Page 155 - Reservoir Formation Damage

Multi-Phase and Multi-Species Transport in Porous Media 137

(7-49)
= v-

Invoking Eq. 7-33, Eq. 7-46 can be written in an alternative form as:

dHj
p,.[e y

V • (EJ k • V7})+ EJ + (7-50)
L«J.a
a=l
a*;

The equation of motion given by Chase and Willis (1992), for deforming
porous matrix can be written as following:

(7-51)

where T 5 is the shear stress tensor for the solid matrix.
The jump mass balance equations, given by Slattery (1972) can be
simplified to express the boundary conditions as:

(7-52)

(7-53)

(7-54)

The superscript a denotes a quantity associated with the dividing surface,
which is moving at a macroscopic velocity of w°, and n a is the unit
vector normal to the dividing surface. r°, rf and r? are the rates of
addition of mass of the porous matrix, the th phase, and the species i