Page 165 - Reservoir Formation Damage

Paniculate Processes in Porous Media 147

and its other forms such as those "relating to the shear gradient, the
relative velocity between particle and liquid, the angular velocity of the
rotating particle, and the frequency of pulsation liquid have been suggested."
Khilar and Fogler (1987) expressed the hydrodynamic lift force pulling
a spherical particle off the pore surface by the following equation given
by Hallow (1973):
1/2
(8-7)

where u s is the slip velocity, K is the linearized velocity gradient near
the particle, and d is the diameter of the spherical particle.

Forces Related to the Attachment Mechanisms
These forces act on the particles when they are near the grain surface
less than a 1 Jim distance (Ives, 1985). These forces and the characteristic
dimensionless groups are described below.

London—van der Waals Force. This is the attractive force due to the
electromagnetic waves generated by the electronic characteristics of atoms
and molecules. The attraction force is expressed by (Ives, 1985):

1
F vw(s) = (8-8)

in which X is a dimensionless wavelength of the dispersion force divided
by nd product and F n is a function assuming different forms for (s - 2)/X
less and greater than unity.

Friction—Drag Force and Hydrodynamic Thinning. Particles approach-
ing the grain surfaces experience a flow resistance because they must
displace the liquid at the surface radially as they attach to the grain
surface (Ives, 1985; Khilar and Fogler, 1987).

Forces Related to the Detachment Mechanisms

Shearing Force. This is the friction or drag force. When the shear stress
of the liquid flowing over the deposited particles creates a shearing force
greater than those attaching the particles to the grain surface, then the
particles can be detached and mobilized (Ives, 1985):

dv
(8-9)
dr