Advection-dispersion Model Research Articles

Research on the hydraulic response characteristics during the water conveyance process of water diversion projects

Abstract During the initial trial period, the Hanjiang-to-Weihe River Valley Water Diversion Project (HWRVWD) sourced water from the Sanhekou water conservancy junction. It then transferred water through the Qinling water conveyance tunnel and distributed it at the Huangchigou water distribution hub, ultimately transporting it to the Guanzhong area. The hydraulic simulation and real-time control of the water conveyance system play a crucial role in ensuring the safe and efficient operation of this engineering project. To maintain water transfer safety and reasonable scheduling during the water supply process, the hydraulic characteristics of the transient process were calculated and analyzed in this paper. The one-dimension (1D) hydrodynamic mathematical model and advection-dispersion model were established to calculate the hydraulic factors of the 81.78 km Qinling water conveyance tunnel and the Huangchigou water distribution hub within the HWRVWD. Validation results showed that the root mean squared error tended toward zero and the coefficient of determination exceeded 0.97 between the measured values and the simulated values. The opening of gates and upstream inflow directly affected water level variations and storage. Smaller gate openings led to increased water level amplitudes before the gate and faster reaching of maximum water levels, but it also led to opposite trends in flow rates behind the gate compared to upstream water levels. The impact of incoming water flow rates on flow variations at different channel sections was significant. The time for water heads to reach each section and the rate of flow variation positively correlated with incoming water flow rates. Gradual increases in upstream inflow resulted in progressively larger water level amplitudes both before and behind the gate, with an increased maximum value, but more water might be discarded. When the water demand changes, the primary focus is on controlling the upstream inflow, with gate opening adjustments as a secondary measure, to achieve the goal of minimizing or eliminating water wastage.

Comparison of non-reactive solute transport models for the evaluation of fluid flow in packed beds with implications for heap leaching practice

This study investigated the effects of mean particle size fraction, bottom particle size, particle porosity and wettability on solution scale preferential flow behaviour via step input tracer tests in drip irrigated, narrowly and mixed-sized beds under steady state fluid flux. Nine solute transport models were used to quantify this behaviour reflected in the residence time distribution (RTD) profiles. Four were empirical models: three compartmental model configurations (CM-1, CM-2, CM-3) and tanks-in-series (TIS) model. The remainder five models were semi-empirical: advection dispersion (AD), piston exchange (PE), piston exchange - diffusion variant (PE-D), piston dispersion and exchange (PDE) and piston dispersion and exchange - diffusion variant (PDED). The model fit results showed that the mono-porosity TIS, AD and CM-2 models were the worst performers, while the dual porosity PDE and novel PDE-D models achieved the lowest average error values across the various systems. Higher levels of particle wettability coupled with capillary effects produced peculiar RTD curves that were relatively more difficult for the mono-porosity models to simulate. The model parameters investigated included the longitudinal dispersion coefficient (Dds), dead to total volume fraction (VD/VT), dynamic to total saturation fraction (βd/βT), overall mass transfer coefficient (Kma) and maximum diffusional pore length (X). The results showed that an increase in the average particle size within the beds led to higher VD/VT, Dds and X values, but lower βd/βT and Kma values. These indicate an overall increase in solution scale preferential flow behaviour. Decreased capillary suction and connectivity between particle pores and inter-particle voids were deemed responsible for the results. Higher levels of particle porosity acted as a buffer against these effects. Overall, the results highlight the benefit of the addition of fines (0.1–1 mm particles) during the agglomeration process in heaps to help reduce solution scale preferential flow behaviour and increase liquid hold-up. This is more necessary when the ore has low to moderate levels of porosity (surface area: <2 m2/g) and will also increase the modelling options available as most models performed better fitting data from such beds.

Rapid determination of the migration parameters of nuclides in intact granite rock under the action of electric field

Deep geologic disposal has been widely accepted as a strategy for long-term disposal of the high-level radioactive waste. It is principal to obtain the migration parameters of radionuclides in natural barrier, such as granite, of a high-level radioactive waste repository for safety assessment of the repository. To quickly determine the diffusion and sorption properties of nuclides in intact granite, two tracers, I− and ReO4−, were tested with a modified electromigration device, by imposing a constant voltage over an intact Beishan granitic rock sample. The breakthrough curves of I− and ReO4− were obtained under condition of five different voltages. To interpret the electromigration experimental results with more confidence, an advection-dispersion model based on first-order adsorption kinetics was developed in this study. Data analysis of the breakthrough curves by this model suggest that the effective diffusion coefficients of I− and ReO4− in intact Beishan granodiorite rock are (6.81 ± 0.53) × 10−13 m2/s and (6.45 ± 0.07) × 10−13 m2/s, respectively. While the distribution coefficient of the two ions are (9.06 ± 1.13) × 10−7 m3/kg and (9.81 ± 0.13) × 10−7 m3/kg, respectively. This indicates that I− and ReO4− hardly adsorb in Beishan granodiorite rock.

Multicomponent mass transfer modeling of antagonistic binary adsorption of metallic pollutants from water using helical fixed-bed columns

A multicomponent advection-dispersion model was proposed to simulate the breakthrough curves of antagonistic adsorption of zinc, nickel and cadmium cations from water using helical fixed-bed columns packed with bone char. It was formulated using a linear driving force model, empirical multicomponent Langmuir-based isotherm and retardation coefficient to correlate the experimental breakthrough curves obtained for different binary (metal 1 + metal 2) aqueous solutions, which showed a higher asymmetry degree because of the antagonistic adsorption and axial dispersion impact in this complex fixed-bed configuration. Several parameters of this model were handled as column feed concentration dependent to improve the results of data fitting. The experimental results indicated the presence of a strong antagonistic adsorption effect of zinc and cadmium cations, causing the nickel breakthrough curves to show a clear desorption process (i.e., a displacement effect of the ions already adsorbed on the bone char surface commonly known as roll up) during helical column operation. Experimental bed adsorption capacities ranged from 0.03 to 0.74 mmol/g. The proposed advection-dispersion model fitted the experimental breakthrough profiles satisfactorily for the tested binary adsorption systems, including the desorption zone where the mean modeling errors were lower than 10 % for tested mixtures. Several column operation and mass transfer parameters were calculated and discussed to analyze the separation performance of the tested helical fixed-bed bone char columns. These results suggest that the proposed advection-dispersion model can simulate the multicomponent antagonistic adsorption of relevant water pollutants using intensified adsorption equipment such as helical fixed-bed columns.

Dynamics of radionuclide electromigration in intact granite: An kinetic adsorption-advection-dispersion model and its application

Granite, as the natural barrier for the disposal of high-level radioactive waste, plays an important role in ensuring environmental and public safety. The safety assessment of the repository depends on the reliable migration parameters of radionuclides in granite. In this study, we developed a kinetic adsorption-advection-dispersion model based on first-order adsorption kinetics. It introduces a first-order adsorption rate coefficient to describe the kinetics of adsorption process and accounts for other crucial mechanisms affecting the migration of radionuclide ions, namely, the electromigration, electroosmosis, and dispersion. This model is then applied to interpret the experimental results of electromigration of tracer ions in intact granite. The results show that for the weakly adsorbed radionuclides studied, iodide and selenite, the effective diffusion coefficients and formation factors calculated by this model are in constant with those derived from the classical advection-dispersion model based on linear adsorption equilibrium. By contrast, for the moderately or strongly adsorbed tracer ions studied, including cobalt, cesium, and strontium, the migration parameters calculated by this model exhibit significantly less uncertainty than those obtained from the advection-dispersion model simulations. The advection-dispersion model based on the first order adsorption kinetics introduces the first order adsorption rate coefficient, and considers the influence of electromigration, electroosmosis and dispersion mechanism, which helps to explain the migration mechanism of nuclide ions in intact granite more accurately.

Dispersion of artificial tracers in ventilated caves

Artificial CO2 was used as a tracer along ventilated karst conduits to infer airflow and investigate tracer dispersion. In the karst vadose zone, cave ventilation is an efficient mode of transport for heat, gases and aerosols and thus drives the spatial distribution of airborne particles. Modelling this airborne transport requires geometrical and physical parameters of the conduit system, including the cross-sectional areas, the airflow and average air speed, as well as the longitudinal dispersion coefficient which describes the spreading of a solute. Four gauging tests were carried out in one mine (artificial conduit) and two ventilated caves (natural conduits). In this paper, we demonstrate that it is possible to gain reliable airflow rates and geometric information of ventilated karst conduits using CO2 as a tracer. Airflow was gauged along two caves and one mine and compared with punctual measurements made with a hot-wire anemometer. Cross-sectional areas estimated with CO2 tests were compared with those measured in situ. Moreover, breakthrough curve (BTC) analysis displayed an accentuated tailing along the investigated natural conduits due to the presence of dispersive singularities which possibly enable aerosol deposition. The long tailing observed in Milandre and Longeaigue Caves is probably due to cross-section variations. A 1-D advection-dispersion model tested for these sites was unable to fit BTC tailing in natural conduits. In Baulmes artificial conduit, where long tailing is not observed, the dispersion coefficient has been estimated using Chatwin’s method, and compared with the prediction of Taylor’s theory. Despite the regular geometry of Baulmes Mine, Taylor’s correlation significantly underestimates the dispersion coefficient deduced from field data, showing the need for more theoretical work on turbulent dispersion in mines. This paper gives a first insight into air motion and matter dispersion along ventilated karst conduits, preparing for proper aerosol dispersion modelling.

Hydrodynamics and phosphorus loading in an urbanized river channel influences response to future managed change: Insights from advection-dispersion modelling

There is a need to understand what makes certain targeted measures for in-river phosphorus load reduction more effective than others. Therefore, this paper investigates multiple development scenarios in a small lowland polluted river draining an urban area (The Cut, Bracknell, UK), using an advection-dispersion model (ADModel-P). A comparative analysis is presented whereby changes in concentrations and fluxes of soluble reactive phosphorus (SRP) and organic phosphorus (OP) have been attributed to specific transformations (mineralization, sedimentation, resuspension, adsorption-desorption, and algal uptake) and correlated to controlling factors. Under present day conditions the river stretch is a net source of SRP (10.4 % increase in mean concentration) implying a release of previously accumulated material. Scenarios with the greatest impact are those based on managed reduction of phosphorus load in sources (e.g., 20 % increase in afforestation causes an in-river SRP and OP reduction of 1.3 % to 12.6 %) followed by scenarios involving changes in water temperature (e.g., 1 °C decrease leads to in-river SRP reduction around 3.1 %). Measures involving increased river residence time show the lowest effects (e.g., 16 % decrease in velocity results in under 0.02 % in-river SRP and OP reduction). For better understanding downstream persistence of phosphorus pollution and the effectiveness of mitigation measures the research demonstrates the importance of establishing when and where reaches are net adsorbers or desorbers, and whether sedimentation or resuspension is important.

Ability of equilibrium and non-equilibrium models to simulate the effects of vermicompost and hydraulic conditions on nitrate and DOC leaching

ABSTRACT This study aims to model the effects of saturated−unsaturated flow rates and initial moisture content on nitrate and dissolved organic carbon (DOC) leaching in soils amended and unamended with vermicompost using equilibrium and non-equilibrium models. Flow rates ranging from 0.4 to 5.1 cm3/min were applied to the columns filled with the soils under initial saturated and air-dried conditions. The leaching of nitrate and DOC was simulated using a one-dimensional advection–dispersion model coupled with the equilibrium and non-equilibrium models. The accuracy of equilibrium without distribution coefficient (K D), equilibrium with K D, one-site, two-site and dual porosity models for modelling the nitrate leaching was 21.8, 33.6, 67.5, 82.2 and 83.9%, respectively, indicating the higher accuracy of dual porosity and two-site models compared to the other models. According to the results of the two-site model, the kinetic release was the most dominant process in all leaching experiments due to the fractions of equilibrium soil sites (F) < 0.5. Vermicompost decreased the diffusion coefficient (D 0), distribution coefficient (K D), first-order rate constant (β) and retardation factor (RF). In comparison to the air-dried condition, the initial saturated condition compared to the air-dried condition resulted in less F and D 0, higher K D and RF lower β for nitrate and lower K D and RF and higher β for DOC. Leaching using a desaturation flow rate of 0.4 cm3/min was more time-dependent, which reduced RF values from 22.6 to 1.09 and 21.5 to 3.68 for nitrate and DOC, respectively. Moreover, the desaturation flow rate reduced D 0 and K D and increased β.

Recharge dynamic and flow-path geometry controls of solute transport in karst aquifer

Solute transport is complex in karst aquifer due to its heterogeneous structure and polytropic hydrodynamic condition. Hydrological monitoring and artificial tracer test were conducted in two flow paths under different recharge conditions, and the Advection–Dispersion Equation and Dual Region Advection–Dispersion models were successfully calibrated to simulate the breakthrough curves. Intermittent concentrated recharge at sinkholes and quick hydrological response at spring outlet often occur after rainstorms. Single symmetrical shape and bimodal shape with long tail were characterized in the breakthrough curves. Stronger recharge hydrodynamic condition drives a larger transport velocity with higher solute transport efficiency. The tracer injection time during a concentrated recharge event is found to significantly affect the solute transport process. Constantly pushed by the follow-up recharge water, the piston transport process of solute in conduit enables higher recovery rate for the tracer injected at the initial recharge process. Solute transient storage in fissures occurs while tracer is injected at the peak flow. A negative correlation between dispersivity and flow velocity is found in karst conduits. The reduction in cross-section area of karst conduits causes high dispersivity and obvious tailing in breakthrough curves due to the blocking function of solute by the uneven bottom surface in karst conduits. The solute transport process is significantly controlled by the changes in hydrodynamic and flow cross-section due to concentrated recharge events, which deepen our understanding of solute transport in karst groundwater.

Insights into the transport and bio-degradation of dissolved inorganic nitrogen in the biochar-pyrite amended stormwater biofilter using dynamic modeling

The stormwater biofilter is a prevailing green infrastructure for urban stormwater management, but it is less effective in dissolved nitrogen removal, especially for nitrate. The mechanism that governs the nitrate leaching and performance stability of stormwater biofilters is poorly understood. In this study, a water quality model was developed to predict the ammonium and nitrate dynamics in a biochar-pyrite amended stormwater biofilter. The transport of dissolved nitrogen species was described by advection-dispersion models. The kinetics of adsorption and pyrite-based autotrophic denitrification are included in the model and simulated with a steady-state saturated flow. The model was calibrated and validated using eleven storm events. The modeling results reveal that the contribution of pyrite-based autotrophic denitrification to nitrate leaching alleviation improves with the increased drying duration. The nitrate removal efficiency was affected by a series of design parameters. Pyrite filling rate has a minor effect on nitrate removal promotion. Service area ratio and submerged zone depth are the key parameters to prevent nitrate leaching, as they influence the emergence and discharge time of nitrate breakthrough. The high inflow volume (high service area ratio) and small submerged zone can lead to earlier and increased discharge of peak nitrate otherwise the peak nitrate could be retained in the submerged zone and denitrified during the drying period. The developed mechanistic model provides a useful tool to evaluate the treatment ability of stormwater biofilters under varying conditions and offers a guideline for biofilter design optimization.

Sub-volume analysis of pore-network simulations: Determining the asymptotic longitudinal dispersion coefficient

This work introduces a new method called sub-volume analysis (SVA) to calculate macroscopic model parameters with their uncertainties from pore-scale simulations. We apply the SVA to calculate the longitudinal dispersion coefficient of the advection–dispersion model (ADM) from continuous tracer injection problems simulated with pore-network models. The SVA application presented here allows for verifying if a given network has enough length to reach an asymptotic dispersion regime where ADM applies. We tested the method using statistically constructed pore networks and pore networks built by joining several network units extracted from Berea sandstone images. There is complete agreement within the error margins for the asymptotic longitudinal dispersion coefficients obtained with the SVA and those obtained from breakthrough curve fitting. We also showed that the SVA gives more accurate results than those from the breakthrough curve fitting and much more accurate results than those from the method of spatial moments. Unlike the other methods, the SVA estimates the parameter uncertainty using a single pore-network realization.

A New Compact Numerical Scheme for Solving Time Fractional Mobile-Immobile Advection-Dispersion Model

This work is focused on the derivation and analysis of a novel numerical technique for solving time fractional mobile-immobile advection-dispersion equation which models many complex systems in engineering and science. The scheme is derived using the effective combination of Euler and Caputo numerical techniques for approximating the integer and fractional time derivatives respectively, and a fourth order exponential compact scheme for spatial derivatives. The Fourier analysis technique is used to prove that the proposed numerical scheme is unconditionally stable and perform convergence analysis. To assess the viability and accuracy of the proposed scheme, some numerical examples are demonstrated with constant as well as variable order time fractional derivatives for this model.

A predictive assessment of the uranium ore tailings impact on surface water contamination: Case study of the city of Kamianske, Ukraine

In this study, we present an assessment of the uranium ore tailings impact on groundwater and surface water contamination. The radioactive materials were deposited in the tailings storage facility “Dniprovske” (the city of Kamianske, Ukraine) from 1954 to 1968; now it contains about 5.85·106 m3 of hazardous waste on the area of about 76 ha in the floodplain of the Dnipro river. The lack of a proper waterproof screen below deposited tailings and in the earthen dam led to permanent watering of radioactive materials, their leaching and migration in groundwater into the nearest small Konoplianka river. We used the reports on previous site-specific studies conducted in 1999–2016, monitoring results, and the field studies conducted in 2022 with the authors’ team participation. The calculations performed with the advection-dispersion model to simulate transport of radionuclides 238U, 230Th, 226Ra and 210Pb through the embankment to the Konoplianka river and dilution relations were compared to the monitoring data of the surface water quality. Among four radionuclides, uranium poses the greatest risks today; the subsurface runoff increases its concentration in the Konoplianka river water by several times over the background value. It is estimated that due to much more intensive sorption in the shallow aquifer, the contribution of 226Ra and 210Pb to the increase in radioactivity of Konoplianka river water is insignificant compared to uranium, whereas the migration front of 230Th has probably not yet reached the riverbank. In the next 50 years the radionuclide fluxes will increase by 1.3–3.7 times for different isotopes, with the uranium subsurface runoff growing at a slower rate than nowadays. These results are of high significance for improving hydrological, hydrogeological, and geotechnical monitoring on this hazardous facility to maintain its radiation safety.

Study on CO2 transport in fractal porous media for a Hausdorff fractal derivative advection-dispersion model

PurposeThe classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO2 transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.Design/methodology/approachAnomalous dispersion behaviors of CO2 transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.FindingsThe physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.Originality/valueTo the best of the authors’ knowledge, first time these results are presented.

Stable Computational Techniques for the Advection–Dispersion Variable Order Model

In this paper, a novel approximation to the Caputo time fractional derivative of variable order (VO) [Formula: see text] ([Formula: see text]) is established. Since time fractional derivatives are integral, with a weakly singular kernel the discretization on the uniform mesh may not lead to satisfactory accuracy. So, numerical approximation is constructed on nonuniform meshes based on Newton interpolation polynomial. As a result, the novel approximation can be viewed as the modification of the existing method [Shen, S., Liu, F., Chen, J., Turner, I. and Anh, V. [2012] “Numerical techniques for the variable order time fractional diffusion equation,” Appl. Math. Comput. 218(22), 10861–10870]. The truncation errors and some significant properties of coefficients are analyzed. Furthermore, we derived Scheme-I and Scheme-II with second-order accuracy in spatial direction to solve the mobile–immobile advection–dispersion model (MIMADM) based on the VO Caputo derivative. The designed scheme converts the considered problems into a linear system of equations. Moreover, the stability properties of Scheme-I are discussed in detail. Ultimately, the proposed scheme is examined on several text examples demonstrating the high precision and effectiveness of the scheme. Also, comparative study between the outcomes achieved by implementing the suggested scheme with other numerical scheme in the existing literature is provided and also the acquired numerical results of these applications indicate that the suggested technique performs extremely well in terms of reliability and capability.

Application of q-HATM over Fractional in Time Model for Advection-Dispersion Equation with Variable Migration Parameters

In this article, an extended and more generalized method of homotopy analysis method (HAM), known as q-homotopy analysis transform method (q-HATM) is employed to develop solutions for highly nonlinear form of various time-fractional advection-dispersion models (TFADE). The proposed methodology of q-HATM is a conjunction of two different strong methodologies, that are HAM and Laplace transform technique (LTT) which makes the scheme much more capable to develop the convergent series solutions for differential equations with high nonlinearity. In this work, two different examples are constructed for the nonlinear time-fractional form of dispersion models corresponding to distance dependent dispersion and velocity components and also for the time dependent decay rate system and solutions are constructed by using q-HATM in generalized form. The graphical comparison is made for different types of variable functions and also for the different fractional order indexes. Prominent impact of fractional derivative indexes is significantly observed over both the examples of dispersion models. Hence, proposed examples shows that the q-HATM is much convenient to handle the nonlinear systems of fractional models.

Transport model simulation prediction and environmental risk assessment of pyrethroid insecticides in urban artificial lakes caused by rainfall: A case study of Cloud Mountain Park in subhumid climate zone

Pyrethroid insecticides are among urban parks' most widely used and harmful insecticides. The advanced prediction method is the key to studying the pollution and diffusion risk of plant conservation insecticides in parks. A two-dimensional advection-dispersion model was established for the North Lake of Cloud Mountain Park in the subhumid area of Hebei Province. The temporal and spatial distribution of lambda-cyhalothrin pollution required by plant growth in artificial lakes under different rainfall intensities and the time of water renewal after rainfall was simulated and predicted. According to the model efficiency (E: 0.98), mean absolute error (MAE: 0.016–0.064 cm), and root mean square error (RMSE: 0.014–0.041 cm), the prediction results showed that the model fits well. The results showed that the concentration of lambda-cyhalothrin in the artificial lake was positively correlated with the increase in rainfall intensity. Under the three scenarios of moderate rain, heavy rain, and rainstorm, the variation of total pollutants into the lake over time conformed to the first-order dynamic equation (R2＞0.97), and the cumulative rates were 0.013 min−1, 0.019 min−1 and 0.022 min−1, respectively. Under light rain, the accumulation rate of lambda-cyhalothrin showed a double-linear relationship, which was in accordance with the second-order kinetic equation (R2＞0.97). The rapid accumulation rate of early-stage rainfall was 0.0024 min−1, and the slow accumulation rate of late-stage rainfall was 0.0019 min−1. The human health risk assessment predicted by the simulation was lower than the hazard value (Rtgn(a-1): 9.65 E−11–1.12 E−10 a-1). However, the potential risk value to aquatic species was higher (RQ: 0.33–23.05). In addition, the increase in rainfall intensity has no significant effect on the acceleration of water renewal time. The two-dimensional dispersion model of pollutants driven by water dynamics provided relevant examples for evaluating the impact of runoff on pesticide scour in parks and supplied scientific support for improving the management of artificial lakes in urban parks.

Spatiotemporal velocities, aggregation, and false dispersion: numerical considerations for the modeling of colonial and motile harmful algae

PurposeThe purpose of this study is to investigate the errors arising from the numerical treatment of model processes, paying particular attention to the impact of key system features including widely variable dispersion coefficients, spatiotemporal velocities of algal cells, and the aggregation of algae from single cells to large colonies. An advection–dispersion model has been presented to describe the vertical transport of colonial and motile harmful algae in a lake environment.Design/methodology/approachModel performance is examined for two different numerical treatments of the advective term: first-order upwind and quadratic upwind with a stability-preserving flux limiter (SMART). To determine how these schemes impact predictions, comparisons are made across a sequence of models with increasing complexity.FindingsUsing first-order upwinding for advection–dispersion calculations with a time oscillating velocity field leads to oscillatory numerical dispersion. Subjecting an initially uniform distribution of large-sized algal colonies to a spatiotemporal velocity creates a concentration pulse, which reaches a steady-state width at high-grid Peclet numbers when using the SMART scheme; the pulse exhibits contraction–expansion behavior throughout a velocity cycle at all Peclet numbers when using first-order upwinding. When aggregation dynamics are included with advection-dominated spatiotemporal transport, results indicate the SMART scheme predicts larger peak concentration values than those predicted by first-order upwind, but peak location and the time to large colony appearance remain largely unchanged between the two advective schemes.Originality/valueTo the best of the authors’ knowledge, this study is the first numerical investigation of a novel advection–dispersion model of vertical algal transport. In addition, a generalized expression for the effective dispersion coefficient of temporally variable flow fields is presented.

Analytical solutions for the advection-dispersion model for radon-222 production and transport in shallow porewater profiles

Quantifying the water flux between surface water (SW) and groundwater (GW) bodies is important for determining water balances and understanding controls on surface water quality and sustainable allocation of water resources. Methods that quantify water exchange at point scales are highly desirable due to the heterogeneous nature of SW-GW connectivity. Porewater radon-222 (222Rn) profiles can be easily collected and variations of 222Rn activity within the sediments below SW bodies can be used to infer water flow and residence times. The current models used to interpret these profiles assume downward flows, limiting their use in gaining, or dynamic environments. We investigate the use of a new analytical solution based on a finite solution of the advection dispersion equation to predict bi-directional water fluxes using 222Rn profiles in riverbed sediments. We apply this solution to profiles collected from the Swan Estuary in Western Australia. The estimated fluxes of water from the estuary to groundwater were up to 2.07 m/day, and fluxes from the groundwater to the estuary were up to 1.79 m/day at various times. Estimates made with a previously applied piston-flow model were broadly consistent when predicting fluxes from the estuary to the groundwater; however, the method was unable to predict fluxes from the groundwater to the estuary, as degassing in the surface water meant that all profiles indicated ageing with depth and hence downward flow. The reversal of fluxes was predicted for a period of seasonally high groundwater levels. Our results highlight that not accounting correctly for upward flows can impact predictions of groundwater exchange with surface water bodies such as estuaries. This may lead to errors in water and chemical balances in stream, lake and estuarine environments and sustainable allocation of freshwater resources between ecosystems and human demands.

A modified and rapid method for the single-well push-pull (SWPP) test using SF6, Kr, and uranine tracers

In the present study, a single-well push-pull (SWPP) test was conducted with multi-component tracers, including inert gas (SF6 and Kr) and uranine (conservative), to understand the volatile/semi-volatile component transport characteristics in the groundwater system. In an SWPP test, it is essential to obtain an initial breakthrough curve (BTC) of the inert gas concentration at the beginning of the pulling stage to analyze the hydraulic properties of the groundwater system. As a result of the SWPP test using a proposed method in this study, physicochemical parameters of the groundwater and BTC of gas tracers and uranine were acquired simultaneously and successfully. In addition, on-site measurements of uranine, pCO2, and water quality data, such as electrical conductivity (EC), temperature, pH, and dissolved oxygen, were undertaken. Modification of an existing pCO2 measuring system allowed the gas samples to be collected, transported, and analyzed for inert gas components within a few hours. As a result, reliable and interpretable data with a recovery ratio of 26%, 85%, and 95% for SF6, Kr, and uranine, respectively, were obtained. The differences in the recovery ratio were utilized to identify the environmental system, whether it contains gas inside the isolated system (closed) or not (open), and to understand plume behavior characteristics in the experimental zone. By applying a two-dimensional advection-dispersion model to the acquired tracer test data and comparing the observed and computed tracer concentrations, helpful information was obtained on the hydraulic and transport characteristics of the targeted zone. This method can be extended to the design of dissolved CO2 transport monitoring of an aquifer above a CCS site.