Fluid-driven fracture propagation in heterogeneous media: Probability distributions of fracture trajectories

David Santillán, Juan-Carlos Mosquera, and Luis Cueto-Felgueroso
Phys. Rev. E 96, 053002 – Published 17 November 2017

Abstract

Hydraulic fracture trajectories in rocks and other materials are highly affected by spatial heterogeneity in their mechanical properties. Understanding the complexity and structure of fluid-driven fractures and their deviation from the predictions of homogenized theories is a practical problem in engineering and geoscience. We conduct a Monte Carlo simulation study to characterize the influence of heterogeneous mechanical properties on the trajectories of hydraulic fractures propagating in elastic media. We generate a large number of random fields of mechanical properties and simulate pressure-driven fracture propagation using a phase-field model. We model the mechanical response of the material as that of an elastic isotropic material with heterogeneous Young modulus and Griffith energy release rate, assuming that fractures propagate in the toughness-dominated regime. Our study shows that the variance and the spatial covariance of the mechanical properties are controlling factors in the tortuousness of the fracture paths. We characterize the deviation of fracture paths from the homogenous case statistically, and conclude that the maximum deviation grows linearly with the distance from the injection point. Additionally, fracture path deviations seem to be normally distributed, suggesting that fracture propagation in the toughness-dominated regime may be described as a random walk.

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  • Received 3 July 2017
  • Revised 9 October 2017

DOI:https://doi.org/10.1103/PhysRevE.96.053002

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
General Physics

Authors & Affiliations

David Santillán*

  • Departamento de Ingeniería Civil: Hidráulica, Energía y Medio Ambiente, Universidad Politécnica de Madrid, Spain

Juan-Carlos Mosquera

  • Departamento de Mecánica de Medios Continuos y Teoría de Estructuras, Universidad Politécnica de Madrid, Spain

Luis Cueto-Felgueroso

  • Departamento de Ingeniería Civil: Hidráulica, Energía y Medio Ambiente, Universidad Politécnica de Madrid, Spain

  • *david.santillan@upm.es

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Issue

Vol. 96, Iss. 5 — November 2017

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