Page 209 - Reservoir Formation Damage

190 Reservoir Formation Damage

The instantaneous porosity of a given cross-sectional area is given by:

ty = ty 0-£ p (10-23)

and (() denote the initial and instantaneous porosity values, e is the
(|) 0
fractional bulk volume of porous media occupied by the deposited
particles, given by

(10-24)
e p=m p/p p
is the mass of particles retained per unit volume of porous media and
m p
is the particle grain density. For convenience, these quantities can be
p p
expressed in terms of initial and instantaneous open flow areas, A fo and
Ay> and the area covered by the particle deposits, A , as
ty = A f/A (10-25)

$ 0=A fo/A (10-26)

e p=A p/A (10-27)

Substituting Eqs. 10-25 through 10-27, Eqs. 10-23 and 24 become,
respectively

A / 0 =A / + A p (10-28)

(10-29)
A p=Am p/p p
The particle mass balance for a thin core slice is given by:

+ m )} = 0 (10-30)

subject to the initial conditions:

(10-31)

and (Ppf) are the particle mass concentrations in the flowing phase
at themlet and outlet of the core. Wojtanowicz et al. (1987, 1988) omitted
the accumulation of particles in the thin core slice and simplified Eq. 10-30
to express the concentration of particles leaving a thin section by: