ABSTRACT
Let us examine the three possible ways to modify or extend the governing equations accounting for the proper modeling of the intermediate (partly saturated) region, which were given at the end of Section IV. To implement extension (1), one must eliminate the capillary pressure in Eq. (27a). Here we
present how one can directly extend (2) with the help of an example case study. Darcy’s law and the continuity equation (which must now account for the continuous change of the saturation with time) take the form [87]:
(27a)
(27b)
In Eq. (27a), k denotes the relative permeability, having values in closed interval (0,1) and being a function of the degree of saturation. More about the relative permeability will be discussed later. It is useful to point out that if s= 1, then Pc=0 and Eqs. (21a) and (27b) (in the fully saturated region) coincide with Eqs. (1) and (2). In numerical simulations, it is necessary to introduce an initial saturation, si, in the unfilled part, because the capillary pressure for zero saturation tends to infinity. Modifications of Darcy’s law according to Eq.
