Theoretical model for the elastic properties of cracked fluid-saturated rocks considering the crack connectivity

Cracks are a common rock microstructure and have a large effect on elastic properties during wave propagation. The fluid flow between a crack and its adjacent pore space can cause wave attenuation and dispersion. In this work, we introduce a crack connectivity parameter which is meant to improve the expression of local flow by weighting the contributions of fully connected and isolated cracks. We then update the analytical expression for frequency-dependent moduli by modifying the boundary conditions of the linearized Navier-Stokes equation and mass conservation equation. The proposed model contains the effect of cracks and stiff pores, in which the attenuation and dispersion are determined by squirt-flow and stiff-pore relaxations. The resulting model shows the squirt-flow relaxation frequency depends on not only the crack aspect ratio but also the crack connectivity. However, their contributions are different. The crack connectivity has little effect on the attenuation amplitude of shear modulus, but affects the attenuation amplitude of bulk modulus when multiple sets of cracks exist in the rock. The attenuation frequency band is also affected by the crack connectivity. As the crack connectivity deteriorates, the attenuation peak moves to low frequencies. In addition, by comparing the crack connectivity with the fluid viscosity coefficient, it is observed that the crack connectivity only affects the attenuation frequency band of cracks, whereas the fluid viscosity coefficient affects the attenuation frequency bands of cracks and stiff pores simultaneously. Thus, the introduction of crack connectivity is a supplement to the theoretical model of cracked fluid-saturated rocks. It helps understand the local fluid flow induced by seismic waves and provides a reasonable variation analysis of moduli and attenuation, especially for tight reservoirs.