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138 Reservoir Formation Damage

in the j th phase, respectively. [I ... I] denotes a jump in a quantity across
a dividing surface defined by:

f-H-r -(•••)• (7-55)

where the signs + and - indicate the post and fore sides, respectively, of
the dividing surface.

Exercises

1. Show that the balance of species / in phase j can also be expressed
in the following forms:

-V(c iy/p,.
jD 9 (7_ 56)

(7-57)

2. Show that, for incompressible flow and incompressible species, Eq.
7-56 simplifies as

(7-58)

References

Blick, E. F., & Civan, F., "Porous Media Momentum Equation for Highly
Accelerated Flow," SPE Reservoir Engineering, Vol. 3, No. 3, 1988,
pp. 1048-1052.
Chang, M.-M., Bryant, R. S., Stepp, A. K., & Bertus, K. M. "Modeling
and Laboratory Investigations of Microbial Oil Recovery Mechanisms
in Porous Media," Topical Report No. NIPER-629, FC22-83FE60149,
U.S. Department of Energy, Bartlesville, Oklahoma, 1992, p. 27.
Chase, G. G., & Willis, M. S., "Compressive Cake Filtration," Chem. Eng.
Sci., Vol. 47, 1992, pp. 1373-1381.