Applicability of the Biot theory. I. Low-porosity materials

Abstract

The Biot theory of wave propagation in porous, saturated materials contains 13 parameters. We discuss empirical and theoretical ways to predict values of these parameters for natural materials. The self-consistent theory of composites is used to predict the elastic moduli of the skeletal frame assuming that the inclusions (pore fluid, sediment grains) are needle-shaped at low concentrations. The Biot theory is then used to predict compressional and shear wave speeds in consolidated materials. In a man-made material (porous sintered glass), the predictions agree with experimental data to within 3% (experimental uncertainty is also 3%); these samples were distilled-water-saturated. The predictions agree with data to within 1% for Berea sandstone, and to within 5% for Bedford limestone; all of these samples were brine-saturated. The predictions agree with data to within 8% for distilled-water-saturated Bedford limestone. In the natural sedimentary rocks, the experimental uncertainty in measured wave speeds is estimated at 5%, and the comparisons apply at high effective pressures (>0.3 kbar), where the experimentally determined wave speeds approach ‘‘limiting velocities.’’ In distilled-water-saturated Massilon sandstone, predicted shear wave speeds are about 25% to 35% higher than measured speeds; this may indicate a reduction of the frame shear modulus due to interaction of the pore fluid with the minerals of the rock.