Growth of hydraulic fractures with constricted opening and leakoff

Fracture growth in rocks is not continuous; the fracture traces exhibit numerous interruptionsand overlapping. This is an indication of the presence of bridges distributed (in 3D) all overthe fracture. While the bridges themselves make little obstruction for the fluid flow in thehydraulic fracture, they constrict the fracture opening and thus narrow the channel transmittingthe fracturing fluid. The effect of distributed bridges on the fracture opening can be modelledby introducing a Winkler layer in the fracture with an effective stiffness combining the averagebridge stiffness and the number of bridges per unit area of the fracture.When the fracturing fluid is injected and the leakoff is not negligible, the fracture size iscontrolled by the fracturing fluid left in the fracture after leakoff rather than by the stressconcentration/singularity at the fracture contour. The flow of the fluid and filling of the fracturedepends upon the fracture geometry and is also controlled by the bridges. However, the bridgesweakly influence the time dependence of the fracture dimensions: the KGD and PKN fracturesgrow proportionally to the square root of time: the effect is only in coefficients. Only in disc-like cracks the constriction reduces the rate of crack growth and weakens the time dependenceof the fracture radius.Acknowledgement. The authors acknowledge support from the Australian Research Councilthrough project DP190103260.