Thermoelastic relaxation and its effects on the compressibility of pore fluid and P wave velocities

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In poroelastic models, the effective compressibility of rock saturating fluid is conventionally taken as the adiabatic compressibility. This compressibility is valid for seismic waves having frequencies large enough to neglect heat exchanges between the rock matrix and the pore fluid, which are subjected to undergo temperature variations in response to seismic wave propagation. For low enough frequencies, heat flows back and forth across the rock/fluid interfaces, which leads the fluid to smaller temperature variations resulting in a higher compressibility than in the absence of the rock. An analysis of the characteristic heat conduction time over the pore and grain lengths shows that the rock-fluid composite should be considered under thermal relaxation in the surface seismic frequency band rather than the conventional high-frequency (unrelaxed) limit. Our analysis for a rock-fluid system shows that in the low-frequency limit, the effective compressibility of the saturating fluid is neither isothermal nor adiabatic but is equal to the average of the adiabatic and isothermal fluid compressibilities weighted by the volumetric heat capacities of the fluid and rock, respectively. The resulting bulk moduli and compressional velocities of fluid-saturated rock are lower than the conventional values. P wave velocity dispersion, in poorly consolidated rocks, is about 15–20 % subject to the type of saturating fluid is rich in acidic gases (CO2, H2S).