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The pressure dependence of elastic parameters of rocks is mainly controlled by the geometry of the pore space. In general, the compliant-stiff pore structure model can be used to reasonably describe this pressure dependence. However, our experiment measurements revealed that for tight sandstone rock with complex pore structures, the contribution of the compressibility of the stiff pores to the elastic modulus is significant. The dual porosity is not sufficient to explain the variation of ultrasonic velocity with pressure. For this reason, we adopted a triple pore structure to divide the rock pore space into equant pores, intermediate pores and compliant pores. Our laboratory measurement and model results show that this pore space division can better describe the pressure dependence of the elastic moduli of rocks. The low-frequency stress–strain measurements show that the fluid-saturated tight sandstone has obvious dispersion in the seismic frequency band, which is primarily attributed to the squirt flow effect. In order to study the pressure and frequency dependence of the elastic moduli of tight sandstone, we retrieved the geometric parameters of the pore structure from the pressure variation of the ultrasonic velocities under dry conditions. Based on this complex pore structure and the extension of the squirt flow model, we constructed an elaborate rock physics model to explain the pressure and frequency dependence of velocity. The model does not require adjustable parameters, and all parameters are measured and calculated by the laboratory, which improves the accuracy of theoretical modelling. The modified squirt flow model can be used to describe dispersion and attenuation in a wide frequency band, and fit well with the velocity measurements in both the low-frequency range and the ultrasonic frequency range under different pressures. Therefore, this rock physics model could be applied in the extraction of pore microstructure and fluid properties provided elastic moduli or velocities can be estimated accurately.

Effects of different pore shapes on the pressure and frequency dependence of velocities of oil-saturated tight sandstone