Page 261 - Reservoir Formation Damage

Two-Phase Formation Damage by Fines Migration 241

throats. These regions are denoted by wS, nS, and tS, respectively, as
indicated schematically in Figure 11-1. The areal fractions of the wetting
and nonwetting sites can vary as a result of the various rock, fluid, and
particle interactions during formation damage, such as by asphaltene,
paraffin, and inorganic deposition. Therefore, a parameter f ks indicating
the fraction of the pore surface, that is wetting for species k, is introduced
in the formulation.
Because the applications to describe and interpret the laboratory core
damage data, conducted at mild temperature and pressure conditions are
intended, the formulation is carried out for one-dimensional flow in
homogeneous core plugs, isothermal conditions, and incompressible
particles and fluids. This allows the use of a simplified formulation based
on volumetric balances and a fractional flow concept. However, the
derivation can be readily extended for compressible systems encountered
at the prevailing elevated pressure conditions of the reservoir formations.

Fluid and Species Transport
Assuming incompressible species, the volumetric balance of species j
transported via phase J through porous media is given by:

(11-1)
J = W, N, /, wS, nS, tS and j = w,«, wp, np, ip

where e y indicates the volume fraction of phase J in porous media, o ;7
is the volume fraction of species j in phase /, u } is the volumetric flux
of phase J through porous media and q jJL represents the volume rate of
transfer of species j from phase J to phase L. D- } denotes the coefficient
of dispersion of species j in phase /, and p y is the density of phase J,
which varies by its composition even if the individual constituent species
may be considered incompressible, jc and t denote the distance along the flow
direction and time. The dispersion term for particles is usually neglected.
The volumetric rate of particle lost per unit bulk media by various
processes is given by:

tjJL (11-2)

in which q ju denotes the volume rate of transformation of species j type
to species / type in phase J expressed per unit bulk volume. Summing