Study on the influence of rock vertical heterogeneity on the vertical extension law of hydraulic fracture

Abstract The vertical extension of fractures in the hydraulic fracturing process of low-permeability bottom-water oil and gas reservoirs are an essential issue to consider, which affects the stimulation effect of oil and gas reservoirs to a certain extent. During hydraulic fracturing, the hydraulic fracture extends in all three directions of length, height, and width simultaneously, and the fracture height gradually decreases as the construction time and fracture length increase. In the absence of a barrier layer, fractures may extend freely up and down; even if there is a barrier layer, if there is not sufficient strength and thickness, the fracture may jump up and down, penetrate into or even penetrate the barrier layer, forming an "indomitable" fracture, which will hurt the success of fracturing operations and reconstruction results. In this paper, we develop a set of nonlinear equations for the mathematical model of the vertical extension of a hydraulic fracture and calculate the stress intensity factors at the upper and lower tip of the fracture. Based on the fast descent method and the Newton iteration method, we solve the numerical model of fracture height extension and systematically analyze the effect of vertical heterogeneity of the reservoir rock on the vertical fracture extension law and sensitivity analysis. A reasonable choice of fracturing design parameters improves the fracturing success rate and stimulation effectiveness considerably.