In spite of the fact that multistage hydraulic fracturing from horizontal wells is the fastest growing and arguably the most economically important application for well stimulation, there remain a number of fundamental questions relevant to determining how long to make each isolated interval and how many perforation clusters to place within each interval. This paper provides new insights to this problem by predicting how many hydraulic fractures can be expected to grow simultaneously from multiple perforation clusters pressurized by a single injection stage. These predictions are obtained from a coupled mathematical model that includes the contributions of fluid flow, rock breakage, and pressure loss through the perforations to the total power requirements for growth of arrays of multiple hydraulic fractures. For typical shale gas stimulations, radial hydraulic fractures are predicted to grow from all perforation clusters, with progressive reduction in the number of hydraulic fractures so as to maintain a ratio of the radius to the spacing that is a bit less than one. If the hydraulic fractures are contained to a height H, then multiple PKN-like hydraulic fractures are predicted to continue growing, with the length of each hydraulic fracture increasing throughout the injection and with a spacing that is approximately 1.5H when perforation losses are strong and approximately 2.5H when perforation losses are negligible. These geometric predictions are consistent with previously published observations based on microseismicity associated with stimulations in the Barnett Shale.

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