Page 259 - Reservoir Formation Damage

Two-Phase Formation Damage by Fines Migration 239

formation damage requires the consideration of other factors, such as the
wettability affect and partitioning of particles between various phases.
In this chapter, mutual interactions and affects between the two-phase
flow systems, fine particles, and porous matrix are described mathe-
matically to develop a predictive model for formation damage by fines
migration in two-phase systems flowing through porous formations. The
formulation is carried out by extending the Liu and Civan (1993, 1994,
1995, 1996) model for more realistic applications. The tests and case
studies used by Liu and Civan (1995, 1996) are presented for demon-
stration and verification of the model. Although the model presented here
involves some simplifications pertaining to the laboratory core damage
experiments, it can be readily modified and generalized for the actual
conditions encountered in petroleum reservoirs.

Formulation

The equations describing the various aspects for formation damage by
fines migration during two-phase fluid flow through porous formations
are formulated here. However, the formulation can be extended readily
to multi-phase fluid systems. It is safe to assume that the gas phase does
not carry any solid particles (i.e., it is nonwetting for all particles).
For convenience in modeling, the bulk porous media is considered in
four phases as schematically depicted in Figure 11-1: (1) the solid matrix,
(2) the wetting fluid, (3) the nonwetting fluid, and (4) the interface region.
These phases are indicated by S, W, N, and /, respectively. The porous
matrix is assumed nondeformable. Therefore, it is stationary and its
volumetric flux is zero. The wetting and nonwetting phases flow at the
volumetric fluxes denoted, respectively, by u w and U N. The interface
region is located between the wetting and nonwetting phases and is
assumed to move at a flux equal to the absolute value of the difference
between the fluxes of the wetting and nonwetting phases (i.e., its flux is
«/ = U W-U N\).
The various particles involving the formation damage are classified
as (1) the foreign particles introduced externally at the wellbore,
(2) the indigeneous particles existing in the porous formation, and (3) the
particles generated inside the pore space by various processes, such as
the wettability alteration considered in this chapter. Another classification
of particles is made with reference to the wettability as (1) the wetting
particles, (2) the nonwetting particles, and (3) the intermediately wetting
particles. These particles are identified, respectively, by wp, np, and ip.
The latter classification is more significant from the modeling point of
view. Because, as explained by Muecke (1979), the wettability affects the
behavior of these particles in a multi-phase fluid system. By means of