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Swarm Theory Framework for Evaluating Suitability of Models for Predicting Simultaneous Growth of Multiple Hydraulic Fractures

Banff International Research Station for Mathematical Innovation and Discovery

Swarming morphologies, that is, those involving multiple aligned members separated by a finite spacing, emerge from systems involving interplay among three fundamental drivers: 1) Alignment: Move in the same direction as neighboring members, 2) Avoidance: Not running into other members, and 3) Attraction: Do not move too far away from other members. As with other systems resulting in swarm-like morphologies, simulation of multiple hydraulic fractures requires a model accounting for the interplay of these fundamental drivers. Specifically, alignment corresponds to the control of the ambient stress field on hydraulic fracture orientation that leads to predominance of certain strike directions. Avoidance drives hydraulic fractures to separate from one another and/or suppress one anotherâ s growth due to the energetic consequences of propagation within the region of elevated compressive stresses surrounding each fracture. Finally, attraction arises from the reduction of viscous energy dissipation associated with splitting the injected fluid among many growing hydraulic fractures rather than just one dominant fracture. When combined, theoretically predicted alignment and emergent spacing in hydraulic fracture swarms matches match with field observations for both hydraulic fractures and naturally occurring dyke swarm analogues. Unfortunately, however, some of the most tempting simplifications, such as neglecting fluid flow or using a two-dimensional modeling domain, result in omitting or fundamentally altering the energetics associated with one or more of the three drivers of hydraulic fracture swarms. As a result, certain simplifications result in a complete loss of model fidelity. On the other hand, reasonably accurate simulations can be obtained from heavily simplified models as long as they preserve the three basic drivers and first principles such as volume balance.

Mathematics; Mechanics of deformable solids; Fluid mechanics

video/mp4

Author affiliation: University of Pittsburgh

2019-03-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68885

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/