A 2D volume conservative numerical model of hydraulic fracturing

A volume conservative numerical approach is suggested for the modelling of propagation of a hydraulic fracture away from an injection well. A regular finite element grid is applied at the reservoir scale without any special gridding of the fracture. Models for critical fluid pressure are used to derive exact solutions for the propagation of hydraulic fractures in impermeable and homogeneous rocks. The numerical model is verified by these exact solutions for hydraulic fracturing. Numerical examples of hydraulic fracturing of permeable and inhomogeneous rocks are given, where the volume balance is given as a function of time.