Page 182 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 157

3.7 TWO-PHASE FINES MIGRATION DURING LOW-
SALINITY WATERFLOOD: ANALYTICAL MODELING
All discussions so far of formation damage due to fines migration
have been solely in a single-phase flow environment. Most scenarios of
fluid flow in porous media, especially in the petroleum industry, contain
more than one mobile phase. Low-salinity water is used primarily to
increase the oil-recovery in petroleum reservoirs. As such, in most cases
of low-salinity water injection, where fines migration is most prominent,
both mobile oil and water phases are present.
The two primary characteristics of two-phase flow are the relative vol-
ume of each of the phases in the pore space, or the saturation:

V water
s 5 ; (3.199)
V oil
and the relative permeability for each phase:

k i
k ri 5 ; (3.200)
k
where k ri denotes the relative permeability for phase i, k i denotes the
absolute permeability for phase i, and k is the rock permeability as before.
In this section, subscripts w and o will be used for water and oil,
respectively.
As suspended colloids are typically contained in the water phase only,
the effect of particle straining is suspected to influence only the water
flux. Thus, the effect of particle straining will not only be a net reduction
in fluid flux, but also a shift in the relative flow of the two mobile phases.
In the following discussion, a mathematical model is presented which
incorporates the effects of fines migration into two-phase flow.

3.7.1 Fines migration in two-phase flow

Ignoring capillary effects on fluid transport, the mass balance equation for
an incompressible, immiscible water phase is:

@s 1 @ rfUÞ
ð
φ 1 5 0; (3.201)
@t r @r