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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.
