Time-dependent initiation of multiple hydraulic fractures in a formation with varying stresses and strength

The premise of classical hydraulic-fracture-breakdown models is that hydraulic-fracture growth can only start when the wellbore pressure reaches a critical value that is sufficient to overcome the tensile strength of the rock. However, rocks are well-known to exhibit static fatigue; that is, delayed failure at stresses less than the tensile strength. In this paper, we explore the consequences of delayed failure on axially oriented initiation of multiple hydraulic fractures. Specifically, given a certain breakdown pressure, we investigate the conditions under which subsequent hydraulic fracture( s) can begin within the time frame of a stimulation treatment in regions of higher stress and/or strength because of delayed-failure mechanisms. The results show that wells completed in shallower formations are more sensitive to variations in strength, whereas wells completed in deeper formations are more sensitive to variations in stress. Furthermore, cases in which all hydraulic fractures break down according to the same pressurization regime-that is, all are "fast" (nonfluid-penetrating) pressurization or else all are "slow" (uniformly pressurized fluid-penetrating) pressurization cases-are highly sensitive to small stress/ strength variability. On the other hand, if the first hydraulic-fracture initiation is in the "fast"-pressurization regime and subsequent fracture(s) are in the "slow"-pressurization regime, then the system is robust to a much-higher degree of variability in stress/ strength. Practically, this work implies that methods aimed at moderately reducing the variability in stress/strength among the possible initiation points (i.e., perforation clusters) within a particular stage can have a strong effect on whether multiple hydraulic fractures will begin. In addition, this analysis implies that pumping strategies that encourage "fast," nonpenetrative breakdown of the first initiation point followed by the opportunity for fluid-penetrating, "slow" breakdown of subsequent initiation points could be effective at encouraging multiple-hydraulic-fracture initiation.