Biot‐Gardner theory of extensional waves in porous rods

Abstract

Many measurements have been made on fluid‐saturated porous rods executing extensional, flexural, and torsional motion. Measurements for extensional and flexural motion yield a loss parameter for Young's modulus waves [Formula: see text], and the measurement for torsional motion yields [Formula: see text] for shear waves. [Formula: see text] has then been calculated for compressional waves in bulk rock, on the assumption that the fluid‐saturated rock is an isotropic solid. I point out the fallacy of computing [Formula: see text] from these measurements and also urge workers to recognize the losses due to simple fluid viscosity in interpreting their data on extensional waves in rods. By application of published theory, I show that peaks in attenuation of extensional waves are to be expected at frequencies of several hertz to several kilohertz, depending upon rod radius. Computed curves are compared with published measurements on Navajo sandstone saturated with water, ethanol, and n‐decane. In each case, computed peak frequency agrees with published measurements. Shift of the peak frequency with temperature from 4 °C to 25 °C is due to change of viscosity of the saturating fluid (water).