Page 54 - Reservoir Formation Damage

38 Reservoir Formation Damage

= 4> - 4> 0 = 4>, - 1 - (2-28)
where k sw is the formation swelling rate constant, t is the actual time of
contact with water. Therefore, the swelling rate constant can be deter-
mined by fitting Eq. 2-27. However, due to the lack of experimental data,
the application of Eq. 2-28 could not be demonstrated. It is difficult to
measure porosity during swelling. Permeability can be measured more
conveniently. Ohen and Civan (1993) used a permeability-porosity rela-
tionship to express porosity reduction in terms of permeability reduction.

Permeability Reduction by Swelling

Civan and Knapp (1987) assumed that the rate of permeability reduc-
tion by swelling of formation depends on the rate of the water absorp-
tion and the difference between the instantaneous permeability and
terminal permeability that will be attained at saturation as:

= a swS(K-K t) (2-29)

subject to the initial condition

K = K 0,t = 0 (2-30)

where a sw is a rate constant.
Thus, solving Eqs. 2-29 and 30 yield:

(2-31)

where a sw is the rate constant for permeability reduction by swelling, from
which the permeability variation by swelling is obtained as:

- exp(-a w5)] (2-32)

Civan and Knapp (1987) and Civan et al. (1989) have confirmed the
validity of Eq. 2-31 using the Hart et al. (1960) data for permeability
reduction in the outlet region of a core subjected to the injection of a
suspension of bacteria. Because bacteria is essentially retained in the inlet
side of the core, the permeability reduction in the near-effluent port of
the core can be attributed to formation swelling by water absorption. The