Elastic wave equation for porous media saturated with non-Newtonian fluid

Non-Newtonian fluids like heavy oil, polymer and fracturing fluid are common in oil and gas exploration and development. The Biot theory ignores the nonlinear changes in the fluid viscosity coefficient and shear stress. Although it can be used to describe the interaction between fully saturated solids and classical Newtonian fluids under the action of wave field, it is not correct for the pore filling of non-Newtonian fluids. After establishing a fractional order derivative Maxwell model of non-Newtonian fluid, we found that there was a significant difference in the features of wave field propagation between regular wave equation and elastic wave equations in porous media saturated with non-Newtonian fluid. Resonance phenomenon exists in wave dispersion and attenuation. Such special effects have not been found in wave field dispersion and attenuation in porous media satura-ted with Newtonian fluid. At the same time, the rheological parameters and fractional derivatives of the constitutive relations of non-Newtonian fluids have obvious effects on the fluid-solid coupling. Numerical results show that the wave equation with non-Newtonian fluid effect is more accurate to predict the P wave velocity of heavy oil sandstone. Non-Newtonian constitutive relation brings new changes to fluid-solid coupling mechanism, which cannot be ignored for the influence on wave field dispersion and attenuation. This study explored the petrophysical model for field seismic survey. The results are useful to other related fields, such as seismic exploration of dense oil reservoir, and micro seismic simulation in cracked reservoirs filled with fracturing fluid. © 2021, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.