One-dimensional Transport Model Research Articles

A One-Dimensional Reactive Transport Model for Microbially Induced Calcium Carbonate Precipitation (MICP) in Phreeqc

Microbially induced calcium carbonate precipitation (MICP) is a geotechnical solution with a low ecological footprint. Conducting MICP inside a porous medium can be used for biocementation. Despite many models and tools being published for simulating MICP, a computationally light, easy-to-use, and freely-available simulation tool is lacking. In this work, we present a reactive transport model using the native capabilities of the Phreeqc software (a free and open-source geochemical solver). We model MICP inside a column packed with sands and inoculated with bacteria. Our model is a one-dimensional representation of the column that accounts for the kinetics of precipitation and ureolysis as well as porosity change. We verify our model by simulating previously published MICP experiments to show our model gives reasonably well predictions. Sensitivity analysis of our model’s input parameters and discussions around their range are presented. Additionally, we calculate the supersaturation of calcite as a function of space and time—a feature that could be important for precipitation, but it is commonly ignored in MCIP modeling. Our scripts developed for running simulations are accessible publicly. Due to the low computational effort required for the simulations, our Phreeqc scripts can be used to design and test different treatment recipes for conducting MICP.

Assessing field scale spatiotemporal heterogeneity in salinity dynamics using aerial data assimilation

Soil moisture and salinity shifts within the root zone can significantly alter crop yields. Thus, spatiotemporal dynamics of these parameters are essential for precision crop management. Airborne or spaceborne earth observation methods based on vegetation and soil observations have sometimes been used with limited success to indirectly understand parameters like soil salinity. These datasets lack spatiotemporal resolution to discern field-scale heterogeneities, and estimates’ accuracy is poor. A Metropolis-Hasting Markov Chain-Monte Carlo (MCMC) based method was developed to estimate field-scale soil salinity by assimilating estimated evapotranspiration (ET) data obtained from aerial canopy temperature sensing with ET outputs from a one-dimensional soil-water transport model. By aligning the two estimated ET values, we inferred anticipated soil salinity levels in a mature pecan orchard (28,951 m2). Our results aligned closely with in-situ measurements with a spatial cross-correlation more than 0.86 and highlighted the expected heterogeneities and nonlinearities. This research offers an approach to refine the current state-of-the-art crop models by accounting for field scale heterogeneities using remotely sensed data. This assimilation method will pave the way for a more inclusive agricultural system modeling that can infer critical but hard-to-measure soil properties from easier-to-obtain remotely sensed datasets. Though this paper concentrates on aerial observations, we anticipate similar methods can be used for satellite-based imagery, especially those with high spatial, temporal, and spectral resolutions.

Channel-facilitated transport under resetting dynamics.

The transport of particles through channels holds immense significance in physics, chemistry, and biological sciences. For instance, the motion of solutes through biological membranes is facilitated by specialized proteins that create water-filled channels. Valuable insights can be obtained by studying the transition paths of particles through a channel and gathering information on their lifetimes inside the channel as well as their exit probabilities. In a similar vein, we consider a one-dimensional model of channel-facilitated transport where a diffusive particle is subject to attractive interactions with the walls of the channel. We study the statistics of conditional and unconditional escape times in the presence of resetting-an intermittent dynamics that brings the particle back to its initial coordinate stochastically. We determine analytically the physical conditions under which such a resetting mechanism becomes beneficial for the faster escape of the particles from the channel, thus enhancing transport. Our theory has been verified with the aid of Brownian dynamics simulations for various interaction strengths and extents. The overall results presented herein highlight the scope of resetting-based strategies to be universally promising for complex transport processes of single or long molecules through biological membranes.

One-dimensional model for vertical hydraulic transport of high-concentration mineral particles

A novel model is proposed for analyzing high-concentration granular flow systems comprising equally sized spherical particles within vertical, long straight pipelines. This model is specifically tailored for simulating the vertical hydraulic transport of ore particles in marine mining projects. The proposed model treats the granular system akin to a pseudo-fluid and operates through three mechanisms. First, fluid characteristics of the granular system are derived from particle–particle collisions. Second, the resistance exerted by the pipe wall on the granular system is calculated based on the momentum loss of particles during particle–wall collisions. Third, the interaction between individual particles and the surrounding fluid is transformed into an interaction between the carrier fluid and the pseudo-fluid. Additionally, the present work develops a dedicated numerical format and iterative method for solving the one-dimensional two-fluid governing equations. The one-dimensional (1D) model notably enhances computational efficiency and facilitates accurate tracking of high-concentration particles over extended distances within straight pipelines. Notably, the proposed 1D model demonstrates a high degree of predictive accuracy when compared against experimental data as well as results from computational fluid dynamics and discrete element method simulations.

Measuring thermal diffusivity and gap conductance in uranium nitride and Zircaloy relevant for microreactor applications

Heat transfer across nuclear fuels and structural interfaces is an important factor for evaluating the performance of nuclear power systems. Specifically, heat generated as nuclear fuel fissions must be transported through the cladding material and through the reactor to reach the steam turbine for power generation. As new microreactor designs emerge, maximizing the efficiency of this heat transfer process becomes crucial to make them commercially viable. This article examines thermal diffusivity and gap conductance in uranium nitride (UN) fuel and Zircaloy-4 (Zry4) cladding using light flash analysis (LFA). Thermal diffusivity measurements were made on monolithic UN pellets and Zry4 exposed to carbon at peak operating temperatures of microreactors and show that carbon ingress has a minimal effect on thermal diffusivity when compared with identical materials not exposed to carbon. Evaluation of gap conductance at the UN-Zry4 interface was done using one-dimensional two-layer thermal transport models as a function of applied pressure. The results show that increasing pressure on the UN-Zry4 interface leads to gains in gap conductance per unit area in fuel-cladding assemblies at microreactor operating temperatures. While many other variables are expected to influence UN-Zry4 interfacial gap conductance (e.g. contact surface roughness, porosity, localized heating, environmental gas pressure), the work offers a demonstration of using a conventional LFA apparatus to determine this parameter at elevated temperatures.

Model-Based Analysis of the Oxygen Budget in the Black Sea Water Column

Climate change and anthropogenic impacts drastically affect the biogeochemical regime of the Black Sea, which contains the largest volume of sulphidic water in the world. The Sea’s oxygen inventory depends on vertical mixing that transports dissolved oxygen (DO) from the upper euphotic layer to deeper layers and on dissolved oxygen consumption for the oxidation of organic matter (OM) and reduced species of S, Fe, and Mn. Here we use a vertical one-dimensional transport model, 2DBP, forced by Copernicus data, that was coupled with the FABM-family N-P-Si-C-O-S-Mn-Fe Bottom RedOx Model BROM. The research objective of this study was to analyze the oxygen budget in the upper 350 m of the Sea and demonstrate the role of the parameterization of the acceleration of the sinking of particles covered by precipitated Mn(IV). The analysis of the oxygen budget revealed distinct patterns in oxygen consumption within different depths. In the oxic zone, the primary sink for DO is the mineralization of organic matter, whereas in the suboxic zone, dissolved Mn(II) oxidation becomes the predominant sink. The produced Mn(IV) sinks down and reacts with hydrogen sulphide several meters below, making possible the existence of the suboxic layer without detectable concentrations of DO and H2S.

Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes

We investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as the Lévy-Lorentz gas. To gain insight into the microscopic properties of such a stochastically complex system, deterministic dynamics known as the slicer map and fly-and-die dynamics are used. We analytically derive the generalized position autocorrelation function of these dynamics and study the special case, the 3-point position correlation function. For this, we derive single-parameter-dependent scaling and compare it with the numerically estimated 3-point position autocorrelation of the Lévy-Lorentz gas, for which the analytical expression is still an open question. Here we obtained a remarkable agreement between them, irrespective of any functional relationship with time. Moreover, we demonstrate that the position moments and the position autocorrelations of these systems scale in the same fashion, provided the times are large enough and far enough apart. Other observables, such as velocity moments and correlations, are reported to distinguish the systems. Published by the American Physical Society 2024

A Detailed Survey of the Parallel Mean Free Path of Solar Energetic Particle Protons and Electrons

In this work, more than a dozen solar energetic particle (SEP) events are identified where the source region is magnetically well connected to at least one spacecraft at 1 au. The observed intensity–time profiles, for all available proton and electron energy channels, are compared to results computed using a numerical one-dimensional SEP transport model in order to derive the parallel mean free paths (pMFPs) as a function of energy (or rigidity) at 1 au. These inversion results are then compared to theoretical estimates of the pMFP, using observed turbulence quantities with observationally motivated variations as input. For protons, a very good comparison between inversion and theoretical results is obtained. It is shown that the observed inter-event variations in the inversion pMFP values can be explained by natural variations in the background turbulence values. For electrons, there is relatively good agreement with pMFPs derived assuming the damping model of dynamical turbulence, although the theoretical values are extremely sensitive to the details of the turbulence dissipation range, which themselves display a high level of variation.

Dimensional effects in analysis of laser-induced-desorption diagnostics data

The accurate assessment of the local tritium concentration in the tokamak first wall by means of the laser-induced desorption (LID) diagnostics is sought as one the key solutions to monitoring the local radioactive tritium content in the first wall of the fusion reactor ITER. Numerical models of gas desorption from solids used for LID simulation are usually closed with the one-dimensional transport models. In this study, the temperature and particle dynamics in the target irradiated by a short laser pulse during LID are analyzed by means of the two-dimensional model to assess the validity of using one-dimensional approximation for recovering the diagnostics signal. The quantitative estimates for the parameters governing the heat and particle transfer are presented. The analytical expressions for the sample spatiotemporal temperature profiles driven by the target irradiation with a Gaussian laser beam with the trapezoid temporal shape are derived. The obtained relations are used to simulate tritium desorption from a tungsten sample driven by pulsed heating. It is shown that depending on the ratio between the laser spot radius and the heat diffusion length, the one-dimensional approach can noticeably overestimate the sample temperature in the limit of small laser spot radius (estimated for tungsten as ∼0.5–1.0 mm), resulting in more than 100% larger amounts of tritium desorbed from the target, compared to the two-dimensional approximation. In the limit of large laser spot radius (≥1.5 mm), both approaches yield comparable amounts of tritium desorbed from the sample.

New Lie Symmetries and Exact Solutions of a Mathematical Model Describing Solute Transport in Poroelastic Materials

A one-dimensional model for fluid and solute transport in poroelastic materials (PEMs) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary cases, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated, and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

A one-dimensional diffusive transport model to evaluate H2S generation in salt caverns hydrogen storage sites

Salt caverns are considered a potential hydrogen storage site given the ductility, tightness, and chemical inertness of halite. In addition, unlike porous media, salt caverns require less cushion gas and allow more cycles of injection and production within a year. However, hydrogen is an electron donor for many hydrogenotrophic microorganisms including halophilic sulfate-reducing microbes (SRM) and hydrogen sulfide (H2S) can be generated in a cavern once sulfate and hydrogen become available in the aqueous phase. As salt deposits are often associated with large amounts of impurities such as anhydrite and gypsum, their dissolution during the leaching phase can release the required sulfate ions for SRMs to produce H2S once hydrogen diffuses and dissolves in the brine at the bottom of the cavern. In this study, a one-dimensional diffusive transport model was developed using PHREEQC to simulate sulfate reduction and H2S generation in a cavern at the gas-brine interface. The solution of Fick's diffusion equation was used to calculate the hydrogen concentration at each level of the 1D model while the kinetic rates of reactions were derived from reported experimental and field site observations of brine samples taken from salt caverns. The results obtained indicated that hydrogen consumption at the gas-brine interface can trigger H2S and methane formations. This is followed by a reduction in sulfate and carbonate concentration and a slight increase in pH due to the reduction of protons in the solution. It was also observed that the presence of Fe2+ ions can reduce the amount of the hydrogen sulfide production while Ca2+ ions slightly favour sulfate reduction due to the production of methane. Although the kinetic reaction rate of the reactions in the model is subject to a certain degree of uncertainty, the workflow and results this study can serve as a guide for the future storage of hydrogen in salt caverns.

Evidence of deviations between experimental and empirical mixing lengths: Multi-discharge field tests in an arid river system

Despite advances in wastewater treatment plant (WWTP) efficiencies, multiple contaminants of concern, such as microplastics, pharmaceuticals, and per- and poly-fluoroalkyl substances (PFAS) remain largely untreated near discharge points and can be highly concentrated before they are fully mixed within the receiving river. Environmental agencies enforce mixing zone permits for the temporary exceedance of water quality parameters beyond targeted control levels under the assumption that contaminants are well-mixed and diluted downstream of mixing lengths, which are typically quantified using empirical equations derived from one-dimensional transport models. Most of these equations were developed in the 1970s and have been assumed to be standard practice since then. However, their development and validation lacked the technological advances required to test them in the field and under changing flow conditions. While new monitoring techniques such as remote sensing and infrared imaging have been employed to visualize mixing lengths and test the validity of empirical equations, those methods cannot be easily repeated due to high costs or flight restrictions. We investigated the application of Lagrangian and Eulerian monitoring approaches to experimentally quantify mixing lengths downstream of a WWTP discharging into the Rio Grande near Albuquerque, New Mexico (USA). Our data spans river to WWTP discharges ranging between 2-22x, thus providing a unique dataset to test long-standing empirical equations in the field. Our results consistently show empirical equations could not describe our experimental mixing lengths. Specifically, while our experimental data revealed “bell-shaped” mixing lengths as a function of increasing river discharges, all empirical equations predicted monotonically increasing mixing lengths. Those mismatches between experimental and empirical mixing lengths are likely due to the existence of threshold processes defining mixing at different flow regimes, i.e., jet diffusion at low flows, the Coanda effect at intermediate flows, and turbulent mixing at higher flows, which are unaccounted for by the one-dimensional empirical formulas. Our results call for a review of the use of empirical mixing lengths in streams and rivers to avoid widespread exposures to emerging contaminants.

One-Dimensional Model of Vertical Transport of Chemical Components in the Mars Atmosphere up to the Lower Thermosphere

One-Dimensional Model of Vertical Transport of Chemical Components in the Mars Atmosphere up to the Lower Thermosphere

Coupling of sediment transport phenomena with turbulent surface flows: mathematical modeling, finite volume approximation and test simulations

Several sediment transport models coupled with shallow water equations have been developed in the literature over the past few decades. The water flow in the presence of abrupt bottom slopes distorts and cause turbulence. This phenomenon is well-known in the sediment transport theory. Sediment transport models based on shallow water equations do not include turbulence effects or the phase-lag between water velocity and bottom velocity. In this study, we consider a one-dimensional free surface turbulent water flow with sediment and morphodynamic. We propose a new one-dimensional acceleration-dissipation mathematical sediment transport model that considers the distortion of horizontal profile velocity in transport. The model is an improved version of existing averaged sediment transport models. In the new model, there is a distinction between fluid velocity and bottom velocity through a new bedload equation. The mathematical model is a system of nonlinear hyperbolic partial differential equations that are approximated by a stable and robust finite volume scheme presented in the path-conservative framework. Numerical tests are performed to demonstrate the efficiency of the developed theory.

Modeling water transport in polymer electrolyte membrane electrolyzers using a one-dimensional transport model

In this paper, we present a one-dimensional transport model for water transport across Nafion® membranes in a proton exchange membrane electrolyzer. This physics-based model is based on the three main water transport mechanisms: diffusion, electro-osmotic drag, and pressure-driven flow. A good agreement is obtained between the model predictions using the measured values of the physical parameters as inputs and the previously reported experimental data. Further, with the help of this simple transport model, the numerical analysis is performed to delineate the effect of electrolyzer operating conditions on the net water transport across the membrane, water condensation at the cathode, individual contribution of the transport fluxes, and electrolyzer design. Finally, the model is exercised to simulate the dependence of water transport as a function of membrane thickness. This confirms the validity of the current approach of using thin reinforced membranes by electrolyzer fabricators.

Carbon dioxide removal via weathering of sugarcane mill ash under different soil conditions

Sugarcane mill ash has been suggested as having high potential for carbon dioxide removal (CDR) via enhanced weathering (EW), but this had not been quantitatively assessed. The aims of this study were to 1) assess the CDR potential of various sugarcane mill ashes via EW, and 2) investigate the impact of soil conditions and mill ash properties on the CDR. This was done by characterising physical and chemical properties of five mill ashes from Australia and simulating weathering using a one-dimensional reactive transport model. The model was parameterised to simulate weathering of 100 t/ha of wet ash (47–65% water) or crushed basalt for 15 years under various combinations of soil pH and carbon dioxide partial pressure (pCO2). A sensitivity analysis was undertaken in a two-level factorial design to test the effect of pH, pH buffering, material surface area, infiltration rate, plant uptake of nutrients, organic matter cation exchange surfaces, and pCO2 on modelled CDR. The simulated CDR of the mill ashes was significantly less than the basalt (p < 0.001) but mostly did not differ significantly between ashes (p > 0.05). Weathering of mill ash removed 0.0–4.0 t CO2/ha (0.00–0.040 t CO2/t wet ash) cumulatively, similar to some basalts and olivine modelled in the literature. The theoretical maximum CDR of the mill ashes (based on amount of weatherable material applied) was achieved in around 5 years. The estimate of CDR varied by orders of magnitude depending on conditions. It was least when initial soil solution pH was lowest (4.5, unbuffered), pH was at 6.5 or less with constant buffering, and pCO2 was low (600 ppm). CDR was also significantly lower when calculated directly from accumulation of carbon in dissolved and solid phases rather than stoichiometrically from cation release. The effects of pH and pH buffering quantified here may explain low measured CDR from EW in field trials on acidic soils and highlight the need for more realistic modelling of pH buffering capacity. Overall, mill ash shows high potential for CDR via EW, especially if lifecycle benefits are considered, although this must be validated in the field.

Comparing the Fate and Transport of MS2 Bacteriophage and Sodium Fluorescein in a Karstic Chalk Aquifer.

Groundwater flow and contaminant migration tracing is a vital method of identifying and characterising pollutant source-pathway-receptor linkages in karst aquifers. Bacteriophages are an attractive alternative tracer to non-reactive fluorescent dye tracers, as high titres (>1012 pfu mL-1) can be safely released into the aquifer, offering improved tracer detectability. However, the interpretation of bacteriophage tracer breakthrough curves is complicated as their fate and transport are impacted by aquifer physicochemical conditions. A comparative tracer migration experiment was conducted in a peri-urban catchment in southeast England to characterise the behaviour of MS2 bacteriophage relative to sodium fluorescein dye in a karstic chalk aquifer. Tracers were released into a stream sink and detected at two abstraction boreholes located 3 km and 10 km away. At both sites, the loss of MS2 phage greatly exceeded that of the solute tracer. In contrast, the qualitative shape of the dye and phage breakthrough curves were visually very similar, suggesting that the bacteriophage arriving at each site was governed by comparable transport parameters to the non-reactive dye tracer. The colloid filtration theory was applied to explain the apparent contradiction of comparable tracer breakthrough patterns despite massive phage losses in the subsurface. One-dimensional transport models were also fitted to each breakthrough curve to facilitate a quantitative comparison of the transport parameter values. The model results suggest that the bacteriophage migrates through the conduit system slightly faster than the fluorescent dye, but that the former is significantly less dispersed. These results suggest that whilst the bacteriophage tracer cannot be used to predict receptor concentrations from transport via karstic flow paths, it can provide estimates for groundwater flow and solute contaminant transit times. This study also provides insight into the attenuation and transport of pathogenic viruses in karstic chalk aquifers.

Detection and transport of environmental DNA from two federally endangered mussels.

Environmental DNA (eDNA) offers a novel approach to supplement traditional surveys and provide increased spatial and temporal information on species detection, and it can be especially beneficial for detecting at risk or threatened species with minimal impact on the target species. The transport of eDNA in lotic environments is an important component in providing more informed descriptions of where and when a species is present, but eDNA transport phenomena are not well understood. In this study, we used species-specific assays to detect eDNA from two federally endangered mussels in two geographically distinct rivers. Using the eDNA concentrations measured from field samples, we developed a one-dimensional (1D) hydrodynamic transport model to predict the downstream fate and transport of eDNA. We detected eDNA from both federally endangered mussels across several seasons and flow rates and up to 3.5 km downstream from the source populations, but the detection rates and eDNA concentrations were highly variable across and within rivers and study reaches. Our 1D transport models successfully integrated the variability of the eDNA field samples into the model predictions and overall model results were generally within ±1 standard error of the eDNA field concentration values. Overall, the results of this study demonstrate the importance of optimizing the spatial locations from where eDNA is collected downstream from a source population, and it highlights the need to improve understanding on the shedding mechanisms and magnitude of eDNA from source populations and biogeomorphic processes that influence eDNA transport.

Pollutant transport behavior through polymer cutoff wall: Laboratory test and analytical model investigation

Polymer cutoff wall has emerged as a new and promising technology for anti-seepage and anti-pollution in geotechnical engineering. With notable advantages such as rapid sealing, high efficiency, and environmental friendliness, this technology has garnered significant attention. This study presents a systematic investigation into the transport characteristics of pollutants in polymer materials, with a specific focus on the transport mechanisms through polymer cutoff wall. The research investigates various factors that influence the pollutant transport characteristics in polymer materials. The objective is to analyze the pollutant transport behavior and obtain the transport parameters. Moreover, the study develops and solves a one-dimensional transport model incorporating partition-diffusion-partition mechanisms, aiming to determines the long-term service performance of polymer wall. These findings contribute to a better understanding of pollutant transport through polymer walls, which is crucial for the future advancement and utilization of this technology.

Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling and experimental observations. In contrast to most prior work, models are not designed or tuned with the aim to produce a specific auxin pattern. Instead, we use well-established techniques from dynamical systems theory to uncover and classify ranges of auxin patterns as exhaustively as possible as parameters are varied. Previous work using these techniques has shown how a multitude of stable auxin patterns may coexist, each attainable from a specific ensemble of initial conditions. When a key parameter spans a range of values, these steady patterns form a geometric curve with successive folds, often nicknamed a snaking diagram. As we introduce growth and cell division into a one-dimensional model of auxin distribution, we observe new behaviour which can be explained in terms of this diagram. Cell growth changes the shape of the snaking diagram, and this corresponds in turn to deformations in the patterns of auxin distribution. As divisions occur this can lead to abrupt creation or annihilation of auxin peaks. We term this phenomenon 'snake-jumping'. Under rhythmic cell divisions, we show how this can lead to stable oscillations of auxin. We also show that this requires a high level of synchronisation between cell divisions. Using 18 hour time-lapse imaging of the auxin reporter DII:Venus in roots of Arabidopsis thaliana, we show auxin fluctuates greatly, both in terms of amplitude and periodicity, consistent with the snake-jumping events observed with non-synchronised cell divisions. Periodic signals downstream of the auxin signalling pathway have previously been recorded in plant roots. The present work shows that auxin alone is unlikely to play the role of a pacemaker in this context.