Prediction of Vertical DNAPL Vapour Fluxes in Soils Using Quasi-Analytical Approaches: Bias Related to Density-Driven and Pressure-Gradient-Induced Advection

This study focuses on a detailed analysis of the errors introduced by two quasi-analytical approaches based on either Fick’s first law or a combination of Fick’s and Darcy’s laws to evaluate the vapour flux of chlorinated solvents from a source zone located in the unsaturated zone towards the atmosphere. A coupled one-dimensional numerical flow and transport model was developed and applied to three case studies characterised by different water content profiles in the vadose zone and under different levels of maximum dense nonaqueous-phase liquid vapour concentrations and vapour pressure conditions of the source zone. The steady-state concentration and pressure profiles obtained were then used in the two quasi-analytical approaches to estimate the flux towards the atmosphere. When mass fluxes due to density-driven advection become dominant and the vertical advective mass fluxes are increased due to strong pressure gradients in the soil air, the error was observed to increase when using the pure diffusion approach in the quantification of the surface flux calculated by the numerical model with increasing dimensionless Rayleigh numbers. Without taking into account the advective transport in the approach, the relative error calculated with only Fick’s law overestimates the real vapour flux when density-driven advection is dominant and underestimates it when pressure-gradient-driven advection dominates. The more advanced advective–diffusive quasi-analytical approach fits reasonably well with the numerically obtained mass fluxes except near soil layer discontinuities, where the evaluation of both the concentration gradient and pressure gradient in the porous media as well as the determination of the average effective diffusion coefficients are rendered more difficult.