Page 57 - Reservoir Formation Damage

Mineralogy and Mineral Sensitivity of Petroleum-Bearing Formations 41

Although the validity of Eq. 2-34 for porosity variation could not be dem-
onstrated because of the lack of experimental data, porosity variation is
also expected to follow the same trend because it is a result of solid ex-
pansion by water absorption, for which case the validity of the proposed
mechanism was confirmed with experimental data.
Let / denote the properties of clayey formations that vary by swell-
ing, that is /e(w,a,(t),AT),/ 0 and/, denote the initial and final values of
/ over the swelling period, t is time, k f is the rate constant for the prop-
erty /, and S is the rate of water absorption controlled by the hindered
diffusion of water into the solid according to Eq. 2-6.
The analytic solution of Eqs. 2-34 and 35 can be written in the fol-
lowing form:

In (2-36)
f-f t
As demonstrated by Eq. 2-23, it is also possible to relate a property
of f£(w,a,§,K) to another property of ge(w,oc,(|>,AT) for f*g. This
can be accomplished by first applying Eq. 2-36 for g as:

(2-37)

The quantity S can then be eliminated between Eqs. 2-36 and 37 to
obtain:

(2-38)

Eq. 2-38 is particularly useful to correlate between w,a,<|),and K with-
out the involvement of the time variable. For example, applying Eq.
2-38, porosity and permeability variations can be correlated by the power
law equation:

(2-39)
K-K

where k K and are the rate coefficients for permeability and porosity
reduction by swelling, respectively.