One-dimensional Transport Model Research Articles

Transport of Organic Contaminants in Composite Vertical Cut-Off Wall with Defective HDPE Geomembrane.

Soil-bentonite vertical cut-off wall is an emergency technique used for contaminant control in geo-environmental engineering, high-density polyethylene (HDPE) geomembrane (GM) with an extremely low-permeability coefficient is expected to enhance the contaminant barrier effect of the vertical cut-off wall. To evaluate the barrier performance of the composite barrier composed of GM and soil-bentonite mixture towards organic contaminant, while also quantitively revealing the impact of GM defects and placement, a one-dimensional transport model for organic contaminants in composite barrier is solved under semi-infinite boundary conditions. The proposed transport model is validated by numerical simulations using COMSOL Multiphysics 5.4, and the effects of GM defect rate, placement within the composite isolation wall, and contact level with soil-bentonite on contaminant transport behavior are further studied. The results show that as the average frequency of GM defects increases from 2.5 to 50 holes per hectare, the breakthrough time of organic contaminants through composite barrier decreases by almost 70%. Poor contact level between GM and soil-bentonite mixture may reduce the breakthrough time of the composite cut-off wall by 65%. Although the selection of GM placement has limited impact on the transient flux of contaminants, it does affect the total flux of contaminants over a certain period of time. The effects of permeability coefficient, effective diffusion coefficient, distribution coefficient, and hydraulic head of the composite cut-off wall can be considered by the proposed analytical solution, which would provide guidance and reference for the design and service performance evaluation of the composite cut-off wall.

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

Although superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs made of long finite-length longitudinal grooves located on both walls. We assume that bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting long-wave theory and accounting for the difference between the rapid transverse and slower longitudinal Marangoni flows, we derive a one-dimensional model for surfactant transport from the full three-dimensional transport equations. Our one-dimensional model allows us to predict the drag reduction and surfactant distribution across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, bulk and interfacial advection, shear dispersion and surfactant exchange between the bulk and the interface. We map out asymptotic regions in the high-dimensional parameter space, and derive explicit closed-form approximations of the drag reduction, without any fitting or empirical parameters. The physics underpinning the drag reduction effect and the negative effect of surfactant is discussed through analysis of the velocity field and surfactant concentrations, which show both uniform and non-uniform stress distributions. Our theoretical predictions of the drag reduction compare well with results from the literature solving numerically the full three-dimensional transport problem. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.

Hydrogen production using aluminum-water splitting: A combined experimental and theoretical approach

Hydrogen generation from aluminum hydrolysis with NaOH as an activator is investigated experimentally. A theoretical model is developed using the Density Functional Theory (DFT) and a one-dimensional transport model formalism. The effects of NaOH concentration and reaction temperature on hydrogen production rates are investigated. The kinetic parameters calculated by DFT are used in the COMSOL transport equations and compared. A transport model is implemented for a reaction-diffusion problem of water over the Al surface. The activation barrier increases as the reaction progresses and adsorption of H2O molecules is limited due to space constraints. The reaction rate constants depend on temperature, species convection, and vibrational frequency. The three chemical reaction steps have activation barriers ranging from 7.72 to 61.75 kJ/mol. The activation barrier of the first H2O dissociation step is Ea,1 = 7.72 kJ/mol, whereas the second and third steps have activation barriers of Ea,2 = 15.44 kJ/mol and Ea,3 = 61.75 kJ/mol, respectively. The estimated DFT harmonic vibrational frequency of H2O stretching mode is 3788 cm−1.

An Explicit Solution for Characterizing Non-Fickian Solute Transport in Natural Streams

One-dimensional solute transport modeling is fundamental to enhance understanding of river mixing mechanisms, and is useful in predicting solute concentration variation and fate in rivers. Motivated by the need of more adaptive and efficient model, an exact and efficient solution for simulating breakthrough curves that vary with non-Fickian transport in natural streams was presented, which was based on an existing implicit advection-dispersion equation that incorporates the storage effect. The solution for the Gaussian approximation with a shape-free boundary condition was derived using a routing procedure, and the storage effect was incorporated using a stochastic concept with a memory function. The proposed solution was validated by comparison with analytical and numerical solutions, and the results were efficient and exact. Its performance in simulating non-Fickian transport in streams was validated using field tracer data, and good agreement was achieved with 0.990 of R2. Despite the accurate reproduction of the overall breakthrough curves, considerable errors in their late-time behaviors were found depending upon the memory function formulae. One of the key results was that the proper formula for the memory function is inconsistent according to the data and optimal parameters. Therefore, to gain a deeper understanding of non-Fickian transport in natural streams, identifying the true memory function from the tracer data is required.

Two-Dimensional Model for Consolidation-Induced Solute Transport in an Unsaturated Porous Medium

Solute transport through porous media is usually described by well-established conventional transport models with the ability to account for advection, dispersion, and sorption. In this study, we further extend our previous one-dimensional model for solute transport in an unsaturated porous medium to two dimensions. The present model is based on a small-strain approach. The proposed model is validated with previous work. Both homogeneous landfill and pointed landfill conditions are considered. A detailed parametric study shows the differences between the present model and previous one-dimensional model.

Analytical solution of three-dimensional particle transport in porous media considering a dual deposition mode

Based on the classical one-dimensional particle transport model, a three-dimensional particle transport model with a dual deposition mode considering sieving and adsorption effects was established. Through Laplace and Fourier transforms, general solutions for particle transport in saturated semi-infinite porous media under one-dimensional seepage and three-dimensional dispersion conditions were derived. According to the basic solution in the case of a point source injection on the surface of a semi-infinite body, the analytical expression in the case of a circular surface source injection was obtained by the integration method. The analytical solution is verified using two well-established numerical simulation solvers. The influence of parameters such as the hydrodynamic dispersion coefficient, sieving coefficient, adsorption coefficient, and desorption coefficient, on the mechanism of the particle transport process was analyzed under the conditions of constant concentration and circulating concentration injection of the circular surface source. The results showed that the hydrodynamic dispersion effect accelerated the transport of particles, shortened the breakthrough time, and increased the peak concentration. Moreover, a larger sieving coefficient and particle adsorption coefficient meant a smaller particle release coefficient, and more particles deposited on the solid matrix with a smaller peak particle concentration in the pores.

Inventories, profiles and deposition fluxes of 210Pbex in mineral and organic (peatlands) Southern Hemisphere soils

Unsupported 210Pb (210Pbex) activity profiles have been determined in both mineral soils from Argentina (La Plata region) and organic soils from Brazil (Serra do Espinhaço Meridional). For the Argentine mineral soils, no significant differences in the 210Pbex inventories are found (ranging from 2920 ± 560 to 4570 ± 460 Bq/m2). The measured activity profiles are properly fitted by the one-dimensional transport model by effective diffusion and migration developed by He and Walling and the resulting parameters were analyzed considering the soil properties. It was observed that the migration rate is inversely proportional to the illite content, that the soils with higher amounts of smectite exhibit higher migration rates, and that the higher the pH, the higher the migration rate. These results agree with the higher Pb sorption capacity of smectite than illite, at identical conditions, and the Pb speciation with pH, that gives raise to different interactions between Pb and soil components. For organic soils, 210Pbex accumulates in superficial layers (5 cm depth) and the 210Pbex inventories (ranging from undetectable value to 5100 ± 200 Bq/m2) depend on the altitude of the sampling points. The activity values of 210Pbex and 137Cs (previously reported) are not significantly correlated, probably because the 137Cs fallout occurred more than 50 years ago, allowing the 137Cs profiles to develop. Finally, the deposit fluxes were determined for both regions studied and were incorporated into the global curve elaborated in previous works, contributing to a better definition of the general trend reported for the Southern Hemisphere.

Initial Neutronics Investigation of a Chlorine Salt–Based Breeder Blanket

Tritium breeding blankets within D-T-fueled fusion reactors contain lithium compounds and typically require neutron multiplier materials to achieve a tritium breeding ratio (TBR) consistent with self-sustaining operation. Liquid breeder blankets have some advantages over solid blankets, and previous blanket studies have investigated liquid metal as well as liquid salt–based blankets. Liquid salts have reduced magnetohydrodynamic effects as compared to liquid metals, but typically have a lower TBR. Recently, advanced fission reactor concepts have considered chloride-based salts in their design, and there is a significant amount of research work occurring to study these salts. Chloride salts have previously been considered for fusion reactors, but studies have typically found lower breeding ratios than for fluoride salts, such as 2(LiF)-BeF2 (flibe) so they have not been further developed. In this work, we use a one-dimensional cylindrical radiation transport model of a conceptual tokamak fusion reactor to investigate the neutronics feasibility of using a chloride salt–based blanket that uses chlorine enriched in 37Cl, which has both a low capture cross section and a substantial (n,2n) cross section. It is found that chloride salts (LiCl mixed with BeCl2 and/or PbCl2) can potentially achieve a ~3% to 5% higher TBR than fluoride molten salts, notably flibe, in the absence of a solid multiplier. Including a solid multiplier, however, does narrow this advantage, with TBRs estimated within ~1% of flibe with a 2-cm Be multiplier. Chloride salts can also reach lower melting points than flibe, potentially improving the scope for the use of reduced activation ferritic-martensitic steel as a structural material. There is substantial uncertainty in the calculations driven by limited thermochemical data for the Cl salts, plus cross-section uncertainties. The production of 36Cl through 35Cl(n,g) and 37Cl(n,2n) has the potential to challenge the waste disposal rating of the blanket. Calculations indicate that, while this is not an immediate showstopper, this case depends upon the exact waste disposal rating criteria used for 36Cl. Further work could reduce these uncertainties with improved thermochemical data, higher-fidelity modeling for downselected salts, and more refined waste disposal calculations and regulatory guidance. Finally, it must be recognized that, as for all molten salts, corrosion and chemistry can present appreciable technical challenges that require further assessment in developing a practical blanket concept, and also that the enrichment of chlorine presents an additional technical and supply chain challenge.

Temporal moments of one-dimensional advective-dispersive transport with exchange represented via memory function models: Application to river corridor transport

Practical simulation of solute transport in river corridors often relies on one-dimensional transport models with solute flux between river and hyporheic zone governed by a mass exchange term, perhaps most generally expressed using the ‘memory function’ formalism. While expressions for temporal moments of solute breakthrough curves (BTCs) are available for a number of such models, those for memory function forms are not, to our knowledge. Here we report closed-form BTC temporal moment expressions for memory function forms, found by exploiting the connection to phase exposure-dependent exchange (PhEDEx) formulations. We use these results to investigate the general capability of the memory function form to accommodate specific scaling of river tracer temporal moments reported in the literature, and we apply the method to identification of parameters in application to two recent tracer tests. The applications involve a simple numerical solution to the memory function river corridor transport model calibrated using measured temporal moments of the tracer test BTCs. The numerical model is validated only for the classical case of the transient storage model without lateral inflow, the analytical solution for which we adapt from the Lassey solution for mobile-immobile exchange in porous media. It should be noted that the temporal moments results obtained here in the context of river corridor transport also apply to one-dimensional transport in two-domain (mobile-immobile) porous media, when governed by a two-domain memory function model.

MacCormack method for solving one-dimensional bed-load sediment transport model

In this work, we investigate the numerical solution of one-dimensional bed-load sediment transport model using two steps finite difference method which so-called MacCormack method. Bed-load sediment transport model is composed by the shallow water equation and Exner equation. The Meyer-Peter and Muller (MPM) formula and Wu formula will be used to determine the Grass factor of the bed-load sediment transport. These governing equations will be discretized into predictor and corrector steps of the MacCormack method. The numerical results of the MacCormack method will be validated with an analytical solution of the bed-load sediment transport model. In addition, the MacCormack solution will also be compared with experimental solutions and another numerical method solutions that have existed previously. The numerical results based on MacCormack method give excellent results in which the numerical and the analytical results are hardly differentiated with RMSE of around 00042 or 4,2 .

New Perspective on Electron Transfer through Molecules.

Motivated by experiments which display unusual length and temperature effects for electron transfer in the nanometer length regime, we propose a new approach for describing long-range electron transfer (ET) processes through molecules. We posit that the electron reorganization in the molecules (e.g., the electronic polarization of a macromolecule or organic film by an applied electric potential, or the injected charge generating a dipole moment) should be included in the description. We numerically solve a one-dimensional model for the electron transport, which includes electron-electron interactions explicitly, and we show that it generates a power law distance dependence for electron transport similar to that observed in experiments. The model does not include vibrations explicitly and should be consistent with the weak temperature dependences observed experimentally. This approach emphasizes the need to treat the electronic changes in the molecule(s) more explicitly to understand the behavior.

B-value definition in Galvele’s pit model

We use one-dimensional mass transport models to investigate the chloride concentration effect on the potential drop inside a pit cavity. Galvele’s pitting model predicts a B value of 59 mV, independent of the complexation reactions and concentration-dependent diffusivity when ions can migrate freely. Higher B values (>59 mV) at 25 °C are commonly attributed to ion interactions in the pit solution, also explaining the material and electrolyte effect on the B value in Galvele’s pit model. Our analysis suggests that practical pitting corrosion models require a comprehensive mass transport component that includes multi-species interactions.

The distribution and transport of water in oil paintings: A numerical moisture diffusion model

Oil paintings are complex, multi-layered systems that are prone to chemical degradation. While it is increasingly recognised that water plays an important role in these degradation reactions, little is known about moisture concentrations in oil paint systems and their temporal variation in response to fluctuating ambient air humidity. This knowledge is necessary to further preventive conservation, specifically to establish optimal environmental conditions to safeguard works of art for future generations. We developed a transient one-dimensional moisture transport model based on Fickian diffusion enabling the integration of experimentally recorded relative humidity data. Moisture sorption and transport data for painting materials have been reviewed from literature showing that each component of a painting has rather distinct properties. Including the properties of the individual layers enabled predicting the behaviour of a multi-layered painting system. A sensitivity study indicated that the response of a multilayer is determined by the combination of diffusion coefficients, isotherm shapes, maximum water contents, layer thicknesses, period of RH fluctuation and stacking order of the layers. Finally, the model was employed to investigate a case study of 18th-century painted wall hangings in a historic house to illustrate the insights that can be gained from this approach and the types of conservation-related questions that can be answered.

One-dimensional numerical model for unsteady solute transport in open channels under multi-point loading

A numerical method for solving the unsteady-one-dimensional advection-dispersion equation for solute transport in streams and channels imposed with multiple point-loading is presented. The numerical technique proposes to solve the equation, which also includes a first-order decay term and a loading term, using techniques similar to those employed by the finite volume method (FVM). The channel length is segmented into cells and the solution aims at evaluating the concentrations at the cell interfaces or the internal nodes, at prescribed time steps for the steady condition of the flow. The results are computed commencing from a specified time level with known spatial concentration within the domain. It is assumed that the boundary nodes at the two ends of the channel, one each at the upstream and the downstream, are specified with solute concentration values or its spatial gradient at all times. Unlike the standard within-the-cell spatial approximations of a variable assumed in the finite volume or finite element schemes, the proposed method models the spatial variation of the solute concentration within a cell by an analytical expression in terms of the concentrations at the two boundary nodes of the cell and the influx rate of point-loading, if any, located within the cell. Using such a closed-form function based upon the true nature of the problem not only helps in capturing the spatial variation of concentration within a cell more precisely but also allows a better approximation of its spatial gradients at the cell interfaces, thus helping to achieve a more accurate computation of the inter-cell dispersive fluxes. The performance of the proposed algorithm is evaluated against analytical benchmarks, a standard finite difference scheme, and one public-domain computational package. Data sets reported from field tests are used for demonstrating the potential of the technique in simulating real situations.

Non-isothermal One-Dimensional Two-Phase Model of Water Transport in Proton Exchange Membrane Fuel Cells with Micro-porous Layer

Non-isothermal One-Dimensional Two-Phase Model of Water Transport in Proton Exchange Membrane Fuel Cells with Micro-porous Layer

(Digital Presentation) Effects of Catalyst Dimension Parameters on Local Oxygen Transport in Cathode Catalyst Layer of Proton Exchange Membrane Fuel Cell

Improving the performance of proton exchange membrane of fuel cell (PEMFC) can save materials and then reduce costs, which is helpful to accelerate its large-scale commercial application. In this paper, an agglomerate model is proposed and developed by coupling a one-dimensional local oxygen transport model with a one-dimensional multiphase non-isothermal fuel cell model to study the influence of catalyst dimension parameters (Pt radius, Pt average dispersity, carbon radius) on local oxygen transport in the cathode catalyst layer (CCL) comprehensively. And this elaborate model shows that the smaller Pt radius, carbon radius, and the higher Pt average dispersity can reduce the transport distance of oxygen molecules from the pores to the active sites, and then decrease the local resistance. Based on the above understanding, the performance of the optimized cell with a Pt loading of 0.2 mg cm-2 is improved by 22%, slightly higher than the original cell with a Pt loading of 0.4 mg cm-2, which achieves a 50% reduction in Pt loading while maintaining the cell performance. This research will give a guide for improving cell performance.

Improvement of the delayed neutron precursor transport model in RELAP5 for liquid-fueled molten salt reactor

The Liquid-Fueled Molten Salt Reactor (LF-MSR) with high-temperature molten salt is one of the Generation IV nuclear power systems. One of the significant differences between the LF-MSR and the Pressurized Water Reactor (PWR) is that the delayed neutron precursors (DNP) circulate in the primary loop of the LF-MSR and leads to different neutron kinetics between LF-MSR and PWR. Consequently, a system code for PWR is not applicable to LF-MSR, and the safety analysis code RELAP5-TMSR is modified by adding a one-dimensional DNP transport model to improve its applicability to LF-MSR. A second-order Godunov method is adopted in this 1-D DNP model. Then the improved code is tested with experimental benchmarks from Molten Salt Reactor Experiment (MSRE) designed and operated by Oak Ridge National Laboratory (ORNL) and the results show good consistency. Moreover, the modified RELAP5-TMSR code is applied to analyzing transient characteristics of the single-fluid Molten Salt Breeding Reactor (MSBR) so that the applicability of the modified RELAP5-TMSR code is further verified. It is concluded that the one-dimensional DNP transport model can describe effectively the movement of the DNP and the improved RELAP5-TMSR code is suitable for modeling and simulation of reactor transient responses in LF-MSR.

(Digital Presentation) Effects of Catalyst Dimension Parameters on Local Oxygen Transport in Cathode Catalyst Layer of Proton Exchange Membrane Fuel Cell

Improving the performance of proton exchange membrane fuel cells (PEMFCs) can help accelerate their large-scale commercial application. In this paper, an agglomerate model is proposed and developed by coupling a one-dimensional local oxygen transport model with a one-dimensional multiphase non-isothermal fuel cell sub-model to study the influences of catalyst dimension parameters (Pt radius, Pt average dispersity, carbon radius) on local oxygen transport and cell performance. And this elaborate model shows that the smaller Pt radius, carbon radius, and the higher Pt average dispersity can reduce the transport distance of oxygen molecules from the pores to the active sites, and then decrease the local resistance. Based on the above understanding, the optimum performance of the optimized cell with a Pt loading of 0.2 mg cm-2 is improved by 22%, slightly higher than the original cell with a Pt loading of 0.4 mg cm-2, which achieves a 50% reduction in Pt loading while maintaining the cell performance. This research will give a guide for improving cell performance.

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.

Estimation of China Fusion Engineering Test Reactor performance and burning fraction in different pellet fueling scenarios by a multi-species radial transport model

Tritium self-sufficiency in future deuterium–tritium fusion reactors is a crucial challenge. As an engineering test reactor, the China Fusion Engineering Test Reactor requires a burning fraction of 3% for the goal to test the accessibility to the future fusion plant. To self-consistently simulate burning plasmas with profile changes in pellet injection scenarios and to estimate the corresponding burning fraction, a one-dimensional multi-species radial transport model is developed in the BOUT++ framework. Several pellet-fueling scenarios are then tested in the model. The results show that the increased fueling depth improves the burning fraction by particle confinement improvement and fusion power increase. Nevertheless, by increasing the depth, the pellet cooling-down may significantly lower the temperature in the core region. Taking the density perturbation into consideration, the reasonable parameters of the fueling scenario in these simulations are estimated as pellet radius injection rate and pellet injection velocity without drift or with high-field-side drift.