One-dimensional Solute Transport Model Research Articles

Multipeaked breakthrough curves in karstic rivers: effects of a diffluence-confluence system

In karstic environments, it is not unusual for an underground river to split into two or more streams (diffluence) and merge back together downstream (confluence). This kind of behavior can generate multipeaked breakthrough curves (BTCs) in dye tracing at a sampling site located downstream of the confluence(s). It is also possible that such a phenomenon is difficult to highlight with dye tracing if the tracer clouds coming from the different streams reach the sampling locations at the same time. In this study, an attempt at quantifying the importance of different criteria in the occurrence of a multipeaked BTC is done by performing a dye tracing campaign in a two-tributaries diffluence-confluence (DC) system and using a one-dimensional solute transport model. The results from both field data and the solute transport model suggest that a double-peaked BTC occurs downstream of a DC system if the following conditions are met: (1) the injection is done close enough to the diffluence, (2) the sampling point is located not too far from the confluence, and (3) the two (or more) streams have sufficiently contrasted travel times from the diffluence to the confluence. The paper illustrates that, even if a diffluence occurs in a karstic river, multipeaked BTCs are not necessarily observed downstream of the confluence if these three conditions are not met. Therefore, characterizing a DC system using dye tracing is a real challenge. This could explain why publications that report studies involving multipeaked BTCs are quite rare.

Surrogate prediction of the breakthrough curve of solute transport in rivers using its reach length dependence

Techniques for predicting the contaminant cloud propagation along a stream are necessary for swift action against contaminant spill accidents in fluvial systems. Due to their low computational cost, one-dimensional solute transport models have conventionally been employed, in which the complex channel characteristics are considered using model parameters. However, the determination of such parameters relies predominantly on optimization techniques based on pre-measured tracer data, which are usually unavailable for unexpected accidents. The present paper suggests an alternative method for predicting a breakthrough curve (BTC) variation along an unmeasured stream reach where no flow information is provided. In this study, we investigated the relationship between directly-measured flow properties and BTC characteristics based on field tracer experiments. Using statistical features of the tracer BTCs, we devised a regressive prediction method for estimating the BTC features as a function of travel distance, and validated the method by comparison with simulations using both a one-dimensional advection–dispersion equation (ADE) and transient storage model (TSM), whose parameters were calibrated at upstream reaches. The proposed regressive predictions were relatively accurate than those from parameter-calibrated models, and this advantage was more apparent for long-distance predictions for the unmeasured river reach.

Evaluating the dynamics of groundwater, lakebed transport, nutrient inflow and algal blooms in Upper Klamath Lake, Oregon, USA

Transport of nutrients to lakes can occur via surface-water inflow, atmospheric deposition, groundwater (GW) inflow and benthic processes. Identifying and quantifying within-lake nutrient sources and recycling processes is challenging. Prior studies in hypereutrophic Upper Klamath Lake, Oregon, USA, indicated that ~60% of the early summer phosphorus (P) load to the lake was internal and hypothesized to be lakebed sediment release. Dynamic nutrient transport processes were examined to better characterize the nutrient sources. One-dimensional heat transport models calibrated to observed lakebed temperatures and a cross-sectional GW flow model provided estimates of GW-inflow rates that were greatest in spring and decreased through summer. One-dimensional solute transport models calibrated to observed lakebed pore-water dissolved silica (Si) and dissolved phosphate-phosphorus (DP) concentrations indicated that nutrients were transported from the lakebed by advection, diffusion, and enhanced mixing by benthic organisms and waves, and that DP removal occurred near the lakebed interface. Estimated water, Si, DP and total-phosphorus (TP) budgets indicated that GW contributed 21% of lake water inflow and at least 26, 20 and 16% of total Si, DP and TP inflow, respectively, when conservatively assuming background GW nutrient concentrations. However, lakebed GW (LGW) is enriched in nutrients during flow through lakebed sediment and the estimated GW contribution increased to 29 (33), 49 (67) and 43% (61%) of total Si, DP and TP inflow, respectively, if 20% (50%) of GW inflow to the lake was assumed to have LGW concentrations. Net nutrient inflow to the lake was greatest in spring and coincident with the annual diatom bloom. Inflowing dissolved nutrients appear to be assimilated by diatoms during the spring and become available for the summer Aphanizomenon flos-aquae bloom when the diatoms senesce. Thus, nutrient-enriched GW inflow and nutrient recycling by successive algal blooms must be considered when evaluating internal nutrient loading to lakes.

Solute transport model equation for mobile phase in semi-infinite porous media

An analytical solution of one-dimensional solute transport model equation for mobile phase is derived for semi-infinite heterogeneous porous media. The transport equation considers advection, longitudinal dispersion, linear isotherm, and porosity in its formulation. The dispersion is assumed to be Fickian, characterized by a constant dispersion coefficient. Temporally dependent velocity patterns are employed for the prediction of contaminant concentration. The analytical solution is compared with two reported solutions and can be used for benchmarking numerical codesand also as a preliminary predictive tool for groundwater management. Also, the obtained analytical solution of the proposed model may be helpful in the groundwater hydrology areas.

Influence of Chemical Osmosis on Solute Transport and Fluid Velocity in Clay Soils

AbstractSolute transport through the clay liner is a significant process in many waste landfills or unmanaged landfills. At present, researchers mainly focus on the test study about semi-membrane property of clay material, however, the influence of chemical osmosis caused by membrane effect on solute transport and fluid velocity is insufficient. In this investigation, based on the classical advection-diffusion equation, a one-dimensional solute transport model for low-permeable clay material has been proposed, in which the coupled fluid velocity related with hydraulic gradient and concentration gradient is introduced, and the semi-membrane effect is embodied in the diffusion mechanism. The influence of chemical osmosis on fluid velocity and solute transport has been analyzed using COMSOL Multiphysics software. The simulated results show that chemical osmosis has a significant retarded action on fluid velocity and pollutant transport. The proposed model can effectively reveal the change in process of coupled fluid velocity under dual gradient and solute transport, which can provide a theoretical guidance for similar fluid movement in engineering.

One-dimensional solute transport in open channel flow from a stochastic systematic perspective

Solute transport by river and stream flows in natural environment has significant implication on water quality and the transport process is full of uncertainties. In this study, a stochastic one-dimensional solute transport model under uncertain open-channel flow conditions is developed. The proposed solute transport model is developed by upscaling the stochastic partial differential equations through their one-to-one correspondence to the nonlocal Lagrangian–Eulerian Fokker–Planck equations. The resulting Fokker–Planck equation is a linear and deterministic differential equation, and this equation can provide a comprehensive probabilistic description of the spatiotemporal evolutionary probability distribution of the underlying solute transport process by one single numerical realization, rather than requiring thousands of simulations in the Monte Carlo simulation. Consequently, the ensemble behavior of the solute transport process can also be obtained based on the probability distribution. To illustrate the capabilities of the proposed stochastic solute transport model, various steady and unsteady uncertain flow conditions are applied. The Monte Carlo simulation with stochastic Saint–Venant flow and solute transport model is used to provide the stochastic flow field for the solute transport process, and further to validate the numerical solute transport results provided by the derived Fokker–Planck equations. The comparison of the numerical results by the Monte Carlo simulation and the Fokker–Planck equation approach indicated that the proposed model can adequately characterize the ensemble behavior of the solute transport process under uncertain flow conditions via the evolutionary probability distribution in space and time of the transport process.

Parameter uncertainty with flow variation of the one-dimensional solute transport model for small streams using Markov chain Monte Carlo

The transient storage model (TSM) is a popular solute transport model among hydrologists and ecologists for characterizing solute retention potential of small headwater streams. TSM parameters are most commonly estimated in an inverse modeling framework using tracer breakthrough data. A key challenge in interpreting TSM parameters is the inherent difficulty in the estimation process and relating these parameters with the physical characteristics of streams. While often recognized that multiple sources of uncertainty impact transient storage modeling, rigorous evaluation of TSM parameter uncertainty is rare. Stream flow magnitude has been identified as a key variable in characterizing stream solute transport dynamics, yet no study has shown the impact of flow magnitude on TSM parameter uncertainty. In this paper we study the impact of flow magnitude on TSM parameter uncertainty by using tracer data from repeated tracer studies with changing stream flow magnitudes, and introduce a software tool to perform Markov chain Monte Carlo based parameter estimation and uncertainty evaluation. The software tool developed is capable of performing thousands of model runs within a few hours, which is necessary for Monte Carlo based parameter estimation, and provides a potentially attractive framework for model testing and improvement. TSM parameters were found to be relatively less important during higher flows with large uncertainty bounds and clear evidence of parameter correlations. The importance of TSM parameters on solute transport seemed to increase as flow decreased with seasonal baseflow recession. Our findings highlight the need for improved field methodologies to reduce parameter uncertainty and the need for further improvement in the model structure for successful stream characterization.

Contribution of flow conditions and sand addition on hyporheic zone exchange in gravel beds

AbstractWe conducted a series of tracer test experiments in 12 outdoor semi-natural flumes to assess the effects of variable flow conditions and sand addition on hyporheic zone conditions in gravel beds, mimicking conditions in headwater streams under sediment pressure. Two tracer methods were applied in each experiment: 2–5 tracer-pulse tests were conducted in all flumes and pulses were monitored at three distances downstream of the flume inlet (0 m, 5 m and 10 m, at bed surface), and in pipes installed into the gravel bed at 5 m and 10 m distances. The tracer breakthrough curves (total of 120 tracer injections) were then analysed with a one-dimensional solute transport model (OTIS) and compared with data from the gravel pipes in point-dilution pulse tests. Sand addition had a strong negative effect on horizontal fluxes (qh), whereas the fraction of the median travel time due to transient storage (F200) was determined more by flow conditions. These results suggest that even small additions of sand can modify the hyporheic zone exchange in gravel beds, thus making headwater streams with low sediment transport capacity particularly vulnerable to sediments transported into the stream from catchment land use activities.

Investigation of fly ash for sorption of copper ions in multiple contaminant system: An implication on re-use of waste material under concept of sponge city

Many previous studies of soil contaminant treatment have primarily analysed heavy metal contaminant ion retention in fly ash (FA) in a single isolated medium whereas, factoring out the competitive systems. This study seeks to determine the interaction of the heavy metal copper ion (Cu+2) with fly ash under single and competitive systems and also to expound its impact on fate prediction. Freundlich and Langmuir non-linear isotherms were adopted to quantify the sorption results. The retardation factor attained from Freundlich isotherm predicts more than Langmuir. The Langmuir isotherm break-through-curves (BTC) was slightly earlier in break through, with a sharp front and prolonged tailing, whereas the Freundlich isotherm appears considerably after the production of a spreading pollutant front. Freundlich retardation factors established in this study was employed to one-dimensional (1-D) solute transport model, which successfully stimulated good prediction for sorption by fly ash. Conversely, significant inconsistencies were identified from the Langmuir isotherm for evaluating the fate of Cu+2 at high concentration range. This study recommends Freundlich isotherm for modelling transport of copper ions in a competitive environment in fly ash.

The effect of soil physical amendments on reclamation of a saline-sodic soil: simulation of salt leaching using HYDRUS-1D

Poor soil physical conditions such as low hydraulic conductivity can limit salt depletion from surface soil. Altering the pore system by addition of organic and inorganic amendments may improve salt leaching as a reclamation strategy. Column studies were conducted to investigate salt leaching in amended and non-amended soil profiles. A one-dimensional water and solute transport model (HYDRUS-1D) was also assessed for its applicability to simulate salt leaching for amendment strategy. Columns of length 300mm were filled with saline-sodic soil at the lower end (100–300mm) and then covered with soil amended with 40% (wt/wt) fine sand and 20% (wt/wt) wood chips, separately. A control column was filled with saline-sodic soil only. One rainfall scenario typical for a location in south-west Queensland (Australia) was applied to the columns. Water potentials were monitored using tensiometers installed at three depths: 35, 120 and 250mm. The concentrations of individual cations (Na+, Ca2+, Mg2+ and K+), electrical conductivity and sodium adsorption ratio of the soil solutions were also monitored for the investigated depths. A reduction in surface salinity (up to 28.5%) was observed in the amended soil profiles. This study indicated that the addition of wood chips to surface soil improved salt leaching under the tested conditions. The simulation successfully predicted both hydrology and chemistry of the columns. This study also concluded that HYDRUS-1D is a powerful tool to simulate salt leaching in the amended soil profiles, and can be applied to predict the success of amendment strategy under natural climatic conditions.

Corrigendum to “Palaeohydrogeology and Transport Parameters Derived from 4He and Cl Profiles in Aquitard Pore Waters in a Large Multilayer Aquifer System, Central Australia”

A study of chloride and 4He profiles through an aquitard that separates the Great Artesian Basin from the underlying Arckaringa Basin in central Australia is presented. The aquitard separates two aquifers with long water residence times, due to low recharge rates in the arid climate. One-dimensional solute transport models were used to determine the advective flux of groundwater across the aquitard as well as establish any major changes in past hydrological conditions recorded by variations of the pore water composition. This in situ study showed that both diffusion and slow downward advection ( mm/yr) control solute transport. Numerical simulations show that an increase in chloride concentration in the upper part of the profile is due to a reduction in recharge in the upper aquifer for at least 3000 years. Groundwater extraction since 2008 has likely increased chloride and 4He concentrations in the lower aquifer by pulling up water from deeper layers; however, there has been insufficient time for upward solute transport into the pore water profile by diffusion against downward advection. The transport model of 4He and chloride provides insight into how the two aquifers interact through the aquitard and how climate change is being recorded in the aquitard profile.

Palaeohydrogeology and Transport Parameters Derived from 4He and Cl Profiles in Aquitard Pore Waters in a Large Multilayer Aquifer System, Central Australia

A study of chloride and 4He profiles through an aquitard that separates the Great Artesian Basin from the underlying Arckaringa Basin in central Australia is presented. The aquitard separates two aquifers with long water residence times, due to low recharge rates in the arid climate. One-dimensional solute transport models were used to determine the advective flux of groundwater across the aquitard as well as establish any major changes in past hydrological conditions recorded by variations of the pore water composition. This in situ study showed that both diffusion and slow downward advection (vz=0.7 mm/yr) control solute transport. Numerical simulations show that an increase in chloride concentration in the upper part of the profile is due to a reduction in recharge in the upper aquifer for at least 3000 years. Groundwater extraction since 2008 has likely increased chloride and 4He concentrations in the lower aquifer by pulling up water from deeper layers; however, there has been insufficient time for upward solute transport into the pore water profile by diffusion against downward advection. The transport model of 4He and chloride provides insight into how the two aquifers interact through the aquitard and how climate change is being recorded in the aquitard profile.

Role of submerged vegetation in the retention processes of three plant protection products in flow-through stream mesocosms

Quantitative information on the processes leading to the retention of plant protection products (PPPs) in surface waters is not available, particularly for flow-through systems. The influence of aquatic vegetation on the hydraulic- and sorption-mediated mitigation processes of three PPPs (triflumuron, pencycuron, and penflufen; logKOW 3.3–4.9) in 45-m slow-flowing stream mesocosms was investigated. Peak reductions were 35–38% in an unvegetated stream mesocosm, 60–62% in a sparsely vegetated stream mesocosm (13% coverage with Elodea nuttallii), and in a similar range of 57–69% in a densely vegetated stream mesocosm (100% coverage). Between 89% and 93% of the measured total peak reductions in the sparsely vegetated stream can be explained by an increase of vegetation-induced dispersion (estimated with the one-dimensional solute transport model OTIS), while 7–11% of the peak reduction can be attributed to sorption processes. However, dispersion contributed only 59–71% of the peak reductions in the densely vegetated stream mesocosm, where 29% to 41% of the total peak reductions can be attributed to sorption processes. In the densely vegetated stream, 8–27% of the applied PPPs, depending on the logKOW values of the compounds, were temporarily retained by macrophytes. Increasing PPP recoveries in the aqueous phase were accompanied by a decrease of PPP concentrations in macrophytes indicating kinetic desorption over time. This is the first study to provide quantitative data on how the interaction of dispersion and sorption, driven by aquatic macrophytes, influences the mitigation of PPP concentrations in flowing vegetated stream systems.

The significance of model structure in one-dimensional stream solute transport models with multiple transient storage zones – competing vs. nested arrangements

Transient storage models are commonly used to simulate solute transport in streams to characterize hydrologic controls on biogeochemical cycling. Recently, 2-storage zone (2-SZ) models have been developed to represent in-channel surface transient storage (STS) and hyporheic transient storage (HTS) separately to overcome the limitations of single storage zone (1-SZ) models. To advance biogeochemical models, we seek to separate the effects of these storage zones on solute fate and cycling in streams. Here we compare and contrast the application and interpretations from two model structures that include STS and HTS storage: a competing model structure, where both zones are connected to the stream at the same location and the stream interacts with the STS and HTS separately, and a nested model structure, where STS is an intermediary between the stream and HTS. We adapt common residence time metrics used to compare single transient storage models for the competing and nested 2-SZ models. As a test case, we investigated the transient storage characteristics of a first-order stream in Pennsylvania, using 1-SZ, nested 2-SZ, and competing 2-SZ model configurations at several different flow conditions. While both 2-SZ models fit the observed STS and in-stream breakthrough curves well, calibrated model parameters and solute molecule travel paths differ, as evident by the faster exchange rate displayed by the nested model, and therefore so does the interpretation of associated transient storage metrics and its relationship with biogeochemical cycling processes. In addition, a study of hypothetical zone-specific reaction rates was very illustrative of the differences in discrimination characterized by each model structure, particularly for the case where reactions would predominantly occur in the STS (i.e. photochemical reactions), because of the compounding effects to the HTS for the nested 2-SZ; however, for the case where reactions would predominantly occur in the HTS, the influence of model structure was found to be relegated only to the HTS.

Modeling Contaminant Spills in the Truckee River in the Western United States

Originating at Lake Tahoe, the Truckee River provides 85% of drinking water for the Reno/Sparks metropolitan area. Major highways and a railroad run adjacent to the river, which increases risk of a contaminant spill into the river that could have detrimental effects on drinking water supplies. A one-dimensional solute transport model (OTIS) was applied to the Truckee River. Data from dye studies on the river were used to determine a relationship to estimate dispersion coefficients for the Truckee River and calibrate the model. Two sizes of hypothetical contaminant spills from 9 locations under 13 flow scenarios were simulated. Travel times to the first water intake for a train spill of 130,000 L ranged from 3 to 46 h and maximum simulated concentrations of a conservative water soluble contaminant at the intake ranged from 340 to 4,800 mg=L. Model output was influenced by uncertainties in the equation for longitudinal dispersion, so model runs were executed with estimated dispersion values that were a factor of 1.5 greater and less than the equation-estimated value of dispersion. DOI: 10.1061/(ASCE)WR.1943-5452.0000338. © 2014 American Society of Civil Engineers.

Management of Groundwater Quality in Sodic Soils using Semi-analytical One-dimensional Solute Transport Model

A semi-analytical one-dimensional solute transport model to manage and predict groundwater quality was tested for its application in Golewala, Punjab. The model being semi-discrete and continuous in time has significant computational advantage over the existing ones, especially for long-term predictions. The model was tested for transport of soluble Ca + Mg, CO3 and HCO3 and EC in soil profile with respect to time under barren soil. The results showed that the model can be used to predict the status of total salt concentration at different depths with time and to manage ground water quality in sodic soils.

Investigating the redox sensitivity of para-toluenesulfonamide (p-TSA) in groundwater

The groundwater downstream of a former sewage irrigation farm in Berlin is contaminated with ammonium (NH4 +) and para-toluenesulfonamide (p-TSA), besides other anthropogenic pollutants. In the field, in situ removal of NH4 + by gaseous oxygen (O2) and air injection is currently being tested. A laboratory column experiment using aquifer material and groundwater from the site was performed to determine whether this remediation technology is also feasible to reduce high p-TSA concentrations in the anoxic groundwater. First, the column was operated under anoxic conditions. Later, compressed air was introduced into the system to simulate oxic conditions. Samples were collected from the column outlet before and after the addition of compressed air. The experiment revealed that whereas p-TSA was not removed under anoxic conditions, it was almost fully eliminated under oxic conditions. Results were modelled using a transient one-dimensional solute transport model. The degradation rate constants for p-TSA increased from 2.8E−06 to 7.5E−05 s–1 as a result of microbial adaption to the change of redox conditions. Results show that O2 injection into an anoxic aquifer is a successful strategy for p-TSA remediation.

One-Dimensional Surface Flow and Solute Transport Model for Basin Irrigation in Traditional Surface Application of Fertilizer

A basis of contrast for advanced basin fertigation method can be provided by simulating the one-dimensional surface flow and solute transport process of basin irrigation in traditional surface application of fertilizer. A nonuniform distribution field of water flow velocity and solute concentration along the basin and its arbitrary cross section were constructed on the basis of vertical linear and logarithmic law in turbulence theory and continuous equation of incompressible hydrodynamics. A one-dimensional surface flow and solute transport model for basin irrigation in traditional surface application of fertilizer was proposed. At the same time, validation of the proposed model was carried out by using the results of typical basin irrigation tests. Results show that the proposed model can efficiently simulate the water flow and solute transport processes of basin irrigation, and exhibits good potential in conservation of water and solute quantity. Thus, the proposed model provides a research numerical to...

Use of finite element method as a simulation technique for bioremediation of naphthalene, anthracene and pyrene contaminated soil in a fixed bed reactor

In this work, the finite element method was applied to solve one-dimensional advective-dispersive solute transport model with linear equilibrium sorption and first-order degradation. This mathematical approach was adopted to adequately predict the effluent concentrations and breakthrough profiles of naphthalene, anthracene and pyrene. Simulation results showed that the concentrations of naphthalene, anthracene and pyrene within a contact period of 49 days, decreased in the direction of flow from 100 mg/l at the surface to zero at 9 cm subsurface depth. The residual concentrations of naphthalene, anthracene and pyrene were found to be 0, 35.79 and 0% respectively by the 49th day of exposure. The theoretical predictions when compared with actual experimental results from the soil column showed an average deviation of 3.92%, an indication of a reasonable agreement between the model and data from experiment. The finite element method has been found to be satisfactory as a predictive tool to show the distribution of the contaminant solutes. This is significant as it displays the capacity of ascertaining the behaviour of these contaminants over long spatial and temporal scales and predicting the extent of bioremediation of the contaminated sites.

Modeling of Solute Transport and Macrodispersion by Unsteady Stream Flow under Uncertain Conditions

A numerical simulation for a longitudinally one-dimensional upscaled solute transport model is developed in order to predict the mean solute concentration in natural streams subject to irregular variations in various flow and transport parameters and forcing conditions. A solute transport equation at the local scale of a river cross section is deterministic, but the equation at the river reach scale is stochastic due to various uncertainties in flow and transport parameters in every reach. The upscaling transformation makes a transport equation at the river reach scale deterministic. Compared with the transport equation at local scale, the upscaled equation at the river reach scale has seven covariance integrals, which incorporate the influence of the stream variabilities on the mean value of solute concentration. One of these integrals provides the explicit model of the macrodispersion coefficient as it varies in time and space under varying flow conditions. Lagrangian trajectories of flow are simulated to compute the time-space covariance integrals (including macrodispersion) of the flow properties. The Monte Carlo simulation of the stochastic solute transport is implemented to verify the upscaling methodology. The validation exercise confirms that the upscaled model is accurate, feasible, and physically meaningful. The Monte Carlo simulation with the stochastic Saint-Venant flow model also supplies all the random flow information used in both the predictive transport model and the validation transport model.