Summary
Equations are formulated to account for the effects of temperature on the dynamical behavior of two-phase materials typified by liquid-saturated rocks. The constitutive relations reveal the existence of several interesting coupling coefficients, two of which appear to have gone unnoticed heretofore and a third, though noticed, never before measured. Specifically, the first two coefficients are associated with thermal expansion and the third with local heat flow between the phases. Experimental work is reported on the measurement of these quantities for a kerosene-saturated sandstone.
Solutions of the field equations are then studied appropriate to the propagation of plane waves, and it is shown that in an isotropic, “thermoporoelastic” medium there exist, in general, four distinct dilatational motions. Two of these represent modifications of the “fast” and “slow” waves in a two-phase medium at constant temperature, the other two are diffusion-like modes analogous to theT-waves in a single-phase thermoelastic solid.
Finally, for values of material constants corresponding to the kerosene-filled sandstone mentioned above, results of numerical calculations are displayed for the dispersion and attenuation of these waves at seismic frequencies.
Zusammenfassung
Gleichungen zur Berücksichtigung des Temperatureinflusses auf das dynamische Verhalten von zweiphasigen Werkstoffen, wie z. B. durchtränkte Gesteine, werden angegeben. Die Werkstoffgleichungen zeigen das Auftreten verschiedener Kopplungskoeffizienten. Zwei dieser Koeffizienten scheinen unbekannt zu sein, der dritte bekannt, aber bisher noch nie gemessen. Die ersten beiden Koeffizienten stehen in Zusammenhang mit der thermischen Ausdehnung, der dritte mit dem lokalen Wärmefluß zwischen den Phasen. Über die Messung dieser Größen für kerosingefüllten Sandstein wird berichtet.
Die der Ausbreitung ebener Wellen entsprechenden Lösungen der Gleichungen werden untersucht und es wird gezeigt, da\ in einem isotropen “thermoporoelastischen” Körper im allgemeinen vier verschiedene Dilatationsbewegungen auftreten. Zwei entsprechen Modifikationen der “schnellen” und “langsamen” Wellen eines Zweiphasengemisches bei konstanter Temperature, die beiden anderen sind diffusionsähnliche Bewegungsarten entsprechend denT-Wellen eines einphasigen thermoelastischen Festkörpers.
Abschließend werden numerische Ergebnisse für die Dispersion und das Abklingen dieser Wellen bei seismischen Frequenzen für kerosingefüllten Sandstein angegeben.
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Pecker, C., Deresiewicz, H. Thermal effects on wave propagation in liquid-filled porous media. Acta Mechanica 16, 45–64 (1973). https://doi.org/10.1007/BF01177125
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DOI: https://doi.org/10.1007/BF01177125