The effective fracture toughness in hydraulic fracturing

摘要

This paper examines the effective fracturetoughness approach which is used in hydraulic fracturing in orderto explain the high net-pressures that are often observed in fieldoperations. The effective fracture toughness is calculated using afully deterministic elasto-plastic hydraulic fracturing model.Rock is modelled by Mohr-Coulomb flow theory of plasticity forcohesive-frictional dilatant material. Fluid flow is modelled bylubrication theory. A cohesive crack model which takes intoaccount the softening behaviour of rocks is employed as thepropagation criterion. The fully coupled model is solvednumerically by the finite element method and the effectivefracture toughness is calculated using the path independent J-integral. The results show that plastic yielding near the tip of apropagating fracture provides an effective shielding, resulting inan increase in the rock effective fracture toughness by more thanan order of magnitude. It is demonstrated that an elastic modelbased on the concept of effective fracture toughness matches theresults of plasticity quite well. The effective fracture toughnessincreases with formation yielding, which is influenced by thedeviator of the in-situ stresses, the rock strength, the elasticmodulus and the pumping parameters. Tables of effectivefracture toughness for a representative set of physical parametersare presented.