Page 167 - Reservoir Formation Damage

Paniculate Processes in Porous Media 149

Surface Deposition

The rate of surface deposition is proportional to the particle mass flux,
uo p, where G p is the particle volume concentration in the flowing
suspension, and the pore surface available for deposition that relates to
(|> 2/3 (Lichtner, 1992; Civan, 1995, 1996); k d is a deposition rate constant;
a is a stationary deposition factor expressing deposition at stationary
conditions; and z d is the volume fraction of the particles in the bulk
media retained at the pore surface. Thus, the surface deposition rate
equation is given by:

'd _
(8-11)
dt

subject to

(8-12)

Pore Filling After Pore Throat Plugging
As stated by Chang and Civan (1991, 1992, 1997) and Ochi and
Vernoux (1998), pore throats act like gates connecting the pores and create
a "gate or valve effect," indicated by a severe reduction of permeability
as they are plugged by particles and shut off (see Figure 8-2). Let 8 r
represent the volume fraction of the particles in the bulk media captured
and retained behind the pore throats. The pore filling following the pore
throat plugging leads to an internal cake formation at a rate proportional
to the particle flux, ua p, and the pore volume, (|), available.

(8-13)

subject to

e ? =e r o ,? = 0 (8-14)

is a pore filling rate constant given by:
k t
k t * 0 for t> t cr when p < p cr (8-15)