Hydrogen Absorption Model Research Articles

Modeling heat and mass transfer in metal hydride hydrogen storage systems: Impact of operating parameters and reactor geometry

This work introduces a transient 2D axis-symmetrical model for hydrogen absorption in a cylindrical LaNi5 reactor employing finite volume method with a fully implicit Euler's time integration scheme, coupling equations for heat, mass, and momentum transport. The validated model is used to investigate the impacts of pressure, cooling fluid temperature, and variations in reactor geometry and size on temperature and reacted fraction profiles. The findings reveal that the charging pressure affects both peak temperature and reaction kinetics, whereas cooling fluid temperature predominantly impacts the absorption kinetics. A comparative analysis of two models, one incorporating Darcy's velocity and one without, demonstrates that while Darcy's law introduces numerical instability in the coupled equations, its impact on the model outcomes is negligible. The effect of changing the non-homogeneous Neumann to Dirichlet boundary condition is also demonstrated to anticipate the utilization of phase change materials (PCM) instead of the cooling fluid.

水素センシングおよび物質への吸蔵現象の理論的解釈

This report introduces hydrogen sensing with Membrane-type Surface stress Sensor (MSS) coated with two kinds of hydrogen adsorbent materials : Pd and PdCuSi. The equilibrium hydrogen pressure can be measured by detecting surface stress associated with a volume change of the material caused by hydrogen absorption. For Pd on MSS, it takes a long time for the hydrogen absorption reaction to reach saturation. However, it is possible to shorten the determination time by using the initial absorption rate as an index. As for PdCuSi on MSS, it needs a short time to reach saturation. We show that the relationship between the hydrogen concentration and the respective index of the absorption rate or the saturation value of the absorption can be well explained by using a 2-step reaction kinetic model for hydrogen absorption into bulk via adsorption on surface.

Spatially and temporally heterothermic kinetic model of hydrogen absorption and desorption in metals with heat transport

Numerical modelling of hydrogen transport is effective for designing and optimizing various energy systems, including hydrogen storage devices, fuel cells, and nuclear fusion reactors. In the present study, we propose and demonstrate a spatiotemporally heterothermic, autonomous kinetic model of hydrogen absorption and desorption in metals for precise simulations. Our bidirectional transport model comprises elementary mass transfer processes of surface adsorption and desorption, subsurface transport, and bulk diffusion. Also implemented are heat generation and conduction stemming from the absorption enthalpy, to determine the evolution of temperature distribution in the metal body, as well as the hydrogen concentration profile. Simulations by our transport model reproduce experimental hydrogen absorption and desorption curves for various temperature levels and metal scales with a single identical set of numerical equations and kinetic parameters, to thus verify the validity of the model.

Improved kinetic model of hydrogen absorption and desorption in titanium with subsurface transport

We improve our previous kinetic model of hydrogen transport in Ti [Y. Hamamoto et al., Nucl. Mater. Energy 23 (2020) 100751]. The model becomes applicable to both the directional processes of absorption and desorption. The limitation in the covered range of hydrogen molar fraction, previously up to 1 mol-H/mol-Ti, is dissolved. The numerical calculations based on the model with a single set of kinetic parameters closely reproduce a series of experimental hydrogen absorption and desorption data for various temperatures, and thus verify the validity of the model.

Heat and mass transfer crisis in a metal hydride reactor

We present a simple lumped mathematical model of hydrogen absorption in a metal hydride reactor with a constant flow rate (sub-critical regime) and use it to predict a heat and mass transfer crisis in the reactor. To verify the model we compare calculations with the experiment on hydrogen absorption in the reactor filled with 5 kg of LaNi4.8Mn0.3Fe0.1 alloy with a hydrogen flow rate of 60 stL/min. The analytical model predicts the heat and mass transfer crisis with good precision.

Kinetic model for hydrogen absorption in tungsten with coverage dependent surface mechanisms

In this work, a kinetic model is presented to describe hydrogen absorption and desorption from tungsten at different surface coverages. Activation energies for hydrogen absorption into the bulk and desorption from the surface of tungsten are modelled by functions that depend explicitly and continuously on the hydrogen surface coverage. A steady-state model is developed to derive these activation energies from experimental data. The newly developed coverage dependent activation energies are then implemented in the non steady-state rate-equation code MHIMS. Published experimental results on D uptake and retention of self-damaged tungsten exposed to 0.28 eV deuterium atoms at different temperatures ranging from 450 K to 1000 K can be successfully described with this approach. Finally, the steady-state model is applied to determine surface concentration, bulk concentration and migration depths of hydrogen isotopes in tungsten exposed to various atomic fluxes and temperatures ranging from milder conditions in laboratory experiments to divertor strike point conditions in tokamaks.

Hydrogen absorption performance of a novel cylindrical MH reactor with combined loop-type finned tube and cooling jacket heat exchanger

A novel cylindrical metal hydride (MH) reactor with loop-type finned tube and jacket heat exchanger was proposed in this work. This MH reactor is expected to possess high performance due to the enhanced heat transfer, compact structure and good gas tightness. A three-dimensional multi-physical model for hydrogen absorption was presented to investigate the evolutions of temperature and concentration in the MH bed, as well as the mean reaction rate of hydrogen absorption process. The effects of different fin configurations on the performance of the proposed MH reactor were also examined. It was indicated that the evolution curve of the mean reaction rate for the whole hydrogen absorption process can be divided into two stages. The reaction rate in the first stage is mainly dependent on the initial conditions (i.e., temperature and gas pressure) of MH bed, whereas the second stage is mainly influenced by the heat dissipation from MH bed to cooling fluid. For the proposed MH reactor, the total charging time for reaching 90% hydrogen saturation can be decreased by 56.8% and 81.9% as compared with that for cylindrical MH reactor with finned double U-shape tube heat exchanger and cylindrical MH reactor with finned single-tube heat exchanger, respectively. Also, it was found that the interlaced layout design of inner and outer fins can improve the uniformity of the temperature distribution inside the MH bed as compared with the parallel layout configuration. Besides, it was showed that increasing the number of fins with keeping the total fin volume constant, the absorption performance of the reactor can be improved.

Correction: Ono, S., et al. A Heterothermic Kinetic Model of Hydrogen Absorption in Metals with Subsurface Transport. Metals, 2019, 9(10), 1131

The authors wish to make the following corrections to this paper [...]

A Heterothermic Kinetic Model of Hydrogen Absorption in Metals with Subsurface Transport

A versatile numerical model for hydrogen absorption into metals was developed. Our model addresses the kinetics of surface adsorption, subsurface transport (which plays an important role for metals with active surfaces), and bulk diffusion processes. This model can allow researchers to perform simulations for various conditions, such as different material species, dimensions, structures, and operating conditions. Furthermore, our calculation scheme reflects the relationship between the temperature changes in metals caused by the heat of adsorption and absorption and the temperature-dependent kinetic parameters for simulation precision purposes. We demonstrated the numerical fitting of the experimental data for various Pd temperatures and sizes, with a single set of kinetic parameters, to determine the unknown kinetic constants. Using the developed model and determined kinetic constants, the transitions of the rate-determining steps on the conditions of metal-hydrogen systems are systematically analyzed. Conventionally, the temperature change of metals during hydrogen adsorption and absorption has not been a favorable phenomenon because it can cause errors when numerically estimating the hydrogen absorption rates. However, by our calculation scheme, the experimental data obtained under temperature changing conditions can be positively used for parameter fitting to efficiently and accurately determine the kinetic constants of the absorption process, even from a small number of experimental runs. In addition, we defined an effectiveness factor as the ratio between the actual absorption rate and the virtually calculated non-bulk-diffusion-controlled rate, to evaluate the quantitative influence of each individual transport process on the overall absorption process. Our model and calculation scheme may be a useful tool for designing high-performance hydrogen storage systems.

An experimental study of the wave effect in fuel equipment using hydrogen additives to diesel fuel

The object of research is the hydrodynamic wave effects in the fuel equipment of high pressure diesel engines. One of the most problematic phenomena when using hydrogen additives to diesel fuel is the change in the maximum fuel injection pressure, which leads to deterioration of fuel separation parameters. For research on the nature of hydraulic oscillations in the fuel equipment, an experimental booth has been created that allows the study of the wave effect with the use of small additives of hydrogen to the main fuel. In the development of an experimental stand, modern precision measuring instruments were used. According to the results of experimental studies, it is established that in the high pressure fuel line a characteristic «wave effect» of oscillations appears. This effect is caused by the landing of the pressure valve on the saddle in the fuel pump of high pressure, as well as the landing of the needle nozzle. The nature of the oscillation depends on factors such as the length of the pipeline between the pump and the nozzle, the maximum injection pressure of diesel fuel, the speed of propagation of the pressure wave. This speed, in turn, depends on the frequency of rotation of the crankshaft of the engine. The frequency of rotation of the fuel pump shaft is changed with the help of an inverted regulator and frequency meter of the drive motor. As a result, the fuel injection characteristics are obtained, which reflect the nature of the change in the pressure wave, depending on the presence of hydrogen additive. It is determined that the hydrogen additive in the amount of 0.1 % of the cycle fuel supply (by mass) leads to the suppression of wave oscillations and the shortening of the oscillation region by 12...20. The characteristics of absorption of hydrogen by diesel fuel are obtained. The amount of hydrogen additive depends on the pump rotation frequency, the injection pressure and the supply pressure of the additive. This kind of hydrogen consumption is explained by the time frame of the restriction of the absorption process, the difference in the minimum value of the «pressure wave» of the excess pressure of the additive. The resulting data can be used to confirm the mathematical model of hydrogen absorption when used as an additive to the fuel line.

Development of a hydrogen absorption model to determine absorption kinetics and diffusion coefficients by means of carrier gas hot extraction

Precise description of the hydrogen charged state of mechanical test specimens including the spatial and energetic hydrogen distribution is considered to be essential for understanding the mechanisms of hydrogen embrittlement. Here, a simple hydrogen absorption model for hydrogen charging in liquids was developed for cylindrical specimens. The absorption model is based on an approximate solution of Fick's laws of diffusion and allows determining hydrogen diffusion coefficients and surface concentrations by measuring the total amount of absorbed hydrogen as a function of the cylinder height. Total hydrogen contents after charging of several cylinders consisting of quenched and tempered steel 42CrMo4 (1.7225) were measured by carrier gas hot extraction and the applicability of the absorption model on the measurement was demonstrated by mathematical fitting. The diffusion coefficient for this material was determined to be D=3.810−11m2/s and the hydrogens surface concentration increases with increasing charging time.

Numerical investigation of hydrogen absorption in a stackable metal hydride reactor utilizing compartmentalization

In this paper, a three-dimensional model for hydrogen absorption in a metal alloy has been developed, validated against the experimental data in the literature, and then applied to a novel design for a hydrogen storage unit. The proposed design is similar to the fuel cell stack, but here the Membrane Electrode Assembly (MEA) has been replaced by a metal hydride (MH) reactor placed between the flow-field plates. These are stacked together to achieve the required amount of hydrogen storage. The flow-field plates have channels engraved on one side for hydrogen supply and on the other, for coolant/heating medium. It is known that the effectiveness of a hydrogen storage unit is directly related to its heat transfer area, and therefore, the choice of its geometry is very important. The larger the size, the more the resistance to heat transfer. Although, the internal tubular heat exchangers have proven to be effective in heat transfer, they pose severe challenges such as cooling/heating medium leakage due to tube erosion, stresses generated, etc. and they displace the active metal hydride from the tank. The present stacked MH reactor configuration helps to overcome these challenges by stacking small MH reactors together and there is no chance of the cooling/heating medium leaking into the metal hydride. Numerical simulations were performed to investigate the effect of coolant flow rate and percentage of flow-field plate rib area exposed to the MH reactor on temperature evolution and the amount of hydrogen stored. Further, a detailed study was carried out to understand the effect of compartmentalization of the MH reactor on temperature distribution. The results revealed that compartmentalization substantially helps to uniformly distribute the temperature in the metal bed, which is very important to maintain uniform utilization of the metal powder. Consequently, the uniform metal powder density for repeated absorption-desorption cycles without significant loss of its hydrogen storage capabilities.

Development of a kinetic model of hydrogen absorption and desorption in magnesium and analysis of the rate-determining step

Mg is promising as a new light-weight and low-cost hydrogen-storage material. We construct a numerical model to represent the hydrogen dynamics on Mg, comprising dissociative adsorption, desorption, bulk diffusion, and chemical reaction. Our calculation shows a good agreement with experimental data for hydrogen absorption and desorption on Mg. Our model clarifies the evolution of the rate-determining processes as absorption and desorption proceed. Furthermore, we investigate the optimal condition and materials design for efficient hydrogen storage in Mg. By properly understanding the rate-determining processes using our model, one can determine the design principle for high-performance hydrogen-storage systems.

Numerical modeling of heat transfer during hydrogen absorption in thin double-layered annular ZrCo beds

Abstract In this work a three-dimensional (3D) hydrogen absorption model was proposed to study the heat transfer behavior in thin double-layered annular ZrCo beds. Numerical simulations were performed to investigate the effects of conversion layer thickness, thermal conductivity, cooling medium and its flow velocity on the efficiency of heat transfer. Results reveal that decreasing the layer thickness and improving the thermal conductivity enhance the ability of heat transfer. Compared with nitrogen and helium, water appears to be a better medium for cooling. In order to achieve the best efficiency of heat transfer, the flow velocity needs to be maximized.

Numerical comparison of heat-fin- and metal-foam-based hydrogen storage beds during hydrogen charging process

We numerically studied the effects of additional components for internal heat transfer enhancement—that is, heat fins and metal foams—on the hydrogen charging performance. First, we applied a three-dimensional transient hydrogen absorption model developed in our previous works to two different experimental MHBs: one with heat fins and the other with metal foam. The simulation results were then compared with the experimental data measured during the hydrogen charging processes. The model predictions were found to be in good agreement with the experimental data in terms of the bed temperature evolution and hydrogen charging time. In addition, a parametric study was conducted on various MHBs with heat fins or metal foams that were designed to contain the same amount of ZrCo powder for the sake of comparison. The detailed analysis of the hydrogen absorption behavior with different MHB designs clearly demonstrated that superior MHB design should exhibit a higher effective conductivity in the metal powder region and lower overall thermal mass; these two advanced features can be achieved by using a metal foam with optimum porosity.

A numerical comparison of hydrogen absorption behaviors of uranium and zirconium cobalt-based metal hydride beds

In this paper, the hydrogen loading capability of uranium and zirconium cobalt (ZrCo) is numerically compared and evaluated, in order to determine optimum getter materials for the storage of tritium. A three-dimensional hydrogen absorption model is applied to two identically designed cylindrical beds (one with uranium and the other with ZrCo) and hydrogen absorption simulations are then conducted for comparison. The simulation results show different hydrogen loading characteristics between the two beds, with that containing uranium exhibiting superior hydrogen loading performance and easier thermal management capability. This is owing to a lower hydrogen equilibrium pressure for absorption, faster absorption kinetics, lower thermal mass, and a higher thermal conductivity of uranium compared to ZrCo. Detailed analysis of hydrogen absorption behaviors with uranium and ZrCo assists in determining and optimizing proper bed material/design and operating conditions for the storage and delivery system in the International Thermonuclear Experimental Reactor.

삼중수소 저장을 위한 ZrCo 저장재에서의 수소 흡장에 대한 수치해석적 연구 (I)

In this paper, a three-dimensional hydrogen absorption model is applied to a thin double-layered annulus ZrCo hydride bed and validated against the temperature evolution data measured by Kang et al. The present model reasonably captures the bed temperature evolution behavior and the 99% hydrogen charging time. The equilibrium pressure expression for hydrogen absorption on ZrCo is derived as a function of temperature and the H/M atomic ratio based on the pressure-composition isotherm data given by Konishi et al. In addition, this present model provides multi-dimensional contours such as temperature and H/M atomic ratio in the thin doublelayered annulus metal hydride region. This numerical study provides fundamental understanding during hydrogen absorption process and indicates that efficient design of the metal hydride bed is critical to achieve rapid hydrogen charging performance. The present three-dimensional hydrogen absorption model is a useful tool for the optimization of bed design and operating conditions.

A numerical investigation of hydrogen absorption phenomena in thin double-layered annulus ZrCo beds

In this paper, a three-dimensional (3-D) hydrogen absorption model is applied to a thin double-layered annulus ZrCo hydride bed and validated against the temperature evolution data measured by Kang et al. [1]. In their experiment, the monitored hydrogen tank pressure decreased with time due to continuous hydrogen supply to a ZrCo hydride bed; hence, the effect of decreasing hydrogen feed pressure is considered for simulations. The equilibrium pressure expression for hydrogen absorption on ZrCo is derived as a function of temperature and the H/M atomic ratio based on the pressure–composition isotherm data given by Konishi et al. [2]. In general, the calculated results agreed well with the temperature evolution data, and the hydrogen charging time for 99% absorption was accurately captured by the model. In addition, detailed simulation results, including multidimensional contours, clearly elucidate the hydrogen absorption behavior of the thin double-layered ZrCo MHB.

Orbital and spin phase-resolved spectroscopy of the intermediate polar EX Hya using XMM-Newton data

We present the orbital phase-resolved spectra of an intermediate polar, EX Hya, together with the spin phase-resolved spectra during two different epochs using the X-ray Multi-Mirror Mission (XMM–Newton), European Photon Imaging Camera (pn instrument). We find that the source at the two epochs has the same X-ray luminosity of ∼6.5 × 10 31 erg s −1 . We detect spectral variations between the 2000 and 2003 observations of the source. We fitted the spectrum using a neutral hydrogen absorption model with or without covering fraction together with Gaussians for emission lines, two collisional equilibrium plasma emission models (MEKAL) and a cooling-flow plasma emission model (VMCFLOW). We find that two of the three emission components (kT = 0.6–0.8 and 1.3–1.7 keV) fitted by the MEKAL models are almost constant over the spin and orbital phases and also over the two different epochs with the normalization varying directly proportional to the flux when the data are folded according to the orbital and spin phase indicating that the slight variation may be due to occultation. The emission modelled by the VMCFLOW changes over the spin and orbital phases and the 2000 and 2003 observations reveal two different ranges of temperatures (3–33 and 8–61 keV, respectively) that model the shock zone in the accretion column(s). The ratios of the spin maximum to minimum and the orbital maximum to minimum spectra along with the increase in the plasma temperatures indicate that the spectrum gets harder in the minimum phases of both orbital and spin periods. In the 2003 observation, a 6.4 keV fluorescent Fe emission line is present at the orbital minima in a range of phases from 0.9 to 1.3 and it is absent otherwise. This indicates that there is reflection from the disc most likely from a large bulge at the accretion impact zone.

A model of hydrogen absorption by metals

The influence of the electron spectrum of transition metals on the hydrogen absorption process is considered. An absorption model is proposed where electrons, followed by protons, from adsorbed molecules or atoms of hydrogen transit into the metal. In terms of this model, the driving force of the absorption process ΔX is equal to the difference of the total electron energies in a hydrogen atom and in a metal at the Fermi level: ΔX = E H − (E F + A work). The equilibrium state in the absorption process corresponds to the equation 13.53 = E F + A work, which makes it possible to find the Fermi energy of transition metals and the valence of hydrogen absorbing metals, to define the molecular formula of hydrides, and to calculate the maximum hydrogen content in hydride phases. The hydrogen content in the composition of hydrides is shown to decrease in approaching the middle of the transition-metal rows. In groups, on the contrary, the hydrogen content grows as the atomic weight of metals increases. A good agreement of calculated and experimental compositions of hydride phases is found for the transition metals whose d band is less than half-filled with electrons.