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Hydrogeology Journal

, Volume 24, Issue 7, pp 1623–1649 | Cite as

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

  • Richeng Liu
  • Bo LiEmail author
  • Yujing Jiang
  • Na Huang
Paper

Abstract

Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.

Keywords

Groundwater flow Hydraulic properties Fracture network Permeability Mathematical expression 

Revue: Les expressions mathématiques pour estimer la perméabilité équivalente de réseaux de fracture de roche

Résumé

Les réseaux de fracture jouent un rôle plus significatif dans l’écoulement d’un fluide et du transport de soluté dans les massifs rocheux fracturés, en comparaison avec celui de la matrice rocheuse. Une estimation précise de la perméabilité des réseaux de fracture aiderait les chercheurs et les ingénieurs à mieux évaluer la performance des projets liés à l’écoulement du fluide dans les massifs rocheux fracturés. Cette étude présente un examen des travaux antérieurs qui ont porté sur l’estimation de la perméabilité équivalente de réseaux de fractures discrétisés (RFDs) en deux dimensions (2-D) compte tenu des influences des propriétés géométriques des massifs rocheux fracturés. Les expressions mathématiques pour les effets de neuf paramètres importants qui ont une incidence significative sur la perméabilité équivalente des RFDs sont résumées, comprenant (1) la distribution des longueurs de fracture, (2) la distribution des ouvertures, (3) la rugosité de la surface des fractures, (4) les fractures sans issues , (5) le nombre d’intersections, (6) le gradient hydraulique, (7) les conditions aux limites, (8) l’anisotropie, et (9) l’échelle. Les développements récents des réseaux de fractures en 3-D sont brièvement revus afin de souligner l’importance de l’utilisation de modèles 3-D dans les recherches futures.

Revisión: Las expresiones matemáticas para estimar la permeabilidad equivalente en redes de fracturas de roca

Resumen

Las redes de fracturas juegan un papel significativo en la conducción del flujo del fluido y en el transporte de solutos en las masas de roca fracturada, en comparación con el de la matriz de la roca. La estimación precisa de la permeabilidad de las redes de fracturas ayudaría a los investigadores e ingenieros a evaluar mejor el rendimiento de los proyectos relacionados con el flujo de fluido en masas de rocas fracturadas. Este estudio proporciona una revisión de trabajos previos que se han centrado en la estimación de la permeabilidad equivalente de redes bidimensionales (2-D) discretas de fractura (dfns) teniendo en cuenta las influencias de las propiedades geométricas de las masas de rocas fracturadas. Se resumen las expresiones matemáticas para los efectos de los nueve parámetros importantes que impactan significativamente sobre la permeabilidad equivalente de dfns, incluyendo (1) la distribución de la longitud de la fractura, (2) la distribución de las aberturas, (3) la rugosidad de la superficie de fractura, (4) las fracturas cerradas, (5) el número de intersecciones, (6) el gradiente hidráulico, (7) la tensión límite, (8) la anisotropía, y (9) la escala. Se revisa brevemente el reciente desarrollo de redes de fracturas 3-D para resaltar la importancia de la utilización de modelos 3-D en futuras investigaciones.

综述: 岩体裂隙网络渗透系数的数学表达式

摘要

裂隙网络相对于岩石基质对裂隙岩体内流体流动和污染物运移等性质有着更为重要的影响。准确预测裂隙网络的渗透系数将有助于研究人员更好的评估与裂隙岩体渗流相关的各项工程的安全稳定性。本综述回顾了前人利用裂隙岩体几何信息计算二维离散裂隙网络渗透系数的相关研究,讨论了裂隙网络模型中9个重要参数对渗透系数数学表达式的影响,这9个参数包括:(1) 裂隙长度分布, (2) 裂隙开度分布, (3) 裂隙表面粗糙度, (4) 裂隙断头, (5) 交点数量, (6) 水力梯度, (7) 边界应力, (8) 各向异性, (9) 模型尺寸。本文也介绍了三维裂隙网络模型的发展现状,并强调了在将来的工作中采用三维模型来评估渗透系数的重要性。

Revisão: Expressões matemáticas para estimar permeabilidade equivalente para redes de fraturadas em rochas

Resumo

Redes fraturadas desempenham um papel mais significante no fluxo de condução do fluido e no transporte de soluto na massa da rocha fraturada, comparado com o mesmo na rocha matriz. Estimativa precisa da permeabilidade das redes de fratura pode ajudar pesquisadores e engenheiros a melhor avaliar o desempenho dos processos associados com o fluxo de fluido na massa de rocha fraturada. Esse estudo fornece uma revisão de trabalhos anteriores que focaram na estimativa de permeabilidade de redes de fratura discretas (RFDs) bidimensionais (2-D) considerando a influência de propriedades geométricas de massa de rochas fraturadas. As expressões matemáticas para os efeitos de nove parâmetros importantes de impacto significante da permeabilidade equivalente das RFDs foram resumidas, incluindo (1) distribuição no comprimento da fratura, (2) distribuição da abertura, (3) rugosidade da superfície da fratura, (4) final da fratura, (5) número de intersecções, (6) gradiente hidráulico, (7) stress do limite, (8) anisotropia e (9) escala. Desenvolvimentos recentes de redes de fraturas 3-D foram brevemente revisados para destacar a importância da utilização de modelos 3-D em pesquisas futuras.

Notes

Acknowledgements

This study has been partially funded by the National Natural Science Foundation of China (Grant Nos. 41427802, 51379117, 51579239). These supports are gratefully acknowledged.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.School of EngineeringNagasaki UniversityNagasakiJapan
  3. 3.Rock Mechanics and Geo-Hazards CenterShaoxing UniversityShaoxingChina
  4. 4.State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and TechnologyShandong University of Science and TechnologyQingdaoChina

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