Page 230 - Reservoir Formation Damage

210 Reservoir Formation Damage

P
= — (10-141)
J r

in which 9 is the inclination angle and Z 0 is a reference level. A^ is
the non-Darcy number given by

(10-142)

The inertial flow coefficient, |3 can be estimated by the Liu et al.
(1995) correlation:

8
8.91xl0 T
(10-143)
Brinkman's application of Einstein's equation is used to estimate the
viscosity of the suspension:
2.5
(10-144)

where \k w is the viscosity of water.
Substituting Eq. 10-140 into Eq. 10-139 yields the following equation
for the flow potential:

(10-145)

The particle volume fraction and the flow potential can be calculated
by solving Eqs. 10-138 and 145 simultaneously, using an appropriate
numerical method such as the finite difference method used by Ohen and
Civan (1993), subject to the initial and boundary conditions given by:

(10-146)

t>0 (10-147)

(10-148)

The volumetric rate of water absorption is estimated by (Civan et
al., 1989):