Flow and transport predictions during multi-borehole tests in fractured chalk using discrete fracture network models

Multi-borehole pumping and tracer tests on the 10 to 100-m scale were conducted in a fractured chalk aquitard in the Negev Desert, Israel. Outcrop and core fracture surveys, as well as slug tests in packed-off intervals, were carried out at this site to obtain the parameters needed for construction of a stochastic discrete fracture network (DFN). Calibration of stochastic DFNs directly to the multiple borehole test data was inadequate. Instead, two equivalent deterministic DFN flow models were used: the vertical-fractures (VF) model, consisting of only vertical fractures, and the fractures’ intersections (INT) model, consisting of vertical and horizontal fractures with enhanced transmissivity at their intersections. Both models were calibrated against the multi-borehole response of one pumping test and their predictions were tested against three other independent pumping tests. The average accuracies of all transient drawdown predictions of the VF and INT models were 65 and 66%, respectively. In contrast to this equality in average drawdown predictions of both models, the INT model predicted better important breakthrough curve features (e.g., first and peak arrival times), than the VF model. This result is in line with previously assumed channeled flow, derived from analytical analysis of these pumping and tracer tests. Ronit Nativ, deceased, may her memory be blessed.     

Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.     

裂隙岩体溶质运移模型综述

本文综述了裂隙岩体系统中溶质运移的概念模型和数学模型。分析了目前各种裂隙岩体系统中溶质运移的数学模型的适用性和优缺点，为选取合理的数学模型求解具体的问题提供了参考依据。最后提出了有待进一步研究的问题。     

Solute transport in a single fracture with negligible matrix permeability: 1. fundamental mechanisms

This report describes the fracture-scale mechanisms acting on solute transport in fractured aquifers under natural-flow conditions. It focuses on low-permeability rocks where advection in the matrix is negligible compared with that in fractures. The relevant transport mechanisms detailed have been identified by experimental and theoretical studies over the past 30 years: advection and hydrodynamic dispersion, channeling effects, matrix diffusion, and sorption reactions. This review is intended to emphasize the fundamental concepts and to draw up a reader's guide through an extensive bibliography by linking key problems to key papers. These concepts might be integrated into transport models, but their influence at the large scale, however, remains an open question that is not dealt with in this review.

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Resumen Este informe describe los mecanismos que actúan a escala de fractura en el transporte de solutos en acuíferos fracturados, bajo condiciones de flujo natural. Se centra en rocas de baja permeabilidad en las que la advección en la matriz es despreciable en relación con la advección en las fracturas. Los mecanismos de transporte relevantes han sido identificados mediante estudios experimentales y teóricos realizados en los últimos 30 años. Consisten en advección y dispersión hidrodinámica, influencia de los canales, difusión en la matriz y reacciones de sorción. Esta revisión pretende enfatizar en los conceptos fundamentales y generar una guía para el lector por medio de una bibliografía abundante que relaciona los problemas clave con artículos clave. Estos conceptos podrían ser integrados en modelos de transporte, pero su influencia a gran escala es todavía un tema no resuelto, el cual no se aborda en este trabajo.

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Résumé Ce rapport décrit les mécanismes agissant sur le transport de soluté dans les aquifères fissurés en régime d'écoulement naturel. L'accent est mis sur les roches peu perméables, où le transport par convection dans la matrice est négligeable devant la convection dans les fractures. Les mécanismes de transport sont analysés à l'échelle de la fracture: convection et dispersion hydrodynamique, chenalisation, diffusion dans la matrice et réactions de sorption. L'objectif de ce travail est double: d'une part, mettre en avant les concepts fondamentaux pouvant être intégrés dans les modèles de transport, et d'autre part, établir un "guide" permettant au lecteur de s'orienter à travers une bibliographie abondante, en reliant chaque sujet abordé à quelques articles clés. Notons que l'influence de ces mécanismes sur le transport à grande échelle reste un problème clé qui ne sera pas abordé ici.

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In situ estimation of the effective chemical diffusion coefficient of a rock matrix in a fractured aquifer

An in situ method of estimating the effective diffusion coefficient for a chemical constituent that diffuses into the primary porosity of a rock is developed by abruptly changing the concentration of the dissolved constituent in a borehole in contact with the rock matrix and monitoring the time-varying concentration. The experiment was conducted in a borehole completed in mudstone on the campus of the University of the Free State in Bloemfontein, South Africa. Numerous tracer tests were conducted at this site, which left a residual concentration of sodium chloride in boreholes that diffused into the rock matrix over a period of years. Fresh water was introduced into a borehole in contact with the mudstone, and the time-varying increase of chloride was observed by monitoring the electrical conductivity (EC) at various depths in the borehole. Estimates of the effective diffusion coefficient were obtained by interpreting measurements of EC over 34 d. The effective diffusion coefficient at a depth of 36 m was approximately 7.8×10^?6 m²/d, but was sensitive to the assumed matrix porosity. The formation factor and mass flux for the mudstone were also estimated from the experiment.     

Roughness control on hydraulic conductivity in fractured rocks

The influence of joint roughness on the typologies of fluid flow inside fractures is well known and, thanks to experiences in the field of hydraulics, it has been studied from both a physical and mathematical point of view. Nevertheless, the formulations adopted by traditional hydraulic models are hardly applicable in the geological field, because of the difficulty encountered in the roughness parameter estimation. Normally this parameter can be estimated using the joint roughness coefficient (JRC), which considers both the asperity height and its regularity and directional trend. The main advantage in using the JRC arises from the fact that it can easily be obtained from geological-technical surveys and from comparison with the standard Barton profiles. Some relationships have been built up that allow for the estimation of the hydraulic conductivity tensor (an essential parameter for understanding water flow in fractured rock masses), not only as a function of traditional parameters like aperture, spacing, dip and dip direction, etc., but also of joint roughness, precisely expressed in terms of the roughness coefficient. These relationships have been studied initially from a theoretical point of view and then practically, through laboratory investigations.

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Resumen  Se conoce muy bien la influencia de la rugosidad de las grietas en las tipologías del flujo de fluidos a lo interior de las fracturas y gracias a las experiencias en el campo de hidráulica ha sido posible estudiarla desde puntos de vista matemáticos y físicos. Sin embargo, las formulaciones adoptadas por los modelos hidráulicos tradicionales tienen poca aplicabilidad en el campo geológico debido a la dificultad relacionada con la estimación del parámetro de rugosidad. Normalmente este parámetro puede estimarse usando el coeficiente de rugosidad de grieta (JRC) el cual considera tanto la altura de la aspereza como su regularidad y tendencia direccional. La principal ventaja de utilizar el JRC se deriva del hecho que puede obtenerse fácilmente de levantamientos técnico-geológicos y de la comparación con los perfiles Standard Barton. Se han construido algunas relaciones que permiten la estimación del tensor de conductividad hidráulica (un parámetro esencial para el entendimiento del flujo de agua en masas de roca fracturadas), no solo en función de parámetros tradicionales como apertura, espaciado, buzamiento y dirección de buzamiento, etc., sino también en función de la rugosidad de la grieta estimada con precisión en términos del coeficiente de rugosidad. Estas relaciones se han estudiado inicialmente desde un punto de vista teórico y luego de modo práctico a través de investigaciones de laboratorio.

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Résumé  L’influence de la rugosité des joints sur les types d’écoulement de fluide dans les fractures est bien connue et a été étudiée aussi bien du point de vue physique que mathématique grace à des expériences menées dans le domaine de l’hydraulique. Cependant les formulations adoptées dans les modèles hydrauliques traditionnels sont difficilement applicables dans le domaine de la géologie à cause de la difficulté rencontrée pour estimer la rugosité. Ce paramètre peut normalement être apprécié grace au coefficient de rugosité du joint (JRC), lequel prend en compte à la fois la hauteur de l’aspérité ainsi que sa régularité et sa direction. Le principal avantage dans l’utilisation du JRC réside dans le fait qu’il peut facilement être obtenu à partir d’études techniques-géologiques et par comparaison avec la classification de Barton. Des relations qui permettent une estimation du tenseur de conductivité hydraulique (un paramètre essentiel pour comprendre l’écoulement de l’eau dans les masses rocheuses fracturées) ont été élaborées, pas seulement en fonction de paramètres traditionnels tels que l’ouverture, l’espacement, l’inclinaison et la direction d’inclinaison, etc , mais aussi en prenant en compte la rugosité des joints à travers le coefficient de rugosité. Ces relations ont initialement été étudiées d’un point de vue théorique puis expérimentalement à travers des recherches en laboratoire.

     

裂隙岩体地下水溶质运移的尺度问题

核废料的安全贮存、地下污染的预测控制等目前面临的许多重大问题要求对大尺度裂隙岩体地下水溶质运移问题进行研究,然而裂隙岩体地下水溶质运移问题的尺度效应给这项研究带来了极大的挑战.本文介绍了裂隙岩体地下水溶质运移的多尺度概念模型及其物理和数学模拟方法,并探讨了模拟尺度与观测尺度、预测尺度、裂隙介质尺度之间的关系及尺度效应的分形特征.     

裂隙岩体溶质运移模型研究

核废料的地下深部贮存、垃圾填埋造成的污水下渗、海水入侵、输油管道老化引起渗漏等诸多应用领域的发展,要求从机理、试验和模型等方面发展裂隙岩体溶质运移理论。基于裂隙岩体系统溶质运移的多尺度概念模型,分析了目前描述裂隙岩体系统中溶质运移各种数学模型的适用性和优缺点,为选取合理的数学模型求解具体的问题提供了参考依据。最后提出了需要进一步研究的问题。     

Numerical modeling of the transient hydrogeological response produced by tunnel construction in fractured bedrocks

Groundwater inflows into tunnels constructed in fractured bedrocks not only constitute an important factor controlling the rate of advancement in driving the tunnel but may pose potential hazards. Drawdowns caused by tunnel construction may also induce geotechnical and environmental impacts. Here we present a numerical methodology for the dynamic simulation of the hydrogeological transient conditions induced by the tunnel front advance. The methodology is based on the use of a Cauchy boundary condition at the points lying along the tunnel according to which water discharge, Q, is computed as the product of a leakage coefficient, , and the head difference, (H−h), where H is the prescribed head at the tunnel wall and h is the hydraulic head in the fractured rock in the close vicinity of the tunnel. At a given position of the tunnel, is zero until the tunnel reaches such position when it is assigned a positive value. The use of step-wise time functions for allows an efficient and accurate simulation of the transient hydrogeological conditions at and around the tunnel during the excavation process. The methodology has been implemented in TRANMEF-3, a finite element computer code for groundwater flow in 3D fractured media developed at the University of A Coruña, Spain, and has been used to simulate the impact of a tunnel on the groundwater system at the Äspö island (Sweden). This tunnel was constructed to access an underground laboratory for research on radioactive waste disposal. The large amount of available data at this site provides a unique opportunity to test the performance of the numerical model and the proposed methodology for tunnel advance. With just minor calibration, the numerical model is able to reproduce accurately the measurements of inflows into the tunnel at several reaches and hydraulic heads at surface-drilled boreholes. These results obtained at the Äspö site lead us to conclude that accurate predictions of the transient hydrogeological responses induced by tunneling works in fractured bedrocks, can be achieved provided that a sound hydrogeological characterization of large-scale fracture zones is available.     

三维裂隙网络溶质运移粒子追踪法

本文讨论了利用粒子追踪方法模拟岩体三维裂隙网络中溶质迁移的问题.在本研究中裂隙为圆盘形,具有一定的张开宽度;其中流体的流动为面状流,发生在整个裂隙圆盘范围内.粒子追踪时考虑了对流、纵向弥散和横向弥散.利用提出的方法模拟了一个野外实际钻孔示踪试验.对模拟得到的示踪剂恢复曲线与实测的回收曲线进行了对比,二者的结果基本一致.     

The relationship between regional stress field,fracture orientation and depth of weathering and implications for groundwater prospecting in crystalline rocks

In a uniform granite gneiss study area in central Zimbabwe, lineaments oriented parallel to the maximum regional compressive stress orientation exhibit the thickest regolith development, while lineaments oriented perpendicular to the maximum compressive stress show the shallowest development of weathered regolith. The principal fracture set orientations were mapped using aerial imagery. The regional stress field, estimated from global stress maps, was used to determine the stresses acting on each principal lineament orientation. Multi-electrode resistivity profiling was carried out across fractures with different orientations to determine their subsurface regolith conditions. The results indicate that the 360 and 060° lineaments, which are sub-parallel to the principal compressive stress orientation (σ₁) exhibit maximum development of the regolith, while 130° lineaments perpendicular to σ₁ do not exhibit significant regolith development. Since regolith thickness has been positively correlated with groundwater resources, it is suggested that fractures with orientations sub-parallel to the principal compressive stress direction constitute favourable groundwater targets. Knowledge of the regional stress field and fracture set orientations can be used as an effective low cost tool for locating potentially higher yielding boreholes in crystalline rock terrains.     

单裂隙介质中的溶质运移研究综述

总结了有关单裂隙介质中溶质运移的基本特点和实验研究的成果,得出影响单裂隙介质中溶质运移的几个重要因素,例如骨架扩散、弥散、表面吸附等,介绍了几个具有代表性的数学模型,同时对模型的有效性和局限性进行了初步讨论.     

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that(1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.     

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that (1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy’s law satisfactorily; (2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.     

Numerical modeling of contaminant transport resulting from dissolution of a coal-tar pool in an experimental aquifer

A previously developed two-dimensional numerical model is further developed for simulating the transport of dissolved contaminants originating from dissolution of a coal tar pool in a stratified, saturated porous medium. The model is used to simulate contaminant transport resulting from a rectangular-shaped coal-tar-pool dissolution experiment conducted in a large-scale experimental aquifer. The experimental porous medium consists of two sand strata, a high-hydraulic-conductivity upper stratum and a low-hydraulic-conductivity bottom stratum. The experiment was conducted to a time of 354 days and the groundwater velocity was changed several times within this duration. Model simulations show good agreement against observed contaminant concentrations, and simulations show that dissolved solute below the pool migrated deeper into the bottom stratum as compared to the upper stratum. Furthermore, simulations also suggest that contaminant concentrations in the lower stratum never reached quasi steady-state during the experimental time frame.     

Simulations of solute transport in fractured porous media using 2D percolation networks with uncorrelated hydraulic conductivity fields

Two-dimensional percolation networks have been used to model a disordered and fractured porous medium. The advantage of percolation networks is that they allow the flow and transport properties of the system to be systematically studied as a function of the connectivity of the fractures and/or the permeable regions. The aim of this research is to study hydrodynamic dispersion in such networks, and to investigate the behavior of the longitudinal dispersion coefficient D_L with binary and log-normally distributed hydraulic conductivity fields. In particular, the study focuses on the behavior of D_L at the percolation threshold p_c, where the insufficiency of flow field homogenization and the limited number of tortuous paths for flow and transport force D_L to behave anomalously, i.e., to be scale- and time-dependent. The simulations indicate that the D_L population taken over a large number of the network realizations resembles a log-normal distribution, hence indicating that, unlike the hydraulic conductivity, D_L is not a self-averaged property whose variance should tend to zero when the size of the system tends to infinity. In addition, it was found that the power law that characterizes the scale dependence of D_L is contingent upon its computation method. Moreover, D_L is found to have a completely different behavior in networks with low and high connectivities.

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Resumen Simulaciones de transporte de solutos en medio heterogéneo utilizando redes de precolación 2D con campos de conductividad no correlacionados. Se han utilizado redes de percolación en dos dimensiones para modelizar un medio poroso fracturado y desordenado. La ventaja de redes de percolación es que permiten estudiar sistemáticamente las propiedades de flujo y transporte del sistema en función de la conectividad de las fracturas y/o regiones permeables. El objetivo de esta investigación es estudiar la dispersión hidrodinámica en las redes mencionadas, e investigar el comportamiento del coeficiente de dispersión longitudinal DL con campos de conductividad hidráulica que tienen distribución log-normal y binaria. El estudio se enfoca particularmente en el comportamiento de DL cuando se alcanza el threshold de percolación pc, donde la insuficiencia de homogenización del campo de flujo y el número limitado de trayectorias tortuosas de flujo y fuerza de transporte DL se comportan de manera anómala, i.e., son dependientes del tiempo y la escala. Las simulaciones indican que la población DL tomada en un número grande en las redes realizadas se asemeja a una distribución log-normal, indicando por lo tanto que, a diferencia de la conductividad hidráulica, DL no es una propiedad auto-promediable cuya variación tienda a cero cuando el tamaño del sistema tiende al infinito. Se encontró además que la ley potencia que caracteriza la dependencia en escala de DL es dependiente del método de cálculo. Más aún, se encontró que DL tiene un comportamiento completamente distinto en las redes de alta y baja conectividad.

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Résumé Des réseaux de percolation bi-dimensionnels ont été utilisés pour modéliser des milieux poreux fracturés et désordonnés. Lavantage de ces réseaux est quils permettent détudier les propriétés découlement et de transport en fonction de la connexité des fractures et/ou des zones perméables. Lobjectif est dappréhender la dispersion hydrodynamique et dinvestiguer le comportement du coefficient de dispersion longitudinal D_L pour des réseaux ayant une distribution des conductivités hydrauliques binaire et log-normale. En particulier, le comportement de D_L a été étudié au seuil de percolation p_c, là où linhomogénéité des vitesses du fluide et le nombre limité de chemins tortueux disponibles pour lécoulement et le transport entraînent un comportement anormal de D_L, à savoir, une dépendance vis-à-vis des échelles de temps et despace. Les simulations montrent que les populations de D_L définies pour un grand nombre de réseaux ressemblent à des distributions log-normales, indiquant que, contrairement à la conductivité hydraulique, D_L nest pas une propriété dont la variance tend vers zéro lorsque la taille du système tend vers linfini. Il a également été trouvé que les lois de puissance qui caractérisent la dépendance déchelle de D_L découlent directement de la méthode de calcul. Enfin, les simulations engendrent un comportement très différent de D_L dans des réseaux faiblement ou fortement connectés.

     

PHREEQC在地下水溶质反应-运移模拟中的应用

由于地下水污染的加剧,对地下水中污染物运移规律的研究日益受到重视。地下水中的溶质在运移过程中伴随着溶质组分间的化学反应,因此需要建立地下水溶质运移与化学反应的耦合模型。PHREEQC是近年来发展起来的描述局部平衡反应、动态生物化学反应的水文地球化学模拟软件。本文利用该模拟软件对一维地下水流动过程中溶质离子交换反应和动态氧化还原反应进行了模拟。结果表明,PHREEQC能够成功地进行溶质运移情况下复杂水化学反应模拟,但对于复杂地下水流和溶质运动的情况,有必要耦合其它的地下水流动和溶质运移软件来共同完成。     

稀疏不规则裂隙岩体模型三维水流-传热对温度和应力影响的试验研究

选取高放射核废物处置库重要预选场区甘肃北山地区的花岗岩,制作750 mm（宽）×300 mm（厚）×1 000 mm（高）的稀疏不规则裂隙岩体模型,该模型由18块花岗岩和竖向与斜向各两条裂隙组成,在裂隙及岩石内部埋置温度传感器、水压计、直角应变花,并在模型一侧设置局部热源,研究热源温度和裂隙水流速对岩石温度和应力的影响。结果表明,竖裂隙水主要从顶部进水口流向底部出水口,斜裂隙水主要从侧部进水口流向侧部出水口,竖裂隙与斜裂隙在交汇处存在微小流量交换;由于热源处在两条斜裂隙进水口之间,并且斜裂隙长度小于竖裂隙,岩石热传导与斜裂隙水流对岩石温度分布起控制作用,竖裂隙水流对岩石横向热传导起阻滞作用;由于热传导和水流传热的不规则性,上层岩石形成从左向右为主的传热路径,中层和下层岩石形成从上向下为主的传热路径;由于上、下层岩石温度梯度较小,岩石收缩受热拉应力,而中层岩石温度梯度较大,岩石膨胀受热压应力,大主应力的方向大致垂直于斜裂隙面与竖裂隙面的交线,岩石应力增量随斜平面方向的温度梯度增大而增大;热源温度越高,裂隙水流速越低,岩石温度越高、岩石应力越大,系统达到稳态需要的时间越长。