Multi-Parameter Regression Models
Efforts for development of empirical correlations and theoretical models for prediction of the permeability of porous media are being pursued by many investigators because the applications of the theoretical models in the formation damage prediction have had limited success. Because of their inherent simplifications, these models are not able to represent the complicated nature of the relationship of the permeability to the petrographical, petrophysical, and mineralogical parameters of geological porous materials. Empirical models, such as by Nolen et al. (1992) have been shown to incorporate such parameters to accurately predict permeability. However, the mathematical form of such models varied in the literature.
Network models facilitate representations of porous media by prescribed networks of nodes (pore bodies) connected with bonds (pore throats). Network models have been used by many researchers, including 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.
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
If the mineral grains forming the scales and the rock are assumed of spherical shapes, the / t h grain volume can be approximated by:
Consider that there are a total of n, of the z t h grains and the number of different mineral grains is Nm. Therefore, Liu et al. (1997) express Eq. 5- 67 as:
and use a modified form of the Fair-Hatch equation (Bear, 1972, p. 134) to relate the texture, porosity, and permeability as:
in which J(- 5) is a packing factor and 6;(- 6 for spherical grains) is a geometric factor.
Power-Law Flow-Units Equation
Civan (1996, 2000) expressed the mean-pore diameter as a threeparameter power-law function of the pore volume to solid volume ratio: in which a, P and y are empirical parameters, and usually a = 1. P and y depend on the pore connectivity and can be correlated as a function of the coordination number, Z, respectively, by:
The interconnectivity parameter can also be approximated by a power law function of porosity as (Civan, 1996):
in which c and n are empirical parameters, y is zero when the pores are blocked by deposition. Civan (2000) verified the validity of Eqs. 5-71 through 74 using the data by Rajani (1988), Verlaan et al. (1999), and Bhat and Kovscek (1999).
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