Growth of hydraulic fractures with constricted opening and leakoff

Fracture growth in rocks is not continuous; the fracture traces exhibit numerous interruptions
and overlapping. This is an indication of the presence of bridges distributed (in 3D) all over
the fracture. While the bridges themselves make little obstruction for the fluid flow in the
hydraulic fracture, they constrict the fracture opening and thus narrow the channel transmitting
the fracturing fluid. The effect of distributed bridges on the fracture opening can be modelled
by introducing a Winkler layer in the fracture with an effective stiffness combining the average
bridge 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 is
controlled by the fracturing fluid left in the fracture after leakoff rather than by the stress
concentration/singularity at the fracture contour. The flow of the fluid and filling of the fracture
depends upon the fracture geometry and is also controlled by the bridges. However, the bridges
weakly influence the time dependence of the fracture dimensions: the KGD and PKN fractures
grow 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 dependence
of the fracture radius.
Acknowledgement. The authors acknowledge support from the Australian Research Council
through project DP190103260.