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Anisotropy in Fracking: A Percolation Model for Observed Microseismicity

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Abstract

Hydraulic fracturing (fracking), using high pressures and a low viscosity fluid, allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high pressures and an extensive distribution of natural fractures which reduce the pressures. With time these fractures heal, sealing the remaining oil and gas in place. High volume fracking opens the healed fractures allowing the oil and gas to flow to horizontal production wells. We model the injection process using invasion percolation. We use a 2D square lattice of bonds to model the sealed natural fractures. The bonds are assigned random strengths and the fluid, injected at a point, opens the weakest bond adjacent to the growing cluster of opened bonds. Our model exhibits burst dynamics in which the clusters extend rapidly into regions with weak bonds. We associate these bursts with the microseismic activity generated by fracking injections. A principal object of this paper is to study the role of anisotropic stress distributions. Bonds in the y-direction are assigned higher random strengths than bonds in the x-direction. We illustrate the spatial distribution of clusters and the spatial distribution of bursts (small earthquakes) for several degrees of anisotropy. The results are compared with observed distributions of microseismicity in a fracking injection. Both our bursts and the observed microseismicity satisfy Gutenberg–Richter frequency-size statistics.

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Acknowledgments

The research of JQN and JBR has been supported by a grant from the US Department of Energy to the University of California, Davis #DE-FG02-04ER15568.

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Authors and Affiliations

  1. Department of Physics, University of California, One Shields Ave., Davis, CA, 95616, USA

    J. Quinn Norris & John B. Rundle

  2. Department of Earth and Planetary Sciences, University of California, One Shields Ave., Davis, CA, 95616, USA

    Donald L. Turcotte & John B. Rundle

  3. Santa Fe Institute, Santa Fe, NM, 87501, USA

    John B. Rundle

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  1. J. Quinn Norris
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  2. Donald L. Turcotte
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Correspondence to J. Quinn Norris.

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Norris, J.Q., Turcotte, D.L. & Rundle, J.B. Anisotropy in Fracking: A Percolation Model for Observed Microseismicity. Pure Appl. Geophys. 172, 7–21 (2015). https://doi.org/10.1007/s00024-014-0921-9

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