Table of Contents

Cover

Title

Preface

Introduction

I.1. Context
I.2. Principle of the technique and illustrative experiments

1 Experiments in a Representative Environment

1.1. Mechanical set-up
1.2. Pulsed arc electric generator
1.3 Material properties
1.4. Measurements of radial permeability
1.5. X-ray tomography
1.6. Results on model materials
1.7. Summary of the results on sandstone
1.8. Discussion

2 Computational Modeling of the Process: Principles

2.1. Pressure generated by the pulsed arc electrical discharge
2.2. Mechanical modeling of rocks under dynamic loads
2.3. Coupled effects between damage and permeability
2.4. Summary and conclusions

3 Validation of the Computational Model

3.1. Simulation of the experiments in uniaxial compression
3.2. Confined tests on hollow cylinders
3.3. Isotropic versus anisotropic permeability
3.4. Conclusions

4 Computations on Representative Reservoir Geometries

4.1. Effect of repeated shocks
4.2. Simulation on a typical reservoir geometry
4.3. Optimization of the process

Concluding Remarks and Future Outlook

Bibliography

Index

End User License Agreement

List of Illustrations

1 Experiments in a Representative Environment

Figure 1.1.Overall view of the triaxial cell
Figure 1.2.Hydraulic frame hosting the triaxial cell
Figure 1.3.Experimental set-up – electrical part
Figure 1.4.Specimen characteristics
Figure 1.5.Schematic representation of the permeability cell
Figure 1.6.Evolution of following a permeability with injected electrical energy, single shock on mortar specimens
Figure 1.7.Evolution of the permeability of mortar specimens with the number of shocks, under an injected energy equal to 2.7 kJ and high confinement
Figure 1.8.Cross-section after computed tomography scanning of a mortar specimen
Figure 1.9. Three-dimensional tomography scans after one shock under high confinement. For a color version of the figure, seewww.iste.co.uk/pijaudier/drystone.zip
Figure 1.10. Three-dimensional tomography scans after one shock (left), three shocks (middle) and nine shocks (right). Tests under high confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 1.11. Evolution of pore size distribution with the number of shocks. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 1.12 . Evolution of the permeability of sandstone specimens with injected energy before and after the shock test

2 Computational Modeling of the Process: Principles

Figure 2.1.Saturation curve of water
Figure 2.2.Example of the evolution of injected energy with time
Figure 2.3.Test configuration for the calibration of the model which simulates pressure wave generation
Figure 2.4.Boundary condition and the numerical mesh of the simulation
Figure 2.5.Comparison of the experimental and the numerical pressure
Figure 2.6.Propagation of the pressure wave at different distances from the interelectrode space
Figure 2.7. Comparison between the numerical peak pressures and equation [2.6]
Figure 2.9.Elastic domains in the case of plane stress
Figure 2.10.Uniaxial tensile response of the rate-dependent model according to increasing strain rates
Figure 2.11.Strain rate effect of the tension strength of concrete (after [MAL 98])
Figure 2.12.Variation of the relative permeability of concrete with damage at various temperatures (after [CHO 07])
Figure 2.13. Evolution of the intrinsic permeability with damage. The solid line corresponds to the fit of equation [2.25]. Experimental results from [BAR 96]

3 Validation of the Computational Model

Figure 3.1.Finite element mesh of the simulation
Figure 3.2. Radial damage at different pressure levels for increasing peak pressure applied (from left to right: 28, 79, 105,193 and 216 MPa). For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.4. Vertical damage at different pressure levels for increasing peak pressure applied (from left to right: 28, 79, 105,193 and 216 MPa). For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.5. Largest principle damage at different pressure levels for increasing peak pressure applied (from left to right: 28, 79, 105,193 and 216 MPa). For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.6. a) Vertical cross tomography scans of a specimen submitted to one shock under 250 MPa; b) principal damage distribution computed under 216 MPa. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.7.Comparison of the experimental and numerical permeability as a function of the amplitude of the pressure wave
Figure 3.8.Finite element model of the simulation of tests on hollow cylinders
Figure 3.9. Typical evolution of the pressure overtime during the calculation for low confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.10. Evolution of damage in the model with injected energy for low confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.11. Evolution of damage and the flux vector with different levels of injected energy under low confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.12.Comparison of the experimental and the numerical average permeability under low confinement
Figure 3.13. Radial damage upon an increase in injected energy (from left to right: 470 J, 2.24 kJ, 7.1 kJ, 11.4 kJ) under medium confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.14. Maximum principal damage upon the increase in injected energy (from left to right: 470 J, 2.24 kJ, 7.1 kJ, 11.4 kJ) under medium confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.15. Evolution of the principal value of damage with time under an injected energy of 11.4 kJ (from left to right: 0, 15, 35, 55 and 140 µs) under medium confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.16.Evolution of the permeability as a function of the injected energy in the case of medium confinement
Figure 3.17. Evolution of radial damage with different levels of injected energy under high confinement (from left to right: 470 J, 5.11 kJ, 11.4 kJ). For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.18. Evolution of tangential damage with different levels of injected energy under high confinement (from left to right: 470 J, 5.11 kJ, 11.4 kJ). For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.19. Evolution of damage and flow under different levels of injected energy under high confinement. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 3.20.Comparison of the experimental and the numerical average permeability under high confinement with variable injected energy
Figure 3.21.Variations in average isotropic and anisotropic permeability of the specimen over time while under transient load

4 Computations on Representative Reservoir Geometries

Figure 4.1.The cumulative effect of energy injections over time
Figure 4.2.Evolution of damage with the number of shocks under high confinement
Figure 4.3.Finite element mesh for the analysis of a representative reservoir geometry
Figure 4.4.Damage due to a single shock under medium confinement
Figure 4.5.Radial depth of penetration of damage in the reservoir as a function of the injected energy for a single shock
Figure 4.6.Influence of a second shock on the radial depth of penetration of damage
Figure 4.7. Wave reflector – parabola with a symmetry of revolution. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 4.8.Finite element mesh with a reflector
Figure 4.9. Distribution of damage (maximum principal damage) for an injected energy equal to 400 kJ. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 4.10. Distribution of damage (maximum principal damage) for an injected energy equal to 400 kJ with a wave reflector. For a color version of the figure, see www.iste.co.uk/pijaudier/drystone.zip
Figure 4.11.Parametric waveform generated on the surface of the borehole
Figure 4.12.Finite element mesh used for the study of the influence of the waveform
Figure 4.13.Influence of the rising time in the waveform on the extent of damage. The curve with the higher plateau corresponds to the shortest rising time and the curve with the lower plateau corresponds to the longest rising time
Figure 4.14.Influence of the duration of the plateau in the waveform on the extent of damage. The curve with the higher plateau corresponds to the longest duration and the curve with the lower plateau corresponds to the shortest duration
Figure 4.15.Influence of the decaying duration of the waveform on the extent of damage. The curve with the higher plateau corresponds to the shortest duration and the curve with the lower plateau corresponds to the longest duration

Electrohydraulic Fracturing of Rocks

Gilles Pijaudier-Cabot

Christian La Borderie

Thierry Reess

Wen Chen

Olivier Maurel

Franck Rey-Berbeder

Antoine de Ferron

FOCUS SERIES

Series Editor Gilles Pijaudier-Cabot

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Gilles Pijaudier-Cabot, Christian La Borderie, Thierry Reess, Wen Chen , Olivier Maurel, Franck Rey-Berbeder and Antoine de Ferron to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2015959670

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISSN 2051-2481 (Print)

ISSN 2051-249X (Online)

ISBN 978-1-84821-710-2