Page 110 - Reservoir Formation Damage

Permeability Relationships 93

Sharma and Yortsos (1987), Rege and Fogler (1987, 1988), and Bhat and
Kovscek (1999). Although, network models may serve as useful research
tools, their implementation in routine simulations of formation damage
problems may be cumbersome and computationally demanding. Therefore,
they are not included in this chapter.

Modified Fair-Hatch Equation

Liu et al. (1997) formulated the texture, porosity, and permeability
relationship for scale formation. Here, their approach is presented in a
manner consistent with the formulation given in this section. By definition
of fractional volumes <|), <|> s, and § r occupied in the bulk volume,
respectively, by the pore space, deposited scales, and the non-reacting
rock grains, we can write

(5-67)

If the mineral grains forming the scales and the rock are assumed of
spherical shapes, the / t h grain volume can be approximated by:

v t=nD?/6 (5-68)

Consider that there are a total of n, of the z t h grains and the number of
different mineral grains is N m. Therefore, Liu et al. (1997) express Eq. 5-
67 as:

(5-69)

and use a modified form of the Fair-Hatch equation (Bear, 1972, p. 134)
to relate the texture, porosity, and permeability as:

'fl-
Z,\J
2 9ft „. (5-70)
,.,~Q

in which J(~ 5) is a packing factor and 6 ;(~ 6 for spherical grains) is a
geometric factor.

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