A Mori-Tanaka scheme-based model for gas-water two-phase cracked rocks and its application

Microporous structure and pore fluid are two important components of poroelastic rocks that influence the variation of rock modulus. Cracks are special microstructures that are more likely to be compressed during wave propagation than stiff pores, resulting in squirt flow. In addition, the distribution of different fluids, such as water and gas, may be characterized by patchy saturation and generate fluid pressure gradients. By combining the Mori-Tanaka scheme and these two local fluid flows, a new rock physics model for gas-water two-phase cracked rocks is developed. Among effective medium models, the Mori-Tanaka model is of superiority in describing non-dilute-inclusion rocks and has an explicit expression. It is used to provide a reasonable variable range of the rock modulus. First, it is re-derived by assuming that the pore structure contains cracks and stiff pores. Then, the pore fluid pressures are investigated by considering the effects of squirt flow and patchy saturation simultaneously. The proposed model agrees well with the boundary models and is consistent with the variation of the experimental and well-logging data. With the new model, the joint effect of two different local fluid flows on rock moduli with frequency can be analyzed in detail.