Analytical modeling dynamic drainage volume for transient flow towards multi-stage fractured wells in composite shale reservoirs

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• 作者：Da Zheng ; Bin Yuan ; ^biny@ou.edu ; Rouzbeh G. Moghanloo
• 关键词：Multi-stage fractured horizontal well ; Dynamic drainage volume ; Composite reservoirs ; Shale ; Stimulated-reservoir volume ; Analytical model
• 刊名：Journal of Petroleum Science and Engineering
• 出版年：2017
• 出版时间：20 January 2017
• 年：2017
• 卷：149
• 期：Complete
• 页码：756-764
• 全文大小：1828 K
• 卷排序：149

文摘

This paper presents an analytical solution to predict the expansion of drainage volume for a composite transient linear flow system consisting of stimulated-reservoir volume (SRV) and unstimulated reservoir volume. Correct prediction of dynamic drainage volume (DDV) is essential in production data analysis and well space evaluation. With the prediction of DDV, we can calculate the average pressure and average saturation with different time, which can assist designing different exploitation scenarios.The compound linear flow solution within both SRV and unstimulated matrix is derived under constant-flowing-bottomehole-pressure (FBHP) and constant-rate boundary conditions. Laplace transform and numerical inversion are implemented to obtain the analytical solution. The location of pressure front is calculated using the impulse response concept, which is the maximum rate of pressure response. A multi-variable regression method is applied to determine an empirical equation indicating the relationship between DDV and the square root of time; the empirical equation includes conductivities of both SRV and unstimulated matrix volume, fracture length, and fracture spacing.The results suggest that the DDV demonstrates a linear relationship with square-root-of-time for both linear flow regime within SRV and the compound linear flow in composite fractured reservoirs. The advancement of DDV within stimulated-reservoir volume is much faster than unstimulated matrix, which is approximately 100 times in general. To verify the accuracy of newly derived DDV equations, we analyze the synthetic production data from series of fine-grid numerical simulations. Finally, we make a sensitivity analysis of hydraulic fracture spacing with respect to DDV, which can be implemented to evaluate the fracturing design. In practice, the solution derived can be used to determine optimal fracture spacing.