Migration of petroleum hydrocarbons from ground surface to groundwater accounting for a liquid Arrhenius model

Abstract

The process of petroleum hydrocarbons migration from the ground surface to groundwater was analyzed. We assumed that the diffusivity is linearly dependent on the concentration in soils. A liquid Arrhenius model of diffusion was adopted in groundwater. The nonlinear diffusion equation of the system was solved numerically. In this sense, we introduced the method of fourth-and-fifth-order Runge-Kutta using the DOPRI5 code as integrator. We sought for conditions under which petroleum products spilled on the ground surface can reach water tables. Three hydrocarbon products were involved in the calculations: benzene, toluene and xylene. We assessed the concentration of pollutants, when they reach the groundwater, for different depths to water. We found that the reachability and the degree of contamination of the water table depend on four main parameters: 1) the value of the initial concentration on the soil surface, 2) the depth to water, 3) the time period and 4) the type of hydrocarbon. For instance, calculations have shown that 5.0kg/m3 Xylene takes about one hour to reach a water table located at 120 m. This study presents separate curves describing the contaminant distribution in soil and groundwater. When Benzene reaches the water table, it takes about 250 days to cover 10 cm depth in the water. Here, the descending motion is significantly slowed.

Keywords: Petroleum-contaminated soils and water, drinkable water, porous media, diffusion, liquid Arrhenius model, biodegradation, DOPRI5 Runge-Kutta integrator