Page 48 - Reservoir Formation Damage

32 Reservoir Formation Damage

(2-13)

V and V w are the volumes of the solid and the water absorbed,
respectively.
Ohen and Civan (1991) used the expression given by Nayak and
Christensen (1970) for the swelling coefficient:

(2-14)

in which c is the water concentration in the solid and CI is the plasticity
index. <;, and q t are some empirical coefficients, m is an exponent.
Chang and Civan (1997) used the expression given by Seed et al.
(1962):

c - 10) 244 (2-15)

where C c is the clay content of porous rock as weight percent, PI is the
plasticity index, and k' is an empirical constant.

Water Content During Clay Swelling

The rate of water retainment of clay minerals is assumed proportional
with the water absorption rate, 5, and the deviation of the instantaneous
water content from the saturation water content as:

= k wS(w t-w) (2-16)

subject to the initial condition

(2-17)

where k w is a water retainment rate constant, w denotes the weight per-
cent of water in clay and the subscripts o and t refer to the initial (t = 0)
and terminal (t -» °o) conditions, respectively. An analytical solution of
Eqs. 2-16 and 17 yields:

= w t-(w t-w 0) exp (-k wS) (2-1 8)

Osisanya and Chenevert (1996) measured the variation of the water
content of the Wellington shale exposed to deionized water. Figure 2-20