A semi-analytical mathematical model for predicting well performance of a multistage hydraulically fractured horizontal well in naturally fractured tight sandstone gas reservoir

• Presented a semi-analytical mathematical model for gas productivity calculation in MFHWs.
• Emphatically considers flow in natural fractures, the novel model is applicable to more complex conditions in SRV.
• Fractures at arbitrary angles and unequal, asymmetric hydraulic fractures were considered in physical modeling.
• Numerical simulation of a conceptual model has been conducted for model validation.
• Sensitivity analysis of relevant parameters were analyzed based on the novel model.

Multiple fractured horizontal well (MFHW) is one of the key technologies to exploit low permeability reservoirs. The accuracy of productivity evaluation after fracturing not only affects the effectiveness of fracturing treatment, but also affects the optimum design of parameters in horizontal wells. This paper is the first investigation into the semi-analytical mathematical modeling for gas productivity calculation of multi-staged horizontal wells in fractured tight sandstone gas reservoirs that emphatically considers the impact of flow in fracture network (natural fracture system). Herein, a production forecast model of complex hydraulic fractures was created where the impact of nature fractures was simulated, and a semi-analytical solution was obtained by using Gaussian elimination method. As extension of historical work, this novel model could be applicable to more actual conditions such as fractures at arbitrary angles and unequal, asymmetric fractures.In the subsequent work, a numerical simulation of a simple conceptual model has been conducted, which validated the accuracy of this novel model. Then a real case application was successfully implemented. The modeling calculation result and actual production data of well X in Surig gas field is in good accordance. Besides, the impact of reservoir parameters upon production and morphology optimization were specifically analyzed. Using this new model, the production performance decline curves were drawn up based on computing results and were thoroughly analyzed for the sensitivity of reservoir parameters, especially the natural fractures. As presented in the performance curves, the post-frac production is greatly influenced by the change of permeability in fracture network, also confirming the applicability of this new model in fractured tight sandstone gas reservoirs.

This paper presented a semi-analytical mathematical model for gas productivity calculation in MFHWs that emphatically considers the impact of flow in natural fracture system. This novel model is applicable to more complex conditions such as fractures at arbitrary angles and unequal, asymmetric hydraulic fractures in SRV caused by the existence of mass natural fractures as well as stress interference of MFHWs.Figure optionsDownload high-quality image (221 K)Download as PowerPoint slide