MODELING OF THE WATER AND NITROGEN TRANSFERS IN UNSATURATED– SATURATED POROUS MEDIUM

A. Maslouhi , O. Bamba Yacoub
Laboratoire Interdisciplinaire en Ressources Naturelles et en Environnement
Université Ibn Tofail, , Faculté des Sciences de Kenitra, BP133, Morocco
maslouhi_a@yahoo.com

Water flow and nitrogen transport in a porous unsaturated-saturated environment constitute a
very difficult problem to study because of the nature of the equations governing the transfers
between the saturated zone and the unsaturated zone. The first difficulty comes owing to the
fact that the water-table, which constitutes the lower condition of the unsaturated zone is not
known and depends on the exchanges between the two zones. The second difficulty is the
reactive nature of nitrogen particularly in the unsaturated zone. In this study, a mathematical
modeling tool was developed to simulate the water flow and nitrogen transfers in unsaturated–
saturated porous medium. We used a mathematical formulation which consists in considering
as a single continuum the saturated and the unsaturated zones. The model is based on the
finite elements method using the Freefem++ code. This code was adapted to the equations
used in this study, namely: Richards’ equation to study the water flow in the unsaturated zone,
the diffusivity equation for the groundwater flow and the transport equation of advection–
dispersion type to study the nitrogen transfer. The advantage of the Freefem++ is that it
generates self-adapting grids. The modelling tool was validated using experimental data
measured on the small-scale physical model. A comparative study with the ADI method was
carried out and showed that the use of the finite elements Freefem++ code presents an
advantage and provides more accurate results.

Key words modeling; unsaturated-saturated; flow; nitrogen; finite elements; self-adapting
grids