Page 265 - Reservoir Formation Damage

Two-Phase Formation Damage by Fines Migration 245

(11-21)

The zero capillary pressure and zero gravity fractional flow term is
given by:

FW= 1 + - (11-22)

In the fractional flow formulation, the saturation of the wetting phase
is calculated by solving Eq. 11-19. But the pressure of the wetting phase is
still determined by solving Eq. 11-17.
As explained by Civan (1996), the solution of equations presented
above requires the capillary pressure and relative permeability data for
the two-phase system. These data continuously vary during formation
damage and empirical models, such as those given in Chapter 4, are
required to incorporate these affects in the solution. This problem can be
alleviated in a practical manner by resorting to an end-point mobility ratio
formulation similar to Civan (1996) and Luan (1995), by extending and
generalizing the unit mobility ratio formulations given by Craig (1971),
Collins (1961) and Dake (1978). In view of the uncertainties in deter-
mining the exact nature of the variations of these data, it is reasonable
to make the following assumptions.
First, similar to Liu and Civan (1996), the capillary pressure affect can
be neglected. Second, the relative permeabilities can be approximated by
linear relationships with respect to the phase saturations as (Yokoyama
and Lake, 1981):

k rJ=k° rJSj (11-23)

where k° r] is the end-point relative permeability. Third, the end-point
mobility ratio parameter as defined below can be implemented:

(11-24)
k rN
Under these conditions, Eqs. 11-20 and 22, respectively, become: