How Energy Dissipation Mode Controls the Evolution of Multiple Plane‐Strain Hydraulic Fractures Under Isotropic Stresses

The geometrical prediction of multiple hydraulic fractures fed from a single fluid source is a major challenge due to transient stress interference among fractures and nonlinear coupling between rock deformation and fluid flow. Here we find that the evolution of multiple hydraulic fractures under isotropic stresses is controlled by a dimensionless toughness, which measures the ratio of the energy dissipated in rock fracturing to that dissipated in viscous fluid flow. The existence of a relation between the dimensionless toughness and the dimensionless length of the arrested fractures is demonstrated by using a bifurcation analysis. The numerical results show that the fractures tend to grow simultaneously in the viscosity‐dominated regime, and the scaling remains effective when the number of fractures varies. This study provides a quantitative and efficient tool for predicting the fracture pattern in engineered and natural fracture systems.