A Split-node Method for Modeling Pulse and Hydraulic Fracturing

Reservoir stimulation is a key technology to enabling carbon and renewable resources recovery from the subsurface. The combination of pulse- and fluid-driven fracture propagation has great potential to revolutionize the hydro-fracturing industry. In this study, we present a novel method that extends the existing traction-at-split-node method to allow mode-I fracture propagation in both dynamic and quasi-static time frames. We implement this method in an open-source code, Defmod, that adaptively alternates between quasi-static and dynamic governing equations. We introduce a quasi-linear weakening failure criterion that allows irreversible tensile failures. To couple the fracture development and fluid flow inside and outside the fracture, we introduce a method to modify the fracture's neighboring elements by an anisotropic permeability as a function of fracture width. To ensure mass conservation, we balance the fluid-injection volume with the fracture-opening volume, by defining virtual fluid sources in the neighboring elements. We first compare an example of two-dimensional (2D) pulse-driven fracturing with experimental results. Then we compare an example of 3D penny-shaped hydraulic fracture, developing from a pressurized borehole, against the analytical Kristianovich-Geertsma-de Klerk (KGD) solution.