A Model For The Determination Of Water Saturation From Dielectric Permittivity Measurements

The dielectric permittivity of a saturated formation is controlled mainly by the amount of water present in the pores; thus, the porosity calculated from the dielectric permittivity is related to the water-filled porosity. The percentage of water present in the pore space is the ratio of water-filled porosity to total porosity. Because the geometrical distribution of the water in the pores changes with water saturation, a direct comparison of the calculated water-filled porosity from dielectric mixing laws to the total porosity is not always a good estimate of water saturation. A more reliable prediction method is to relate the water saturation to the porosity ratio using a saturation exponent analogous to the saturation exponent in Archie's Water Saturation Equation. An equation using an exponent to relate water saturation to the water-filled porosity has been developed using the Hanai-Bruggeman Equation to determine the water-filled porosity. The water saturation equation is analogous to, and reduces to, Archie's Saturation Equation when the conductivity of the rock dominates the electrical response. The magnitude of the exponent varies between formations and can be determined from laboratory measurements. Laboratory measurements on core samples show a high correlation between the water saturation and the ratio of calculated water-filled porosity to total porosity. An approximate relationship between the dielectric saturation exponent and Archie's saturation exponent has been derived and verified.