Effects of non-Newtonian pore-fluid rheology on frequency-dependent wave dispersion and attenuation in porous rocks

Summary Non-Newtonian pore-fluid behaviour is incorporated into a generalized Lagrangian–dissipation framework for wave propagation in fluid-saturated porous media. In contrast to approaches that rely on prescribed pore-scale flow patterns, pore geometries, or other microscopic structural assumptions, the present formulation introduces nonlinear rheological effects directly at the macroscopic constitutive level. The resulting model remains consistent with continuum mechanics and Biot-type poroelasticity while allowing non-Newtonian effects to enter three fluid-related dissipation mechanisms: Darcy-type fluid–solid friction, local-deformation (LD) relaxation, and bulk-viscous dissipation. Nonlinear dissipation potentials are constructed for these mechanisms and then reduced, through a first-harmonic approximation, to effective frequency-dependent coefficients for harmonic wave analysis. Numerical examples show that the non-Newtonian Darcy-friction and LD mechanisms primarily modify the characteristic frequencies of the corresponding relaxation processes, whereas the non-Newtonian bulk-viscosity mechanism affects both the frequency range and the strength of attenuation and dispersion, with a strong sensitivity to the assumed magnitude of the pore-fluid bulk viscosity. The framework also allows alternative nonlinear representations of Darcy-type fluid–solid friction to be compared within the same Lagrangian–dissipation structure; an alternative nonlinear dissipation operator produces wave-propagation predictions nearly indistinguishable from those obtained using the power-law Darcy-friction model, suggesting that different nonlinear constitutive assumptions may lead to similar effective attenuation structures at the macroscopic scale. Calibration against laboratory measurements on tight carbonate rocks shows that the observed attenuation and velocity-dispersion behaviour can be reproduced using physically interpretable non-Newtonian parameters. These results suggest that non-Newtonian pore-fluid rheology may contribute to frequency-dependent wave-propagation effects in fluid-saturated porous media and provide a flexible macroscopic framework for investigating fluid-related dissipation beyond conventional Newtonian poroelastic models.