ISSN 2542–0380 Труды Института механики им. Р.Р. Мавлютова Электронный научный журнал | Electronic Scientific Journal Proceedings of the Mavlyutov Institute of Mechanics

им. Р.Р. Мавлютова
УФИЦ РАН

Ilyasov A.M. A new approach to the hydraulic fracture geometric dimensions determination Proceedings of the Mavlyutov Institute of Mechanics. 2017. 12(1). 126–134.
2017. Vol. 12. Issue 1, Pp. 126–134
URL: http://proc.uimech.org/uim2017.1.018
DOI: 10.21662/uim2017.1.018
A new approach to the hydraulic fracture geometric dimensions determination
Ilyasov A.M.
Ufa State Aviation Technical University, Ufa

### Abstract

Based on the generalized Perkins-Kern-Nordgren model (PKN) for the development of a hyperbolic type vertical hydraulic fracture, an exact solution is obtained for the hydraulic fracture self-oscillations after terminating the fracturing fluid injection. These oscillations are excited by a rarefaction wave that occurs after the injection is stopped. The obtained solution was used to estimate the height, width and half-length of the hydraulic fracture at the time of stopping the hydraulic fracturing fluid injection based on the bottomhole pressure gauge data.

Keywords

hydraulic fracture,
rarefaction wave,
hydraulic fracture self-oscillations,
fracture geometry

## Article outline

Purpose: To develop a mathematical model and to investigate the bottomhole pressure oscillation process after water injection stopping at the fracturing test termination.

Methodology: An exact solution of the hydraulic facture self-oscillation problem was obtained for linearized equations.

Findings:

On the basis of the generalized PKN model of hyperbolic fracture development, a mathematical model was proposed to describe natural oscillations of a symmetric hydraulic fracture after stopping water injection wen terminating the fracturing test.

Neglecting of water filtration through the fracture walls, an analytical solution for the direct problem of natural fracture oscillations was obtained.

Using the obtained solution on the basis of the bottomhole pressure gauge data, the fracture geometry was evaluated, including half-length l, average width w0 and height h after stopping the hydraulic fracturing fluid injection.