One of the most effective ways to increase well productivity is hydraulic fracturing. As a result of hydraulic fracturing the high conductivity fractures in the reservoir are formed, which reduce the filtration resistance of the bottomhole zone and increase the effective wellbore radius. In the works of I.V. Krivonosov, I.A. Charny and M. Prats, it was found that an “ideal” fracture (infinite conductivity fracture) is equivalent to a well whose diameter is equal to half the fracture length. Earlier, a similar conclusion was made in the fundamental works of F. Forchheimer and N.E. Zhukovsky, where steady-state water flow to the slit and gallery of finite length was investigated. An important step in planning a hydraulic fracturing operation is determining the optimal fracture parameters (length, width and conductivity), which are able to provide the maximum production rate at a fixed fracture volume and known values of the reservoir thickness, drainage radius, reservoir and proppant permeability’s.
The article presents a theoretical analysis of the pseudo-skin factor for rectangular and elliptical fractures and expressions for the optimal fracture half-length and width. It is shown that the effective radius of fracture with optimal conductivity is half the effective radius of an “ideal” fracture. A system of integral equations is obtained for determining the steady-state fluid flow to a finite conductivity fracture in a circular reservoir. Based on the numerical solution of a system of integral equations, graphs of flux and pressure distribution along the fracture wings were presented for different values of the dimensionless fracture conductivity, which are in good agreement with the results of M. Prats and H. Cinco-Ley. It is shown that the pseudo-skin factor is explicitly expressed through the flux distribution along the fracture.
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