Finite element simulations of hydraulic fracturing: A comparison of algorithms for extracting the propagation velocity of the fracture

The finite element method is a powerful and general numerical method used to simulate subsurface processes. In this paper, we take recent hydraulic fracturing propagation algorithms and assess their performance when used within the finite element framework. In particular, we evaluate aperture and energy-based methodologies that are capable of extracting the propagation velocity of a hydraulic fracture propagating throughout the toughness and viscous regime. Such algorithms have the benefit of a quicker convergence on the fracture front. The aperture-based methodology consists of the multi-scale aperture asymptote that is yet to be applied with finite elements. On the other-hand, the energy-based methodology consists of a recently developed procedure for predicting the propagation velocity from the energy release rate, which is calculated using a J-integral devised for hydraulic fracturing. A comparison of the accuracy and the number of iterations required to converge on the fracture length is undertaken, and found to produce similar results for both methods. Consequently, we conclude that the higher accuracy of energy-based methods in extracting stress intensity factors does not immediately translate to a higher accuracy in extracting propagation velocities, most notably in the toughness-dominated propagation regime. Given the similar performance of the methods, and the simplicity of the aperture-based approach, we then extend the evaluation of the multi-scale aperture asymptote to the case of buoyancy-driven propagation. As a result, the aperture asymptote is shown to be a simple and efficient method for the simulation of subsurface processes using a finite element framework.