A Simple Model of Soil‐Gas Concentrations Sparged into an Unlined Unsaturated Zone

Abstract

We derive an analytical model of soil‐gas contamination sparged into an imlined unsaturated zone. A nonaqueous phase liquid (NAPL) source lies in the capillary fringe, with an exponential sparge constant within the radius of influence and a constant ambient evaporation rate beyond. Advection, diffusion, and dispersion govern the conservative soil‐gas response, expressed as a quasi‐steady series solution with radial Bessel and hyperbolic vertical dependence. Simulations suggest that sparged contamination initially spreads beyond the radius of influence down a negative gradient. This gradient eventually reverses, leading to a subsequent influx of ambient contamination. Soil‐gas concentrations accordingly reflect slowly varying source conditions as well as slowly varying diffusive transport through the radius of influence. The two time scales are independent: One depends on NAPL, airflow, and capillary fringe characteristics, the other on soil moisture, gaseous diffusivity, and unsaturated zone thickness. The influx of ambient contamination generates an asymptotic soil‐gas concentration much less than the initial source concentration. The simple model is applied to a pilot‐scale sparging study at Plattsburgh Air Force Base in upstate New York, with physically plausible results.