Modeling of viscoelastic properties of nonpermeable porous rocks saturated with highly viscous fluid at seismic frequencies at the core scale

Abstract

AbstractA core scale modeling method for viscoelastic properties of rocks saturated with viscous fluid at low frequencies is developed based on the stress‐strain method. The elastic moduli dispersion of viscous fluid is described by the Maxwell's spring‐dash pot model. Based on this modeling method, we numerically test the effects of frequency, fluid viscosity, porosity, pore size, and pore aspect ratio on the storage moduli and the stress‐strain phase lag of saturated rocks. And we also compared the modeling results to the Hashin‐Shtrikman bounds and the coherent potential approximation (CPA). The dynamic moduli calculated from the modeling are lower than the predictions of CPA, and both of these fall between the Hashin‐Shtrikman bounds. The modeling results indicate that the frequency and the fluid viscosity have similar effects on the dynamic moduli dispersion of fully saturated rocks. We observed the Debye peak in the phase lag variation with the change of frequency and viscosity. The pore structure parameters, such as porosity, pore size, and aspect ratio affect the rock frame stiffness and result in different viscoelastic behaviors of the saturated rocks. The stress‐strain phase lags are larger with smaller stiffness contrasts between the rock frame and the pore fluid. The viscoelastic properties of saturated rocks are more sensitive to aspect ratio compared to other pore structure parameters. The results suggest that significant seismic dispersion (at about 50–200 Hz) might be expected for both compressional and shear waves passing through rocks saturated with highly viscous fluids.