A dual‐porosity model incorporating uniaxial stress effect and its application in wave velocity estimation with well‐logging data

Abstract The elastic properties and wave propagation of porous rocks are sensitive to the stress variation. The existing theories mainly focus on the impacts of effective stress, confining and pore pressures. The physics of uniaxial stress effect on rock elasticity and wave propagation is seldom well studied, although the uniaxial stress case is frequently encountered in several scenarios, such as the laboratory loading and the subsurface tectonic deformation. Therefore, we propose a new dual‐porosity model to describe the effect of uniaxial effective stress on elastic properties of dry porous rocks, based on the Palmer equation and Shapiro dual‐porosity model. The Gurevich squirt‐flow model is then incorporated to model the dispersion and attenuation of wave velocities of fluid‐saturated porous rocks. Modelling results show that the increase of uniaxial effective stress inflates the P‐ and S‐wave velocities along the stress direction until the velocities asymptotically reach their maximum values within the elastic limit. However, the relevant wave dispersion and attenuation gradually decline with the elevating stress possibly due to the gradual closure of cracks. The effect of viscosity, fluid modulus and crack aspect ratio on wave dispersion is investigated in detail as well. By comparing our model to the published laboratory ultrasonic measurements, we confirm the validity of our model. Furthermore, our dual‐porosity model is used to establish a rock‐physics approach to estimate the wave velocities with the well‐logging data. The well‐logging examples show the reasonable agreement between the predicted results and real data, illustrating the feasibility of our approach.