface; and (2) depletion from the soil following an initially contaminated soil profile. Sensitivity analysis with respect to different dimensionless parameters is conducted and the effect on solute concentration and vapor flux of such parameters as volatilization mass transfer velocity relative to infiltration, soil Peclet number, biochemical decay, and diffusive mass transfer into the immobile phase, is plotted and the results are discussed. The mass transfer rate coefficients and the analytical solutions are applied to simulate transport of an example volatile organic compound in an aggregated soil. The simulated results indicate that macropore-aggregate vapor phase diffusion may profoundly impact transport of volatile compounds in aggregated soils.