Page 164 - Reservoir Formation Damage

146 Reservoir Formation Damage

dimensionless group, which relates the Stokes and convection velocities
as (Ives, 1985):

(8-3a)
18jiv fl

Centrifugal Forces. The centrifugal forces are generated by external
acceleration. The centrifugal force created with an angular velocity of w
and a radius of R is expressed in dimensionless form by

G = (8-3b)

Diffusion Force. Particles smaller than 1 mm diameter tend to move
irregularly in a liquid media and disperse randomly. This phenomena is
called the Brownian notion. The diffusivity of fine particles undergoing
a Brownian notion is given by Einstein (McDowell-Boyer et al., 1986):

(8-4)

The diffusion force can be expressed by the Peclet number as the ratio
of the convection velocity to the average Brownian velocity given by
(Ives, 1985).

(8-5)
KT
,-23
where TI = 3.1459... and K = 1.38 x 10 is Boltzmann's constant.
Hydrodynamic Force. Hydrodynamic forces are the fluid shearing and
pressure forces (Wojtanowicz et al., 1987, 1988). Ives (1985) explains
that during fluid flow secondary circulation flows can be formed around
the particles, which can generate out-of-balance hydrodynamic forces
acting on the particles to move them across the flow field. Ives (1985)
states that a proper dimensionless group rigorously expressing the
hydrodynamic force is not available. Ives (1985) points out that the
Reynolds number given by:

(8-6)