An accurate prediction of elastic parameters is crucial for predicting minimum horizontal stress in wellbore stability, drilling design of horizontal borehole azimuth and hydraulic fracturing in petroleum engineering. For a transversely isotropic shale formation, the vertical and horizontal mechanical properties can be obtained from five independent elastic stiffnesses C11, C33, C44, C66 and C13, which also are the necessary parameters for horizontal stresses estimation. Among these stiffness coefficients, C33 and C44 can be obtained from the P- and S-wave velocities while C66 is calculated from the Stoneley wave velocity if there is. The other two elastic stiffness C11 and C13 have to be obtained from the empirical model, such as ANNIE model, M-ANNIE model, M-ANNIE2 model and V-reg model. However, the adaptability and accuracy of the above models to a formation are very different from each other, which need optimization analysis for a specific formation. The objective of this paper is to evaluate the discreteness of stiffness coefficients of the above four empirical models by applying datasets of the ultrasonic velocities of Wufeng–Longmaxi shale of the Sichuan Basin in China, for finding a suitable model of this shale formation for predicting horizontal stress. These four models are divided into two types by whether or not there is Stoneley wave in model, which is group 1 including ANNIE model and M-ANNIE model with Stoneley wave, and group 2 including M-ANNIE2 and V-reg model which lack for Stoneley wave. The results show that the elastic parameters obtained from M-ANNIE model has the smallest deviation with the measured results in group 1. While the elastic parameters calculated by V-reg model makes lower deviation compared to M-ANNIE2 in group 2. But for both groups, the goodness-of-fit of V-reg model is better than other models. Finally, the two models M-ANNIE2 and V-reg are used to a field log example missing Stoneley wave. The results of minimum horizontal stress show that the average error between calculated solution from V-reg model and measured values is less than 10%, which can reflects the actual formation more accurately and exhibit good application potential for drilling and fracturing.

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