Multiple Hydraulic Fractures in Horizontal Wells

摘要

A well model is required to relate the well rate to the well pressurernand the block pressure containing the well for the modelingrnwells in simulators. The well index is calculated automaticallyrnby simulators for conventional wells, but it is generallyrncalculated by the user and supplied in the input while modelingrnnon-conventional wells, when the default procedure availablernin commercial simulators is not adequate.rnIn this paper we describe a new analytical solution for horizontalrnwells with multiple fractures. The fractures can be rotatedrnat any horizontal angle to the well and they need not fullyrnpenetrate the formation in the vertical direction. This threedimensionrnsolution for hydraulically fractured wells is obtainedrnby applying Fourier analysis to a two-dimensional solution,rntherefore this three-dimension solution is easy to obtain whenrnthe two-dimensional solution is available. The analytical solutionrnprovides the well pressure that can be combined with arnnumerically computed gridblock pressure to obtain the well indexrn(WI). Results of our rigorous solution are compared withrnempirical approaches currently in use for calculating the wellrnindex and the productivity index. Examples are given whenrnhorizontal wells with fractures are modeled using our new approachrnand conventional methods. These results demonstraternthe need for computing the correctWI.