Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part I: A Review Of Biot's Theory

Abstract

Hydrocarbon exploration is especially concerned with two phase media. Following Biot, such finite porosity rocks are modeled as statistically isotropic materials composed of a solid elastic matrix permeated by a network of interconnected pores saturated with a compressible viscous liquid. In a first step, the constitutive equations of a saturated porous medium are reviewed, using mixtures theory and homogenization theory. This study focuses on the assumptions which are necessary but not always explicit. Biot's formulation is then modified by the introduction of a unified definition of the viscous and mass coupling coefficients which are both frequency dependent. The continuity equations at different kinds of interfaces are also analyzed. The body wave velocities and attenuations are then computed, using the cylindrical duct model for pores. The effects of the saturant fluid, the permeability and the porosity are studied.