Ascent rates of 3D fractures driven by a finite batch of buoyant fluid

This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: https://doi.org/10.1017/jfm.2022.986. This is version 3 of this Preprint.

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Authors

Timothy Davis , Eleonora Rivalta , Delphine Smittarello, Richard Katz

Abstract

Propagation of fluid-filled fractures by fluid buoyancy is important in a variety of settings, from magmatic dykes and veins to water-filled crevasses in glaciers. Industrial hydro-fracturing utilises fluid-driven fractures to increase the permeability of rock formations, but few studies have quantified the effect of buoyancy on fracture pathways in this context. Analytical approximations for the buoyant ascent rate facilitate observation-based inference of buoyant effects in natural and engineered systems. Such analysis exists for two-dimensional fractures, but real fractures are 3D. Here we present novel analysis to predict the buoyant ascent speed of 3D fractures containing a fixed-volume batch of fluid. We provide two estimates of the ascent rate: an upper limit applicable at early time, and an asymptotic estimate (proportional to t^(-2/3)) describing how the speed decays at late time. We infer and verify these predictions by comparison with numerical experiments across a range of scales and analogue experiments on liquid oil in solid gelatine. We find the ascent speed is a function of the fluid volume, density, viscosity and the elastic parameters of the host medium. Our approximate solutions predict the ascent rate of fluid-driven fractures across a broad parameter space, including cases of water injection in shale and magmatic dykes. Our results demonstrate that in the absence of barriers or fluid loss, both dykes and industrial hydro-fractures can ascend by buoyancy over a kilometre within a day. We infer that barriers and fluid loss must cause the arrest of ascending fractures in industrial settings.

DOI

https://doi.org/10.31223/X5393K

Subjects

Fluid Dynamics, Geology, Glaciology, Mechanics of Materials, Volcanology

Keywords

Brittle fracture, lubrication theory, Volume, Fluid, Hydro-fracture

Dates

Published: 2022-06-20 03:44

Last Updated: 2023-01-03 11:22

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License

CC BY Attribution 4.0 International