Electric Resistivity of Vuggy Fractured Media

Abstract

Abstract A theoretical and experimental study on electric resistivity of vuggy fractured media is presented. In order to have a rigorous control of the involved variables, a vuggy fractured medium is idealized by a cubic array of cubes having hemispherical cavities drilled in each cube face. In this model, the spaces between the cubes represent fractures and the hemispherical cavities represent vugs. The theoretical developments lead to a simple relationship expressing formation resistivity factor as the product of two factors, one depending on vug porosity and the other on fracture porosity. This formulation has been validated with experimental data obtained with a special resistivity cell. The proposed formulation can easily be generalized to be applicable to real rocks, and so it is a useful tool for interpretation of electric well logs of vuggy fractured formations. Introduction It is well known that an important part of the world oil production comes from vuggy fractured reservoirs. This type of reservoirs are commonly found in Saudi Arabia, Iran, Iraq, Mexico, Oman and Syria, hence the importance of developing reliable analytical formulations concerning the geometrical properties, storage capacity, and flow properties of the porous space. A practical way of knowing the internal geometry of a porous medium consists in using the so called formation resistivity factor.1 By knowing the formation resistivity factor, it is possible to determine, for instance, the magnitude and type of porosity, and the tortuosity. However, in the case of vuggy fractured media, no previous well established expressions relating formation resistivity factor and the various kinds of porosities have been proposed to date. In this paper, expressions for the formation resistivity factor of vuggy fractured media are developed in terms of fracture and vug porosities. To establish these formulations, the vuggy fractured medium is idealized by a cubic array of cubes with hemispherical cavities drilled in each face. In this model, the spaces between the cubes represent fractures, and the hemispherical cavities represent vugs.2 The theoretical work is based on the idea that, in a vuggy fractured medium saturated with a conducting fluid, the vugs are zones of very low resistivity (or very high conductivity) in comparison with that of the fractures. In this way, one arrives at an equation expressing formation resistivity factor as the product of two components, one depending exclusively on fracture porosity, and the other on vug porosity. This equation was validated with experimental data obtained with a special resistivity cell. The Fractured Medium Due to the geometrical complexity of a vuggy fractured medium, a rigorous analytical study of the formation resistivity factor is not an easy task; however, by making certain logical idealizations it is possible to manage this problem in a relatively simple way. But before entering the study of vuggy fractured media, the case containing no vugs will be considered in this section. The simple fractured medium (i.e., with no vugs), has previously been treated analytically by several authors. For its study, the following basic considerations are made:When a potential difference is applied across the medium saturated with a conducting fluid, the electric current flows much more easily through the fractures than through de matrix, so that the current through the matrix can be considered as negligible, andthe fractured medium can be idealized by a cubic array of cubes (Warren and Root model3), as shown in Fig. 1. This same model has been used by Towle4 and by Aguilera5 for studying the relationship that exists between porosity and formation resistivity factor of fractured media.