An analytical solution for vertical transport of volatile chemicals in the vadose zone

An analytical solution is presented for one-dimensional vertical transport of volatile chemicals through the vadose zone to groundwater. The solution accounts for the important transport mechanisms of the steady advection of water and gas, diffusion and dispersion in water and gas, as well as adsorption, and first-order degradation. By assuming a linear, equilibrium partitioning between water, gas and the adsorbed chemical phases, the dependent variable in the mathematical model becomes the total resident concentration. The general solution was derived for cases having a constant initial total concentration over a discrete depth interval and a zero initial total concentration elsewhere. A zero concentration gradient is assumed at the groundwater table. Examples are given to demonstrate the application of the new solution for calculating the case of a non-uniform initial source concentration, and estimating the transport of chemicals to the groundwater and the atmosphere. The solution was also used to verify a numerical code called VLEACH. We discovered an error in VLEACH, and found that the new solution agreed very well with the numerical results by corrected VLEACH. A simplified solution to predict the migration of volatile organic chemical due to the gas density effect has shown that a high source concentration may lead to significant downward advective gas-phase transport in a soil with a high air-permeability.