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Study on selection and direct inversion method of brittleness index for shale reservoir

Qin Ziyu, Wen Xiaotao, Pan Shulin, Chen Jing-yi, Gou Qiyong

Acta Geophysica

2023

Vol. 71, no. 2

757--768

The brittleness index can be indirectly converted by elastic parameters which are obtain by pre-stack amplitude variation with offset inversion and extended to the whole work area. However, indirect conversion will bring cumulative errors. In order to improve the accuracy of obtaining the brittleness index, the exact Zoeppritz equation including different brittleness indices is derived. Before inversion, we analyzed the characteristics of the brittleness index under the changes of brittle minerals, porosity and organic matter content through rock physics model, and selected the brittleness index most suitable for the work area. Based on the Bayesian framework, we introduce the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method to invert theoretical and actual data. Theoretical data inversion results demonstrate this method can achieve good results in both PP- and PS-wave joint inversion as well as only PP-wave inversion. To further verify the effectiveness of the algorithm, the brittleness index of actual data is directly inverted by using the studied algorithm and process. The inversion results of the borehole-side trace are in good agreement with the brittleness index calculated by log data. Both theoretical and practical data prove the feasibility of our proposed method.

Prestack AVO inversion for brittleness index of shale based on BI_Zoeppritz equation and NSGA II

Bi Chenchen, Wang Yanchun, Xie Wei, Sun Wei, Liu Wei

Acta Geophysica

2020

Vol. 68, no. 4

1067--1082

As one of the evaluation characteristics of shale sweet spots, the brittleness index (BI) of shale formations is of great sig nifcance in predicting the range of sweet spots, and guiding hydraulic fracturing. Based on the three elastic parameters of P-wave velocity (VP), S-wave velocity (VS) and density obtained by conventional prestack AVO inversion, BI can be calcu lated indirectly using the Rickman formula. However, the conventional AVO inversion based on Zoeppritz approximation assumes that incident angle is small and elastic parameters change slowly, which afects the inversion accuracy of the three elastic parameters. Additionally, using these three elastic parameters to obtain BI indirectly also leads to cumulative errors of the inversion results. Therefore, we propose an inversion method based on BI_Zoeppritz equation to directly estimate VP, VS and BI. The BI_Zoeppritz equation is an exact Zoeppritz equation for BI, which is used as the forward operator for the proposed method. The multi-objective function of the inversion method is optimized by a fast nondominated sorting genetic algorithm (NSGA II). An initial model and an optimized search window are used to improve the inversion accuracy. The test results of model data and actual data reveal that this method can directly obtain the BI with high precision. In addition, the stability and noise immunity of the proposed method are verifed by the seismic data with random noise.