An acoustic theory of thermally cracked rocks

High temperatures in rocks lead to thermal cracking, whereby porosity and permeability increase and the P and S wave velocities as well as the Q (quality) factor decrease. In addition, the crack density increases and the crack aspect ratio decreases. There are many ultrasonic data in the literature, usually for dry, stiff rocks (granite, basalt) and ambient pressure, which can be processed and described using appropriate theories. The data were usually measured up to a temperature of about 600–800 (Formula presented.) C before melting of the grain minerals. In this work, we use Gassmann equations based on Pride’s dry-rock moduli and estimate the consolidation coefficient, mass density, wave velocities, quality factor and permeability as a function of temperature. Fluid substitution is then applied to determine the density and velocities of the rock saturated with steam and water under supercritical conditions. The equivalent inclusion average stress (EIAS) model is used in combination with the Zener model to model attenuation and estimate crack fraction, density and aspect ratio. We compare the results with the simplified approach of O’Connell and Budiansky to determine the crack density. The permeability mainly follows power laws as a function of porosity. The inversion method uses a simulated annealing algorithm.