Study for Electrical Conductivity Model of Fractal Porous Media

摘要

Natural porous media,such as reservoir rocks and unconsolidated sediment,generally have complex internal systems,and the geometry and size-distribution of pores as well as their interconnectivity greatly influence the transport properties of these materials.Archie’s equation is an empirical electrical conductivity-porosity model that has been used to predict the formation factor of porous rock for more than 70 years.However,the physical interpretation of its parameters,e.g.,the cementation exponent m remain questionable.Many natural porous media have been shown to be fractal in nature,and fractal geometry has been widely used to study transport properties of porous media.In this study,a theoretical electrical conductivity equation is derived based on the fractal characteristics of porous media.The proposed model is expressed in terms of the tortuosity fractal dimension,the pore fractal dimension,the electrical conductivity of the pore liquid,and the porosity.The empirical parameter m is then determined from physically based parameters,such as tortuosity fractal dimension and pore fractal dimension.Furthermore,a distinct interrelationship between tortuosity fractal dimension and pore fractal dimension is obtained.We find reasonably good match between the predicted formation factor by our model and experimental data.