Coupled effects of pressure and frequency on velocities of tight sandstones saturated with fluids: measurements and rock physics modelling

Elastic moduli and velocities of tight sandstones are strongly influenced by rock-frame heterogeneity, pore microstructure and fluid in addition to pressure and probing-wave frequency. The effects of pressure and frequency on the elastic moduli and velocities are different from those of conventional sandstones with high porosity and high permeability due to complexity of pore microstructure. To investigate these effects, we measured two tight sandstone samples for their velocities in the dry and fluid saturation conditions using the ultrasonic transmission technique and the low-frequency stress–strain method. The variations in the ultrasonic velocities with pressure see a transition from non-linear to linear increase for the dry samples, in contrast to a gradual increase for the fluid-saturated samples. The low frequency velocities of the saturated sample T1 and T2 directly show significant dispersion in a wide range of frequencies (1–100 Hz), and the magnitudes of the dispersion are suppressed by the pressure. The low-frequency velocities also increase with pressure, showing increasing trends bounded by the ultrasonic velocity–pressure curves for the dry and fluid saturation conditions. An elaborate rock physics model, considering a discrete aspect ratio spectrum and the simple squirt flow model, was constructed to account for the pressure and frequency dependence of the velocities. The predictions from the modified squirt flow model can fit well the measured velocities at varying pressures, both in the low-frequency range and the ultrasonic frequency range. The real measurements and the modelling results suggest that the pressure- and frequency-dependence cannot be modelled without considering such aspect ratio spectra. The effects of pressure and frequency are coupled in that they are interconnected by the microstructure of the pores. Changes in the pressure and fluid saturation (and thus wave frequency) both contribute to stiffening of the rock frame, and they both strongly depend on the presence of microcracks in the rock. Therefore, this rock physics model could be applied in extraction of pore microstructure and fluid properties provided elastic moduli or velocities can be estimated accurately.