MECHANICS

A new approach for modeling the development of injection-induced hydraulic fractures

K. M. Fedorov^a, A. P. Shevelev^a, A. Ya. Gilmanov^a, A. A. Izotov^b, A. V. Kobyashev<sup>b

a</sup> University of Tyumen, Tyumen, Russian Federation
^b Tyumen Petroleum Research Center, Tyumen, Russian Federation

Abstract: A new approach for modeling the development of injection-induced hydraulic fractures is proposed in this paper. The fracture is assumed to be elliptical in the cross-section. The initial fracture length is determined by the mass conservation law and Darcy's law. A quasi-stationary mathematical model of injection-induced hydraulic fracture growth is based on the specification of two characteristic areas of the fracture: in the first, the dispersed particles settle down near the boundaries of the developed fracture; in the second, the fracture expands with the retarded motion of the suspension front. The mathematical formulation of the problem includes the law of conservation of phase mass, Darcy's law, and the equation for the integral hydraulic resistance. Boundary conditions correspond to the injection of water with dispersed particles through the well into the fracture. The resulting integro-differential system of equations is solved analytically. The effect of the reservoir and fluid parameters on the growth of injection-induced hydraulic fracture is shown. The fracture growth decelerates over time. The increased rock-damage factor leads to faster fracture growth.

Keywords: fracture growth, mass conservation law, particle concentration, integral hydraulic resistance, model of deep bed penetration of particles, rock damage factor.

UDC: 532.5-1/-9

Received: 29.08.2023

DOI: 10.17223/19988621/91/11