Well Models of Hydraulically Fractured Horizontal Wells

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A well model is required to relate the well rate to the well pressure and the block pressure containing the well for the modeling of wells in simulators. The well index is calculated automatically by simulators for conventional wells, but it is generally calculated by the user and supplied in the input while modeling non-conventional wells, when the default procedure available in commercial simulators is not adequate. In this report we describe a new analytical solution for horizontal wells with multiple fractures. The fractures can be rotated at any horizontal angle to the well and they need not fully penetrate the formation in the vertical direction. This three-dimensional solution for hydraulically fractured wells is obtained by applying Fourier analysis to a two-dimensional solution, therefore this three-dimension solution is easy to obtain when a two-dimensional solution is available. The analytical solution provides the well pressure that can be combined with a numerically computed gridblock pressure to obtain the well index (WI). Results of our rigorous solution are compared with empirical approaches currently in use for calculating the well index and the productivity index. Examples are given when horizontal wells with fractures are modeled using our new approach and conventional methods. These results demonstrate the need for computing the correct WI.


Type of resource text
Date created June 1999


Author Wan, Jing
Primary advisor Aziz, Khalid
Degree granting institution Stanford University, Department of Petroleum Engineering


Subject School of Earth Energy & Environmental Sciences
Genre Thesis

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Preferred Citation
Wan, Jing. (1999). Well Models of Hydraulically Fractured Horizontal Wells. Stanford Digital Repository. Available at: https://purl.stanford.edu/xf270cm2526


Master's Theses, Doerr School of Sustainability

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