Page 112 - Reservoir Formation Damage

Permeability Relationships 95

saturation ratio, and n is a process rate exponent. The porosity, (|), and
the volume fraction of the deposits in the pore volume, a, are related,
respectively, by:

§o =<)> + £ (5-77)

e = <j> 0a (5-78)

Once the porosity is calculated, the permeability can be determined by
Eq. 5-71. Civan (2000) verified this approach using the Koh et al. (1996)
data for permeability impairment by silica deposition.

Effect of Deposition/Dissolution and
Stress on Porosity and Permeability

Civan (2000) modified the equations of Adin (1978), Arshad (1991),
Tien et al. (1997), and Civan (1998) as:

(5-79)

(5-80)
K-K

in which, the subscripts o and °° indicate the initial and terminal porosity
and permeability values, oc ( :« = 1,2,...,8 are empirical parameters, and
denotes the effective overburden stress given according to Nieto et
p eff
al. (1994) and Bustin (1997) as:

Peff=Pob-ap Pf (5-81)

in which a is Biot's constant, and p ob and p pf are the overburden stress
and pore fluid pressure, respectively. Civan (2000) verified these equations
using the data by Nieto et al. (1994) and Bustin (1997).

Effect of Temperature on Porosity and Permeability

Gupta and Civan (1994) and then Civan (2000) formulated the varia-
tion of porosity and permeability by temperature. Representing the
volumetric thermal expansion coefficient of the porous media grains by
the linear equation