A technique for the primary and secondary porosity estimation is proposed. This technique is based on a resistivity model of carbonate formations with double porosity and the analysis of numerous core data. The resistivity model consists of an isotropic conductive matrix with a primary porous system and inclusions, which represent secondary porosity (vugs and fractures). Fracture systems are described by oblate ellipsoids of different sizes (which have the same orientation and aspect ratio) or by thin plates. These rock structures are characterized by an anisotropy of electrical properties. The components of the resistivity tensor have a nonlinear relationship with the matrix porosity and parameters of fracture systems (orientation and porosity). The model with spherical inclusions (Maxwell-Garnett approach) is applied to obtain the resistivity of vugular formations. The fluid type, saturation of matrix and secondary pores influence significantly the formation resistivity and anisotropy coefficient. When both pore systems are completely saturated by the same conductive fluid (the case of core analysis), the effective formation factor depends only on the matrix formation factor and the secondary porosity value. The statistical analysis of core data has shown that Archie's equation with cementation exponent m=2, is the best approximation to describe the matrix formation factor for carbonate formations in Mexico. For verification of the porosity separation technique, the fracture and vuggy porosities have been estimated for core with detailed description of pore structure.


The correct evaluation of carbonate formation with double porosity requires separately determining the primary and secondary porosity. Type, distribution and porosity value of secondary-pore systems (vugs or fractures) influence significantly the estimation of saturation, permeability and hydrocarbon reserves.

For porosity separation in the heterogeneous carbonate formations, the resistivity data from log and core analysis are widely used. Two different approaches that are applied to describe the resistivity of multiporosity system can be distinguished.

The first technique uses the traditional presentation of the formation factor in the form of modified Archie's equation as the function of the total porosity. The cementation exponent varies considerably in the carbonate formations with complex porous system. For its correct calibration the correlation analysis of core data for each lithological type is recommended.1,2 Frequently, to describe the experimental distribution of the formation factor obtained from core data, the variable value of cementation exponent as a function of the total porosity has to be assumed.3,4 The estimation of type and value of secondary porosity applying such methodology is qualitative and it is based on the analysis of the parameters of modified Archie equation.5,6 The influence of porosity variation on the cementation exponent using effective-medium theory was studied by Sen et al.7

In the alternative approach the resistivity model of doubleporosity formation is presented as the host medium with primary porosity in which inclusions of different forms (secondary pores) are placed. The formation factor is expressed as a function of two arguments: the primary and secondary porosities.

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