A unified model including non-Darcy flow and viscoelastic mechanisms in tight rocks

Tight porous media have extremely low porosities and permeabilities, which can induce low-fluid mobility and a significant non-Darcy flow phenomenon. We build a unified mathematical model considering the non-Darcy seepage and the viscoelasticity mechanism, which includes two new parameters related to the non-Darcy flow mechanism. We call this the non-Darcy viscoelastic (NDV) model. Numerical experiments reveal that the two parameters have significant effects on the dispersion and attenuation of the P and S waves. We find that the dispersion and attenuation of the waves depend on the initial amplitude. A comparison is conducted between experimental data for tight porous media in the low (seismic) frequency band and the numerical results of the NDV model. The comparison demonstrates that the NDV model can predict the velocity dispersion in tight oil and gas reservoirs more accurately.