Heterogeneity analysis of shale reservoirs from multi-stage pumping data using Hilbert-Huang transform method

Heterogeneity, as an intrinsic property of shale reservoirs, exhibits long-standing puzzles, which makes it difficult to optimize the hydraulic fracturing design and may render suboptimal good performance. At present, heterogeneity analysis of conventional data, such as geophysical log data and rock core, has been still limited to the application of the near-wellbore zone due to the problem of the up-scaling and low resolution. However, numerous multi-stage pumping data manifesting nonlinear behavior of physical properties with shale reservoirs are usually ignored. In this study, the multi-stage pumping data were selected and the empirical mode decomposition technique (EMDT) as pre-processing of Hilbert–Huang transform method was applied to the multi-stage pumping data to determine the respective intrinsic mode functions (IMF). Meanwhile, the Hilbert spectral analysis (HSA) was only used to further analyze its heterogeneity for multi-stage pumping data of equal IMF number. At last, based on the IMF number decomposed by EMDT and instantaneous amplitude of high-frequency components in Hilbert spectra, the heterogeneity associated with far-wellbore shale reservoirs was comprehensively determined. A shale gas well located in Sichuan Basin, China, was analyzed by using Hilbert–Huang transform method including EMDT and HSA. The results indicate that heterogeneity results from multi-stage pumping data are coincided with the effective stimulation reservoirs volume (ESRV) obtained from micro-seismic events. Not only that, it reveals that there is a strong correlation of IMF number, ESRV, instantaneous amplitude, and degree of heterogeneity within shale reservoirs. This work has demonstrated that heterogeneity analysis combined with Hilbert–Huang transform method has been significantly important and essential to evaluate the degree of heterogeneity within far-wellbore shale reservoirs from multi-stage pumping data, which contributes to optimizing the hydraulic fracturing design and improving good suboptimal performance.