Tracer Concentration Distribution Research Articles

Tracer transport in fractured porous media: Distribution of tracer concentration within the rock matrix and the implementation of time domain random walk algorithm

In this work, a new Time Domain Random Walk (TDRW) algorithm is proposed to estimate the tracer distribution profile within the rock matrix. The development of the new algorithm stems from the statistical properties of the analytical solution to a single fracture-matrix system, in which the particle position at a certain time is calculated and recorded. With the position of each particle determined, the resulting distribution will then provide an estimate of the tracer distribution profile directly. In addition, the newly developed algorithm can readily be extended to a case of more complicated fracture-matrix system, in which an arbitrary injection boundary condition may also be used. To verify the accuracy and applicability of the new algorithm, three benchmark simulations are made, in which the results of different approaches are found to be identical. Nevertheless, the new algorithm has a higher computational efficiency, due to its lower calculation demand.

Solids dispersion in high density circulating fluidized beds

Transient local solid tracer concentration distributions were measured by a novel, simple and accurate measurement system with fast response to obtain axial solids dispersion in the riser of a circulating fluidized bed operated at solids fluxes up to 450 kg/m2s and gas velocities up to 8 m/s. Phosphorescent-coated FCC particles were used as the tracer which were activated by high intensity UV light and injected into the return leg of high-density circulating fluidized bed unit. A radially non-uniform axial dispersion model was utilized to determine axial solids dispersion coefficients, and the results were interpreted with the help of hydrodynamic data obtained in the same column. Comparison of the axial dispersion coefficients at different operating conditions revealed that dispersion decreases when solids circulation flux increases to 450 kg/m2s together with the increase in gas velocity to 8 m/s. Low solids dispersion coefficients (Daz < 0.1) at high solids circulation fluxes and high velocities resulted from the disappearance of the net downward flow of particles at the riser walls, signifying the existence of the dense suspension upflow regime.

A Fractional-order dual-continuum model to capture non-Fickian solute transport in a regional-scale fractured aquifer

Contaminant transport in fractured media exhibits complex dynamics, including multiple peaks in breakthrough curves (BTCs) and non-Fickian diffusion, thereby posing significant challenges to the application of traditional transport models. Here we undertook a detailed study of a natural-gradient tracer test conducted in a regional-scale fractured carbonate aquifer situated in southwestern Germany, where the observed BTCs contained both dual peaks and positive skewness. These BTCs were used to optimize parameters and interpret their physical meanings for several transport models, including the dual-continuum model (DCM) and the fractional derivative equation (FDE) model. Tracer concentration distributions were simulated in both single- and dual-continuum media employing the DCM and FDE models. Our results demonstrated that while the DCM model could reasonably replicate the bimodal BTC, the FDE (which accounts for solute retention) outperformed in capturing the heavy-tailed BTC. This was attributed to the limitations of grid-based numerical models that assume Fickian diffusion and fail to map small-scale medium heterogeneity exhaustively. In contrast, a parsimonious model like the FDE, with upscaled parameters, was found to be more effective in capturing regional-scale non-Fickian transport. To further characterize the multiple BTC peaks the standard FDE missed, we proposed a fractional derivative dual-continuum model (fDCM). This model was found to be adept at capturing both the multi-peak and late-time heavy tail in the BTC. Our study thus opens an alternate pathway for modeling solute transport in regional-scale fractured to partially karstified aquifers.

Experimental analysis and two-region mixing coefficients development for a wire-wrapped tight lattice bundle

Wire-wrapped tight lattice fuel assemblies are widely used in the design of advanced nuclear reactors for their advantages of higher power density and enhanced heat transfer capability. The flow mixing characteristics in this type of assembly are complicated due to the presence of the wire. In this study, a flow mixing experiment has been carried out in a 19-pin wire-wrapped tight lattice bundle with Reynolds numbers ranging from 5000 to 25,000. The mixing and crossflow effects were studied by injecting a tracer substance affecting the electrical conductivity of the fluid and measuring tracer concentration distributions using a wire-mesh sensor system. A set of flow mixing data has been obtained, and the experimental results indicate the mixing characteristics of a wire-wrapped bundle are insensitive to the Reynolds number. Combined with the measured data and the modified CTF code, the two-region mixing coefficients were determined by the least-square method and compared with the mixing coefficients in the literature. This work is an important supplement to the study of the mixing characteristics of wire-wrapped tight lattice bundles, and the data also can be used to validate the computational fluid dynamics codes and develop high-precision mixing models for subchannel analysis.

Effect of swirling addition on the liquid mixing performance in a T-jets mixer

Swirling addition to the stream is beneficial for the fluid mixing. This work aims to study the mixing process intensification in a conventional T-jets mixer by the swirling addition. After experimental verification by the planar laser-induced fluorescence technique, large eddy simulation with the dynamic kinetic energy sub-grid stress model is used to predict how the swirling strength (in terms of swirling number, S w ) and swirling directions affect the mixing performance, e.g . the tracer concentration distribution, mixing time, and turbulent characteristics in the T-jets mixers. Predictions show that the swirling strength is the key factor affecting the mixing efficiency of the process. The overall mixing time, τ 90 , can be significantly reduced by increasing S w . Vortex analysis shows that more turbulent eddies appear in the collision zone and the turbulent kinetic energy dissipation rate increases obviously with the swirling addition. When S w is kept constant, the mixing process can be accelerated and intensified by adding swirling to only one stream, to both streams with the opposite swirling directions, or to both streams with the same swirling directions. Amplification of the mixing process by enlarging the mixer size or increasing the flow rates is also optimized. Thus, this work provides a new strategy to improve the mixing performance of the traditional T-jets mixers by the swirling addition.

Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

This paper reports an analytical study conducted to investigate the behaviour of tracers undergoing creeping flow between two parallel plates in porous media. A new coupled model for the characterisation of fluid flow and transport of tracers at pore scale is formulated. Precisely, a weak-form solution of radial transport of tracers under convection–diffusion-dominated flow is established using hypergeometric functions. The velocity field associated with the radial transport is informed by the solution of the Stokes equations. Channel thickness as a function of velocities, maximum Reynolds number of each thickness as a function of maximum velocities and concentration profile for different drift and dispersion coefficients are computed and analysed. Analysis of the simulation results reveals that the dispersion coefficient appears to be a significant factor controlling the concentration distribution of the tracer at pore scale. Further analysis shows that the drift coefficient appears to influence tracer concentration distribution but only after a prolonged period. This indicates that even at pore scale, tracer drift characteristics can provide useful information about the flow and transport properties of individual pores in porous media.

Effects of Velocity and Permeability on Tracer Dispersion in Porous Media

During micro-scale tracer flow in porous media, the permeability and fluid velocity significantly affect the fluid dispersion properties of the media. However, the relationships between the dispersion coefficient, permeability, and fluid velocity in core samples are still not clearly understood. Two sets of experiments were designed to study the effects of tracer fluid flow velocity and porous medium permeability on the dispersion phenomenon in a core environment, using natural and sand-filled cores, respectively. From experimental data-fitting by a mathematical model, the relationship between the dispersion coefficient, flow velocity, and permeability was identified, allowing the analysis of the underlying mechanism behind this phenomenon. The results show that a higher volumetric flow rate and lower permeability cause a delay in the tracer breakthrough time and an increase in the dispersion coefficient. The core experimental results show that the dispersion coefficient is negatively correlated with the permeability and positively correlated with the superficial velocity. The corresponding regression equations indicate linear relations between the dispersion coefficient, core permeability, and fluid velocity, resulting from the micron scale of grain diameters in cores. The combination of high velocity and low permeability yields a large dispersion coefficient. The effects of latitudinal dispersion in porous media cannot be ignored in low-permeability cores or formations. These findings can help to improve the understanding of tracer flow in porous media, the design of injection parameters, and the interpretation of tracer concentration distribution in inter-well tracer tests.

Influence of Aquatic Vegetation on Dispersive Parameters as a Part of Hydrodynamic Conditions in Natural Streams

Submerged and emergent aquatic vegetation is a natural and organic component of natural rivers and streams. It plays an important role in all physical, chemical and biological processes in the stream biocoenosis. This type of vegetation has also a non-negligible impact on flow conditions. It influences the discharge, hydraulic roughness, velocity as well as other hydraulic parameters. Important part of the river hydrodynamic processes are also dispersive processes and its parameters, which defines the speed and intensity of the dispersive processes in the natural stream. This paper analyses these aspects of the stream hydrodynamics, which are influenced by aquatic vegetation and analyses the influence of the submerged and emerged vegetation on mixing processes in a river. Presented results are findings of hydrometric measurements and tracer experiments at the Šúrsky kanál stream, located in south-west part of Slovakia. The Šúrsky kanál stream is a typical lowland stream, where significant changes in the vegetation are present during different periods of a year. The hydrometric and tracer experiments were performed on 1700 m long straight reach of the stream with a relatively prismatic cross-section profile during the growing as well as non- growing season of a year. The results show, that the level of vegetative growth has a significant influence on the hydrodynamic parameters of the stream, as well as on the dispersive process. The dispersive process is influenced not only by the velocity and concentration gradients, but also by the fact that the vegetation forms in the stream so-called dead zones. Such dead zones modify the velocity profiles of a stream and affect dispersive mass transport within the stream by collecting and separating parts of the tracer from the main current. Subsequently, the tracer is slowly released and incorporated back to the main current in a stream. This process deforms the shape of the tracer concentration distribution in time. All these facts were confirmed by the experiments results described in this paper, which contains also the analysis of the dead zones effect on the dispersive process.

Large Eddy Simulations of Reactive Mixing in Jet Reactors of Varied Geometry and Size

We applied large eddy simulation (LES) to predict the course of reactive mixing carried out in confined impinging jet reactors (CIJR). The reactive mixing process was studied in a wide range of flow rates both experimentally and numerically using computational fluid dynamics (CFD). We compared several different reactor geometries made in different sizes in terms of both reaction yields and mixing efficiency. Our LES model predictions were validated using experimental data for the tracer concentration distribution and fast parallel chemical test reactions, and compared with the k-ε model supplemented with the turbulent mixer model. We found that the mixing efficiency was not affected by the flow rate only at the highest tested Reynolds numbers. The experimental results and LES predictions were found to be in good agreement for all reactor geometries and operating conditions, while the k-ε model well predicted the trend of changes. The CFD method used, i.e., the modeling approach using closure hypothesis, was positively validated as a useful tool in reactor design. This method allowed us to distinguish the best reactors in terms of mixing efficiency (T-mixer III and V-mixer III) and could provide insights for scale-up and application in different processes.

Multitracer irrigation experiments for assessing the relevance of preferential flow for non-sorbing solute transport in agricultural soil

This study addresses the relevance of preferential flow for the transport of a non-sorbing solute in a sandy agricultural field with nitrate-contaminated groundwater. Two multitracer irrigation experiments were conducted 1) in October 2017, and 2) in March 2018 on a 2 m × 2 m plot on an agricultural field in Northern Germany (Cloppenburg region). For irrigation 1, Cl-, H218O, and 15NO3- were used as tracers, for irrigation 2, Br-, 2H2O, and 15NO3- were used as tracers. Between both irrigation events the study plot was subject to natural precipitation. The study plot was instrumented with soil moisture sensors and suction plates. The occurrence of preferential flow was studied based on the following data: (1) tracer breakthrough curves collected by five suction plates; (2) the spatial distribution of resident tracer concentrations in soil at the end of the experiment; and (3) 3D-time lapse electrical resistivity tomography (ERT) during both irrigation events. The spatial distribution of water residence times at the end of the experiment was calculated based on measured tracer concentrations in the soil and the known fingerprints of three sources of water (irrigation 1, rain and irrigation 2) applied to the plot. The relevance of preferential flow for the leaching of a non-sorbing solute was assessed by comparing the observed and Hydrus-1D-modeled cumulative leaching of Cl-.In comparison to the conservative tracers 1–11% of the applied 15NO3- was removed from soil solution most probably due to microbial processes. Continuous preferential flow paths were observed below the plow pan. The same preferential flow paths seem to be used repeatedly by the successive rain/irrigation events. However, the mobile-immobile regions appear to exist only for a short period of time, because fast matrix flow balances the spatial heterogeneity in tracer distribution. The residence time of soil water varied from 1 to 3 months at 40–50 cm depth and was not older than 4 months at 190–200 cm depth. Hydrus-1D transient model calculations predicted 13%-30% less leaching of a conservative tracer during wintertime compared to the experimentally estimated averaged leaching from our study plot. Therefore, our main result is that preferential flow, though responsible for a high spatial heterogeneity in leaching loads within study plot in our non-structured sandy soil, increased only slightly the averaged cumulative solute leaching during wintertime from the plot.

A General Methodology for Beached Oil Spill Hazard Mapping

The current lack of a standardized approach to computing the coastal oil spill hazard due to maritime traffic releases has hindered an accurate estimate of its global impact, which is paramount to manage and intercompare the associated risks. We propose here an hazard mapping approach that is based upon the methodology of ensemble simulations and the statistical analysis of the relevant distributions. Based on more than 20,000 ensemble simulations of oil spills from maritime traffic routes, we demonstrate that beached ocean tracer concentration distributions fit a Weibull curve, a two-parameter fat-tail probability distribution function. Two indicators that quantify the coastal oil spill hazard are proposed and applied to the Algarve coast, Portugal.

Spreading of the South Pacific Tropical Water and Antarctic Intermediate Water Over the Maritime Continent

AbstractThe three‐dimensional climatological spreading of South Pacific waters over the Maritime Continent is examined using eddy‐resolving simulations and a passive tracer method. Four pathways are summarized for the South Pacific Tropical Water and the Antarctic Intermediate Water through the Maritime Continent, including two direct pathways, namely, the Eastern Path and the Torres Strait Path, and two indirect pathways, namely, the Western Path and the South China Sea Path. Among them, according to tracer concentration distribution, the former two contribute most of the volume transport of the Indonesian Throughflow (ITF) originating from the South Pacific. The latter two experience two retroflections (i.e., the South Equatorial Current‐Equatorial Undercurrent and the North Equatorial Countercurrent‐North Equatorial Current) before entering the Indonesian Seas. The vertical distributions of the South Pacific waters along each path throughout the Indonesian Seas are also analyzed, revealing that the South Pacific salinity extrema greatly affect the intermediate and deep layers of the Indonesian Seas and ITF as well as the upper thermocline. Vertical fluxes, especially vertical advection, are vital to these Indo‐Pacific water exchange processes. Sensitivity tests are conducted for the vertical diffusion coefficient and initial conditions, the results of which are robust. According to current study, the South Pacific has substantial impacts on the water properties throughout the Maritime Continent and the mass‐energy exchanges between the Pacific and Indian Oceans.

CFD Simulation of Liquid–Liquid Two-Phase Hydrodynamics and Axial Dispersion Analysis for a Non-Pulsed Disc and Doughnut Solvent Extraction Column

ABSTRACTA two-phase computational fluid dynamics (CFD) simulation for a non-pulsed disc and doughnut solvent extraction column has been developed with commercial CFD software FLUENT. Simulated hydrodynamic results including phase distribution, velocity fields, and holdup are given, which enables predicted holdup to be compared with experimental data. Average absolute relative deviation (AARD) of experimental data and CFD prediction in this study is found to be 10.8%, which is comparable to the estimated error in the experimental data and the predictions from traditional correlations in the literature. To estimate the extent of axial dispersion, a species transport model is used for the continuous phase with a small amount of tracer introduced in the continuous phase, when Sauter mean diameter of the dispersed phase is set to be 3.5 mm. A two-point monitoring method is used to estimate a Peclet number. The tracer concentration distribution in the two-dimensional distance–time space is interpreted with MATLAB along with the experimental measurement. The simulated Peclet numbers are compared with column experiments, and in general the simulation underestimates the experimental data by 60%. Introducing a modified drag law improves the predictions. This work shows that CFD can successfully model the performance of a non-pulsed disc and doughnut solvent extraction column.

Geoscientific process monitoring with positron emission tomography (GeoPET)

Abstract. Transport processes in geomaterials can be observed with input–output experiments, which yield no direct information on the impact of heterogeneities, or they can be assessed by model simulations based on structural imaging using µ-CT. Positron emission tomography (PET) provides an alternative experimental observation method which directly and quantitatively yields the spatio-temporal distribution of tracer concentration. Process observation with PET benefits from its extremely high sensitivity together with a resolution that is acceptable in relation to standard drill core sizes. We strongly recommend applying high-resolution PET scanners in order to achieve a resolution on the order of 1 mm. We discuss the particularities of PET applications in geoscientific experiments (GeoPET), which essentially are due to high material density. Although PET is rather insensitive to matrix effects, mass attenuation and Compton scattering have to be corrected thoroughly in order to derive quantitative values. Examples of process monitoring of advection and diffusion processes with GeoPET illustrate the procedure and the experimental conditions, as well as the benefits and limits of the method.

Investigating hydrodynamic characteristics and peculiarities of the coolant flow behind a spacer grid of a fuel rod assembly of the floating nuclear power unit

The results of experimental investigations of local hydrodynamics of a coolant flow in fuel rod assembly (FA) of KLT-40C reactor behind a plate spacer grid have been presented. The investigations were carried out on an aerodynamic rig using the gas-phase diffusive tracer test. An analysis of spatial distribution of absolute flow velocity projections and distribution of tracer concentration allowed specifying a coolant flow pattern behind the plate spacer grid of the FA. On the basis of obtained experimental data the recommendations were provided to specify procedures for determining the coolant flow rates for the programs of cell-wise calculation of a core zone of KLT-40C reactor. Investigation results were accepted for the practical use in JSC “OKBM Afrikantov” to assess heat engineering reliability of cores of KLT-40C reactor and were included in a database for verification of CFD programs (CFD-codes).

Steady-state CFD simulations of an EPR™ reactor pressure vessel: A validation study based on the JULIETTE experiments

Validating computational fluid dynamics (CFD) models against experimental measurements is a fundamental step towards a broader acceptance of CFD as a tool for reactor safety analysis when best-estimate one-dimensional thermal-hydraulic codes present strong modelling limitations.In the present paper numerical results of steady-state RANS analyses are compared to pressure, volumetric flow rate and concentration distribution measurements in different locations of an Areva EPR™ reactor pressure vessel (RPV) mock-up named JULIETTE. Several flow configurations are considered: Three different total volumetric flow rates, cold leg velocity field with or without swirl, three or four reactor coolant pumps functioning. Investigations on the influence of two types of inlet boundary profiles (i.e. flat or 1/7th power-law) and the turbulent Schmidt number have shown that the first affects sensibly the pressure loads at the core barrel whereas the latter parameter strongly affects the transport and the mixing of the tracer (passive scalar) and consequently its distribution at the core inlet. Furthermore, the introduction of an integral parameter as the swirl number has helped to decrease the large epistemic uncertainty associated with the swirling device. The swirl is found to be the cause of asymmetric loads on the walls of the core barrel and also asymmetries are enhanced for the tracer concentration distribution at the core inlet.The k–ϵ CFD model developed with the commercial code STAR-CCM+ proves to be able to predict quantitatively well both, the mixing at the core inlet and the mechanical loading at the core barrel for most of the different flow configurations considered.

Numerical study on the dynamics and mass transfer characteristics of a radial offset jet

Purpose – A radial offset jet has the flow characteristics of a radial jet and an offset jet, which are encountered in many engineering applications. The purpose of this paper is to study the dynamics and mass transfer characteristics of the radial offset jet with an offset ratio 6, 8 and 12. Design/methodology/approach – Three turbulence models, namely the SST k-? model, detached eddy simulation model, and improved delayed detached eddy simulation (IDDES), were applied to the radial offset jet with an offset ratio eight and their results were compared with experimental results. The contrasting results, such as the distributions of mean and turbulent velocity and pressure, show that the IDDES model was the best model in simulating the radial offset jet. The results of the IDDES were analyzed, including the Reynolds stress, turbulent kinetic energy, triple-velocity correlations, vertical structure and the tracer concentration distribution. Findings – In the axisymmetric plane, Reynolds stresses increase to reach a maximum at the location where the jet central line starts to be bent rapidly, and then decrease with increasing distance in the radial direction. The shear layer vortices, which arise from the Kelvin-Helmholtz instability near the jet exit, become larger scale results in the entrainment and vortex pairing, and breakdown when the jet approaches the wall. Near the wall, the vortex swirling direction is different at both front and back of attachment point. In the wall-jet region, the concentration distributions present self-similarity while it keeps constant below the jet in the recirculation region. Research limitations/implications – The radial offset jet with other offset ratio and exit angle is not considered in this paper and should be investigated. Originality/value – The results obtained in this paper will provide guidance for studying similar flow and a better understanding of the radial offset jet.

Estimating Preferential Flow in Karstic Aquifers Using Statistical Mixed Models

Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory-scale Geo-HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow-dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit-like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study.

Hydraulic Efficiency in RANS of the Flow in Multichambered Contactors

Accurate and practical models are in demand for optimization of ozone contactor designs. This paper reports results from Reynolds-averaged Navier-Stokes simulation (RANS) of the flow and passive nonreactive tracer transport inside a multichambered, laboratory-scale ozone contactor using a structured, collocated, finite volume discretization. Simulations are posed following previously published laboratory experiments. Results are presented in terms of velocity distributions, tracer concentration distributions, and tracer residence times. The flow is characterized by short-circuiting and dead zone regions that reduce the hydraulic (disinfection) efficiency or baffling performance of the contactor. RANS-predicted cumulative residence time distribution (RTD) of the tracer (released at the inflow as a pulse) is shown to be in excellent agreement with published experimental data despite the under resolution of the RANS methodology compared with better-resolved methodologies, such as large-eddy simulation (LES). The authors also compare the baffling performance and friction energy loss (molecular and turbulent) of three ozone contactor configurations by RANS simulation. A trade-off between baffling performance and energy loss is identified for the first time, as previous works have focused on baffling performance only. However, it is seen that the overall energy saving afforded by increasing the hydraulic efficiency (thus requiring less energy for ozone generation) offsets the energy increase required for driving the flow through a more hydraulically efficient contactor (characterized by more baffles). Overall, it is seen that energy considerations associated with contactor hydraulic efficiency (i.e., energy loss due to friction, and thus energy to drive the flow, and energy required for ozone generation) are important for determining the operational costs of a water treatment plant.

Three dimensional imaging of porosity and tracer concentration distributions in a dolostone sample during diffusion experiments using X-ray micro-CT

X-ray micro-computed tomography (micro-CT) techniques for measuring the three-dimensional (3-D) distributions of diffusion-accessible porosity (φ(d)) and temporal tracer-concentrations (C(t)) within a dolostone sample subjected to solute diffusion are developed and tested in this work. The φ(d) and C(t) measurements are based on spatially resolved changes in X-ray attenuation coefficients in sequentially acquired 3-D micro-CT datasets using two (calibration and relative) analytical approaches. The measured changes in X-ray attenuation coefficient values are a function of the mass of X-ray absorbing potassium-iodide tracer present in voxels. Mean φ(d) values of 3.8% and 6.5% were obtained with the calibration and the relative approaches, respectively. The detection limits for φ(d) measurements at individual voxel locations are 20% and 36% with the calibration and the relative methods, respectively. The detection limit for C(t) are 0.12 M and 0.22 M with the calibration and the relative approaches, respectively. Results from the calibration method are affected by a beam-hardening artifact and although results from the relative approach are not affected by the artifact, they are subject to high detection limits. This work presents a quantitative assessment of micro-CT data for studies of solute transport. Despite limitations in precision and accuracy, the method provides quantitative 3-D distributions of φ(d) and C(t) that reflect solute diffusion in heterogeneous porous geologic media.