Iterative use of the Bruggeman-Hanai-Sen mixing model to determine water saturations in sand

Abstract

The accuracy of the Bruggeman-Hanai-Sen (BHS) mixing model has been previously demonstrated for two-material mixtures during BHS model development. Using permittivities determined from modeling ground-penetrating radar (GPR) data, the BHS model has been iteratively applied to three-material mixtures of water, sand, and a dense, nonaqueous-phase liquid (DNAPL). However, the accuracy of this application has not been verified. A 10-cm air-line system driven by a network analyzer is used to measure bulk permittivitities when the water saturations in a sand are varied (frequency range of 20 to 200 MHz). Through iterative use of the BHS mixing model, the measured permittivities are used to calculate water saturations, which are compared to known saturation values. An iterative BHS mixing model for an air/water/sand system must consider which two-material end member (air/sand or water/sand) represents the matrix term in the original two-material BHS model. An air/sand matrix provides the best accuracy for low water saturations, and a water/sand matrix provides the best accuracy for high water saturations; thus, a new weighted model is developed. For a given porosity and a measured bulk permittivity, water saturation is most accurately determined by proportionally weighting the water saturation values determined using air/sand as the matrix and water/sand as the matrix in the BHS model.