Approximate analytical model for transient transport and oxygen-limited biodegradation of vapor-phase petroleum hydrocarbon compound in soil

Volatile organic compounds (VOCs) contamination may occur in subsurface soil due to various reasons and pose great threat to people. Petroleum hydrocarbon compound (PHC) is a typical kind of VOC, which can readily biodegrade in an aerobic environment. The biodegradation of vapor-phase PHC in the vadose zone consumes oxygen in the soil, which leads to the change in aerobic and anaerobic zones but has not been studied by the existing analytical models. In this study, a one-dimensional analytical model is developed to simulate the transient diffusion and oxygen-limited biodegradation of PHC vapor in homogeneous soil. Laplace transformation and Laplace inversion of the Talbot method are adopted to derive the solution. At any given time, the thickness of aerobic zone is determined by the dichotomy method. The analytical model is verified against numerical simulation and experimental results first and parametric study is then conducted. The transient migration of PHC vapor can be divided into three stages including the pure aerobic zone stage (Stage I), aerobic-anaerobic zones co-existence stage (Stage II), and steady-state stage (Stage III). The proposed analytical model should be adopted to accommodate scenarios where the transient effect is significant (Stage II), including high source concentration, deep contaminant source, high biodegradation capacity, and high water saturation. The applicability of this model to determine the breakthrough time for better vapor intrusion assessment is also evaluated. Lower first-order biodegradation rate, higher source concentration, and shallower source depth all lead to smaller breakthrough time.