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Hydrogeology Journal

, Volume 27, Issue 1, pp 87–99 | Cite as

Three-dimensional flow characterization in a joint with plumose pattern

  • Benoit NigonEmail author
  • Andreas Englert
  • Christophe Pascal
Paper
  • 75 Downloads

Abstract

This work numerically simulates fracture flow in natural fractures, specifically in a joint with plumose pattern. A natural fracture surface, previously measured in the field using LiDAR scanning, was used to rebuild an open fracture geometry, assuming mode 1 fracture opening. Three-dimensional fracture flow was modeled by solving Stokes equation in a stationary regime using the finite element method. Three different pressure gradients and apertures were numerically investigated to better understand the impact of plumose patterns with different degrees of roughness. Resulting fracture flow fields were characterized by hydraulic aperture and by statistics on the directional components of the three-dimensional velocity vector. The results show that the hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. Beyond this classical finding, the study shows that the variance of the longitudinal component of the flow velocity vector also decreases with increasing roughness. This behavior can be predicted based on variance estimates connected to the parabolic profile. The results further revealed that the variances of the transverse components of the velocity vector increase with fracture surface roughness. These findings suggest that the roughness-induced reduction in the mean and the variance of the longitudinal component of the velocity vector in joints with rough surfaces is accompanied with a simultaneous increase of the transverse components of the three-dimensional velocity vector.

Keywords

Fractured rocks Natural fractures Numerical modeling Fracture flow 

Caractérisation tridimensionnelle de l’écoulement dans un joint avec des caractéristiques morphologiques en forme de plume

Résumé

Ce travail simule numériquement les écoulements dans des fractures naturelles, en particulier dans des joints avec des caractéristiques morphologiques de plumose. Une surface de fracture naturelle, initialement mesurée sur le terrain à l’aide d’une imagerie LiDAR, a été utilisée pour reconstituer la géométrie d’une fracture ouverte en supposant une ouverture de fracture en mode 1. L’écoulement tridimensionnel dans la fracture a été modélisé en résolvant l’équation de Stokes en régime permanent et en utilisant la méthode des éléments finis. Trois gradients de pression et trois ouvertures ont été étudiés numériquement afin de mieux comprendre l’impact des plumoses avec différents degrés de rugosité sur les écoulements. Les champs d’écoulement résultant dans la fracture ont été caractérisés à l’aide de l’ouverture hydraulique et de l’analyse statistique des composantes directionnelles du vecteur tridimensionnel de la vitesse. Les résultats montrent que l’ouverture hydraulique et la composante longitudinale du vecteur de la vitesse décroissent avec l’augmentation de la rugosité. Au-delà de ces résultats classiques, cette étude montre que la variance de la composante longitudinale du vecteur de vitesse diminue également avec l’augmentation de la rugosité. Ce comportement peut être prédit en fonction des estimations de variance liées au profil parabolique des vitesses dans la fracture. Les résultats ont montré que les variances des composantes transversales du vecteur de vitesse augmentent avec la rugosité des surfaces de fracture. Ces résultats suggèrent que la réduction de la moyenne et de la variance de la composante longitudinale du vecteur de vitesse induite par la rugosité dans les joints est accompagnée d’une augmentation simultanée des composantes transversales du vecteur de la vitesse tridimensionnelle.

Caracterización del flujo tridimensional en una diaclasa con patrón plumoso

Resumen

Este trabajo simula numéricamente el flujo de fractura en fracturas naturales, específicamente en una diaclasa con patrón plumoso. Se usó una superficie de fractura natural, previamente medida en el campo utilizando el escaneo LiDAR, para reconstruir una geometría de fractura abierta asumiendo la apertura de fractura en modo 1. El flujo de fractura tridimensional se modeló mediante la resolución de la ecuación de Stokes en un régimen estacionario utilizando el método de elementos finitos. Se investigaron numéricamente tres diferentes gradientes de presión y aperturas para comprender mejor el impacto de los patrones plumosos con diferentes grados de rugosidad. Los campos de flujo de fractura resultantes se caracterizaron por la apertura hidráulica y por las estadísticas sobre las componentes direccionales del vector de velocidad tridimensional. Los resultados muestran que la apertura hidráulica y la componente longitudinal del vector de velocidad disminuyen con el aumento de la rugosidad. Más allá de este hallazgo clásico, el estudio muestra que la varianza de la componente longitudinal del vector de velocidad de flujo también disminuye al aumentar la rugosidad. Este comportamiento se puede predecir a partir de las estimaciones de varianza relacionadas con el perfil parabólico. Los resultados revelaron además que las varianzas de las componentes transversales del vector de velocidad aumentan con la rugosidad superficial de la fractura. Estos hallazgos sugieren que la reducción inducida por la rugosidad en la media y la varianza del componente longitudinal del vector de velocidad en las diaclasas con superficies rugosas se acompaña con un aumento simultáneo de las componentes transversales del vector de la velocidad tridimensional.

羽状模式节理中的三维水流特征描述

摘要

本研究工作数值模拟了天然断裂中、特别是羽状模式节理中的断裂水流。过去在野外采用LiDAR扫描测量的天然断裂面用来重建假定模式1 断裂缝隙的开放的断裂几何形状。采用有限元方法依靠稳定状态下求解Stokes方程模拟了三维断裂水流。数值上调查了三个不同的压力梯度和缝隙以便更好地了解不同粗糙程度的羽状模式的影响。通过水力缝隙以及对三维速度矢量方向性成分的统计学计算,描述了断裂水流场的特征。结果显示,水力缝隙及速度矢量纵向成分随着粗糙度增加而减少。除了这个经典的发现, 研究还显示,水流速度矢量纵向成分的方差也随着粗糙度的增加而减少。这种状况可根据与抛物线剖面相连的方差估算值预测。结果进一步揭示,速度矢量的横向成分方差随着断裂面的粗糙度的增加而增加。这些发现表明,粗糙度引起的带有粗糙面节理中速度矢量纵向成分平均值和方差的减少伴随着三维速度矢量横向成分的同时增加。

Caracterização do fluxo tridimensional em uma diaclase com padrão plumoso

Resumo

Este trabalho simula numericamente o fluxo fraturado em fraturas naturais, especificamente em uma diaclase com padrão plumoso. Uma superfície de fratura natural, previamente medida no campo utilizando a varredura LiDAR foi utilizada para reconstruir uma geometria de fratura aberta assumindo como abertura de fratura o modo 1. O fluxo de fratura tridimensional foi modelado aplicando-se a equação de Stokes em um regime estacionário utilizando o método de elementos finitos. Três diferentes gradientes de pressão e aberturas foram numericamente investigados para melhor entender o impacto do padrão plumoso com diferentes graus de rugosidade. Os campos de fraturas resultantes foram caracterizados por abertura hidráulica e estatísticas nos componentes direcionais do vetor de velocidade tridimensional. Os resultados mostram que a abertura hidráulica e o componente longitudinal do vetor de velocidade diminuem com o aumento da rugosidade. Além deste achado clássico, o estudo mostra que a variância do componente longitudinal do vetor de velocidade de fluxo também diminui com o aumento da rugosidade. Este comportamento pode ser previsto baseado nas estimativas de variância conectadas ao perfil parabólico. Os resultados revelaram ainda que as variâncias dos componentes transversais do vetor velocidade aumentam com a rugosidade da superfície da fratura. Isto sugere que a redução da média e da variância da componente longitudinal do vetor velocidade em articulações com superfícies irregulares induzidas pela rugosidade é acompanhada de um aumento simultâneo dos componentes transversais do vetor de velocidade tridimensional.

Notes

Acknowledgements

We acknowledge two anonymous reviewers for their constructive comments. The authors are thankful to Mandy Duda (International Geothermal Centre, Bochum) for her priceless help to improve the quality of the manuscript. We are grateful to Aline Saintot (Ruhr-Universität Bochum) for her help in identifying and performing surface elevation measurements on joints. Also we thank Rolf Bracke (GZB) for his support.

Funding information

The first author benefited from a PhD grant from the Applied Research on Enhanced Geothermal Energy System (AGES) graduate school, a joint venture between the International Geothermal Centre Bochum (GZB) and the Institute of Geology, Mineralogy and Geophysics, Ruhr-Universität Bochum.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.International Geothermal CenterBochumGermany
  2. 2.Institute of Geology, Mineralogy and GeophysicsRuhr University BochumBochumGermany

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