Page 205 - Reservoir Formation Damage

186 Reservoir Formation Damage

The Darcy and Hagen-Poiseuille equations given respectively by

(10-5)
and
(10-6)

are considered as two alternative forms of the porous media momentum
equations, q is the flowrate of the flowing phase and Ap is the pressure
differential across the thin core slice. Thus, equating Eqs. 10-5 and
10-6 and using Eqs. 10-1 and 10-2 the relationship between permeability,
K, and open flow area, A is obtained as:

I C\ (10-7)
K = A fA h
in which the new constant is defined by

C\ = (10-8)

The permeability damage in porous media is assumed to occur by three
basic mechanisms: (1) gradual pore reduction (pore narrowing, pore
lining) by surface deposition, (2) single pore blocking by screening (pore
throat plugging) and (3) pore volume filling by straining (internal filter
cake formation by the snowball effect).
Gradual pore reduction is assumed to occur by deposition of particles
smaller than pore throats on the pore surface to reduce the cross-sectional
area, A, of the flow tubes gradually as depicted in Figure 10-2. Thus,
the number of tubes open for flow, N np, at any time remains the same as
the total number of tubes, N h, available. Hence,

N h=N np,N p=Q (10-9)

Then, using Eq. 10-9 and eliminating A between Eqs. 10-4 and 10-7
leads to the following equation for the permeability to open flow area
relationship during the surface deposition of particles:

(10-10)

in which the new constant is defined by

_ c N 1/2
c
^—"i ~~~ *—"> * * fc (10-11)
Single pore blocking is assumed to occur by elimination of flow tubes
from service by plugging of a pore throat or constriction, that may exist