A weighted averaging technique for the linearized governing equation for sharp interface LNAPL transport models

Abstract

The modeling of the spreading of contaminant non-aqueous phase liquid (NAPL) as free-phase in groundwater has been gaining interest in the last decade due to the increasing importance for the accurate prognosis of the expansion of the contaminated area in aquifer. Under certain conditions and assumptions the governing equation of free-phase NAPL-flow is a non-linear partial differential equation (PDE) in terms of NAPL thickness ( h NAPL ) as a function of time and of the plane coordinates only. Solutions presented in the last decade consider Light NAPL (LNAPL) mound and use for calculation of the spreading/floating semi-analytical and numerical methods which are based on the linearized form of the governing equation. The linearized PDE is an advective-dispersive equation in terms of h NAPL and can be obtained trough introduction of an averaged reference thickness ( h a NAPL ). The central problem of the linearized PDE is the estimation of this averaged reference thickness for each time-step. Currently, the simple domain averaging method is applied (e.g., mound volume of LNAPL per unit area). This paper discusses the reliability of the averaging method. It will be shown that this method, which has been used over the last decade leads to significantly large approximation errors for the time dependent LNAPL mound thickness and its plane expansion. A new weighted domain averaging technique is proposed, which reduces substantially these errors and consequently allows the improvement of the existing numerical and semianalytical calculation methods for free-phase LNAPL and Dense NAPL (DNAPL) mound spreading and migration with ambient groundwater flow in an aquifer. Numerical results are presented to demonstrate the effectiveness of this new weighted averaging technique.