Abstract

Abstract: The speed at which elastic waves travel through a fluid-saturated porous rock depend on the mineral composition, the pore geometry, and the pore fluid properties. Since the pore structure of a rock will vary with the external stress, the wave speeds will generally vary with stress. Since the ability of the pore fluid to contribute to the elastic stiffness of the rock-fluid system depends on the ease with which the fluid can move into or out of a pore as it is compressed by a passing wave, the wave speeds will also be functions of the pore fluid viscosity and wave frequency. Various effective medium theories, such as the Mori-Tanaka model or the differential effective medium approach, can be used to relate the elastic moduli of the rock to its pore structure. The effect of stress on the elastic moduli can be accounted for by combining an effective medium prediction for cracked rocks with an equation that describes crack closure under stress. The effect of pore fluids, however, depends on the frequency regime. At “high” frequencies, the pore fluid will not have sufficient time to travel between adjacent pores during the period of the wave, and can be considered to be “trapped” in each individual pore. In this regime, the effective moduli of the fluid-saturated rock can be calculated from an effective medium theory, with the fluid-filled pores considered as isolated inclusions in a rock matrix. At very low frequencies, the fluid has sufficient time to drain out of any pore that is compressed by the wave, and the effective elastic moduli of the rock-fluid system will correspond to the drained (i.e., dry) limit. It is generally assumed that there is an intermediate range of frequencies in which the fluid is able to travel between adjacent pores, so as to locally equilibrate the fluid pressure, but cannot fully drain out of the region of rock that is compressed by the passing wave. In this case, Gassmann’s equation is used to predict the stiffening effect that the fluid has on the rock-fluid system. I will present some of the models that have been developed to relate the elastic moduli and wavespeeds to pore structure, and to account for the effect of stress. The model predictions will be tested against experimental data on sandstones. Finally, the applicability of Gassmann’s equation will be discussed in light of available experimental results.