The Effective Fracture Toughness in Hydraulic Fracturing

This paper examines the effective fracture toughness approach which is used in hydraulic fracturing in order to explain the high net-pressures that are often observed in field operations. The effective fracture toughness is calculated using a fully deterministic elasto-plastic hydraulic fracturing model. Rock is modelled by Mohr–Coulomb flow theory of plasticity for cohesive-frictional dilatant material. Fluid flow is modelled by lubrication theory. A cohesive crack model which takes into account the softening behaviour of rocks is employed as the propagation criterion. The fully coupled model is solved numerically by the finite element method and the effective fracture toughness is calculated using the path independent J-integral. The results show that plastic yielding near the tip of a propagating fracture provides an effective shielding, resulting in an increase in the rock effective fracture toughness by more than an order of magnitude. It is demonstrated that an elastic model based on the concept of effective fracture toughness matches the results of plasticity quite well. The effective fracture toughness increases with formation yielding, which is influenced by the deviator of the in-situ stresses, the rock strength, the elastic modulus and the pumping parameters. Tables of effective fracture toughness for a representative set of physical parameters are presented.