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There has been a recent increase of interest in sewer network water quality, both for pollutants and wastewater epidemiology. Of particular interest is the ability to perform cost-effective small-scale monitoring to understand the sewer network and perform source localization (the process of identifying the sources of materials of interest within the network), enabling prioritization of combined sewer overflow (CSO) interventions and targeted response to the detection of infectious diseases. Rhodamine WT fluorescent dye tracing was carried out in the combined sewer networks of four UK cities, for which network geometries were available. Over 100 dye concentration profiles were recorded, from which discharge, travel time (velocity), and dispersion were quantified. A simplified hydraulic and water quality (conservative solute transport) modeling approach was used to investigate dispersion further. A theoretical method for calculating dispersion over a reach with nonuniform properties was derived and used with the models and recorded data to develop a method for estimating the dispersion coefficient in sewers. Novel simultaneous injections into multiple manholes within one sewer network were conducted. Modeling of these injections validated the modeling approach and explained the measured concentration profiles, demonstrating both the potential of hydraulic and solute transport modeling and the new dispersion coefficient predictor for source localization. Such modeling can be used to develop sewer network "fingerprints" and source location probability plots based on residence time distribution (RTD) theory to maximize information from limited water quality monitoring. This will aid managers and operators in identifying potential intermittent sources of material within the network. [ABSTRACT FROM AUTHOR]

Physical interactions of microplastics within vegetation and turbulent flows of freshwater systems are poorly understood. An experimental study was conducted to investigate the underlying physical transport mechanisms of microplastics over submerged canopies across a range of flow conditions common in the natural environment. The effects of changing canopy heights were investigated by testing two model canopies of varying stem heights, simulating seasonal variation. This study determined and compared the mixing and dispersion processes for microplastics and solutes utilizing fluorometric tracing techniques. A hydrodynamic model was developed based on the advection‐dispersion equation for quantifying microplastic mixing in submerged canopies. Longitudinal dispersion coefficients for neutrally buoyant microplastics (polyethylene) and solutes were significantly correlated within submerged model vegetation irrespective of the complexity of the flow regime. Hydrodynamic and solute transport models were shown to be capable of robust predictions of mixing for neutrally buoyant microplastics in environmental flows over a canopy, facilitating a new approach to quantify microplastic transport and fate. We compare the mixing processes for microplastics and solutes then propose a hydrodynamic model for quantifying the mixing in submerged canopies. Plain Language Summary: Microplastic movement and fate within vegetation and turbulent flows of freshwater systems is poorly understood. A study was conducted within a laboratory flume, scaled for real‐world river systems, to investigate the transport of microplastics over submerged canopies across a range of flow conditions common in the natural environment. The effects of changing vegetation heights were investigated by testing two model canopies of varying stem heights, simulating seasonal variation. To measure microplastic movement in real‐time this study determined and compared the mixing of microplastics and solutes using fluorometric techniques that measure fluorescence at specific wavelengths of light produced by the stained microplastics and Rhodamine WT dye (solute). Models utilizing velocities over depth and solute dispersion were adapted to quantify microplastic mixing in submerged canopies. The dispersion of neutrally buoyant microplastics (polyethylene), microplastics of a similar buoyancy to water, and solutes were significantly correlated within submerged vegetation irrespective of the complexity of the flow regime. The models were shown to be capable of reliable predictions of mixing for neutrally buoyant microplastics in environmental flows over a canopy, facilitating a new approach to measure microplastic transport and fate. Key Points: Neutrally buoyant microplastics disperse analogous to solutes within the water column of fluvial environments with submerged vegetationA novel fluorometric tracing and particle staining technique is proven to accurately trace stained microplastics within vegetated flowsA robust hydrodynamic model is proven to predict mixing of neutrally buoyant microplastics [ABSTRACT FROM AUTHOR]

Solute transport in rivers is controlled by mixing processes that occur over a wide spectrum of spatial and temporal scales. Deviations from the classic advection–dispersion model observed in tracer test studies are known to be generated by the temporary trapping of solutes in storage zones where velocities and mixing rates are relatively small. In this work, the relation between the early and late-time behavior of solute breakthrough curves (BTCs) and the key parameters of the Transient Storage Model (TSM) is analyzed using non-asymptotic approximations of the model equations. Two main slopes are identified corresponding to the rising and decreasing limbs of the BTCs which are linked by specific relationships to transport and storage parameters. The validity of the proposed approximations is demonstrated with both synthetic and experimental data. Consistent with the TSM assumptions, the range of validity of the proposed approximations represents the limit of separability between surface dispersion and transient storage and can be expressed as a function of a nondimensional parameter. The results of this work can help environmental scientists identify solute transport and transient storage parameters and support the design of enhanced field tracer experiments. [ABSTRACT FROM AUTHOR]

• The relationships between upstream flow, vegetation height, and solute diffusion processes in vegetated waters were investigated. • Placing emergent vegetation upstream of the vegetation zone can increase the magnitude of the solute cloud diffusion in the longitudinal direction. • The longitudinal dispersion coefficients obtained in this study are close to those determined using the theoretical method for the same scenarios. Reasonable estimates of longitudinal dispersion coefficients are essential for predicting solute dispersion processes. However, the current knowledge of solute dispersion processes in vegetated waters is limited. In this work, we coupled a refined hydrodynamic model with scalar transport equations to simulate the flow field and dispersion process of solutes in water under the effect of vegetation. First, the proposed numerical model was verified using laboratory experiments, revealing the excellent performance of the coupled model in complex conditions. Eight different cases were subsequently simulated to analyse the effects of the upstream flow rate and vegetation height on the streamwise velocity, solute concentration, and longitudinal dispersion coefficients. The simulation results show that the upstream flow variation exerts a marked effect on the streamwise velocity and flow field within the vegetation zone, with a velocity difference within the shear layer reaching 54.7 % for an upstream flow of 0.018 m3·s-1. The height of the vegetation affects both the velocity profile and solute dispersion. Placing emergent vegetation upstream can enhance solute dispersion in the longitudinal direction. The correlation analysis reveals that the longitudinal dispersion coefficients obtained using the routing producer are close to those determined using the theoretical method, with correlation coefficients reaching 0.75. This work presents the appropriate application range and parameters that must be considered in deriving formulas for longitudinal dispersion coefficients. [ABSTRACT FROM AUTHOR]

This paper concerns the cadmium sorptive effects by river bed sediments on longitudinal dispersion coefficient in an open-channel flow via experimental and numerical study. For this purpose, a circular flume was used with mean diameter of 1.6 m and a width of 0.2 m. The adsorbing bed was considered as a thin layer of the sediment particles with mean diameter of 0.53 mm and three sediment concentrations of 3, 12, and 20 gr/lit. To determine the sorption parameters of the sediments, some experiments were conducted with three cadmium concentrations of 150, 460, and 770 ppb. Then, the dispersion experiments were carried out with and without the bed sediments with the same cadmium concentration as the sorption experiments. A numerical model was then developed to solve the advection–dispersion equation with considering the sorption term by river bed sediments. The longitudinal dispersion coefficients were estimated by comparing the experimental and numerical breakthrough curves. The results showed that, with increasing the sediment concentrations, the sediment sorption rate increased and the longitudinal dispersion coefficient decreased by about 38, 36 and 33 percent, respectively, for cadmium concentrations of 150, 460 and 770 ppb. In addition, by increasing the cadmium concentrations, the changes in the longitudinal dispersion coefficient are decreased. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion as a function of the new parameter of sorption ratio. From a practical point of view, the results of this study demonstrated that, at the presence of riverbed sediment, the cadmium is longitudinally dispersed with more delay in comparison with no sediment at the river bed. HIGHLIGHTS The advection–dispersion equation was numerically solved with considering the sorption term by river bed sediments.; Longitudinal dispersion coefficients were estimated by comparing the experimental and numerical breakthrough curves.; With increasing the sediment concentrations, the sediment sorption rate increased and the longitudinal dispersion coefficient decreased.;

The effects of bed roughness on the longitudinal dispersion coefficient (DL) were experimentally and numerically investigated in the present study. The tracer experiments were first carried out in a circular flume with a diameter of 1.6 m over both smooth and rough beds (coarse sand) with four sizes (ks = d65) of 1.04, 2.09, 3.01, and 4.24 mm. In addition, the one-dimensional advection–dispersion equation was numerically solved. The longitudinal dispersion coefficient was calculated by comparing the numerical and experimental breakthrough curves. The results showed that by increasing the bed roughness height (from zero to 4.24 mm), the longitudinal dispersion coefficient increased by 34%. In addition, the longitudinal dispersivity (λ = DL/V) increased with increasing relative roughness (ks/h), so that the range of longitudinal dispersivities in smooth bed experiments were 0.037–0.049 m and for rough bed (ks = 4.24 mm) were 0.07–0.084 m. In other words, with increasing the bed roughness height from zero (smooth bed) to 4.24 mm, the longitudinal dispersivities increased from 0.037 to 0.077 m, indicating an increase of about 108%. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion (DL/(Vh)) as a function of relative roughness (ks/h). It can be concluded that taking into consideration bed roughness as the driving force of shear dispersion would improve predictive equations of the longitudinal dispersion in the rivers. As the bottom of all natural rivers has roughness elements with different sizes, the results of this study will definitely be useful in estimating the longitudinal dispersion coefficient in natural rivers and quantifying the effect of roughness in the longitudinal dispersion coefficient equations. HIGHLIGHTS By increasing the bed roughness height (from zero to 4.24 mm), the longitudinal dispersion coefficient increased significantly.; A relationship was developed using non-dimensional longitudinal dispersion (DL/(Vh)) as a function of relative roughness.; Taking into consideration bed roughness as the driving force of shear dispersion would improve predictive equations of the longitudinal dispersion in the rivers.;

There is a need for developing efficient models to simulate the sediment transport phenomenon in ice-covered alluvial channel flows, which is essential in enriching the theory of riverbed evolution. This study establishes a random displacement model parameterized with the time-averaged streamwise velocity U(z), the sediment settling velocity ωs(z), and the turbulent diffusion coefficient Dz(z) to calculate the suspended sediment concentration and the longitudinal dispersion coefficient for ice-covered alluvial channels. The proposed model is first validated to determine if it could be used to predict the sediment concentration profiles by comparing to limited experiments published in the literature. Results show that the simulations agree well with the measurements except for the underestimated concentration near the ice cover boundary. Once validated, the random displacement model is applied to explore the variation law of the suspended sediment concentration and the longitudinal dispersion with different sediment particle release modes. The sediment concentration and the stable value of the longitudinal dispersion coefficient for a given flow condition in the dynamic equilibrium state are not affected by the change of the particle release mode. The Fickian time required for the longitudinal dispersion coefficient converging to a constant, however, has a close relationship with the particle release mode and increases as the water depth increases. [ABSTRACT FROM AUTHOR]

We report new measurements of the concentration‐dependent longitudinal dispersion coefficient of aqueous urea and ethyl acetate solutions in a porous medium at a wide range of concentrations. The longitudinal dispersion coefficient was obtained by injection of a pulse of an aqueous solution of urea (or ethyl acetate) into a carrier phase flowing through a porous column and analysis of the effluent peak using the Taylor dispersion theory. The measured longitudinal dispersion coefficients for different velocities and concentrations showed an increasing trend with concentration and pore velocity. The longitudinal dispersion coefficient measurements show a power‐law relationship with the Peclet number KL∝αlPemβl. The results are compared with experimental data and empirical formulas available in the literature, and a reasonable agreement is achieved over the range of Peclet numbers studied. [ABSTRACT FROM AUTHOR]

Vegetation notably influences transport and mixing processes and can thus be used for controlling the fate of substances in the hydro‐environment. Whilst most work covers fully vegetated conditions, the novelty of this paper is to focus on flows with real‐scale flexible willow patches. We aimed to investigate how longitudinal dispersion varies according to the spatial distribution, density and coverage of the patches and to evaluate the explanatory power of predictors that consider the hydraulics, vegetation and channel geometry. Salt tracer experiments were performed in a trapezoidal channel where we established 3–4 m long and 1–1.6 m wide patches of artificial foliated willows that reproduced the shapes and plant densities observed on woody‐vegetated floodplains. We examined sparsely distributed patches with low areal/volumetric coverage of 6–11%, and non‐vegetated conditions for reference. Flow depths and surface widths were 0.7–0.9 and 6–7 m, respectively, and the mean flow velocities ranged at 0.3–0.6 m/s. The emergent patches generated from a negligible to over a four‐fold increase in the longitudinal dispersion when compared with non‐vegetated conditions. The patches with a preferential location in low‐velocity areas, such as near banks, or with a high plant density and a blockage of the cross‐sectional flow area ⪆0.4, led to the largest dispersion and residence times. Patches under such configurations enhanced the normalized differential velocity defined as the difference between the highest (90th percentile) and lowest (10th percentile) cross‐sectional flow velocities divided by the mean velocity, thus increasing shear dispersion. As existing analytical predictors failed to estimate the effect of different patch configurations, we proposed the change in the normalized differential velocity between vegetated and corresponding non‐vegetated conditions as a basic predictor of the reach‐scale longitudinal dispersion coefficient under patchy vegetation. In contrast, we observed no clear relationship between flow resistance and dispersion. Thus, our findings indicated that bankside vegetation may allow for reduced peak concentrations and lengthened residence times, supporting pollutant management, while ensuring good flow conveyance. Such rare field‐scale analyses improve the estimation of solute transport in real vegetated flows. [ABSTRACT FROM AUTHOR]

Numerous studies focus on flow and mixing within cylinder arrays because of their similarity to vegetated flows. Randomly distributed cylinders are considered to be a closer representation of the natural distribution of vegetation stems compared with regularly distributed arrays. This study builds on previous work based on a single, fixed, cylinder diameter to consider non‐uniform cylinder diameter distributions. The flow fields associated with arrays of randomly distributed cylinders are modeled in two dimensions using the ANSYS Fluent Computational Fluid Dynamics software with Reynolds Stress Model turbulence closure. A transient scalar transport model is used to characterize longitudinal and transverse mixing (Dx and Dy) within each geometry. The modeling approach is validated against independent laboratory data, and the dispersion coefficients are shown to be comparable with previous experimental studies. Eight different cylinder diameter configurations (six uniform and two non‐uniform) are considered, each at 20 different solid volume fractions and with seven different transverse positions for the injection location. The new dispersion data cover a broad range of solid volume fractions, for which simultaneous estimates of Dx and Dy have not been available previously. There are no systematic differences in non‐dimensional Dx and Dy between uniform and non‐uniform cylinder diameter distributions. When non‐dimensionalized by cylinder diameter, both dispersion coefficients are independent of solid volume fraction. When non‐dimensionalized by cylinder spacing, both longitudinal and transverse dispersion can be described as linear functions of the ratio of cylinder diameter to cylinder spacing. Key Points: New dispersion data for non‐uniform and uniform cylinder diameter distributions have been generated using a two‐dimensional numerical modelNon‐dimensional dispersion coefficients are unaffected by cylinder diameter distributionBoth longitudinal and transverse dispersion coefficients can be modeled as linear functions of cylinder diameter and cylinder spacing [ABSTRACT FROM AUTHOR]

Aim of the study: This study presents an opportunity to determine a value of longitudinal dispersion and is focused on the comparison of seasonal variation of the longitudinal dispersion predetermined by natural conditions of the river aquatic zone. Material and methods: The dispersion of a pollutant tracer was simulated by HEC-RAS model and by one dimensional advection-diffusion equation. Determination of longitudinal dispersion coefficient was done on the base of tracer experiments (2 kg NaCl in 10 l H2O) carried out in March, August and October 2019. Both methods were applied to the Okna River localized in the Eastern Slovak Lowland Results and conclusions: Result showed, that model HEC-RAS very sensitive reacted to the changes of dispersion and vegetation in the river. Estimated longitudinal dispersion coefficient for Okna river by equation during the year, was in a range from 0.093 to 1.08 m2s-1 and by the HEC-RAS it was from 0.220 to 1.850 m2s-1. Results could represent different values of longitudinal dispersion simulated by the model or equation. Obtained coefficients have a wide application. A main use of these numbers is with simulation of the spread of accidental pollution in rivers. Also, it can be applied to streams with similar characteristics. Results showed important role of seasonal variation of longitudinal dispersion coefficient that must be assumed in simulation of pollution spreading in rivers.

This study proposes two-dimensional (2D) pollutant migration in a semi-infinite geological formation with spatial varying transport parameters. Because the groundwater flow is bidirectional, the impact of off-diagonal dispersion also was taken into account. A decay parameter was considered in the aqueous phase as well as in the solid phase. We assumed that the groundwater reservoir was not plume-free, because some scale-varying pollutant exists there very initially, decaying with space. A change in the source at the inlet boundary in the presence of off-diagonal dispersion (ODD) alters the strength of pollutant concentration. The existing solutions can be reduced into other existent solutions for various geological formations. The Laplace transform technique (LTT) was applied to obtain the pollutant concentration profile in the 2D anisotropic heterogeneous porous medium. The Crank–Nicolson finite-difference (CNFD) technique was adopted for a numerical simulation. We demonstrated the validity of the analytical result. The numerical result and some previously available data from literature were compared and good agreement was found. [ABSTRACT FROM AUTHOR]

Temporal concentration profiles resulting from an injected pulse of fluorescent tracer were recorded at multiple locations along a pipe during controlled unsteady flow conditions. A linear temporal change in discharge over durations of 5, 10, or 60 s for both accelerating and decelerating flow conditions was studied. Tests were performed for flows that changed within the turbulent range, between Reynolds numbers of 6,500 and 47,000, and for laminar to turbulent flows, between Reynolds numbers of 2,700 and 47,000. Analysis of the data shows the limitations of employing steady-state routing of temporal concentration profiles in unsteady flow. Employing a flow weighted time routing approach, using tracer mean velocity and dispersion coefficients, provides accurate predictions of mixing in unsteady flow. For decelerating flows, longitudinal dispersion coefficients were lower than for the equivalent mean steady discharge. Previously unreported disaggregation of the tracer cloud was observed during all experiments accelerating from laminar to turbulent conditions. [ABSTRACT FROM AUTHOR]

Analytical solutions describing the 1D substance transport in streams have many limitations and factors, which determine their accuracy. One of the very important factors is the presence of the transient storage (dead zones), that deform the concentration distribution of the transported substance. For better adaptation to such real conditions, a simple 1D approximation method is presented in this paper. The proposed approximate method is based on the asymmetric probability distribution (Gumbel’s distribution) and was verified on three streams in southern Slovakia. Tracer experiments on these streams confirmed the presence of dead zones to various extents, depending mainly on the vegetation extent in each stream. Statistical evaluation confirms that the proposed method approximates the measured concentrations significantly better than methods based upon the Gaussian distribution. The results achieved by this novel method are also comparable with the solution of the 1D advection-diffusion equation (ADE), whereas the proposed method is faster and easier to apply and thus suitable for iterative (inverse) tasks.

We present a solute transport model, developed by employing a dynamic pore network modeling approach, to investigate dispersive solute transport behaviors in consolidated porous media. The model is capable of upscaling solute transport processes from pore to core, under two-phase fluid configurations. The governing equations of fluid flow, fluid displacement, and solute transport are solved at the pore level. A heavily parallelized computing scheme is utilized to simulate dynamic fluid displacements and transport processes in a core-scale pore network constructed from micro-computed tomography (micro-CT) images of a Berea sandstone sample. A series of solute transport simulations are conducted under the single-phase condition to validate the model by comparing the computed longitudinal dispersion coefficients against the experimental data over a wide range of Peclet numbers (Pe), i.e., 3 × 10 - 2 ∼ 3 × 10 5 . The model is then used to simulate solute transport under two-phase fluid configurations to examine the effects of the non-wetting phase saturation on solute transport behaviors. More specifically, solute transport is studied at different Pe and different water saturations obtained at the end of imbibition processes. We find that in a two-phase system, the longitudinal dispersion coefficient substantially increases with enhanced convective mixing under the transport regime with high Pe but decreases with restricted diffusive mixing at low Pe. In addition, the results indicate a non-monotonic dispersion–saturation relation under the convective transport condition. We illustrate that a strong correlation exists between the extent of dispersive mixing and the heterogeneity of fluid saturation profile across a core-scale network. [ABSTRACT FROM AUTHOR]

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Mixing in the hyporheic zone plays a key role in controlling the fate and transport of contaminants in streams and rivers. Consistently with recent experimental and numerical results, a physically based one‐dimensional solute transport model is presented that represents hyporheic mixing as a diffusion process exponentially attenuated with depth. When vertical diffusion in the sediment bed is not limited by an impermeable boundary, the moments of the breakthrough curves (BTCs) generated by the model exhibit persistent non‐Fickian behavior and are shown to scale consistently with existing experimental evidence. The ability of the exponentially attenuated mixing model to represent experimental BTCs was tested using data from field and flume tracer experiments, and its performance was compared with that of a classic two‐storage zone model. While both models provided an equally good approximation for the BTCs observed in field tracer tests, the exponentially attenuated mixing model provided better fits for the flume experiments. Analysis of the model equations and their solutions shows that, if the flow cross‐sectional area and wetted perimeter are not predetermined, there are infinite sets of parameter values that produce the same space‐time concentration distributions. The result implies that the physical parameters of hyporheic exchange cannot be determined by sole measurements of the solute BTCs in the surface water unless flow cross‐sectional area and average flow depth can be independently estimated. Key Points: A physically based one‐dimensional solute transport model with vertically attenuated hyporheic mixing is presentedThe behavior of the model breakthrough curves is consistent with experimental evidencePhysical transport parameters cannot be identified solely from surface breakthrough curves unless the cross‐sectional geometry is known [ABSTRACT FROM AUTHOR]

Predicting how pollutants disperse in vegetation is necessary to protect natural watercourses. This can be done using the one-dimensional advection dispersion equation, which requires estimates of longitudinal dispersion coefficients in vegetation. Dye tracing was used to obtain longitudinal dispersion coefficients in emergent artificial vegetation of different densities and stem diameters. Based on these results, a simple non-dimensional model, depending on velocity and stem spacing, was developed to predict the longitudinal dispersion coefficient in uniform emergent vegetation at low densities (solid volume fractions < 0.1). Predictions of the longitudinal dispersion coefficient from this simple model were compared with predictions from a more complex expression for a range of experimental data, including real vegetation. The simple model was found to predict correct order of magnitude dispersion coefficients and to perform as well as the more complex expression. The simple model requires fewer parameters and provides a robust engineering approximation. [ABSTRACT FROM AUTHOR]

In nature, aquatic vegetation is one of the important factors—along with hydraulic characteristics and geometric configuration—determining the dispersion of scalars. Previous research has studied the effects of vegetation on longitudinal dispersion, varying plant population with uniform arrangement. However, since vegetation grows more often in clumped and heterogeneous rather than uniform patterns, the present work investigates the effects of the vegetation arrangement on the flows characteristics such as longitudinal dispersion, mean velocities, and drag coefficients. Several types of vegetation arrangement are described with the isometric and allometric concept and quantified with the standardized Morisita index. Laboratory experiments were performed to investigate variations of hydraulic parameters and longitudinal dispersion coefficients according to vegetation arrangements, which were quantified with the standardized Morisita index. The hydraulic parameters of mean velocity, turbulent kinetic energy, and drag depend on the vegetation arrangements, and in particular, the longitudinal dispersion coefficient varies with these arrangements by a factor of 4 or more. Key Points: The standardized Morisita index can compare vegetation arrangements quantitatively and varies with dispersion parametersThe longitudinal dispersion gets larger as the patterns of vegetation become more allometric even with the same densityVegetation in 2‐D allometric arrangement generates velocity fluctuations in the lateral direction, increasing of longitudinal dispersion [ABSTRACT FROM AUTHOR]

The one‐dimensional advection dispersion equation (1D ADE) is commonly used in practice to simulate pollutant transport processes for assessment and improvement of water quality conditions in rivers. Various studies have shown that the longitudinal dispersion coefficient used within the 1D ADE is influenced by a range of hydraulic and geomorphological conditions. This study aims to quantify the impact and importance of the parameter uncertainty associated with the longitudinal dispersion coefficient on modeled pollutant time‐concentration profiles and its implications for meeting compliance with water quality regulations. Six regression equations for estimating longitudinal dispersion coefficients are evaluated, and commonly used evaluation criteria were assessed for their suitability. A statistical evaluation of the regression equations based on their original calibration data sets resulted in percent bias (PBIAS) values between −47.01% and 20.78%. For a case study, uncertainty associated with the longitudinal dispersion coefficient was propagated to time‐concentration profiles using 1D ADE and Monte Carlo simulations, and 75% confidence interval bands of the pollutant concentration versus time profiles were derived. For two studied equations, the measured peak concentration values were above the simulated 87.5th percentile, and for the other four equations it was close to the 87.5th percentile. Subsequent uncertainty propagation analysis of four diverse rivers show the potential considerable impact on concentration‐duration‐frequency‐based water quality studies, with 1D ADE modeling producing predictions of quality standard compliance which varied over hundreds of kilometers. Key Points: Uncertainty associated with longitudinal dispersion coefficients is quantified and propagated to time‐concentration profiles using 1D ADEApplication to case study found highly variable and considerable levels of uncertainty, influencing assessment of regulatory complianceStatistical criteria for evaluation of dispersion coefficient equations are less suitable for water quality regulation compliance evaluation [ABSTRACT FROM AUTHOR]

Simulation and prediction of the pollution transport is one of the major problems in environmental and rivers engineering studies. The numerical tools have been used in simulation of the concentration profile transmission for description of river water quality. The one-dimensional advection-dispersion equation (ADE) is used in applied water quality modeling and requires the accurate estimation of longitudinal dispersion coefficient (Dx). This paper develops a hybrid numerical-intelligence model for dispersion modeling in open-channel flows. The main contribution of this paper is to improve the results of 1D numerical simulation of pollutant transport in steady flows by estimation of dispersion coefficient (Dx) based on artificial intelligence models and subset selection of maximum dissimilarity (SSMD). The developed hybrid model uses an intelligence module based on optimized adaptive neuro fuzzy inference system (ANFIS) and artificial neural networks (ANNs) for longitudinal dispersion estimation, in which their structures are optimized by genetic algorithm (GA). Intelligence estimates of Dx by ANN, ANFIS, ANFIS-GA, ANN-GA, multiple linear regression (MLR), and empirical equation are compared with observed values of Dx available in 505 river section, and the ANFIS-GA, as the most accurate, is incorporated and integrated with developed 1D-ADE numerical module. The numerical solution of 1D-ADE is done using physically influenced scheme (PIS) for face flux estimation in finite volume method. The performance of hybrid models PIS-ANFIS-GA, PIS-ANFIS, and PIS-empirical is compared using the R2, RMSE, MAE, and NSE values in comparison with analytical solution and measured concentration hydrographs. The results revealed that the hybrid numerical-intelligence model is more accurate than the other classical methods for sediment/pollutant dispersion prediction in open-channel flows. The developed hybrid numerical-intelligence model can accurately simulate the dispersion processes in rivers and is a novel step in applicability of ANFIS-GA and ANN-GA models.ᅟ [ABSTRACT FROM AUTHOR]

Dispersion and mixing of fluids during miscible displacement in porous media are known to be strongly affected by heterogeneity and viscous fingering. In this study, direct pore-level numerical simulations are employed to model flow and solute transport during both stable and unstable miscible displacements in two-dimensional packings of circular grains. Longitudinal dispersion coefficients are then computed by fitting the numerically obtained concentration profiles to the analytical solution of the convection-dispersion equation. We observed that diffusive, mixed diffusive-advective, and mechanical dispersion regimes are present during stable displacements whereas the middle diffusive-advective regime is absent in unstable displacements due to the evolution of viscous fingers. Viscous fingering also increases the longitudinal dispersion coefficient several orders of magnitude compared to the stable displacement. The results reveal that the scale-dependency of longitudinal dispersion is a function of layering direction and viscosity contrast. During stable displacement in porous domains with no layering or with the layering perpendicular to the displacement direction, the longitudinal dispersion coefficient increases along the length of flow until it reaches an asymptotic value. When layering is in the direction of displacement, however, the scale-dependency behavior is a function of the layering pattern. In unstable displacements, however, longitudinal dispersion always exhibits an asymptotic behavior. Finally, it is observed that the effect of heterogeneity and layering on the magnitude of the longitudinal dispersion coefficient diminishes as viscosity ratio increases to higher adverse values. [ABSTRACT FROM AUTHOR]

Suspended vegetation can disturb flow, thereby affecting mass transportation. Although theoretical study of longitudinal dispersion in suspended vegetated flows may be complex, physical factors influencing longitudinal dispersion are well known. The key studying longitudinal dispersion is to obtain time-averaged longitudinal velocity distribution and lateral diffusion coefficient. A four-zone model, which includes the four-zone velocity profile and the four-zone turbulent diffusion coefficient profile, is proposed in this study to incorporate with the random displacement model (RDM) to simulate solute transport in suspended vegetated flows. Considering that the experimental results are measured at the early stage of the longitudinal dispersion, the downstream distance between the instrument and the release position should be considered to determine the longitudinal dispersion coefficient rather than directly using the asymptotic value. Then simulation results are obtained, which are consistent with those data measured in the experiments. In addition, this study confirms that the suspended vegetation can increase Fickian time, that is, it will take longer time for the longitudinal dispersion coefficient to reach stable. Finally, sensitivity analysis proves that the model has good stability. [ABSTRACT FROM AUTHOR]

Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e. , the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e. , the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large Péclet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous aquifers. [ABSTRACT FROM AUTHOR]

This study aims to examine the dispersion of a passive contaminant of solute released in Casson liquid flow through a tube. The wall of the tube is taken to be chemically active where the flow is driven by the constant pressure gradient. To evaluate the transport coefficients, Aris-Barton's Moment technique is considered, a finite difference implicit scheme is adopted to handle the differential equation arises in moment methodology. Also to confirm the results obtained by Aris-Barton's method, the generalized dispersion model has been applied. Unlike the previous studies on dispersion in Casson liquid, the time-dependent behavior of the transport coefficients has been established. Some significant observations have been founded, e.g. exchange coefficient is independent of yield stress while the convection coefficient and dispersion coefficient are inversely proportional to yield stress. Results reveal that transport coefficients are enormously affected by wall absorption. [ABSTRACT FROM AUTHOR]

Heat transfer in a random packed bed of monosized iron ore pellets is modelled with both a discrete three-dimensional system of spheres and a continuous Computational Fluid Dynamics (CFD) model. Results show a good agreement between the two models for average values over a cross section of the bed for an even temperature profiles at the inlet. The advantage with the discrete model is that it captures local effects such as decreased heat transfer in sections with low speed. The disadvantage is that it is computationally heavy for larger systems of pellets. If averaged values are sufficient, the CFD model is an attractive alternative that is easy to couple to the physics up- and downstream the packed bed. The good agreement between the discrete and continuous model furthermore indicates that the discrete model may be used also on non-Stokian flow in the transitional region between laminar and turbulent flow, as turbulent effects show little influence of the overall heat transfer rates in the continuous model. [ABSTRACT FROM AUTHOR]

At small dimensionless timescales T (= tD/H 2 ), where t is the time, H is the depth of the channel and D is the molecular diffusion coefficient, the mean transverse concentration along the longitudinal direction is not in a Gaussian distribution and the transverse concentration distribution is nonuniform. However, previous studies found different dimensionless timescales in the early stage, which is not verified experimentally due to the demanding experimental requirements. In this letter, a stochastic method is employed to simulate the early stage of the longitudinal transport when the Peclet number is large. It is shown that the timescale for the transverse distribution to approach uniformity is T = 0.5, which is also the timescale for the dimensionless temporal longitudinal dispersion coefficient to reach its asymptotic value, the timescale for the longitudinal distribution to approach a Gaussian distribution is T = 1.0, which is also the timescale for the dimensionless history mean longitudinal dispersion coefficient to reach its asymptotic value. [ABSTRACT FROM AUTHOR]

A reliable prediction of dispersion coefficient can provide valuable information for environmental scientists and river engineers as well. The main objective of this study is to apply intelligence techniques for predicting longitudinal dispersion coefficient in rivers. In this regard, artificial neural network (ANN) models were developed. Four different metaheuristic algorithms including genetic algorithm (GA), imperialist competitive algorithm (ICA), bee algorithm (BA) and cuckoo search (CS) algorithm were employed to train the ANN models. The results obtained through the optimization algorithms were compared with the Levenberg-Marquardt (LM) algorithm (conventional algorithm for training ANN). Overall, a relatively high correlation between measured and predicted values of dispersion coefficient was observed when the ANN models trained with the optimization algorithms. This study demonstrates that the metaheuristic algorithms can be successfully applied to make an improvement on the performance of the conventional ANN models. Also, the CS, ICA and BA algorithms remarkably outperform the GA and LM algorithms to train the ANN model. The results show superiority of the performance of the proposed model over the previous equations in terms of DR, R and RMSE. [ABSTRACT FROM AUTHOR]

The presence of instream aquatic vegetation (macrophytes) has an impact on the ecological functioning of rivers through their effects on transport and retention of dissolved and particulate matter, and also on the hydraulic functioning of rivers by increasing the hydraulic resistance, which results in higher water levels and may induce an increased flooding risk. In order to unravel these opposing effects, two field studies were conducted in 2013 and 2014 in a lowland river reach of 50 m with a high initial vegetation cover (>76%). We quantified the effects of three treatments − initial vegetation, partially mowed and vegetation free − on the hydraulic functioning (hydraulic resistance) and ecological functioning (transport and retention of dissolved and particulate tracers). Firstly, the partially vegetated treatment (after partial vegetation removal) resulted in reduced hydraulic resistance compared to the vegetated treatment and in enlarged retention of particulate matter compared to the vegetation free treatments. The longitudinal dispersion and transient storage zones were similar to the vegetated treatment. Moreover, the most heterogeneous flow field was also found in these partially vegetated treatments. Secondly, the vegetation free treatments (after complete vegetation removal) had the lowest hydraulic resistance, the highest flow velocity, the highest longitudinal dispersion coefficient, the largest transient storage zone, and the lowest retention of particulate matter. Thirdly, vegetated treatments had the highest hydraulic resistance, the lowest flow velocity, the lowest longitudinal dispersion coefficient, smallest transient storage zone, and the highest retention for particulate organic matter. We conclude that partial removal of the vegetation leads to an optimal trade-off between minimizing the flow velocity and maximizing the retention of particulate organic matter while minimizing the hydraulic resistance compared to the fully vegetated and vegetation free treatment. [ABSTRACT FROM AUTHOR]

Solute transport in rivers has been traditionally represented using one-dimensional models assuming advection and Fickian dispersion along the main flow direction and transient storage in surface and subsurface dead zones. Experimental evidence from several stream tracer studies has shown that the longitudinal scaling of the moments of the breakthrough curves (BTCs) is inconsistent with classic 1-D solute transport models. In this work, simulations of advection and diffusion in a 2-D and 3-D channel flow over a porous bed are presented assuming an exponentially attenuated profile of the transverse mixing coefficient in the porous medium, as suggested by recent experimental and numerical studies. It is shown that the longitudinal transport in the channel is superdiffusive, and the skewness of the concentration distributions can be almost constant over a broad temporal range, with no sign of approaching zero at large times. A sensitivity analysis shows that, at large times, longitudinal dispersion is controlled by the cross-sectional profile of the in-bed transverse mixing coefficient, and by the difference between the average velocity in the channel and in the porous bed. The normalized concentration distributions can be approximated by beta-distributions with time-dependent parameters, and relationships are derived between the scaling of the parameters under power-law approximation and the scaling of the spatial and temporal moments. The results provide new insights into the physical mechanisms that control the anomalous scaling of the moments observed in field tracer studies and opens new possibilities for predictive and inverse modeling of transport processes in rivers and their catchments. [ABSTRACT FROM AUTHOR]

Accurate prediction of longitudinal dispersion coefficient (K) is a key element in studying of pollutant transport in rivers when the full cross sectional mixing has occurred. In this regard, several research studies have been carried out and different equations have been proposed. The predicted values of K obtained by different equations showed a great amount of uncertainty due to the complexity of the phenomenon. Therefore, there is still a need to make an improvement on the existing predictive models. In this study, a multi-objective particle swarm optimization (PSO) technique was used to derive new equations for predicting longitudinal dispersion coefficient in natural rivers. To do this, extensive field data, including hydraulic and geometrical characteristics of different rivers were applied. The results of this study were compared with those of the previous studies using the statistical error measures. The comparison revealed that the proposed model is superior to the previous ones. According to this study, PSO algorithm can be applied to improve the performance of the predictive equations by finding optimum values of the coefficients. The proposed model can be successfully applied to estimate the longitudinal dispersion coefficient for a wide range of rivers' characteristics. [ABSTRACT FROM AUTHOR]

Numerical solution of steady state partial differential equation (PDE) model is proposed using a stabilized local meshless method (SLMM). The PDE model under consideration is used to approximate longitudinal dispersion of suspended particles of turbulent flow moving with both zero and nonzero settling velocities. In the proposed technique, a shape parameter based SLMM is used to calculate effects of mean velocity and variable eddy diffusivity accurately. In the case of zero settling velocity, when particles are injected from a line source located at some height, numerical results confirm the experimental results. Numerical results of the SLMM also confirm numerical results produced by finite difference method (FDM) as well. [ABSTRACT FROM AUTHOR]

• Numerical estimation of longitudinal dispersion in reticulated porous media. • Peclet number correlation using strut diameter as Characteristic length is proposed. • Modified Peclet numbers of Kelvin structure are validated with literature data. The purpose of this numerical investigation is to characterize the longitudinal dispersion coefficients in open-cell reticulated porous structures. Open-cell foams are modelled using idealized Kelvin cell structures. Using the conventional Navier–Stokes equation, airflow has been calculated through various porous structures. Along with the flow, the dispersion of a tracer fluid is traced across the structures and analyzed in terms of the effective dispersion coefficient. Using direct pore level simulations (DPLS), a parametric study is performed to understand the influence of geometrical parameters on the dispersion in porous media. To evaluate the longitudinal dispersion coefficient (LDC), the analytic solution gradients were fitted into the simulated gradients. From the results, a new characteristic length correlation is proposed to calculate the Peclet number, and it is compared with experimental and numerical data that are available in the literature. [ABSTRACT FROM AUTHOR]

An approximate solution of longitudinal dispersion phenomena occurring in two phase miscible fluid flow through porous media has been obtained by using the group theoretic approach. The longitudinal dispersion coefficient is assumed to be directly proportional to the concentration of the fluid for a distance x and at any time t > 0. The graphical representation for the concentration of the fluid for a distance x and at time t > 0 has been obtained using Mat lab coding.