Self-similar solution for deep-penetrating hydraulic fracture propagation |
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Authors: | Yu. N. Gordeyev A. F. Zazovsky |
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Affiliation: | (1) Institute for Problems in Mechanics, U.S.S.R. Academy of Sciences, prospekt Vernadskogo, 101, 117526 Moscow, Russia |
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Abstract: | The propagation of a vertical hydraulic fracture of a constant height driven by a viscous fluid injected into a crack under constant pressure, is considered. The fracture is assumed to be rectangular, symmetric with respect to the well, and highly elongated in the horizontal direction (the Perkins and Kern model). The fracturing fluid viscosity is assumed to be different from the stratum saturating fluid viscosity, and the stratum fluid displacement by a fracturing fluid in a porous medium is assumed to be piston-like. The compressibility of the fracturing fluid is neglected. The stratum fluid motion is governed by the equation of transient seepage flow through a porous medium.A self-similar solution to the problem is constructed under the assumption of the quasi-steady character of the fracturing fluid flow in a crack and in a stratum and of a locally one-dimensional character of fluid-loss through the crack surfaces. Crack propagation under a constant injection pressure is characterized by a variation of the crack sizel in timet according to the lawl(t)=lo(1+At)1/4, where the constantA is the eigenvalue of the problem. In this case, the crack volume isVl, the seepage volume of fracturing fluidVfl3, and the flow rate of a fluid injected into a crack isQ0l–1. |
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Keywords: | Hydraulic fracturing transient seepage flow self-similar solution |
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