A compositional approach to the modeling of an unsaturated zone

A mathematical model is developed for the simultaneous flow of different phases in porous media. Inertial effects of momentum have been considered in modified Darcy's equation and the obtained hyperbolic equations are solved by the method of lines. This model has been evaluated and compared at limiting conditions with Buckley and Leverett theory and the results of a numerical model. Also the effect of permeability on the predictions obtained by modified Darcy's law and the proposed momentum equation has been discussed. Predictions show that for moderate permeability media, both modified Darcy's law and the model momentum equation approach the same results, but for high permeability media, modified Darcy's law must be extended to take the inertial effects into account.