Filtration to a Vertical Well from a Broken-Down Formation in the Case of Short Fractures
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 6, November, 2020
FILTRATION TO A VERTICAL WELL FROM A BROKEN-DOWN FORMATION IN THE CASE OF SHORT FRACTURES V. Sh. Shagapov,a I. R. Khamidullin,b and Z. M. Nagaevac
UDC 532.546
Consideration has been given to the problem of achieving a steady-state regime in the process of the well operation at a constant pressure drop between bottom-hole and formation values, and also, at a constant flow rate. It has been assumed that in a fracture resulting from the conduct of hydraulic formation fracturing and existing inside the well supply contour, there is uniform pressure, i.e., the characteristic times of the well operation exceed significantly the periods during which the disturbances from the well affect the entire fracture. Appropriate estimates are presented for these characteristic periods depending on the filtration and geometric parameters of the fracture and formation, and also, on the properties of the fluid. Accurate and approximate analytical solutions have been constructed describing the filtration flows in the "well–fracture–formation" system that make it possible to determine the pressure evolution, the well flow rate, and the dynamics of the well operation in achieving a steady-state regime. Formulas have been obtained determining the well flow rate (analogs of the Dupuit formula). Critical conditions have been proposed for the fracture extent and the supply contour radius, when hydraulic fracturing results in a substantial increase in the well flow rate at a steady-state regime. Keywords: hydraulic fracturing, well, fracture, filtration, pressure distribution, flow rate, integrodifferential equation. Introduction. Formation hydraulic fracturing (hydrofracking) is currently one of the main ways of intensifying oil production from low-permeability beds. Theoretical foundations for implementing hydraulic fracturing were laid in the investigations by S. N. Khristianovich and Yu. P. Zheltov [1], R. P. Nordgren [2], and L. F. Kemp [3]. In their book [4], M. Economides, R. Oligney, and P. Valkó give quite an exhaustive account and a detailed description of the current state of the methods of conducting hydraulic fracturing, and also the procedure of engineering and process calculations for the development of productive formations after hydraulic fracturing. A theoretical model representing a system of partial differential equations describing the filtration in the fracture with account for the leakage of the fluid into the formation has been considered in the investigation by H. Cinco-Ley, V. F. Samaniego, and A. N. Dominguez [5]. These investigations have resulted in obtaining the law of pressure variation in the well during the operation in a constant flow rate regime. The methods of calculating filtration flows made on the assumption that the cross section of the fracture has the shape of an ellipse are presented in the monograph by R. D. Kanevskaya [6]. Let us also point out the most interesting investigations of the last few years, for example [
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