Sensitivity of the active fracture model parameter to fracture network orientation and injection scenarios

Active fractures refer to the portions of unsaturated, connected fractures that actively conduct water. The active fracture model parameter accounts for the reduction in the number of fractures carrying water and in the fracture–matrix interface area in field-scale simulations of flow and transport in unsaturated fractured rocks. One example includes the numerical analyses of the fault test results at the Yucca Mountain site, Nevada (USA). In such applications, the active fracture model parameter is commonly used as a calibration parameter without relating it to fracture network orientations and infiltration rates. A two-dimensional, multiphase lattice-Boltzmann model was used in this study to investigate the sensitivity of the active fracture model parameter to fracture network orientation and injection scenarios for an unsaturated, variable dipping, and geometrically simple fracture network. The active fracture model parameter differed by as much as 0.11–0.44 when the effects of fracture network orientation, injection rate, and injection mode were included in the simulations. Hence, the numerical results suggest that the sensitivity of the active fracture model parameter to fracture network orientation, injection rates, and injection modes should be explored at the field-scale to strengthen the technical basis and range of applicability of the active fracture model.     

裂隙岩体中非饱和渗流与运移的概念模型及数值模拟

探讨了裂隙岩体中非饱和地下水渗流与溶质运移的几种概念模型的构造及数值模拟问题 ,如裂隙网络模型、连续体模型、等效连续体模型、双孔隙度 (单渗透率 )模型、双渗透率模型、多组份连续体模型等。在裂隙岩体中 ,非饱和地下水的渗流可能只局限于岩体中的岩石组份、或裂隙网络 ,也可能在裂隙和岩石中同时发生 ;对前一种情形只需考虑单一连续体中的流动 ,而后一种情况则需要包括地下水在岩石和裂隙之间的交换。岩体中的裂隙网络往往是溶质运移的主要通道 ;但当溶质在裂隙与岩石之间的渗透和扩散是重要的运移机制时 ,就需要考虑岩石与裂隙界面处的溶质交换。为了模拟岩石与裂隙之间地下水和溶质的交换 ,就需要了解岩石与裂隙之间相互作用的模式和范围 ,使得这类问题的概念模型较单一连续体模型多了一层不确定性、其数值模拟也变得更为困难。因为在实际问题中不易、甚至根本不能判别非饱和渗流的实际形态 ,具体采用哪种模型主要取决于分析的目的和对现场数据的掌握程度。不论哪种模型都会受到模型及参数不确定性的影响 ,因此必须考虑与其他辅助模型的比较.     

Analyzing unsaturated flow patterns in fractured rock using an integrated modeling approach

Characterizing percolation patterns in unsaturated fractured rock has posed a greater challenge to modeling investigations than comparable saturated zone studies due to the heterogeneous nature of unsaturated media and the great number of variables impacting unsaturated flow. An integrated modeling methodology has been developed for quantitatively characterizing percolation patterns in the unsaturated zone of Yucca Mountain, Nevada (USA), a proposed underground repository site for storing high-level radioactive waste. The approach integrates moisture, pneumatic, thermal, and isotopic geochemical field data into a comprehensive three-dimensional numerical model for analyses. It takes into account the coupled processes of fluid and heat flow and chemical isotopic transport in Yucca Mountain’s highly heterogeneous, unsaturated fractured tuffs. Modeling results are examined against different types of field-measured data and then used to evaluate different hydrogeological conceptualizations through analyzing flow patterns in the unsaturated zone. In particular, this model provides clearer understanding of percolation patterns and flow behavior through the unsaturated zone, both crucial issues in assessing repository performance. The integrated approach for quantifying Yucca Mountain’s flow system is demonstrated to provide a practical modeling tool for characterizing flow and transport processes in complex subsurface systems.     

Influence of flow velocity on conservative solute transport in sets of parallel fractures with fracture skin

Analysis of contaminant transport through fractured crystalline rocks has received considerable attention, particularly with regard to subsurface nuclear waste repositories. Most of the studies have employed the dual continuum approach, with the fractures and the rock matrix as the two continuums, assuming that fractures control the overall conductivity of the rock and the porous matrix just provides storage. However, field observations of rock fractures have shown that the real situation can be very complex. Based on some recent investigations, it has been reported that the portion of the rock matrix adjacent to many open fractures is physically and chemically altered. These alterations, referred to as the fracture skin, can have different sorption and diffusion properties compared to those of the undisturbed rock matrix and this may influence the transport of solutes through such formations. In the present study, a numerical model is developed to simulate conservative solute transport in a fractured crystalline rock formation using the triple continuum approach ?? with the fracture, fracture skin and the rock matrix as the three continuums. The model is solved using a fully implicit finite difference scheme. Contaminant migration in the fractured formation with and without skin has been simulated. It is observed that contaminant penetration along the fracture is enhanced at large flow velocities. The effect of flow velocity on conservative solute transport is investigated for different fracture apertures and fracture skin thicknesses. The influence of flow velocity on contaminant transport is demonstrated to be more with change in fracture aperture than with change in skin thickness.     

基于COMSOL Multiphysics的非饱和裂隙土降雨入渗特性研究

基于COMSOL Multiphysics软件对非饱和裂隙土降雨入渗特性进行数值模拟研究。通过将裂隙和基质分别离散成有限单元,建立了能充分模拟土中裂隙流、基质流以及裂隙-基质流量交换的离散裂隙-孔隙介质模型。结合"空气单元"的概念,对裂隙土的上边界进行模拟。该方法不仅能描述降雨初期雨水沿裂隙优先入渗的现象,还能描述当降雨量大于裂隙土入渗量时雨水沿地表流走的现象。通过对地表以下2 m深度内低渗含裂隙土体进行模拟,分析了裂隙的几何特征、基质的水力特性、前期水分条件以及降雨强度对非饱和裂隙土降雨入渗过程的影响。结果表明,在非饱和裂隙土中,存在两个主要的渗流过程:一是水沿裂隙优先流动;二是水不断从裂隙吸入基质中,基质吸收水的作用抑制了裂隙中优势流的发展。与裂隙的几何特征相比,基质的水力特性对非饱和裂隙土渗流的影响较大。增大基质的饱和渗透系数可能使由裂隙流主导的渗流过程转变为由基质流主导的渗流过程,而基质的非饱和特性与裂隙土的初始含水率改变了土体的储水能力,从而加速或延缓了降雨入渗至某一深度的时间。降雨强度对土体入渗速率和入渗量均有影响,当超过裂隙土的入渗能力时,多余积水沿地表流走,断面入渗率随...     

The role of porous matrix in water flow regulation within a karst unsaturated zone: an integrated hydrogeophysical approach

Some portions of the porous rock matrix in the karst unsaturated zone (UZ) can contain large volumes of water and play a major role in water flow regulation. The essential results are presented of a local-scale study conducted in 2011 and 2012 above the Low Noise Underground Laboratory (LSBB – Laboratoire Souterrain à Bas Bruit) at Rustrel, southeastern France. Previous research revealed the geological structure and water-related features of the study site and illustrated the feasibility of specific hydrogeophysical measurements. In this study, the focus is on hydrodynamics at the seasonal and event timescales. Magnetic resonance sounding (MRS) measured a high water content (more than 10 %) in a large volume of rock. This large volume of water cannot be stored in fractures and conduits within the UZ. MRS was also used to measure the seasonal variation of water stored in the karst UZ. A process-based model was developed to simulate the effect of vegetation on groundwater recharge dynamics. In addition, electrical resistivity tomography (ERT) monitoring was used to assess preferential water pathways during a rain event. This study demonstrates the major influence of water flow within the porous rock matrix on the UZ hydrogeological functioning at both the local (LSBB) and regional (Fontaine de Vaucluse) scales. By taking into account the role of the porous matrix in water flow regulation, these findings may significantly improve karst groundwater hydrodynamic modelling, exploitation, and sustainable management.     

Physical and stable-isotope evidence for formation of secondary calcite and silica in the unsaturated zone,Yucca Mountain,Nevada

Calcite and silica form coatings on fracture footwalls and cavity floors in the welded tuffs at Yucca Mountain, the potential site of a high-level radioactive waste repository. These secondary mineral deposits are heterogeneously distributed in the unsaturated zone (UZ) with fewer than 10% of possible depositional sites mineralized. The paragenetic sequence, compiled from deposits throughout the UZ, consists of an early-stage assemblage of calcite±fluorite±zeolites that is frequently capped by chalcedony±quartz. Intermediate- and late-stage deposits consist largely of calcite, commonly with opal on buried growth layers or outermost crystal faces of the calcite. Coatings on steep-dipping fractures usually are thin (⩽3 mm) with low-relief outer surfaces whereas shallow-dipping fractures and lithophysal cavities typically contain thicker, more coarsely crystalline deposits characterized by unusual thin, tabular calcite blades up to several cms in length. These blades may be capped with knobby or corniced overgrowths of late-stage calcite intergrown with opal. The observed textures in the fracture and cavity deposits are consistent with deposition from films of water fingering down fracture footwalls or drawn up faces of growing crystals by surface tension and evaporated at the crystal tips. Fluid inclusion studies have shown that most early-stage and some intermediate-stage calcite formed at temperatures of 35 to 85 °C. Calcite deposition during the past several million years appears to have been at temperatures <30 °C. The elevated temperatures indicated by the fluid inclusions are consistent with temperatures estimated from calcite δ¹⁸O values. Although others have interpreted the elevated temperatures as evidence of hydrothermal activity and flooding of the tuffs of the potential repository, the authors conclude that the temperatures and fluid-inclusion assemblages are consistent with deposition in a UZ environment that experienced prolonged heat input from gradual cooling of nearby plutons. The physical restriction of the deposits (and, therefore, fluid flow) to fracture footwalls and cavity floors and the heterogeneous and limited distribution of the deposits provides compelling evidence that they do not reflect flooding of the thick UZ at Yucca Mountain. The textures and isotopic and chemical compositions of these mineral deposits are consistent with deposition in a UZ setting from meteoric waters percolating downward along fracture flow paths.     

某核废物处置预选区中核素迁移模拟研究

核素在裂隙介质中的迁移问题是核废物深地质处置中极为关注的问题。为了解裂隙介质中核素的迁移规律,建立了基于双重介质理论的描述核素在裂隙域和基质域中迁移的基本微分方程,利用拉普拉斯变换推导出其解析解;在对西北某核废物处置场预选区地水文地质条件分析的基础上,获取相关参数,利用一维多途径核素迁移模型,选取国内在花岗岩中研究较多的核素Cs-134、Co-57、Tc-99,模拟这几种核素的相对浓度随模拟时间、迁移距离的变化规律。模拟结果表明：在其他条件都相同的情况下,Cs-134的迁移是最快的,而Tc-99迁移是最慢的。     

滴状流条件下非饱和交叉裂隙分流机制研究

交叉裂隙作为裂隙网络的基本结构是控制场地尺度非饱和渗流特性的关键。随着流量的减小,交叉裂隙非饱和渗流将从连续、稳定的线状流转变为非连续、非稳定的滴状流,但目前对后者的研究还很少。在滴状流条件下,开展了交叉裂隙非饱和流动特性的理论和试验研究,发现了交叉裂隙滴状流存在毛细力驱动以及重力与毛细力联合驱动两种分流驱动模式。基于瞬态静力平衡方法,提出了一套液滴分流理论及计算模型,实现了动态分流过程的定量化描述与预测。结合模型预测与可视化试验,详细探究了两种模式下液滴的分流过程,阐明了动态分流行为受重力、毛细力、黏滞力共同控制的细观机制,并揭示了液滴长度、裂隙倾角、通道中液体的累积等因素对界面流速、分流体积比例的影响。研究成果为低流量、低饱和度条件下非饱和裂隙岩体渗流的预测与控制提供了理论及试验支撑。     

Translation of field tracer-test results into bounding predictions of matrix diffusion in the shallow subsurface at Idaho National Laboratory, USA

Matrix-diffusion parameters deduced from an infiltration tracer test at Idaho National Laboratory (INL), USA, are combined with other site information in an analysis involving two dimensionless lumped parameters to assess the effects of matrix diffusion on contaminant transport at the INL over longer distance and time scales than were evaluated in the test. Matrix diffusion was interrogated in the test by comparing, in three different observation wells, the breakthrough curves of two simultaneously injected nonsorbing solutes that have different diffusion coefficients. The matrix-diffusion parameters deduced from the different breakthrough curves were in good agreement, suggesting that the parameters may be broadly applicable at the INL. With this in mind, the uncertainties in the individual parameters that make up the two lumped parameters were estimated, and the resulting ranges of parameter values were used to assess matrix diffusion over larger scales. Assessments of the effects of flow transients, spatial heterogeneity in transport parameters, and sorption on solute transport in the shallow subsurface flow system were also conducted. The methods presented here should be generally applicable to other settings for making bounding assessments of the effects of matrix diffusion while honoring the information obtained from tracer tests and other supporting data.     

Investigations on Diffusion Characteristics of Granite and Chalk Rock Mass

Contaminant transport through fractured rock mass is predominated by diffusion. This is due to the continuous interaction of the mobile water present in the fracture network and relatively immobile pore water, which is adsorbed on the surface and in the rock matrix itself. Even though the advective flow through the fracture network is high, besides sorption of rock mass, the diffusive exchange into the rock mass leads to significant retardation of contaminant transport. Hence, for describing contaminant transport in fractured rock mass, more precisely, the effect of retardation attributed to the matrix diffusion must be taken in account. With this in view, a methodology, which can be employed for determination of the diffusion characteristics of the rock mass, has been developed and its details are presented in this paper. Validation of the methodology has been demonstrated with the help of Archie’s law.     

A dual-continuum model (TOUGH2) for characterizing flow and discharge in a mechanically disrupted sandstone overburden

Underground hard coal mining usually disrupts the mechanical equilibrium of rock sequences, creating fractures within minor permeable rocks. The present study employs a dual-continuum model to assess how both fractured and porous sandstone media influence the percolation process in postmining setups. To test the approach, the software TOUGH2 was employed to simulate laminar fluid flow in the unsaturated zone of the Ibbenbüren Westfield mining area. Compared to other coal mining districts in Germany, this area is delineated by the topography and local geology, leading to a well-defined hydrogeological framework. Results reveal good agreement between the calculated and measured mine water discharge for the years 2008 and 2017. The constructed model was capable of reproducing the bimodal flow behavior of the adit by coupling a permeable fractured continuum with a low-conductivity rock matrix. While flow from the fractured continuum results in intense discharge events during winter months, the rock matrix determines a smooth discharge limb in summer. The study also evaluates the influence of individual and combined model parameters affecting the simulated curve. A detailed sensitivity analysis displayed the absolute and relative permeability function parameters of both continua among the most susceptible variables. However, a strong a priori knowledge of the value ranges for the matrix continuum helps to reduce the model ambiguity. This allowed for calibration of some of the fractured medium parameters for which sparse or variable data were available. However, the inclusion of the transport component and acquisition of more site-specific data is recommended to reduce their uncertainty.

     

Analytical solutions of tracer transport in fractured rock associated with precipitation-dissolution reactions

Precipitation-dissolution reactions are important for a number of applications such as isotopic tracer transport in the subsurface. Analytical solutions have been developed for tracer transport in both single-fracture and multiple-fracture systems associated with these reactions under transient and steady-state transport conditions. These solutions also take into account advective transport in fractures and molecular diffusion in the rock matrix. For studying distributions of disturbed tracer concentration (the difference between actual concentration and its equilibrium value), effects of precipitation-dissolution reactions are mathematically equivalent to a “decay” process with a decay constant proportional to the corresponding bulk reaction rate. This important feature significantly simplifies the derivation procedure by taking advantage of the existence of analytical solutions for tracer transport associated with radioactive decay in fractured rock. It is also useful for interpreting tracer breakthrough curves, because the impact of a decay process is relatively easy to analyze. Several illustrative examples are presented, which show that the results are sensitive to fracture spacing, matrix diffusion coefficient (fracture surface area), and bulk reaction rate (or “decay” constant), indicating that the relevant flow and transport parameters may be estimated by analyzing tracer signals.     

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.     

Stochastic finite element modelling of water flow in variably saturated heterogeneous soils

Water flow is greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently, this heterogeneity results in high variation in hydraulic properties of soil. In order to develop an accurate predictive model for transport processes in soil, the effects of this variability should be considered. In this study a two‐dimensional stochastic finite element flow model was developed for simulation of water flow through unsaturated soils. In this model, the stochastic partial differential governing equation of water flow, obtained from implementation of the perturbation‐spectral stochastic method on classical Richard's equation, was solved using a finite element method in the space domain and a finite difference scheme in the time domain. The effective hydrological parameters embedded in the mathematical model depend on time derivatives of capillary tension head; this makes possible to consider the hysteresis due to large‐scale variability of soil hydrological properties. The model is also capable of simulating infiltration and evaporation events and rapid change in the land surface boundary condition from one type event to another, based on a scheme used in the model for implementation of land surface boundary condition. The model was validated with the data obtained from a layered lysimeter test. The model was also used to simulate water flow under a long irrigation furrow. The results obtained with this model show better agreement with experimental measurements in comparison with a deterministic model. The possible reason for this agreement is that in the developed model, the influence of the variability of the properties of soil and effects of parameter hysteresis on water flow and water content redistribution are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

采用复合单元法模拟裂隙多孔介质变饱和流动

采用复合单元法建立了模拟裂隙多孔介质变饱和流动的数值模型。该模型具有以下特点：裂隙不需要离散成特定单元，而是根据几何位置插入到孔隙基质单元中形成复合单元；在复合单元中，分别建立裂隙流和孔隙基质流的计算方程，二者通过裂隙?基质界面产生联系并整合成复合单元方程；复合单元方程具有和常规有限单元方程相同的格式，因此，可以使用常规有限单元方程的求解技术。采用欠松弛迭代、集中质量矩阵以及自适应时步调节等技术，开发了裂隙多孔介质变饱和流动计算程序。通过模拟一维干土入渗和复杂裂隙含水层内的流动问题，验证了该模型的合理性和适用性。模拟结果为进一步认识非饱和裂隙含水层地下水流动特性提供了理论依据。     

Review: The state-of-art of sparse channel models and their applicability to performance assessment of radioactive waste repositories in fractured crystalline formations

Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. ‘Sparse channels’ refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.     

Evaluation of retention properties of a semi-synthetic fractured block from modelling at performance assessment time scales (Äspö Hard Rock Laboratory, Sweden)

Modelling of radionuclide transport in fractured media is a primary task for safety evaluation of a deep nuclear waste repository. A performance assessment (PA) model has been derived from site characterization data with the aim of improving confidence for quantifying transport of sorbing radionuclides at a safety time scale of 10⁶ y. The study was conducted on a 200?×?200?×?200 m semi-synthetic fractured block, providing a realistic system derived from the Äspö Hard Rock Laboratory (Sweden) dataset. The block includes 5,632 fractures ranging from 0.5 to 100 m in length and a heterogeneous matrix structure (fracture coating, gouge, mylonite, altered and non-altered diorite). The PA model integrates steady-state flow conditions and transport of released radionuclides during the safety time scale. An original simulation method was developed involving Eulerian flow and transport within fracture planes with a mixed hybrid finite element scheme and a semi-analytical source term to account for heterogeneous matrix diffusion. Total mass flux of radionuclides (conservative to strongly sorbing) was computed. A method to simplify the system was demonstrated, leading to a major path of 12 fractures. This is mainly due to the low connectivity of the fracture network. Matrix diffusion and sorption proved to have major impact on block retention properties for PA conditions.