Civan (2000) expressed the precipitation/dissolution rate by:

where, t is time, k1 is a rate constant, Φ0 is the initial porosity, e is the volume fraction of deposits in porous media, F is the solution saturation ratio, and n is a process rate exponent. The porosity, Φ and the volume fraction of the deposits in the pore volume, a, are related, respectively, by:

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:

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

in which a is Biot's constant, and pob and ppf 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 variation of porosity and permeability by temperature. Representing the volumetric thermal expansion coefficient of the porous media grains by the linear equation

where T and To denote the temperature and a reference temperature, respectively, and a and b are empirical parameters, Civan (2000) derived: Civan (2000) verified this formulation using the Okoye et al. (1990) data.


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