Page 227 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 207

results in the pressure equation

(10-126)
3*^)0, dx ) dt

subject to the boundary conditions

p = p. n, x = O (10-127)

p = p ourx = L (10-128)

Then, the pressure obtained by solving Eqs. 10-126 through 10-128 is
substituted into Eq. 10-124 to determine the volume flux.
The preceding formulation of Eq. 10-119 or 120 applies to the overall
system following Gruesbeck and Collins' (1982) assumption that the
particle concentrations in the plugging and nonplugging pathways are the
same according to Eq. 10-113. When different concentrations are con-
sidered, Eq. 10-120 should be applied separately for the plugging and
nonplugging paths, respectively, as suggested by Civan (1995):

(10-129)

(10-130)

subject to

=0, 0 < j c < L , f = (10-131)

(10-132)

k is a particle exchange rate coefficient. A solution of Eqs. 10-129
through 132 along with the particle deposition rate equations, Eqs. 10-
101 and 105, yields the particle volume fractions in the plugging and
nonplugging flow paths.