Advection-dispersion Model Research Articles

Influence of calcium species on SO2 adsorption capacity of a novel carbonaceous materials and their ANN modeling

Due to the sulfur dioxide (SO2) negative effects to the environment and human health, its removal is currently of great importance to policy markers and researchers. In this context, the present work had the aim to study the SO2 dynamic adsorption behavior on two activated carbons rich on calcium species. One material prepared directly from peach stone shell (PC) and the other prepared from raw material treated with CaCl2 (PCCa) with the purpose to increase the interaction of sulfur with calcium compounds on the surface and to augment its surface area. The obtained activated carbons were characterized using N2 adsorption at 77 K, IR, XRD and SEM/EDX analysis. PCCa carbon presented the higher adsorption capacity compared with PC material, indicating that the surface area and the increase of calcium groups (Ca(OH)2, CaCO3, CaO) are playing an important role during the adsorption of SO2. Additionally, the results demonstrated that as temperature increases the adsorption capacity decreases. On the other hand, the dynamic studies revealed that the residence time reached at 150 mL min−1 flow-rate was the most efficient for the mass transfer processes. Also, the results demonstrated that the presence of moisture decreases the adsorption capacity due to the presence of water molecules on the adsorbent surface. The dynamic adsorption results were modeled using: the Advection-dispersion model, FANN and the conventional models Thomas and Yan. The results shown that the FANN model was the best to correlate the adsorption breakthrough curves of SO2.

Long-term alterations of flow regimes of the Mekong River and adaptation strategies for the Vietnamese Mekong Delta

Study regionThe Mekong basin, where climate change and anthropogenic interventions (e.g., dams, sand mining, and sluice gates) have intensified in the recent decades affecting the pristine flow regime and salinity intrusion. Study focusThis paper aims at quantifying the flow regime alterations in the entire Mekong from 1980 to 2015 and linking with the controlling drivers of alterations. In this regard, various indicators, analytical methods, and a semi two-dimensional hydrodynamic and advection-dispersion model were used. New hydrological insights for the regionThe flow regime alterations in the high-dam development period (2009–2015) are more pronounced than in the low-dam development period (1993–2008), compared to the no-dam development period (1980–1992), based on most of the indicators analyzed. In the high-dam development period all existing dams with large reservoir capacity seemed to have cumulatively reduced the flood pulses and frequency and increased the low-flow discharge along the entire Mekong through reservoir operations, exceeding climate change effect. In the recent years the water levels in the low-flow season in the Vietnamese Mekong Delta (VMD) have decreased, possibly because of increased riverbed incision caused by reduced sediment supply and increased sand mining. The reduced water levels together with the increased number of the sluice gates constructed seemed to have increased salinity intrusion in the VMD which may be partly reduced by early emergency water release from upstream dams.

Comparing Simulations of Umbrella-Cloud Growth and Ash Transport with Observations from Pinatubo, Kelud, and Calbuco Volcanoes

The largest explosive volcanic eruptions produce umbrella clouds that drive ash radially outward, enlarging the area that impacts aviation and ground-based communities. Models must consider the effects of umbrella spreading when forecasting hazards from these eruptions. In this paper we test a version of the advection–dispersion model Ash3d that considers umbrella spreading by comparing its simulations with observations from three well-documented umbrella-forming eruptions: (1) the 15 June 1991 eruption of Pinatubo (Philippines); (2) the 13 February 2014 eruption of Kelud (Indonesia); and (3) phase 2 of the 22–23 April 2015 eruption of Calbuco (Chile). In volume, these eruptions ranged from several cubic kilometers dense-rock equivalent (DRE) for Pinatubo to about one tenth for Calbuco. In mass eruption rate (MER), they ranged from 108–109 kg s−1 at Pinatubo to 9–16 × 106 kg s−1 at Calbuco. For each case we ran simulations that considered umbrella growth and ones that did not. All umbrella-cloud simulations produced a cloud whose area was within ~25% of the observed cloud by the end of the eruption. By the eruption end, the simulated areas of the Pinatubo, Kelud, and Calbuco clouds were 851, 53.2, and 100 × 103 km2 respectively. These areas were 2.2, 2.2, and 1.5 times the areas calculated in simulations that ignored umbrella growth. For Pinatubo and Kelud, the umbrella simulations provided better agreement with the observed cloud area than the non-umbrella simulations. Each of these simulations extended 24 h from the eruption start. After the eruption ended, the difference in cloud area (umbrella minus non-umbrella) at Pinatubo persisted for many hours; at Kelud it diminished and became negative after 14 h and at Calbuco it became negative after ~23 h. The negative differences were inferred to result from the fact that non-umbrella simulations distributed ash over a wider vertical extent in the plume, and that wind shear spread the cloud out in multiple directions. Thus, for some smaller eruptions, wind shear can produce a larger cloud than might be produced by umbrella spreading alone.

Numerical analysis of sensor-based flood-floor ebb-and-flow subirrigation system with saline water

ABSTRACT Ebb-and-flow is a well-known and common greenhouse irrigation system. In this paper, a specific numerical model for a sensor-based flood-floor ebb-and-flow irrigation system has been developed using one-dimensional Richards’ equation for water flow and two-site sorption advection-dispersion model for simulation of solute transport. The model was validated against analytical and numerical results proposed in the literature, and acceptable agreement was obtained in all cases. Maximum RMSE (MAE) was 0.053 m (0.273 m) for water flow and 0.021 (0.065) for solute transport. The model was then used for a parametric study of how different factors (such as salinity of irrigation water, triggering and cutoff thresholds, sensor position and flooding depth) would affect transpiration of sensor-equipped solitary pot under ebb-and-flow irrigation system for two different crops. It was revealed that sensor position and water salinity were significantly influential on transpiration of the pots. Finally, the synchronized sensor equipped-sensorless module of the numerical model was used to optimize the flood-floor ebb-and-flow irrigation system considering different factors using Taguchi approach. It was concluded that installing a water content sensor, whose triggering and cutoff thresholds were at −10 and −2 m, at the upper-half of the center-positioned pot would result in higher transpiration and lower unevenness of water distribution.

Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection–dispersion models

Various non-local structural derivative diffusion models have been proposed based on different kernel functions to describe the anomalous time dependence of the mean-squared displacements. In the present study, the fundamental solutions for constant and variable-order structural derivative advection–dispersion models are achieved via scaling transformation and the generalized non-Euclidean Hausdorff fractal distance. Comparative numerical investigations of the structural derivative models have been conducted to reveal the influences of various kernels via the meshless method of fundamental solutions. Numerical results verify the validity of the derived fundamental solutions and the rationality of the employed numerical method for structural derivative advection–dispersion models.

Influence of dual conduit structure on solute transport in karst tracer tests: An experimental laboratory study

We conducted lab-scale experiments to investigate the mechanism of dual-peaked breakthrough curves (BTCs) in karst tracer tests. Three groups of dual conduit structures were constructed by varying: (1) the length ratio between the two conduits for a fixed length of the shorter conduit, (2) the total length of the conduits for a fixed length ratio, (3) the connection angle between the conduits. The BTCs generated by the tracing experiments were fitted by a Dual-Region Advection Dispersion (DRAD) model to derive effective transport parameters.Our results confirm that the dual conduit structure triggers the double-peaked BTCs. Increasing the conduit length for a fixed length ratio or increasing the length ratio increases peak separation. The connection angles between the two conduits θ1 and θ2 also influence the BTCs: increasing θ1 and decreasing θ2 causes the first peak to get smaller and the second peak to get larger. The DRAD model can reproduce the dual-peaked BTCs while its application to the case of single-peaked BTCs may be problematic due to strong interaction between model parameters. A method is proposed for estimating underground karstic conduit lengths from experimental dual-peaked BTCs.

Simple transport models for karst systems

Tracer tests are useful field methods with a wide range of applications in karst aquifers. The measured tracer breakthrough curve at a karst spring allows the estimation of the important transport properties of the karst system. The breakthrough curve is typically characterized by a long tailing and a low tracer recovery that is not captured by the classical one-dimensional advection dispersion model. Partitioning models are often used and require a large number of parameters. In the present work, simplified transport models are proposed to simulate the typical karst breakthrough curve. The model setup consists of a karst conduit that is interacting laterally with the surrounding matrix. The solute transport in both the conduit and matrix are governed by the one-dimensional advection-dispersion equation and the resulting mathematical model consists of a coupled system of differential equations. The Laplace transform method is used to derive the transport models for various flow and boundary conditions. The models are in terms of four physically meaningful parameters that represent the advection and dispersion properties of the flow in the conduit and matrix. Algebraic relationships to estimate the model parameters are also derived in terms of the key features of the breakthrough curves. The main advantage of the proposed models are their simple formulation and ability to capture the long tailing of the breakthrough curve in terms of just a few parameters. Application of the models to two real karst aquifers demonstrate their effectiveness in simulating the observed breakthrough curves and estimating the key transport parameters.

A new method for determination of concentration profile in a transport column by gamma spectroscopy combined with genetic algorithm

A non-collimated gamma spectroscopy with fewer sampling (counting) and shorter sampling periods is developed and used to estimate the concentration profile of the radiotracers within the column. In this method, the radiotracer activity in the whole column is measured in a few different positions of the detector and then, by using an appropriate advection-dispersion model and the genetic algorithm, the concentration profile within the column is constructed. The concentration profile obtained by the new method fits very well to the experimentally obtained thin-section scanning results with RMSE less than 0.046. The uniqueness of the concentration profile obtained by the method was confirmed by a sensitivity analysis. Beside the excellent prediction of the concentration profile, the non-collimated gamma spectroscopy (our method) is much faster than the conventional thin-section gamma scanning method. In our experimental set-up, it took less than 10 min to construct the concentration profile by the non-collimated gamma spectroscopy, much less than 8 h required for thin-section scanning method.

Study of pollution transport through the rivers using aggregated dead zone and hybrid cells in series models

This paper aims at studying the data-based mechanistic pollution transport models of the aggregated dead zone (ADZ) and hybrid cells in series (HCIS) models. For a better understanding of them, it was tried to connect their parameters to the physical parameters of the classical advection–dispersion (ADE) model. A series of experiments were conducted using the laboratory model of the gravel bed river, and the sodium chloride solution was chosen as a conservative tracer. A new analytical solution of HCIS model, including triple dispersion cells, was developed. Also, the theoretical temporal moment equations were derived and attempted to develop explicit relationships for both ADZ and HCIS parameters based on hydraulically and geometrically variables. Detailed descriptions of the Pe number and the skewness coefficients (CSK) were presented, and the theoretical limit of CSK was extracted. It was concluded that the range of (0.93–1.24) for CSK is acceptable, which confirms the finding of previous investigators. A sensitivity analysis was operated to find the importance of different variables in estimating model parameters. Finally, the theoretical breakthrough curves of ADZ and HCIS models were drawn and confirmed with experimental BTCs. Statistical goodness of fit parameters of RMSE, DC, and MAE was calculated as triple sets of (0.0158, 0.99, 21.58 ppm), (0.0188, 0.97, 27.16 ppm), and (0.105, 0.83, 78.84 ppm) for ADZ, HCIS, and ADE models, respectively, which showed the superiority of data-based models to the classical ADE model.

Study on non-Fickian behavior for solute transport through porous media

ABSTRACT In this study, fractional advection-dispersion equation is used to model the conservative solute transport through porous media. Explicit finite difference method has been used to solve the spatial fractional advection dispersion equation. Observed concentration profiles of chloride tracer have been obtained through soil column experiments in the lab. Both advection-dispersion and spatial fractional advection dispersion models have been used to simulate observed concentration profile at various distances in the flow direction. Results indicate that the variation in the value of root mean square error is observed in the case of both homogeneous and heterogeneous porous media. Non-Fickian behavior is more in case of heterogeneous media as compared to homogeneous media. Finally, results indicate that the better simulation has been obtained from spatial fractional advection-dispersion equation model as compared to advection-dispersion equation model in case of heterogeneous porous media.

Predicting Solute Transport Parameters in Saturated Porous Media Using Hybrid Algorithm

This study aims to estimate the solute transport parameters in saturated porous media using a hybrid algorithm. In this study, the Physical Non-Equilibrium (PNE) model was used to describe the transport of solutes in porous media. A numerical solution for the PNE model is obtained using the Finite Volume Method (FVM) based on the Ttri-Diagonal Matrix Algorithm (TDMA). The developed program, written in Matlab, is capable to solve the advection-dispersion (ADE) and the PNE equations for the mobile -immobile (MIM)model with linear sorption isotherm. The Solute transport parameters, (immobile water content, mass transfer coefficient, and dispersion coefficient), are estimated using different algorithms such as the Levenberg-Marquardt algorithm (LM), genetic algorithm (GA), simulated annealing algorithm (SA). To overcome the limitations of deterministic optimization models which are rather unstable and divergent around a local minimum, a hybrid algorithm (GA+LM, SA+LM) permits to estimate of the solute transport parameters. Numerical solutions are verified using the experiments conducted by Semra (2003) which are about the transport of toluene through a column composed of impregnated Chromosorb grains at ambient temperature (20 °C) for three flow rates (1, 2 and 5ml/min). The results show that the hybrid algorithm (GA+LM, SA+LM) is more accurate than others (GA, SA, and LM). Comparing to the ADE model, The PNE with linear isotherm model gives a better description to the BeakThrough Curves (BTCs) with higher values of determination coefficient (R2) and lower values of Root Mean Square Error (RMSE). Also, the solute transport parameters tended to vary with the flow rate.

Development and application of an advection-dispersion model for data analysis of electromigration experiments with intact rock cores

An advection-dispersion model was developed for interpreting the experimental results of electromigration in granitic rock cores. The most important mechanisms governing the movement of the tracer ions, i.e. electromigration, electroosmosis and dispersion were taken into account by the advection-dispersion model, but the influence of aqueous chemistry was ignored. An analytical solution in the Laplace domain was derived and then applied to analyze the measured results of a series of experiments, performed in an updated experimental device using different applied voltages. The modelling results suggested that both studied tracers, i.e. iodide and selenite, are effectively non-sorbing in the intact rock investigated. The effective diffusivities and formation factors evaluated from the model were also found to be in good agreement with data reported in literature and the associated uncertainties are much smaller than those obtained from the classical ideal plug-flow model, which accounts only for the dominant effect of electromigration on ionic transport. To explore further how the quality of parameter identifications would be influenced by neglect of aqueous chemistry, a reactive transport model was also implemented, which may be regarded as a multi-component version of the advection-dispersion model. The analysis showed that the advection-dispersion model works equally well as the reactive transport model but requires much less computational demand. It can, therefore, be used with great confidence to interpret the experimental results of electromigration for studies of diffusion and sorption behavior of radionuclides in intact rock cores.

Analysis of fractal fractional differential equations

Nonlocal differential and integral operators with fractional order and fractal dimension have been recently introduced and appear to be powerful mathematical tools to model complex real world problems that could not be modeled with classical and nonlocal differential and integral operators with single order. To stress further possible application of such operators, we consider in this work an advection-dispersion model, where the velocity is considered to be 1. We consider three cases of the models, when the kernels are power law, exponential decay law and the generalized Mittag-Leffler kernel. For each case, we present a detailed analysis including, numerical solution, stability analysis and error analysis. We present some numerical simulation.

A modification of the electromigration device and modelling methods for diffusion and sorption studies of radionuclides in intact crystalline rocks

To determine the diffusion and sorption properties of radionuclides in intact crystalline rocks, a new electromigration device was built and tested by running with I− and Se(IV) ions. By introducing a potentiostat to impose a constant voltage over the studied rock sample, the electromigration device can give more stable and accurate experimental results than those from the traditional electromigration devices. In addition, the variation in the pH of the background electrolytes was minimised by adding a small amount of NaHCO3 as buffers. To interpret the experimental results with more confidence, an advection-dispersion model was also developed in this study, which accounts for the most important mechanisms governing ionic transport in the electromigration experiments. Data analysis of the breakthrough curves by the advection-dispersion model, instead of the traditional ideal plug-flow model, suggest that the effective diffusivities of I− and Se(IV) are (1.15 ± 0.06) × 10−13 m2/s and (3.50 ± 0.86) × 10−14 m2/s, respectively. The results also show that I− is more mobile than Se(IV) ions when migrating through the same intact rock sample and that their sorption properties are almost identical.

An efficient approximation of non-Fickian transport using a time-fractional transient storage model

The classical transient storage (TS) model is widely used to describe a non-Fickian solute transport process induced by the solute mass exchange between the main channel and the immobile zone. It has been shown that the single rate TS model tends to underestimate the slower exchange that occurs in a deeper or longer hyporheic flow path. This long-term retention can be better described by the fractional mobile/immobile model (FMIM). However, in a real-world application, this method usually overestimates the late time concentrations in a breakthrough curve (BTC), which can be better described by the tempered-time-fractional model (TTFM). In this study, we introduced a fractional-in-time derivative TS model (FTTS), which can describe broad waiting times in a particle motion process. First, a fully-implicit numerical scheme was applied to solve the FTTS and the method was validated by comparing its results with the analytical solutions of the classical advection-dispersion model (ADE) and the FMIM. Then, the FTTS was applied to fit the synthetic data generated by the STAMMT-L and field tracer experiment data. Further, a variance-based global sensitivity analysis was performed to assess the influence rank of the parameters to the heavy tail of the BTCs. The results indicated that the FTTS could fit the BTCs generated by the ADE and FMIM well. In synthetic cases, the FTTS could reproduce different heavy tailing BTCs accurately. In addition, the FTTS could well describe tracer data in natural streams and performed better than the TTFM. The sensitivity analysis indicated that both the fractional-in-time term and the TS term in the FTTS had important impacts on the tail of the BTC, which could make the FTTS more flexible for describing the tailing phenomenon in a BTC.

Near-field hydrothermal plume dynamics at Brothers Volcano (Kermadec Arc): A short-lived radium isotope study

The naturally occurring radium (Ra) isotope quartet was measured for the first time at an intraoceanic arc hydrothermal setting along the Kermadec Island Arc (SW Pacific). 224Ra (3.7 d half life) and 223Ra (11.4 d half life) are assumed to be tracers solely originating from hydrothermal discharge and have been used to resolve near-field hydrothermal plume dynamics by applying both advection and eddy diffusion-based dispersion models. Assuming dominant advective processes, we identified different horizontal plume age structures at Brothers volcano, with a slow moving plume inside the caldera (0.060 cm/s) and a faster moving plume outside the caldera (0.323 cm/s), indicating a longer plume residence time within the caldera structure. The decreasing trend in Ra activity also allows the calculation of horizontal eddy diffusion coefficients inside and outside of the caldera, with 0.164 m2/s and 3.545 m2/s for 224Ra, respectively. These trends are in accordance with the radial horizontal eddy diffusion model. Our results reveal that net advection might not necessarily play a major role at Brothers, as radial horizontal eddy diffusion reproduces the observed Ra activity distribution to the same degree. Additional model simulations based on a combination of advection and diffusion, favor slow net advection to explain the Ra activity distribution. Within the rising non-buoyant plume, Ra isotopes suggested constant dilution along the first 170 m of the vertical water column and a vertical transport velocity on the order of 0.156 cm/s for altitudes up to 150 m above the vent and around 0.004 cm/s for altitudes above 150 m. When a common source of diffuse and focused venting is assumed and only small amounts of Ra are added to the ascending plume, due to recoil originating from high water to rock ratios, fluids from diffuse vents show a slower migration rate through the subsurface than fluids from focused vents. Our data imply that the fluids from diffuse vents needed approximately five days longer to percolate through the underlying subsurface to reach the water column plume, compared to the fluids from direct vents which emanate through chimney structures. This study demonstrates the potential of short-lived Ra isotopes as tracers of near-field plume dynamics, which will improve our understanding of hydrothermal vents as sources for various trace elements to the global ocean.

Granular computing–neural network model for prediction of longitudinal dispersion coefficients in rivers

Successful application of one-dimensional advection-dispersion models in rivers depends on the accuracy of the longitudinal dispersion coefficient (LDC). In this regards, this study aims to introduce an appropriate approach to estimate LDC in natural rivers that is based on a hybrid method of granular computing (GRC) and an artificial neural network (ANN) model (GRC-ANN). Also, adaptive neuro-fuzzy inference system (ANFIS) and ANN models were developed to investigate the accuracy of three credible artificial intelligence (AI) models and the performance of these models in different LDC values. By comparing with empirical models developed in other studies, the results revealed the superior performance of GRC-ANN for LDC estimation. The sensitivity analysis of the three intelligent models developed in this study was done to determine the sensitivity of each model to its input parameters, especially the most important ones. The sensitivity analysis results showed that the W/H parameter (W: channel width; H: flow depth) has the most significant impact on the output of all three models in this research.

Modelling long‐distance floating seed dispersal in salt marsh tidal channels

AbstractSeed dispersal is a primary factor influencing plant community development in salt‐marshes. However, studies on seed dispersal in marsh‐channel system are relatively scarce, and relevant mathematical modelling is particularly lacking. In this study, we developed a one‐dimensional advection–dispersion model to explore the patterns of long‐distance floating seed dispersal in tidal channels. Oscillatory tidal current velocity and water depth were assumed to represent the tidal effects. An exponential decay coefficient was introduced to account for the loss of floating seeds due to water‐logged deposition and retention by trapping agents along the channel banks. An analytical solution in integral form was derived using the method of Green's function. The developed model was applied to simulate floating Spartina densiflora seed dispersal in a real tidal channel. Seed floating duration and seed collection data reported in the literature were used for model calibration and validation. The leptokurtic seed dispersal kernel in the marsh‐channel system was quantified for the first time using the predicted spatio‐temporal distribution of deposited and retained seeds. The range of the long‐distance floating seed dispersal and its distribution concentration that have important implications for salt marsh protection and restoration activities were evaluated through statistical parameters such as the centroid displacement and the variance of the floating seed cloud and floating seed concentration contours. The developed model provides a useful tool for ecological management of tidal marshes, as data on the long‐distance floating seed dispersal are rarely available and hard to gather.

Longitudinal and transverse dispersion coefficients of 2D contaminant transport model for mixing analysis in open channels

In this study, longitudinal and transverse dispersion coefficients of the two-dimensional advection-dispersion model were calculated using both the velocity and concentration data obtained through tracer tests in large-scale meandering channels. The velocity-based dispersion coefficients calculated by applying the theoretical equations to the velocity data were compared with concentration-based dispersion coefficients that were calculated by applying the routing procedure to the measured concentration curves. The results showed that the cross-sectional averaged values of the dimensionless longitudinal dispersion coefficient, DL/HU∗, calculated from the velocity profile data ranged 4.1–6.5, which corresponded to the theoretical value, whereas DL/HU∗ by concentration data ranged 14.7–35.5, which was 4–6 times larger than the velocity-based coefficient. The cross-sectional maximum values of the dimensionless transverse dispersion coefficient, DT/HU∗, by the velocity-based method ranged 0.1–3.3, whereas DT/HU∗ by concentration-based method was 0.9–2.9. These results revealed that the velocity-based longitudinal dispersion coefficient is a fractional value of the concentration-based result, which contained mixing caused by channel irregularities throughout the reach, in addition to shear dispersion by vertical velocity variations, while transverse dispersion coefficients by both methods represented the same dispersion mechanism which was dominated by the secondary currents developed in highly sinuous channels.

ICAT: A numerical scheme to minimize numerical diffusion in advection-dispersion modeling and its application in identifying flow channeling

The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. Discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.