Page 86 - Percolation Models for Transport in Porous Media With

78 CHAPTER 4. MULTIPHASE FLUID FLOW

Figure 22: Impact of the form of the function f(r) on the nature of the depen-
dencies ka,b(S): K- = 0.5; 1 - 3- curves obtained by calculations using functions
j(l>(r), j< 2 >(r), j< 3 >(r), respectively. Code: a

a 1 ,;:.lra~----.,------.k'

0
I lr 1---12
Figure 23: Impact of the parameter K- on the nature of the dependencies ka,b(S):
f(r) = J< 1 >(r); 1, 2- curves for a= 1 and a= -1, respectively. Code: K-

In all cases, the calculations of ka and kb were carried out for K- = 0.5, using
both of the outlined models for computing the saturationS. The obtained curves
are placed beside each other for comparison: those corresponding to model II, in
fig.22, a, and those corresponding to model I, in fig. 22, b. It is evident from the
1
2
plots in fig. 22, a, that as the variance of f(r) increases (a~ ) < a~ ) < a~ >),
3
kb(Su) decreases, while the threshold saturation, which determines the beginning
of the flow of phase b, increases, both for a > 0 and a < 0. When S is calculated
using the pore model (fig. 22, b) the same effects are to be found for ka(SI), i.e.,
as the variance of f(r) goes up, the values of ka(SI) go down, and the threshold
saturation somewhat increases, though not as notably as in the first case.
The impact of the parameter K- on the forms of functions ka and kb is reflected
in fig.23, where, too, the case a corresponds to model II, and the case b, to model
I. The data presented show that when a = -1 for all K-, the ka ( S II) curves lie
below the corresponding curves for a= 1, while the opposite is true for ka(SI ). In
this case the fall (or rise) of the curves with respect to a= -1 is steeper when K-