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An image denoising method is proposed for ultrasonic logging images with severe noise. The proposed method works on a variational Bayesian framework using block sparse prior. First, the sparse coefficients are simulated by a more appropriate distribution-Laplacian distribution. Then the variational Bayesian denoising model in which Laplacian distribution is used as a prior term of sparse coefficients is proposed. Finally, semiquadratic regularization is used to solve the model with a simplified process. Moreover, during the denoising process, a relaxation factor is introduced to improve the accuracy. In the vast majority of cases, the proposed method obtained better results in both the visual quality and the objective evaluation. It achieves better denoising performance than the existing denoising methods when the edge details of the images are contaminated by noise, especially severe noise. The experimental results show that the proposed method is practical in ultrasonic logging images.

During the drilling of shale gas wells, the shape of shale cuttings cut by polycrystalline diamond compact bits has an obvious flaky structure. The accumulation of such flaky cuttings is one of the main reasons for high drilling torque and drag and serious back pressure, which affect the drilling speed of the horizontal section of shale gas wells. Therefore, predicting the thickness of the flaky cuttings bed and restraining it are essential for ensuring safe and efficient drilling of the horizontal section of shale gas wells. However, most of the previous research on migration laws for cuttings were based on spherical particles, which affected the accuracy of cuttings bed thickness prediction. In this study, through visualization experiments combined with computational fluid dynamics numerical simulation, the hole cleaning laws of shale gas wells in the long horizontal section were studied, and a set of cuttings bed thickness prediction models and cuttings bed removal process parameter optimization methods were established. Field application was conducted in the Changning 209H24-1 well in the southern Sichuan Basin, China. The results revealed the following: (1) There are significant differences in the migration laws of flaky cuttings and spherical cuttings in the horizontal section. (2) The fitting accuracy of the established long horizontal fragmentation layer distribution model considering multiple factors and the experimental data is as high as 0.973. (3) Based on this model, the drilling parameters of the Changning 209H24-1 well were optimized, which played a good role in wellbore cleaning and ensured the safe and smooth implementation of the later casing operation.

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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