The flow rate of oil after fracturing is determined by the permeable surface area of the formed crack and its width. The main geometrical parameters of fracture are height, width and length which cannot be directly measured. The only measured data for hydraulic fracturing are wellhead and bottom pressure. Another way to determine the size of the crack is to get a hydraulic fracture design. But it is necessary to know the elastic rock modules in the interval of the hydraulic fracturing operation. Experimental core studies of elastic constants can give quite high errors at least due to the unloading of core samples and the formation of cracks in the core material when lifted to the surface.
This article presents the method and algorithm of determining the size of a hydraulic fracture and the effective Young's modulus of rock within the interval of fracture development after a water hammer according to downhole gauges. The method is based on solving direct problems of the natural fluctuations of a hydraulic fracture after stopping the pump. Natural fluctuations of a hydraulic fracture are described with the use of the linearized generalized Perkins – Kern – Nordgren (PKN) model of a hyperbolic type. The inverse coefficient problem is solved by the least squares method. On the coefficients found it is possible to estimate the rigidity of a hydraulic fracture, its geometrical parameters, as well as the Young's modulus of the rock within the interval of fracture development. A comparison is carried out between geometrical parameters of hydraulic fractures found using the suggested method and the figures of the design test on substitution obtained with the help of the RN-GRID simulator, provided the Young’s modulus is derived from the new accepted method. Calculations showed fine precision.
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