Dynamic and Static Biot's Coefficient of Transversely Isotropic Longmaxi Shale

ABSTRACT: In this work, the dynamic and static Biot's coefficients and elastic parameters of Longmaxi black shale are investigated by using acoustic measurement and triaxial compression tests. The results firstly show that the dynamic and static elastic stiffness, Young's modulus both increase with confining pressure, and the dynamic results is higher than the corresponding static values. The Young's modulus parallel to bedding is higher than that of perpendicular to bedding. However, the Poisson's ratio has no significant rule with confining pressure and bedding direction. Secondly, the dynamic and static Biot's coefficients decrease with confining pressure. And the Biot's coefficients perpendicular to bedding are higher than those parallel to bedding. Moreover, the static Biot's coefficients are higher than the dynamic results. Finally, there is a linear relationship between dynamic and static Biot's coefficients and Young's modulus, respectively. The anisotropic Biot's coefficient and the dynamic to static conversion could improve the accuracy of geomechanical analysis in Longmaxi shale. 1. INTRODUCTION The Biot's coefficient, or effective stress coefficient, is a key parameter in poro-elasticity, which could reflect the contribution of pore pressure to effective stress (Alam et al., 2009; Asadollahpour et al., 2021). This coefficient is widely used in petroleum geomechanics, wellbore stability analysis, fracturing design, reservoir sensitivity analysis and productivity prediction, rock physics and other research fields (Valdes et al., 2016; Aderibigbe et al., 2019). Hence, it is of great practical significance for accurately and efficiently obtaining the Biot's coefficient. The Biot's coefficient can be determined from the subtraction of rock bulk modulus to rock matrix's bulk modulus ratio from one (Alam et al., 2009; Asadollahpour et al., 2021; Vorobiev et al., 2022). In the direct laboratory approach, the bulk modulus is obtained while pore pressure is zero in the jacketed test while the rock matrix's modulus is measured by doing the unjacketed test in which the values of the pore pressure and confining pressure are the same (Ling, et al., 2016; Zhou and Ghassemi, 2019). Moreover, the Biot's coefficient also could be calculated by compressibility, permeability and wave velocity or sonic well logs (Luo et al., 2015; He et al., 2016; Amiri et al., 2019; Nolte et al., 2021; Vorobiev et al., 2022). Commonly, the result calculated from the wave velocity is named as dynamic Biot's coefficient (Asadollahpour et al., 2021; Azadpour et al., 2022). Compared to dynamic Biot's coefficient, the unjacketed and drained hydrostatic compression tests are expensive and laborious while the core samples are mostly unavailable. But the dynamic Biot's coefficient needs to be converted into a static value before using for engineering analysis (Crawford et al., 2020).