A review of some tracer-test design equations for tracer-mass estimation and sample-collection frequency

Determination of necessary tracer mass, initial sample-collection time, and subsequent sample-collection frequency are the three most difficult aspects to estimate for a proposed tracer test prior to conducting the tracer test. To facilitate tracer-mass estimation, 33 mass-estimation equations have been developed over the past century. These 33 equations are reviewed here, 32 of which were evaluated using previously published tracer-test design examination parameters. Comparison of the results produced a wide range of estimated tracer mass, but no means is available by which one equation may be reasonably selected over the others. Each equation produces a simple approximation for tracer mass. Most of the equations are based primarily on estimates or measurements of discharge, transport distance, and suspected transport times. Although the basic field parameters commonly employed are appropriate for estimating tracer mass, the 33 equations are problematic in that they were all probably based on the original developers experience in a particular field area and not necessarily on measured hydraulic parameters or solute-transport theory. Suggested sampling frequencies are typically based primarily on probable transport distance, but with little regard to expected travel times. This too is problematic in that tracer sampling remains a haphazard process that tends to result in false negatives or data aliasing. Simulations from the recently developed efficient hydrologic tracer-test design methodology (EHTD) were compared with those obtained from 32 of the 33 published tracer-mass estimation equations and suggested sampling frequencies. EHTD applies functional relationships developed from hydrologic measurements in a solute-transport model to develop a preliminary tracer-breakthrough curve that has been shown to reasonably predict actual tracer-test results.     

Efficient hydrologic tracer-test design for tracer-mass estimation and sample-collection frequency. 2. Experimental results

Effective tracer-test design requires that the likely results be predicted in advance of test initiation to ensure tracer-test success. EHTD-predicted breakthrough curves (BTCs) for various hydrological conditions were compared with measured BTCs obtained from actual tracer tests. The hydrological conditions for the tracer tests ranged from flowing streams to porous-media systems. Tracer tests evaluated included flowing streams tracer tests conducted in small and large surface-water streams, a karst solution conduit, and a glacial-meltwater stream and porous-media systems conducted as natural-gradient, forced-gradient, injection-withdrawal, and recirculation tracer tests. Comparisons between the actual tracer tests and the predicted results showed that tracer breakthrough, hydraulic characteristics, and sample-collection frequency may be forecasted sufficiently well in most instances as to facilitate good tracer-test design. Comparisons were generally improved by including tracer decay and/or retardation in the simulations. Inclusion of tracer decay in the simulations also tended to require an increase in set average tracer concentration to facilitate matching peak concentrations in the measured BTCs, however. Both nonreactive tracer and reactive tracer predictions produced recommended sample-collection frequencies that would adequately define the actual BTCs, but estimated tracer-mass estimates were less precise.     

Effect of different transport observations on inverse modeling results: case study of a long-term groundwater tracer test monitored at high resolution

Conservative tracer experiments can provide information useful for characterizing various subsurface transport properties. This study examines the effectiveness of three different types of transport observations for sensitivity analysis and parameter estimation of a three-dimensional site-specific groundwater flow and transport model: conservative tracer breakthrough curves (BTCs), first temporal moments of BTCs (m ₁), and tracer cumulative mass discharge (M _d) through control planes combined with hydraulic head observations (h). High-resolution data obtained from a 410-day controlled field experiment at Vandenberg Air Force Base, California (USA), have been used. In this experiment, bromide was injected to create two adjacent plumes monitored at six different transects (perpendicular to groundwater flow) with a total of 162 monitoring wells. A total of 133 different observations of transient hydraulic head, 1,158 of BTC concentration, 23 of first moment, and 36 of mass discharge were used for sensitivity analysis and parameter estimation of nine flow and transport parameters. The importance of each group of transport observations in estimating these parameters was evaluated using sensitivity analysis, and five out of nine parameters were calibrated against these data. Results showed the advantages of using temporal moment of conservative tracer BTCs and mass discharge as observations for inverse modeling.     

水箱-管道系统溶质运移实验研究及其岩溶水文地质意义

为了研究岩溶管道中溶潭对溶质运移的影响,在实验室内构建水箱-管道系统,在不同管道结构和水流条件下进行定量示踪实验并得到相应的穿透曲线(BTCs);采用Qtracer2软件分析溶质运移参数,采用滞后系数R分析实验结果与一维经典对流弥散方程解析解之间的差别。实验结果显示:随着水箱数量的增加,示踪剂(NaCl)峰值质量浓度逐渐降低,弥散系数和弥散度逐渐增加,穿透曲线拖尾逐渐增长,表明水箱的瞬态存储使溶质运移滞后;与不对称水箱相比,对称水箱BTC拖尾较长;峰现时间随着不对称水箱数量的增多明显滞后;出口流量增加时,弥散度减小,BTC拖尾变短。一维经典对流弥散方程解析解仅对单管道最大流量条件下的BTC拟合较好,对流量较小的单管道和水箱-管道系统的BTC拟合较差,需研究适用的模型解释其拖尾现象。     

A comparison of estimated and calculated effective porosity

 Effective porosity in solute-transport analyses is usually estimated rather than calculated from tracer tests in the field or laboratory. Calculated values of effective porosity in the laboratory on three different textured samples were compared to estimates derived from particle-size distributions and soil–water characteristic curves. The agreement was poor and it seems that no clear relationships exist between effective porosity calculated from laboratory tracer tests and effective porosity estimated from particle-size distributions and soil–water characteristic curves. A field tracer test in a sand-and-gravel aquifer produced a calculated effective porosity of approximately 0.17. By comparison, estimates of effective porosity from textural data, moisture retention, and published values were approximately 50–90% greater than the field calibrated value. Thus, estimation of effective porosity for chemical transport is highly dependent on the chosen transport model and is best obtained by laboratory or field tracer tests. Received, March 1997 · Revised, August 1997 · Accepted, August 1997     

裂隙岩体渗透性理论研究进展

裂隙岩体的渗透性是地质灾害、水电工程、矿山工程等研究中需要考虑的重要因素之一。岩体裂隙本身的渗透性取决于它的空间几何参数,因此,可以通过直接测量裂隙的几何要素计算出岩体的渗透系数。岩体的结构及其透水性直接关系到建筑物围岩的稳定及安全.通过水力劈裂试验,可以真实地反映高水压作用下岩体的结构和渗透性的变化规律.以某水电站工...     

Constraining the uncertainty in fracture geometry using tracer tests

In fractured-rock aquifers, the geometric and hydraulic properties of the fractures commonly have a dominant influence on transport. Tracer tests are often used to estimate directly the gross transport properties of a fractured rock mass. The prospects for understanding characteristics of the heterogeneities in a fractured porous medium were explored from evidence provided by tracer experiments. The approach was to simulate flow and transport on a large set of prescribed fracture networks in a two-dimensional homogeneous permeable medium, thus generating synthetic tracer test data. The fracture orientation, aperture, spacing and network geometry were systematically altered from one case to the next. A classification scheme was devised for the tracer breakthrough curves using principal component analysis and this classification was linked to the fracture pattern properties. Even under highly simplified and controlled conditions, quite different fracture patterns can produce very similar breakthrough curves. The classification scheme thus demonstrates that a single breakthrough curve cannot reveal the fracture geometry with any precision. However, the scheme provided a methodology for rejecting geometric properties that do not belong to the fracture pattern under investigation, thus reducing the uncertainty in fracture geometry.     

Characterization of hydrogeologic properties for a multi-layered alluvial aquifer using hydraulic and tracer tests and electrical resistivity survey

A multi-layered aquifer, typical of riverbank alluvial deposits in Korea, was studied to determine the hydrologic properties. The geologic logging showed that the subsurface of the study site was comprised of four distinctive hydrogeologic units: silt, sand, highly weathered and fresh bedrock layers. The electrical resistivity survey supplied information on lateral extension of hydrogeologic strata only partially identified by a limited number of the geologic loggings. The laboratory column tracer test for the recovered core of the sand layer resulted in a hydraulic conductivity of 5.00×10⁻² cm/s. The slug tests performed in the weathered rock layer yielded hydraulic conductivities of 4.32–7.72×10⁻⁴ cm/s. Hydraulic conductivities for the sand layer calculated from the breakthrough curves of bromide ranged between 2.08×10⁻³ and 2.44×10⁻² cm/s with a geometric mean of 6.89×10⁻³ cm/s, which is 7 times smaller than that from the laboratory column experiment. The trend of increasing hydraulic conductivity with an increase in tracer travel length is likely a result of the increased likelihood of encountering a high conductivity zone as more of the aquifer is tested. The combined hydrogeologic site characterization using hydraulic tests, tracer tests, and column test with geologic loggings and geophysical survey greatly enhanced the understanding of the hydrologic properties of the multi-layered alluvial aquifer.     

桂林毛村地下河流域雨季与旱季定量示踪分析

以典型岩溶地区广西桂林市毛村地下河流域为例,基于在线高分辨率监测进行雨季与旱季定量示踪试验,精细刻画流域内含水介质特征。根据示踪试验研究及毛村地下河系统内地下水的径流和分布特征,可将毛村地下河系统划分为社更岩、扁岩地下河系统,大冲里-背地坪系统和大岩前落水洞-毛村出口系统。这三个子系统分布于毛村流域的上游和下游,其示踪剂浓度历时曲线为陡升陡降的尖峰,地下管道相对单一,无较大岔道和溶潭发育。各段地下河水动力作用以对流作用为主,且水流一般呈现为紊流流态。雨季流速快、流量较大,平均运移时间短,示踪剂回收率比旱季高。流域中游含水介质相对均匀,无管道发育,地下水主要赋存于溶蚀裂隙。      

Using Sequential Self-Calibration Method to Identify Conductivity Distribution: Conditioning on Tracer Test data

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases.     

Modeling solute transport in river channels using dispersion theory

Carrying out a series of field tracer experiments in river channels allows recognition of river behavior in different flow conditions and thus investigation of the evolution of a solute, tracer, or pollutant over the range of flow rates considered. In this paper, data from tracing tests conducted on the Artibai River in northern Basque Country are used to demonstrate the approach. In all experiments the tracer used was lithium and it was added to the river as an input pulse. An analytical solution to the instantaneous injection model that accounts for the effective initial amount of tracer injected, calculated from the tracer breakthrough curve, instead of the conventional initial injection concentration, is used. The technique is applied to estimate travel times, Péclet numbers, and dispersion coefficients using an optimization algorithm with the aim of characterizing the tracer movement in the stream and analyzing its evolution. Subsequently, considering the results of various tracer experiments, conducted over different flow rates, empirical relationships between dispersion, velocity, and flow rates may be determined. This information allows characterization of the river behavior and can be used to model transportation and dispersion of a tracer or pollutant.     

Regional-scale analysis of karst underground flow deduced from tracing experiments: examples from carbonate aquifers in Malaga province,southern Spain

Tracer concentration data from field experiments conducted in several carbonate aquifers (Malaga province, southern Spain) were analyzed following a dual approach based on the graphical evaluation method (GEM) and solute transport modeling to decipher flow mechanisms in karst systems at regional scale. The results show that conduit system geometry and flow conditions are the principal factors influencing tracer migration through the examined karst flow routes. Solute transport is mainly controlled by longitudinal advection and dispersion throughout the conduit length, but also by flow partitioning between mobile and immobile fluid phases, while the matrix diffusion process appears to be less relevant. The simulation of tracer breakthrough curves (BTCs) suggests that diffuse and concentrated flow through the unsaturated zone can have equivalent transport properties under extreme recharge, with high flow velocities and efficient mixing due to the high hydraulic gradients generated. Tracer mobilization within the saturated zone under low flow conditions mainly depends on the hydrodynamics (rather than on the karst conduit development), which promote a lower longitudinal advection and retardation in the tracer migration, resulting in a marked tailing effect of BTCs. The analytical advection-dispersion equation better approximates the effective flow velocity and longitudinal dispersion estimations provided by the GEM, while the non-equilibrium transport model achieves a better adjustment of most asymmetric and long-tailed BTCs. The assessment of karst underground flow properties from tracing tests at regional scale can aid design of groundwater management and protection strategies, particularly in large hydrogeological systems (i.e. transboundary carbonate aquifers) and/or in poorly investigated ones.     

A natural-gradient field tracer test for evaluation of pollutant-transport parameters in a porous-medium aquifer

This paper describes a natural-gradient field tracer test to characterise solute-transport properties in a sand and gravel aquifer in the Hebei Province, northern China. Some laboratory-scale column tests on aquifer material and a local-scale field borehole-dilution test have been conducted previously, but the field test reported herein represents the only large-scale tracer test in the aquifer, which is the sole water supply to the city of Shi Jiazhuang and which is threatened by urban pollution. The aim of the study was to quantify the transport behaviour of nonreactive pollutants in this aquifer. Little quantitative data are available concerning its solute-transport properties; thus, the results of the tracer test are significant and critical for understanding pollutant transport and fate. The in-situ tracer test was carried out in the aquifer using a slug injection of the geochemically conservative, radioactive iodine tracer ¹³¹I. The longitudinal (α _L ) and transverse (α _T ) hydrodynamic dispersivities for solute transport in the field are 1.72 and 0.0013 m, respectively. The ratio of longitudinal dispersivity α _L and the flow length at the field scale is 1:10. The ratio between α _L and α _T from the in-situ test (~1,300:1) demonstrates a dominant longitudinal dispersion in this fluvial sand and gravel aquifer. The tracer test further indicates a relatively short transit time for the aquifer (linear velocities ~13 m/d) under natural-gradient conditions. Electronic Publication     

Hydraulic parameters and solute velocities in triple-porosity karstic-fissured-porous carbonate aquifers: case studies in southern Poland

 Rock and flow parameters of three karstic-fissured-porous aquifers in the Krakow-Silesian Triassic formations were measured using various methods and compared. Though cavern and fissure porosities are shown to be very low (cavern porosity below 0.5% and fracture porosity below 0.2%), they contribute dominantly to the hydraulic conductivity (from about 1.3×10^–6 to about 11×10^–6 m/s). Matrix porosity (2–11%) is shown to be the main water reservoir for solute transport and the main or significant contributor to the specific yield (<2%). Though the matrix porosity is shown to be much larger than the sum of the cavern and fissure porosities, its contribution to the total hydraulic conductivity is practically negligible (hydraulic conductivity of the matrix is from about 5×10^–11 m/s to about 2×10^–8 m/s). On the other hand, the matrix porosity (for neglected cavern and fissure porosities) when combined with tracer ages (or mean travel times) is shown to yield proper values of the hydraulic conductivity (K) by applying the following formula: K≅(matrix porosity×mean travel distance)/(mean hydraulic gradient×mean tracer age). Confirming earlier findings of the authors, this equation is shown to be of great practical importance because matrix porosity is easily measured in the laboratory on rock samples, whereas cavern and fracture porosities usually remain unmeasurable. Received: 21 February 1997 · Accepted: 13 May 1997     

岩溶地下河浊度来源及对示踪试验影响的定量分析

定量示踪技术是分析岩溶含水层水力特征和岩溶水系统结构的重要手段,地下河浊度是制约定量示踪试验精确性的关键因素。针对西南典型岩溶地下河,以三次不同水动力条件下示踪试验为研究对象,通过对比分析浊度、流量及示踪剂浓度变化探讨浊度来源及其对示踪剂和管道参数的影响。试验过程中,确定存在上、下临界流量使水流从层流过渡为紊流状态,浊度主要来源从管道内部再悬浮颗粒过渡为外源悬浮物,计算上、下临界流量分别为0.7 m~3/s和0.4 m~3/s。通过浊度与示踪剂的相关关系研究浊度对示踪剂的影响,结果表明当浊度大于25时,浊度与示踪剂浓度呈负相关关系,且浊度越大,对示踪剂的影响越大。最后通过对比确定,第一次示踪试验浊度影响较小,并估算了岩溶管道参数,为进一步水资源评价提供基础。     

Estimating hydraulic conductivity from specific capacity for Hawaii aquifers,USA

Site-specific relationships between specific capacity and hydraulic parameters (transmissivity and hydraulic conductivity) were investigated for volcanic rocks in Maui, Hawaii, USA. Details about well construction were commonly ignored in previous studies. To improve on such efforts, specific-capacity values were normalized by the open interval of the well. Correcting specific capacity for turbulent head losses using step-drawdown tests and including aquifer penetration length improved the correlation between specific capacity and hydraulic conductivity and reduced uncertainty in the prediction of hydraulic parameters. The relationships provide estimates of aquifer parameters with correlation coefficients between 0.81 and 0.99. The relationships for Maui can probably be extended to other Hawaii islands, given the similarity of aquifer formations and a reasonable fit to step-drawdown data from Oahu. Hydraulic conductivity was estimated from 1,257 specific-capacity values in the Hawaii’s well database. Hydraulic-conductivity estimates for dike-free volcanic rocks are consistent on different islands. For all islands, the estimates range from 3 to 8,200 m/d, with a geometric-mean and median value of 272 and 291 m/d, respectively. A geostatistical approach was applied to Maui and Oahu to generate island-wide hydraulic-conductivity maps to facilitate groundwater management efforts.     

基于有机污染物扩散的复合衬垫厚度的概率设计

有机污染物在复合衬垫中的运移以扩散方式为主。目前关于运移参数不确定性及其对衬垫性能影响的研究还不多,复合衬垫厚度的设计也没有考虑不确定性的影响。总结了运移参数已有的成果,采用蒙特卡罗法研究了半无限条件下运移参数的变异性对衬垫底部污染物质量浓度和通量的影响,并对衬垫厚度进行了设计。研究表明:土工膜中有机污染物的分配系数和扩散系数的变异性对质量浓度和通量的影响可以忽略,而土中有机污染物的扩散系数和阻滞系数的变异性对其影响则非常显著。确定性方法计算的结果偏于危险,有必要加强对土中有机污染物的扩散系数和阻滞系数概率特性的研究。以甲苯为例进行黏土衬垫厚度设计,结果表明:概率计算方法得到的黏土衬垫厚度约为确定性方法的1.71~1.81倍,采用概率方法进行衬垫设计更合理。     

Effects of tectonic structures, salt solution mining, and density-driven groundwater hydraulics on evaporite dissolution (Switzerland)

Subsurface dissolution (subrosion) of evaporites such as halite and gypsum can lead to extensive land subsidence. Recent land subsidences have been surveyed at six separate locations in northwestern Switzerland. The diameters of the affected surface areas range from 100 to 1,500 m, and corresponding subsidence rates reached more than 100 mm/year. Based on a geometrical model, three sites could be outlined where land subsidence can likely be attributed to salt solution mining. The effects of increased hydrostatic gradient due to both groundwater withdrawal and fluid density contrasts were evaluated in more detail for the remaining sites with a series of 2D density-coupled solute-transport simulations along an approximately 1,000-m-long and 150-m-deep 2D cross section. Simulation results indicate that the upconing process of saline groundwater into the main aquifer occurs under different distributions of subsurface parameters and hydraulic boundary conditions. For the presented setup, the simulations also revealed that the most sensitive factor for the dissolution rate is the structure or dip of the halite formation, which leads to an increase of dissolution rate with increasing dip. Due to the increased density of the brine, an intrinsic flow dynamic develops which follows the direction of the dip.     

Statistical Analysis of Anisotropic Damage of the Bukit Timah Granite

Summary This paper presents a method to analyze probabilistic anisotropic initial damage of a rock mass. A three-dimensional geometric model of cracks in a rock mass is established in terms of several parameters, such as orientations, spacing and normalized sizes of cracks in the rock mass. The dip, dip direction, spacing, and normalized size of cracks of the Bukit Timah granite in Singapore were obtained from visual inspection of rock cores, color TV imaging, and impression packer tests in the boreholes at a site of geological investigation. Using the measured data, probabilistic distribution laws of geometric parameters of cracks on the surface of the boreholes are derived. Based on these statistical distributions and using Monte-Carlo simulation method, the distribution of anisotropic initial damage of the Bukit Timah granite is derived and found to have a beta distribution. This anisotropic initial damage distribution of a rock mass can be used in probabilistic analysis of rock mass responses to both static and dynamic loads.     

不同流场情况下地下水弥散试验方法分析

针对不同地下水水力梯度进行地下水弥散试验采用不同的方法,直接影响到弥散试验的成功及获取参数的准确性及真实性。其中在不同的水力梯度下采用不同的监测时间间隔监测示踪剂浓度,决定了弥散试验捕捉到示踪剂的初至及峰值的成功机率。同时本项目详细地进行了地下水弥散试验求参过程完整性分析,可做为弥散试验参考实例。