Analytical Transport Model Research Articles

Analysis of coupled proton and water transport in a PEM fuel cell using the binary friction membrane model

Transport of liquid water within a polymer electrolyte membrane (PEM) is critical to the operation of a PEM fuel cell, due to the strong dependence of the membrane transport coefficients on water content. In addition, enhanced predictive abilities are particularly significant in the context of passive air breathing fuel cell designs where lower water contents will prevail in the membrane. We investigate and analyze the numerical predictions of a recently proposed rational model for transport of protons and water in a PEM, when compared to a widely used empirical model. While the performance is similar for a saturated membrane, for PEMs with low water content, the difference in computed current density and membrane water crossover can be substantial. The effects of coupling partially saturated gas diffusion electrodes (GDLs) with the membrane are studied in both a 1D and 2D context. In addition, a simplified 1D analytical membrane water transport model is validated against the complete 1D model predictions. Our numerical results predict a higher current density and more uniform membrane hydration using a dry cathode instead of a dry anode, and illustrate that the strongest 2D effects are for water vapor transport.

A Three‐Dimensional Analytical Tool for Modeling Reactive Transport

In this note, we present a public domain analytical reactive transport modeling tool (ART3D, version 2.0). The tool is developed in FORTRAN and can be used for solving a system of a set of partial differential equations coupled with a first-order reaction network. ART3D uses a novel analytic solution technique proposed by Clement. The new software includes options for performing Monte Carlo simulations and automated parameter estimation.

Quality Criteria for Re-Use of Organotin-Containing Sediments on Land (7 pp)

Background, Aim and Scope The use of organotin compounds as antifouling agents on ships is prohibited at EU level since 1 July 2003. Because of its persistence, the presence of organotin compounds in harbour sediment will however remain a problem for years. Dumping of dredged sediment in sea is subject to very strict quality criteria, stimulating the exploration of re-use alternatives, such as re-use on land. Within the TBT Clean project (EU LIFE Project 02/ENV/B/341) an assessment framework for re-use of organotin containing treated sediment on land as secondary granular building material was developed. Three scenarios were considered: free re-use on land, re-use above groundwater level with cover layer, and re-use under groundwater level (the latter two scenarios are referred to as restricted re-use). Receptors considered were humans, ecosystem and groundwater. Generic upper concentration limits and sediment leaching limits were calculated. Materials and Methods: Upper concentration limits were calculated with the Vlier-Humaan model. This model allows to calculate soil remediation values according to the Flemish legal framework. The focus of the methodology is the protection of human health, although a check for ecotoxicity was included in the project. The soil remediation value for residential land-use was selected within the scenario for free re-use; for restricted re-use (no direct contact possible), the soil remediation value for industrial land-use was selected. Leaching values were calculated with an analytical soil and groundwater transport model. The reference scenario behind the leaching criteria of the European Landfill Directive was modified to fit the project objectives. Default values for application height and length were used. The point-of-compliance was situated at 20 m distance in the groundwater. Physicochemical properties were taken from literature; sorption characteristics were taken from literature and were measured on 6 treated sediment samples during the project. Plant-uptake values were taken from the literature. Toxicological criteria were taken from EFSA. Results: The assessment framework provided an upper limit (SedUL) and an leaching value (SedLV) for each scenario, expressed as mg/kg dm in the sediment. Criteria were calculated for tributyltin (TBT) and dibutyltin (DBT); too few data were available for monobutyltin (MBT). The SedUL equalled 0.51 mg TBT/kg dm and 0.07 mg DBT/kg dm for free re-use and 195 mg TBT/kg dm and 205 mg DBT/kg dm for restricted re-use (two scenarios). For free re-use the SedLV was only limiting for TBT at Kd of < 2000 l/kg in the sediment. Under re-use above groundwater level with coverage SedLV values ranged from 6.9 – 29 mg TBT/kg dm and from 12 – 33.3 mg DBT/kg dm (Kd ranging from 100 – 10000 l/kg); under re-use below groundwater level SedLV values ranged from 0.007 – 0.77 mg TBT or DBT/kg dm (Kd ranging from 100 – 10000 l/kg). Discussion: Results are subject to large uncertainties because of variation in input data; the model output is sensitive to variation in plant uptake (SedUL for free re-use), Koc or Kd (SedUL for restricted re-use, SedLV for re-use with coverage), Henry's law coefficient (SedUL for restricted re-use); all these parameters show orders of magnitude variation. Conclusions: A feasible and consistent framework for evaluation of the re-use of treated organotin containing sediment was developed. However, the resulting quality criteria are still subject to large uncertainties, due to uncertainties in input data. Recommendations and Perspectives: High-quality data on plant uptake and soil sorption of organotin compounds, the influence of soil properties on these processes, and long-term terrestrial toxicity data are needed to refine the calculations. The quality criteria should be reviewed when these data become available.

Analytical model of magnetic nanoparticle transport and capture in the microvasculature

An analytical model is presented for predicting the transport and capture of therapeutic magnetic nanoparticles in the human microvasculature. The nanoparticles, with surface bound drug molecules, are injected into the vascular system upstream from malignant tissue, and are captured at the tumor site using a local applied magnetic field. The applied field is produced by a rare-earth cylindrical magnet positioned outside the body. An analytical expression is derived for predicting the trajectory of a particle as it flows through the microvasculature in proximity to the magnet. In addition, a scaling relation is developed that enables the prediction of the minimum particle radius required for particle capture. The theory takes into account the dominant magnetic and fluidic forces, which depend on the position and properties of the magnet, the size and magnetic properties of the nanoparticles, the dimensions of the microvessel, the hematocrit level of the blood, and the flow velocity. The model is used to study noninvasive drug targeting, and the analysis indicates that submicron particles can be directed to tumors that are several centimeters from the field source.

A Review of Multidimensional, Multifluid Intermediate‐Scale Experiments: Nonaqueous Phase Liquid Dissolution and Enhanced Remediation

A review is presented of original multidimensional, intermediate‐scale experiments involving NAPLs (nonaqueous phase liquids). The experimental approach at this scale can be viewed as an important intermediary between column studies and field trials. The primary advantage of intermediate‐scale flow cell experiments is that field‐scale processes can be simulated under controlled conditions. The experiments are frequently conducted to provide data sets to test and verify numerical and analytical flow and transport models. The controlled setting and laboratory instrumentation reduces the uncertainty in parameter estimation, allowing comparisons between simulation and experimental results to focus on flow and transport processes. A total of about 125 original contributions were identified and reviewed. Depending on the main topic of NAPL experimental research, the papers were divided into the following sections: (i) aqueous dissolution, (ii) enhanced remediation, (iii) flow behavior, (iv) quantification, and (v) imaging. In this review, the first two categories are discussed and suggestions for future research are provided. In a companion review, experimental work related to the other three categories is investigated. The aqueous dissolution category includes experiments in which pooled and entrapped NAPL removal occurs due to water flushing. The enhanced remediation section contains experimental contributions investigating surfactant flushing, alcohol flushing, surfactant and alcohol flushing combinations, dense brine strategies, hydraulic NAPL recovery, soil vapor extraction, air sparging, heat‐based remediation, bioremediation, and other techniques.

An analytical model for solute transport in unsaturated flow through a single fracture and porous rock matrix

An exact analytical solution is presented for solute transport in an unsaturated, vertical fracture and porous rock matrix. The problem includes advective transport in the fracture and rock matrix as well as advective and diffusive fracture‐matrix exchange. Linear sorption and radioactive decay are also treated. The solution is derived under the assumptions that longitudinal diffusion and dispersion are negligible and that the fracture and rock properties are homogeneous. The water flux and saturation within the matrix are assumed to be steady and spatially uniform. The fracture flux, saturation, and wetted fracture‐matrix interface area are steady but are allowed to be spatially variable. The problem is first solved in terms of solute concentrations that result from an instantaneous point source in the fracture. An integrated form of the solution is also derived for cumulative solute mass flux at a fixed downstream position. The closed‐form analytical solution is expressed in terms of algebraic functions, exponentials, and error functions. Analyses indicate limited sensitivity to fracture porosity and fracture retardation under typical conditions but strong sensitivity to matrix diffusion, matrix retardation, and matrix imbibition.

An analytical model of enterococci inactivation, grazing, and transport in the surf zone of a marine beach

An analytical model of enterococci (ENT) concentrations in the surf zone of a long sandy beach is constructed considering the physical processes of dilution by rip currents and alongshore littoral drift, and the biological processes of inactivation and mortality by grazing. The solution is used to construct an expression for the length of shoreline adversely impacted by ENT from a point source. Two non-dimensional parameters are developed whose magnitude can be used to ascertain whether dilution, inactivation, or grazing is the dominant sink for ENT in the surf zone. The model is applied to beaches in southern California, USA. Model input parameters related to physical processes and inactivation are compiled from the literature. Laboratory experiments are conducted to determine grazing mortality rates of ENT ( 6.5 × 10 - 6 s - 1 ) . Results indicate that at the field sites, between 1000 and 5000 m of shoreline are typically impacted by a continuous point source of ENT. Dilution is the primary cause of decline in ENT concentrations within the surf zone, with inactivation secondary and grazing tertiary. Results recommend strategic positioning of point sources and timing of effluent releases to take advantage of high dilution conditions. Our estimates for grazing mortality rates are within the same order of magnitude as some published inactivation rates, thus we cannot rule out the possibility that grazing is an important sink for ENT, especially in low dilution environments like enclosed bays.

Relationship between soil CO 2 concentrations and forest-floor CO 2 effluxes

To better understand the biotic and abiotic factors that control soil CO 2 efflux, we compared seasonal and diurnal variations in simultaneously measured forest-floor CO 2 effluxes and soil CO 2 concentration profiles in a 54-year-old Douglas fir forest on the east coast of Vancouver Island. We used small solid-state infrared CO 2 sensors for long-term continuous real-time measurement of CO 2 concentrations at different depths, and measured half-hourly soil CO 2 effluxes with an automated non-steady-state chamber. We describe a simple steady-state method to measure CO 2 diffusivity in undisturbed soil cores. The method accounts for the CO 2 production in the soil and uses an analytical solution to the diffusion equation. The diffusivity was related to air-filled porosity by a power law function, which was independent of soil depth. CO 2 concentration at all depths increased with increase in soil temperature, likely due to a rise in CO 2 production, and with increase in soil water content due to decreased diffusivity or increased CO 2 production or both. It also increased with soil depth reaching almost 10 mmol mol −1 at the 50-cm depth. Annually, soil CO 2 efflux was best described by an exponential function of soil temperature at the 5-cm depth, with the reference efflux at 10 °C ( F 10) of 2.6 μmol m −2 s −1 and the Q 10 of 3.7. No evidence of displacement of CO 2-rich soil air with rain was observed. Effluxes calculated from soil CO 2 concentration gradients near the surface closely agreed with the measured effluxes. Calculations indicated that more than 75% of the soil CO 2 efflux originated in the top 20 cm soil. Calculated CO 2 production varied with soil temperature, soil water content and season, and when scaled to 10 °C also showed some diurnal variation. Soil CO 2 efflux and concentrations as well as soil temperature at the 5-cm depth varied in phase. Changes in CO 2 storage in the 0–50 cm soil layer were an order of magnitude smaller than measured effluxes. Soil CO 2 efflux was proportional to CO 2 concentration at the 50-cm depth with the slope determined by soil water content, which was consistent with a simple steady-state analytical model of diffusive transport of CO 2 in the soil. The latter proved successful in calculating effluxes during 2004.

Carrier Transport Model for Lateral p-i-n Photodiode in High-Frequency Operation

We present an analytical model for carrier transport in a lateral p-i-n photodiode from DC to high-frequency operation. The model derives a nonstationary description of photodiode behavior in Fourier space. Transient photodiode response calculated by the model is in excellent agreement with measurement at high-applied reverse bias. The model is particularly useful for circuit simulation of optoelectronic integrated circuits where computational accuracy and reduced computational runtime are required.

Development of A Two-Dimensional Analytical Model for Predicting Toxic Sediment Plumes Due to Environmental Dredging Operations

A two-dimensional analytical transport model is developed to predict the dredge induced plume concentration in the horizontal plane under steady-state for simple hydraulic conditions. The derivation of the analytical solution is based on the solution to the advection-diffusion equation. The application of this analytical model is limited to mechanical dredge operations, bucket dredge, which has continuous point source in the water column. The analytical model developed herein is used to simulate sediment concentration distributions from a hypothetical dredging site and compared to results from a similar model using Stokes’ settling. The result shows that Stokes’ settling underestimates settling in the near-field and overestimates settling in the far-field plume. In summary, the model provides the ability to account for the rapid settling of larger particles in the suspended sediment near the dredging operations while simulating the slower settling and diffusive transport of smaller particles moving away from the dredging sites.

Radon‐222 as a Tracer for Nonaqueous Phase Liquid in the Vadose Zone: Experiments and Analytical Model

The potential use of the naturally occurring noble gas 222Rn as a tracer for vadose zone contamination by nonaqueous phase liquids (NAPLs) is studied experimentally and theoretically. n‐Dodecane was chosen as the model NAPL. In batch experiments containing unsaturated alluvial sand, a 2.9‐fold decrease of the steady‐state 222Rn activity in soil gas was measured as a consequence of the increase in the volumetric NAPL content from 0 to 0.074. A one‐dimensional analytical reactive transport model was developed that includes 222Rn production, gas‐phase diffusion, partitioning, and radioactive decay. Radon‐222 soil gas profiles were predicted for homogeneous and heterogeneous sandy profiles where NAPL contamination was restricted to selected depth layers. The resulting depth profiles document that the position of the NAPL has great influence on the 222Rn activity depth profile. An outdoor lysimeter experiment was performed using unsaturated alluvial sand contaminated by NAPL at depths from 1 to 1.2 m. In the lysimeter experiment, a spill of 2 L m−2 NAPL did not alter significantly the 222Rn profile, as predicted also by model calculations. We concluded that 222Rn can be used as a NAPL tracer in the vadose zone only at heavily polluted sites with uniform spatial 222Rn production.

Radon-222 as a Tracer for Nonaqueous Phase Liquid in the Vadose Zone: Experiments and Analytical Model

The potential use of the naturally occurring noble gas 222 Rn as a tracer for vadose zone contamination by nonaqueous phase liquids (NAPLs) is studied experimentally and theoretically. n -Dodecane was chosen as the model NAPL. In batch experiments containing unsaturated alluvial sand, a 2.9-fold decrease of the steady-state 222 Rn activity in soil gas was measured as a consequence of the increase in the volumetric NAPL content from 0 to 0.074. A one-dimensional analytical reactive transport model was developed that includes 222 Rn production, gas-phase diffusion, partitioning, and radioactive decay. Radon-222 soil gas profiles were predicted for homogeneous and heterogeneous sandy profiles where NAPL contamination was restricted to selected depth layers. The resulting depth profiles document that the position of the NAPL has great influence on the 222 Rn activity depth profile. An outdoor lysimeter experiment was performed using unsaturated alluvial sand contaminated by NAPL at depths from 1 to 1.2 m. In the lysimeter experiment, a spill of 2 L m −2 NAPL did not alter significantly the 222 Rn profile, as predicted also by model calculations. We concluded that 222 Rn can be used as a NAPL tracer in the vadose zone only at heavily polluted sites with uniform spatial 222 Rn production.

The effect of cathodic water on performance of a polymer electrolyte fuel cell

A simple analytical model of water transport in the polymer electrolyte fuel cell is developed. Nonlinear membrane resistance and voltage loss due to incomplete membrane humidification are calculated. Both values depend on parameter r, the ratio of mass transport coefficients of water in the membrane and in the backing layer. Simple equation for cell performance curve, which incorporates the effect of cathodic water is constructed. Depending of the value of r, the cell may operate in one of the two regimes. When r ≥ 1, incomplete membrane humidification simply reduces cell voltage; the limiting current density is determined by oxygen transport in the backing layer (oxygen-limiting regime). If r < 1, limiting current density is determined by membrane drying (water-limiting regime). In that case there exists optimal current density, which provides minimal membrane resistance. It is shown that membrane drying may lead to parasitic “in-plane” proton current.

Neutral pressure dynamics in the upper plenums in the DIII-D tokamak

We present the dependence of the neutral pressure rise on strike point geometry in the inner and outer plenums of the upper divertor in the DIII-D tokamak. The upper outer plenum pressure increases in the proximity of the plenum opening in a manner similar to previous reports of the lower outer plenum pressure. The inner plenum pressure measurement is modulated up to a factor of two by edge-localized modes (ELMs) particle flux, due to the small plenum volume and resulting short equilibration time constant. Reasonable agreement is obtained between the measured dependence of the outer plenum pressure on strike point position and simulations with an analytic neutral transport model, using the time-averaged (i.e. long compared with the ELM period) divertor profiles as inputs. The modelling of inner plenum pressure data with time-averaged profiles traces through the middle of the data range. In addition, modelling with two other sets of profiles, one averaged in the vicinity of ELMs and the other between ELMs, covers the upper and lower envelopes of the data. These new data sets represent an independent test and the agreement confirms that the basic physics in the model is responsible for the dependence of pressure rise on strike point geometry in the long mean free path limit.

Analytical model of solute transport by unsteady unsaturated gravitational infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils.

A unified analytical model for charge transport in Heterojunction Bipolar Transistors

A unified analytical charge transport model of HBTs, which is applicable for a wide variety of emitter-base (e–b) structures of HBTs, viz. abrupt or graded heterojunctions and p–n junctions displaced into wider or narrower band gap material is proposed. This is a thermionic field diffusion model, which considers thermionic emission and tunneling at the e–b heterojunction and diffusion in the quasi-neutral base regions. The Fermi-level splitting is considered while calculating the space charge region (SCR) recombination currents, which in turn is taken into account to calculate excess electron concentration at the edge of the depletion region in the base side of the e–b p–n junction. Closed form analytical expressions for the terminal currents are obtained, which has been implemented in a circuit simulator. The accuracy of the model is established by comparison with numerical simulation results and experimental data.

A Simulation-Assessment Modeling Approach for Analyzing Environmental Risks of Groundwater Contamination at Waste Landfill Sites

ABSTRACT An integrated simulation-assessment modeling approach for analyzing environmental risks of groundwater contamination is proposed in this paper. It incorporates an analytical groundwater solute transport model, an exposure dose model, and a fuzzy risk assessment model within a general framework. The transport model is used for predicting contaminant concentrations in subsurface, and the exposure dose model is used for calculating contaminant ingestion during the exposure period under given exposure pathways. Both models are solved through the Monte Carlo simulation technique to reflect the associated uncertainties. Based on consideration of fuzzy relationships between exposure doses and cancer risks, risk levels of different exposure doses for each contaminant can be calculated to form a fuzzy relation matrix. The overall risks can then be quantified through further fuzzy synthesizing operations. Thus, probabilistic quantification of different risk levels (possibilities) can be realized. Results of the case study indicate that environmental risks at the waste landfill site can be effectively analyzed through the developed methodology. They are useful for supporting the related risk-management and remediation decisions.

An Analytical Model for Electron Transport and Luminance in SrS:Cu,Ag ACTFEL Display Devices

An analytical model is developed to explain electron transport and luminance mechanisms in SrS:Cu,Ag ac thin film electroluminescent (ACTFEL) display devices. The model includes shallow and deep interface states, bulk traps, and impact excitation and ionization of activators. Mathematical expressions describing optoelectronic processes in the phosphor layer and interface states are written and numerical solutions for field, current and luminance are obtained. Results of calculations are compared with experimental data. The model is able to simulate the dominant features of the experimental luminance and current waveforms.

Rapid transport pathways for geothermal fluids in an active Great Basin fault zone

We present an analysis of fault hydraulic architecture, based on >700 spatially distributed ground and geothermal spring temperature measurements taken in an active fault zone. Geostatistical simulations were used to extrapolate the measured data over an 800 × 100 m area and develop a high-resolution image of temperatures in the fault. On the basis of the modeled temperatures, a simple analytical model of convective heat transport was used to infer a probability distribution function for hydraulic conductivities in a two-dimensional plane parallel to the land surface, and the partitioning of flow between flow paths of different conductivities was calculated as a fraction of the total flux. The analysis demonstrates the existence of spatially discrete, high-permeability flow paths within the predominantly lower-permeability fault materials. Although the existence of fast-flow paths in faults has been hypothesized for >10 yr, their prevalence and contribution to the total flow of fluid in a fault zone are debated. On the basis of our findings, we conclude that the flux transmitted by an individual fast-flow path is significantly greater than that of an average flow path, but the total flux transported in fast-flow paths is a negligible fraction of the total flux transmitted by the fault.

Analytical and Reynolds stress transport model results for periodically oscillated turbulent flows

Turbulent pipe flows in which the bulk velocity is oscillated harmonically about a mean level (U b = U bo [1 + γ cos ω t]) are considered from both analytical and turbulence modelling perspectives. The analytical development is concerned with the response of the phase-averaged turbulent kinetic energy (k = k0 + k 1 cos(ω t + ψ)) to imposed unsteadiness. An approximate quasi-steady analysis is used to obtain an asymptotic low frequency limit for the modulation of the turbulent kinetic energy, k 1/γ k 0 → 1.75. The analysis is extended to examine the response of ∂k/∂t, the unsteady rate-of-change term of the k-transport equation. A Reynolds stress transport model (RSTM) of turbulence is compared with data for steady and periodic pipe flows and, in most cases, satisfactory agreement is demonstrated. When the model is run for periodic flow over a wide range of frequency it is found that a “resonant” response in k 1/γ k 0 occurs at mid-frequencies; at higher frequencies the RSTM shows the turbulence to become “frozen” at a mean condition (k 1/γ k 0→0). In the final stage of the study the RSTM is used to explore departures from the quasi-steady variation of ∂k/∂t, in particular identifying the onset of frozen behaviour in the balance of the k-equation at higher frequencies.