Hydraulic fracturing is an essential technology for the development of unconventional resources such as tight gas. The evaluation of the fracture performance and productivity is important for the design of fracturing operations. However, the traditional dimensionless fracture conductivity is too simple to be applied in real fracturing operations. In this work, we proposed a new model of dimensionless fracture conductivity (FCD), which considers the irregular fracture geometry, proppant position and concentration. It was based on the numerical study of the multistage hydraulic fracturing and production in a tight gas horizontal well of the North German Basin. A self-developed full 3D hydraulic fracturing model, FLAC3Dplus, was combined with a sensitive/reliability analysis and robust design optimization tool optiSLang and reservoir simulator TMVOCMP to achieve an automatic history matching as well as simulation of the gas production. With this tool chain, the four fracturing stages were history matched. The simulation results show that all four fractures have different geometry and proppant distribution, which is mainly due to different stress states and injection schedule. The position and concentration of the proppant play important roles for the later production, which is not considered in the traditional dimensionless fracture conductivity FCD. In comparison, the newly proposed formulation of FCD could predict the productivity more accurately and is better for the posttreatment evaluation.
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An ensemble Kalman filter based on the Weather Research and Forecasting Model (WRF-EnKF) is used to explore the effectiveness of the assimilation of surface observation data in an extreme local rainstorm over the Pearl River Delta region on 7 May 2017. Before the occurrence of rainstorm, the signals of weather forecasts in this case are too weak to be predicted by numerical weather model, but the surface temperature over the urban area are high. The results of this study show that the wind field, temperature, and water vapor are obviously adjusted by assimilating surface data of 10-m wind, 2-m temperature, and 2-m water vapor mixing ratio at 2300 BST 6 May, especially below the height of 2 km. The southerly wind over the Pearl River Delta region is enhanced, and the convergence of wind over the northern Guangzhou city is also enhanced. Additionally, temperature, water vapor mixing ratio and pseudoequivalent potential temperature are obviously increased over the urban region, providing favorable conditions for the occurrence of heavy precipitation. After assimilation, the predictions of 12-h rainfall amount, temperature, and relative humidity are significantly improved, and the rainfall intensity and distribution in this case can be successfully reproduced. Moreover, sensitivity tests suggest that the assimilation of 2-m temperature is the key to predict this extreme rainfall and just assimilating data of surface wind or water vapor is not workable, implying that urban heat island effect may be an important factor in this extreme rainstorm. 相似文献