The aim of part 2 is to understand the development of complex hydraulic fractures (HFs) that are commonly observed in the field and in experiments but are not explained by most models. Our approach uses finite element simulations and a numerical rheology developed in part 1 to model damage fracturing, the fracturing process by damage propagation in a rock with elastic–plastic damage rheology. Using this rheology and a dynamic solution technique, we investigate the effect of far-field stresses and pressure distribution in the fracture on the geometric complexity of the fractures.

The model is for the vertical propagation of an HF segment into an overlying bed located far from borehole effects. The layer is 2.3 m (7.5 ft) tall, has elastic–plastic damage rheology, and contains a 0.3-m (1-ft)–tall initial vertical fracture. Vertical and horizontal tectonic loads of 50 MPa (7252 psi) and 10 to 45 MPa (1450–6527 psi) are established, and then an internal fracture pressure of 10 MPa/s (1450 psi/s) is applied until the layer fails. The simulated fracturing is sensitive to the stress state and generated patterns range from single straight fractures to treelike networks. Reducing differential stress increases the injection pressure required to fracture and promotes off-plane damage, which increases fracture complexity. Consecutive periods of nonuniform weakening followed by unstable rupture generate multiple branches and segments.

We find that the processes that form HF complexity occur under a range of in-situ reservoir conditions and are likely to contribute to complex far-field fracture geometry and enhanced network connectivity.