Page 43 - Reservoir Formation Damage

Mineralogy and Mineral Sensitivity of Petroleum-Bearing Formations 27

and Knapp (1987) and Civan et al. (1989) that diffusion is the primary
cause of water transfer through clayey porous formations. But, transfer
rates tend to increase with pressure application. Ballard et al. (1994) ob-
served that, beyond a certain threshold pressure, water and ions move at
the same speed. This is because transfer by advection dominates and
diffusion by concentration gradients becomes negligible.
The Civan and Knapp (1987) and Civan et al. (1989) models for varia-
tion of porosity and permeability by swelling assume that the external
surface of the swelling clay is in direct contact with water at all times
and therefore they used a Dirichlet boundary condition in the analytic
solution of the models. Civan (1999) developed improved models by
considering a water-exposed-surface-hindered-diffusion process and used
a Neumann boundary condition in the analytical solution of the models.
By means of a variety of experimental data reported in the literature,
Civan (1999) demonstrated and verified that this boundary condition leads
to improved analytic models which correlate the experimental data bet-
ter as closely as the quality of the data permits. He has also shown that
the various phenomenological parameters, such as the rate constants and
the terminal porosity and permeability values that will be attained at water
saturation, can be conveniently determined by fitting these models to
experimental data. Civan (1999) pointed out that the laboratory swelling
tests are generally carried out using aqueous solutions of prescribed con-
centrations. Whereas, the composition of aqueous solutions in actual res-
ervoir formations may vary, but this effect can readily be taken into
account by incorporating a time-dependent clay surface boundary condi-
tion by applying Duhamel's theorem. As a result, the effect of variable
aqueous solution concentration can be adequately incorporated into the
simulation of formation damage by clay swelling.
As schematically depicted in Figure 2-17, swelling clay particles can
absorb water and expand to enlarge the particle size, and the clayey
porous formations containing swelling clays can absorb water and expand
inward to reduce its porosity and permeability. In this section various
models useful for interpretation of experimental data and modeling for-
mation damage are presented.

Osmotic Repulsive Pressure

Ladd (1960) explains that: "The exchangeable cations are attracted to
the clay particles by the negative electric field arising from the negative
charge on the particles. Hence, the electric field acts as a semi-perme-
able membrane in that it will allow water to enter the double layer but
will not allow the exchangeable cations to leave the double layer." Thus,
when the total ion (cations plus anions) concentration in the double-layer