Extending the inclusion-based effective medium model with fluid pressures caused by wave-induced flow

The wave propagation through a rock system is affected by the rock microstructure and the pore fluid. By considering the rock microstructure, the upper and lower bounds of P-wave modulus can be refined in the inclusion-based effective medium model. However, the effects of patchy saturation and squirt flow are not included. The patchy saturation due to the inhomogeneous distribution of different fluids and the squirt flow induced by wave propagation can lead to a difference in fluid pressures. Thus, we introduce the fluid pressures to the inclusion-based effective medium model to describe the variation of P-wave modulus during the wave propagation. We assume that the fluid pressures mainly generate the variation of the P-wave modulus and update the elastic tensor. By adjusting the model parameter related to effective fluid modulus, the proposed model can keep good consistency with the known boundary models. Finally, we analyze the effect of water saturation, frequency, and the pressure difference of different fluids on P-wave modulus with the proposed model.