Page 216 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 197

The Compartments-in-Series Ordinary
Differential Model

Khilar and Fogler (1987) divided a core into n-compartments as
depicted in Figure 10-5. The contents of these compartments are assumed
well-mixed. Therefore, the composition of the flow stream leaving the
compartments should be the same as the contents of the compartments.
However, because particles having sizes comparable or larger than the
pore throats are trapped within the porous media, the particle con-
centration of the stream leaving a compartment will be a fraction, y, of
the concentration of the fluid in the compartment, y is called the particle
transport efficiency factor.
Pore surfaces are considered as the source of in-situ mobilized particles
and the pore throats are assumed the locations of particle capture. A
particle mass balance over a thin slice yields

+m (10-65)

m p and ra* denote the mass of particles captured at the pore throats and
the indigeneous particles remaining on pore surfaces, respectively. In
Eq. 10-65

(10-66)

(10-67)

p
(pf )l

Figure 10-5. Continuously stirred compartments in series realization in a core
(after Civan, 1994; reprinted by permission of the U.S. Department of Energy;
after Civan 1992 SPE; reprinted by permission of the Society of Petroleum
Engineers).