Constrained and simplified gassmann's equations

Abstract

Summary For isotropic, homogeneous porous materials, Gassmann’s (1951) equations are physically constrained by the Voigt and Reuss bounds and critical porosity. . These bounds provide stricter constraints on input parameters and output results of fluid saturation effects on bulk modulus. We recast the Gassmann's relations in terms of a porositydependent normalized modulus Kn, and pore fluid sensitivity in terms of a rock gain function G. These simplified Gassmann’s relations suggest that correct input of grain bulk modulus and fluid modulus is key for accurate estimation of fluid saturation effects. We have developed new empirical relation (Han & Batzle 2000) to calculate fluid properties. Measured data on sandstone suggest that the gain function for reservoir sandstones (porosity of 2030%) is around 2 and increases with increasing clay content. We also empirically estimate grain bulk modulus for clean and shaly sandstone based on measured velocities.