Hydraulic fracture treatments can be used to increase oil and gas flow rates, and ultimate recovery. A fracture treatment should be designed to optimize profit from the well. To design and optimize the fracture treatment, the engineer must use 1) a fracture propagation model, 2) a reservoir fluid flow model, and 3) an economics model.

To properly simulate the fracture and the reservoir, the engineer should use three-dimensional (3D) models.13 Hydraulic fractures grow up, out, and down from the perforated interval. Oil and gas reservoirs are layered and the flow of reservoir fluids occurs both horizontally and vertically within the reservoir and the fracture. Even though 3D models should be used for most reservoirs, a majority of the fracture treatments are designed using two-dimensional (2D) fracture propagation models. The most common models used by industry are the Perkins-Kern-Nordgren (PKN)4  and the Geertsma-deKlerk-Daneshy (GDK)4  models.

Two-dimensional fracture propagation models are used most often because they are easy to program and run fast on a personal computer. Fortran code for both the PKN and GDK models can be found in Appendix G of SPE Monograph 12.5  We have found that 2D models can be successfully used to design a hydraulic fracture treatment when (1) there are barriers that eventually suppress or restrict vertical growth, and (2) the engineer chooses the correct input value for created fracture height. When these two criteria are met (and all other data are reasonable), a 2D model will provide reasonable estimates of created fracture length and created fracture width.

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