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

Abstract

The vertical expansion of fractures during hydraulic fracturing in low-permeability bottom-water oil and gas reservoirs is a crucial factor that significantly influences stimulation effectiveness. Fractures propagate concurrently in three dimensions; however, as operation time for fracturing and fracture length increase, there is a gradual reduction in fracture height. In the absence of a barrier layer or with inadequate strength and thickness, fractures may extend vertically or oscillate through it leading to an “unyielding” fractured state that impedes successful operations. This study introduces a mathematical model delineating the vertical expansion of hydraulic fractures (HFs) while computing stress intensity factors at upper and lower tips of each individual fracture. We use numerical methods to examine how vertical heterogeneity within reservoir rocks impacts laws governing vertical fracture propagation while conducting sensitivity analysis for making informed decisions on design parameters for hydraulic fracturing operations. The research results indicate that an escalation in stress disparity and increased toughness results in diminished height for HFs. Hydraulic fracturing augments fracture lengths along their respective axes. Nevertheless, if gap stress disparity surpasses net fluid pressure, a reduction in fracture length is observed. With an increasing ratio between local stress gradient versus fluid gravity gradient, HFs persistently advance vertically across cap and bed formations.