Reservoir Formation Damage Episode 1 Part 3 docx

32 Reservoir Formation Damage

(2-13)

V and Vw 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 qt

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 Cc 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:

= kwS(wt-w)

subject to the initial condition

(2-16)

(2-17)

where kw 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:

= wt

-(wt

-w0

) exp (-kwS) (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

Mineralogy and Mineral Sensitivity of Petroleum-Bearing Formations 33

10 15

1

1« (hr

• Osisanya and Chenevert Gage 1 data

Correlation of the Gage 1 data

% Osisanya and Chenevert Gage 2 data

Correlation of the Gage 2 data

X Osisanya and Chenevert Gage 3 data

Correlation of the Gage 3 data

Figure 2-20. Correlation of water pickup during swelling (after Civan, ©1999

SPE; reprinted by permission of the Society of Petroleum Engineers).

shows the correlation of their data with Eq. 2-18 using Eq. 2-6. The best

fits were obtained using w0= 2.7 wt.%, wt= 3.27 wt.%, A = kw(c{

- c0)/

h = 0.26 and h-Jo = \ for their Gage 1 data, w0 = 2.77 wt.%, wt

= 3.28

wt.%, A = 0.06 and h^D = 0.8 for their Gage 2 data, and w0= 2.77 wt.%,

wt

= 3.28 wt.%, A = 0.035 and h-^j~D = 0.8 for their Gage 3 data.

Brownell (1976) reports the data of the moisture content of a dried

clay piece containing montmorillonite soaked in water. Figure 2-21 shows

a correlation of the data with Eq. 2-18 using Eq. 2-6. The best fit was

obtained using w0 = 0%, wt

= 14.2 wt.%, A = 0.2 and

Time-Dependent Clay Expansion Coefficient

By contact with water the swelling clay particles absorb water and ex￾pand. The rate of volume increase is assumed proportional to the water

absorption rate, 5, and the deviation of the instantaneous volume from

the terminal swollen volume that will be achieved at saturation, (Vt

- V).

Therefore, the rate equation is written as: