Numerical simulations for the evaluation of the free surface history in porous media. Comparison between two different approaches

This paper shows an empirical comparison of two different models for the theoretical analysis of the zero pressure surface position during the imbibition of a partially saturated porous medium: the model based on the unsaturatedsaturated approach, and the model which describes the zero pressure surface as a free external boundary for the fully saturated zone. A domain FD technique is applied for solving the governing equations of the first model, whereas a BEM formulation has been chosen for the equations of the second one. The comparison is based on numerical experiments which deal with the imbibition of an academic system. The results obtained highlight the tendency of the fully saturated approximation to provide solutions where the rise of the free surface is much more localized near the injection zone than in the case of the unsaturatedsaturated approach. In addition, owing to the capability of describing the capillary fringe, these latter solutions affect thicker layers of porous matrix. So, the users have to consider the system of interest with the greatest care before they choose the mathematical model which is the most suitable for the aims of the planned simulation.