Fluid-filled cracks are an important feature of the upper crust of the Earth, and the proposed work addresses how fluid-filled cracks interact with one another when several are emplaced closely in space and time. Specifically, most magmas are transported in cracks between the deep crust and volcanoes, thus an understanding of the mechanics of these bodies is important for volcanic processes on the Earth and other planets. Hydraulic fracturing has revolutionized the fossil fuel industry and is another example of fluid-filled cracks under pressure. The mechanics of interacting cracks will be examined by applying a novel method that has been developed in biology: swarm theory. The principal investigator will use three methods to tackle the problem. First, mathematical models will be developed. Second, computational models will examine the parameters that lead to the development of crack swarms. Third, analogue experiments, which use artificial materials at room temperature and pressure, will be applied to simulate the processes in the earth and verify the analytical and computational models. The method has the potential to influence the design of new methods that will influence the conditions by which hydrocarbon and geothermal reservoirs are exploited.

A new modeling paradigm is proposed that is based on swarm theory in order to clarify the mechanisms that lead to self-organization of fluid-filled cracks. The proposed research aims to clarify the origin of the alignment, repulsion, and attraction forces within fluid-filled cracks and to demonstrate how the interplay of these forces leads to emergent length scales that provide a lasting and measureable imprint of the mechanical conditions governing emplacement. Analytical, numerical, and analogue models will be developed to test the hypothesis that the mechanical conditions governing emplacement will be systematically expressed in the emergent geometry of the swarm, applying the results in order to infer emplacement conditions using measurements of spacing, length, and width for naturally-occurring dyke swarms and industrial hydraulic fractures. Observations of natural and manmade systems reveal substantial differences: hundreds of igneous dikes grow together as swarms, but hydraulic fractures tend to localize to 1 or 2 dominant strands. This paradox presents a unique opportunity to understand the physical mechanisms that govern whether or not injection of fluid will result in a fluid-driven fracture swarm.

National Science Foundation (NSF)
Division of Earth Sciences (EAR)
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Dennis Geist
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University of Pittsburgh
United States
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