Page 178 - Reservoir Formation Damage

160 Reservoir Formation Damage

dR •A\ _
Ml = (8-43)

p _ *^M12 _ T, poA _ / T, y pP^
^12— ./^ , x^^Al^Al M2 M12 (8-44)

_ . «4
\ — " 4 9 **• 4 1 "7 (8-45)
-* A2

and are some rate constants; and are some empirical
?i A1 A- A2 a A {3 A
exponents of intensities; and ? A1, t An, and t A2 are the time delays due
to the inertia of the respective transfer processes. The initial conditions are:

= 0 (8-46)

th
The rate of particle transfer can be expressed per unit volume of the I
phase according to the following expression:

(8-47)

The particles captured at the interface are assumed to migrate at a speed
determined by the relative speed of the fluid phases.

Exercise

1. Using Einstein's equation, Eq. 8-4, estimate the Brownian diffu-
sivity of a l|0jn diameter fine particle in water at 20°C temperature.
2
9
(Answer: D = 4.3xl(T cm /s; McDowell-Boyer et al., 1986)
References

Amaefule, J. O., Kersey, D. G., Norman, D. L., & Shannon, P. M.,
"Advances in Formation Damage Assessment and Control Strategies,"
CIM Paper No. 88-39-65, Proceedings of the 39th Annual Technical
Meeting of Petroleum Society of CIM and Canadian Gas Processors
Association, June 12-16, 1988, Calgary, Alberta, 16 p.
Cernansky, A., & Siroky, R., "Deep-bed Filtration on Filament Layers on
Particle Polydispersed in Liquids," Int. Chem. Eng., Vol. 25, No. 2,
1985, pp. 364-375.