A comparison of hydraulic fracture front tracking algorithms

August 5, 2022


The problem of a plane strain hydraulic fracture propagating in a layered formation is considered. Fracture toughnessin-situ stress, and leak-off coefficient are assumed to vary by layer, while the elastic properties are kept constant throughout the domain for simplicity. The purpose of this study is to develop a numerical algorithm based on a fixed mesh approach, which is able to solve the above problem accurately using elements that can even be larger than the layer size. In order to do this, the concept of fictitious tip stress is first introduced for determining the fracture front location. In this technique, additional stress is applied to the tip element to suppress the opening and to mimic the width corresponding to the actual fracture front location. A theoretical basis for this concept has been established and it is further calibrated for piece-wise constant elements. Once the ability to track the crack front location is developed, the effect of layers is included by varying properties as a function of front location. Several numerical examples benchmarking the numerical solution, as well as highlighting the capabilities of the algorithm to tackle multiple thin layers accurately are presented.

Published in the Journal of Petroleum Science and Engineering, Volume 217, October 2022, 110841

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