Air sparging in an aquifer below a less permeable horizontal layer is modeled using a two-phase flow approach. Supported by numerical simulations we show that a steady state situation is reached. For an analysis of the steady state we distinguish three different flow regimes, which occur between the well screen and the unsaturated zone. Just below the interface, that separates the high and the low permeable layers, a regime with almost hydrostatic capillary pressures develops. We use this observation to derive an ordinary differential equation for the pressure at the interface, which leads to an approximation of the air flow pattern just below and within the low permeable layer. The approximation provides an estimate for the radius of influence as a function of the physical parameters. The agreement between the analytical approximation and the numerical steady state results is almost perfect when heterogeneity is increased. With a few modifications the analysis applies also to a DNAPL spill above a less permeable layer. Comparison with an illustrative numerical simulation shows that the analytical approximation provides a good estimate of the radial spreading of the DNAPL flow on top of and within the low permeable layer.

Reaction-diffusion equations (msc 35K57), Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65M60), Flows in porous media; filtration; seepage (msc 76S05), Two-phase and multiphase flows (msc 76Txx)
Modelling, Analysis and Simulation [MAS]

van Dijke, M.I.J, & van der Zee, S.E.A.T.M. (1997). Modelingof air sparging in a layered soil : numerical and analytical approximations. Modelling, Analysis and Simulation [MAS]. CWI.