Accurately determining the anisotropic Biot’s coefficient and its dynamic-static correlations is critical for shale geomechanics. This study investigates the dynamic and static anisotropic Biot’s coefficients of deep Longmaxi shale from the Sichuan Basin through integrating laboratory wave velocity, triaxial tests, and in-situ well logging data. The dynamic and static elastic stiffness coefficients C11, C33, C44, C66, and C13 are calculated from five laboratory velocities at 0°, 45°, and 90° as well as Young’s modulus and Poisson’s ratio in 0° and 90°. The horizontal and vertical Biot’s coefficients αh and αv are then calculated from these elastic stiffness coefficients. The dynamic αh ranges from 0.25 to 0.56 and αv from 0.37 to 0.63, while the static values range from 0.36 to 0.63 for αh and 0.41 to 0.67 for αv. A strong linear regression correlation is observed between the dynamic and static Biot’s coefficients, with R2 values of 0.9777 for αv and 0.9859 for αh. Four log-based models, the ANNIE, M-ANNIE, M-ANNIE2, and V-reg model, are employed to predict values of C13, C11 by using well sonic logging data. The evaluation reveals that the ANNIE model is inapplicable for Longmaxi shale because νv/νh is not always greater than 1. In contrast, the M-ANNIE2 model is also unsuitable due to its poor estimation of C66, which leads to the anomalous result of αh > αv, contradicting all other models. While the M-ANNIE model improves the reliability of C13 predictions, the V-reg model provides accurate estimates of all stiffness coefficients. Thus, the V-reg model is recommended for the geomechanical analysis of Longmaxi shale. Furthermore, the C66 and Biot’s coefficient in ANNIE and M-ANNIE models are highly sensitive to minor changes in drilling fluid density. Applying static parameters significantly improved the accuracy of in-situ horizontal stress predictions, with the M-ANNIE and V-reg models showing the smallest relative errors. The findings of this study enable accurate estimation of anisotropic elastic parameters for wellbore stability analysis and hydraulic fracturing design in shale.

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

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发表日期：

2026年5月26日

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Lichun Jia,
Hu Deng,
Qicong Xu,
Wen Xu,
Lei Li,
Luchun Li

摘要

Accurately determining the anisotropic Biot’s coefficient and its dynamic-static correlations is critical for shale geomechanics. This study investigates the dynamic and static anisotropic Biot’s coefficients of deep Longmaxi shale from the Sichuan Basin through integrating laboratory wave velocity, triaxial tests, and in-situ well logging data. The dynamic and static elastic stiffness coefficients C₁₁, C₃₃, C₄₄, C₆₆, and C₁₃ are calculated from five laboratory velocities at 0°, 45°, and 90° as well as Young’s modulus and Poisson’s ratio in 0° and 90°. The horizontal and vertical Biot’s coefficients α_h and α_v are then calculated from these elastic stiffness coefficients. The dynamic α_h ranges from 0.25 to 0.56 and α_v from 0.37 to 0.63, while the static values range from 0.36 to 0.63 for α_h and 0.41 to 0.67 for α_v. A strong linear regression correlation is observed between the dynamic and static Biot’s coefficients, with R² values of 0.9777 for α_v and 0.9859 for α_h. Four log-based models, the ANNIE, M-ANNIE, M-ANNIE2, and V-reg model, are employed to predict values of C₁₃, C₁₁ by using well sonic logging data. The evaluation reveals that the ANNIE model is inapplicable for Longmaxi shale because ν_v/ν_h is not always greater than 1. In contrast, the M-ANNIE2 model is also unsuitable due to its poor estimation of C₆₆, which leads to the anomalous result of α_h > α_v, contradicting all other models. While the M-ANNIE model improves the reliability of C₁₃ predictions, the V-reg model provides accurate estimates of all stiffness coefficients. Thus, the V-reg model is recommended for the geomechanical analysis of Longmaxi shale. Furthermore, the C₆₆ and Biot’s coefficient in ANNIE and M-ANNIE models are highly sensitive to minor changes in drilling fluid density. Applying static parameters significantly improved the accuracy of in-situ horizontal stress predictions, with the M-ANNIE and V-reg models showing the smallest relative errors. The findings of this study enable accurate estimation of anisotropic elastic parameters for wellbore stability analysis and hydraulic fracturing design in shale.