Coupled influence of non-ideal diffusion and multilayer asymmetric porous supports on Sieverts law pressure exponent for hydrogen permeation in composite Pd-based membranes

The behaviour of the pressure exponent in the Sieverts-type empirical law is evaluated for hydrogen permeation through Pd-based membranes under the influence of non-ideal internal diffusion and transport in an asymmetric multilayer porous support. The results show that the non-ideal diffusion causes the pressure exponent to be non-monotone within the temperature range investigated (300–500 °C), showing a minimum point indicating the passage from slower internal diffusion to slower transport in support. Additionally, a detailed analysis shows that the maximum transmembrane pressure difference (in terms of maximum feed pressure with constant permeate pressure) is the only operating parameter affecting the uncertainty degree by which the pressure exponent is evaluated. This analysis also shows that the Sieverts-type empirical law can be fully used in the presence of supports. This suggests that an overall transport mechanism resulting from a combination in series/parallel of different elementary mechanisms obeying this law can be also described by the same type of law with a different value of pressure exponent and permeance.     

Hydrogen permeation dynamics across a palladium membrane in a varying pressure environment

Permeation dynamic of hydrogen through a palladium (Pd) membrane in an environment of varying pressure is investigated and analyzed experimentally. By monitoring the instantaneous pressure and mass transfer rate of hydrogen in the conducted system, the present study provides a comprehensive and precise measurement on the permeance of the membrane. It is found that a threshold of pressure difference between the both sides of the membrane for hydrogen permeation is exhibited. That is, when the driving force of the mass transfer is below the minimum pressure difference, hydrogen permeation will not occur. Accordingly, a modified equation accounting for the hydrogen permeation flux through the membrane is suggested. As a whole, the hydrogen permeation flux versus the pressure difference is characterized by a linear relationship, regardless of what the pressure exponent is. Nevertheless, the optimal pressure exponent is located between 0.5 and 0.7. A dimensionless time, the permeation number, is derived to describe the permeation process. The characteristic time of hydrogen permeation depends on the pressure exponent. The experiments reveal that the permeation number is around 7–13 for the hydrogen permeation flux in the system reaching the quasi-steady state.     

Transient dynamic of hydrogen permeation through a palladium membrane

Transient dynamic of hydrogen permeation through a palladium membrane is studied in the present study. Three different pressure differences between the two sides of the membrane are considered; they are 3, 5 and 8 atm. The experimental results indicate that the variation in the hydrogen permeation process is notable at the selected pressure differences. When the pressure difference is relatively low (i.e. 3 atm), the hydrogen permeation process proceeds from a time-lag period, then to a concave up period and eventually to a concave down period. Therefore, the transient hydrogen permeation is characterized by a three-stage mass transfer process. When the pressure difference is increased to 5 atm, the time-lag period disappears, thereby evolving the three-stage mass transfer process into a two-stage one. However, the concave up period withers significantly. Once the pressure difference is as high as 8 atm, the transient hydrogen permeation is completely characterized by a concave down curve, yielding a single-stage mass transfer process. A quasi-steady state of hydrogen permeation is defined to evaluate the period of the transient mass transfer process. It suggests that, within the investigated conditions of operation, the time required for hydrogen permeation to reach the steady value is around or over 1 h. For the low pressure difference cases, the transient period is especially long, resulting from the time-lag characteristic. Once the hydrogen permeation is in the steady state, over 80% of hydrogen can be recovered from the membrane.     

Effect of sweep gas on hydrogen permeation of supported Pd membranes: Experimental and modeling

Membrane reactor processes are being increasingly proposed as an attractive solution for pure hydrogen production due to the possibility to integrate production and separation inside a single reactor vessel. High hydrogen purity can be obtained through dense metallic membranes, especially palladium and its alloys, which are highly selective to hydrogen. The use of thin membranes seems to be a good industrial solution in order to increase the hydrogen flux while reducing the cost of materials. Typically, the diffusion through the membrane layer is the rate-limiting step and the hydrogen permeation through the membrane can be described by the Sieverts’ law but, when the membrane becomes thinner, the diffusion through the membrane bulk becomes less determinant and other mass transfer limitations might limit the permeation rate. Another way to increase the hydrogen flux at a given feed pressure, is to increase the driving force of the process by feeding a sweep gas in the permeate side. This effect can however be significantly reduced if mass transfer limitations in the permeate side exist. The aim of this work is to study the mass transfer limitation that occurs in the permeate side in presence of sweep gas. A complete model for the hydrogen permeation through PdAg membranes has been developed, adding the effects of concentration polarization in retentate and permeate side and the presence of the porous support using the dusty gas model equation, which combines Knudsen diffusion, viscous flow and binary diffusion. By studying the influence of the sweep gas it has been observed that the reduction of the driving force is due to the stagnant sweep gas in the support pores while the concentration polarization in the permeate is negligible.     

Hydrogen transport in solution-treated and pre-strained austenitic stainless steels and its role in hydrogen-enhanced fatigue crack growth

Hydrogen solubility and diffusion in Type 304, 316L and 310S austenitic stainless steels exposed to high-pressure hydrogen gas has been investigated. The effects of absorbed hydrogen and strain-induced martensite on fatigue crack growth behaviour of the former two steels have also been measured. In the pressure range 10–84 MPa, the hydrogen permeation of the stainless steels could be successfully quantified using Sieverts' law modified by using hydrogen fugacity and Fick's law. For the austenitic stainless steels, hydrogen diffusivity was enhanced with an increase in strain-induced martensite. The introduction of dislocation and other lattice defects by pre-straining increased the hydrogen concentration of the austenite, without affecting diffusivity. It has been shown that the coupled effect of strain-induced martensite and exposure to hydrogen increased the growth rate of fatigue cracks.     

Modeling of transient hydrogen permeation process across a palladium membrane

Transient mass transfer processes of hydrogen permeating through a Pd membrane are modeled to aid in predicting the hydrogen transport behavior. The model is established in terms of the quasi-steady time and the steady permeation rate. Meanwhile, four important parameters are considered; they are the permeation lag time, the initial permeation rate, the concave up period and the concave down period. A unit step function is embedded in the model to account for the effect of the hydrogen permeation lag at a lower pressure difference. Corresponding to the lower, the moderate and the higher pressure differences (i.e. 3, 5 and 8 atm), though the hydrogen permeation undergoes a three-stage, a two-stage and a one-stage processes, respectively, these processes can be predicted well by an arc tangential function. By introducing an adjusting parameter in the arc tangential function, there exists an optimal value of the adjusting parameter when the pressure difference is lower. In regard to the moderate and higher pressure differences, the predictions agree with experiments well if the adjusting parameter is sufficiently large. Physically, the unit step function is used to account for the controlling mechanisms of hydrogen diffusion toward the membrane and the spillover of the hydrogen across the membrane. The initial jump parameter represents the rapid response of the initial hydrogen permeation. The adjusting parameter can be used to describe the relative importance of the concave up and the concave down periods.     

Enhancement of hydrogen production in a novel fluidized-bed membrane reactor for naphtha reforming

In this work, a novel fluidized-bed membrane reactor (FBMR) for naphtha reforming in the presence of catalyst deactivation has been proposed. In this reactor configuration, a fluidized-bed reactor with perm-selective Pd–Ag (23 wt% Ag) wall to hydrogen has been used. The reactants are flowing through the tube side which is a fluidized-bed membrane reactor while hydrogen is flowing through the shell side which contains carrier gas. Hydrogen penetrates from fluidized-bed side into the carrier gas due to the hydrogen partial pressure driving force. Hydrogen permeation through membrane leads to shift the reaction toward the product according to the thermodynamic equilibrium. This membrane-assisted fluidized-bed reactor configuration solves some drawbacks of conventional naphtha reforming reactors such as pressure drop, internal mass transfer limitations and radial gradient of concentration and temperature. In FBMR the hydrogen which is produced in shell side is a valuable gas and can be used for different purposes. The two-phase theory of fluidization is used to model and simulate the FBMR. Industrial packed bed reactor (PBR) for naphtha reforming is used as a basis for comparison. This comparison shows enhancement in the yield of aromatic production in FBMR for naphtha reforming. Although using FBMR reduces hydrogen mole fraction in reaction side and enhances catalyst deactivation due to coking, but this effect can be compensated using advantages of FBMR such as suitable hydrogen to hydrocarbon molar ratio, lowering deactivation rate due to lower temperature, control of permeation rate by adjusting shell side pressure and shifting the equilibrium reactions. The impacts of hydrogen to hydrocarbon molar ratio, pressure, membrane thickness, flow rate and temperature have been investigated in this work.     

Numerical characterization on concentration polarization of hydrogen permeation in a Pd-based membrane tube

Sieverts’ law has been extensively employed to evaluate hydrogen permeation rate across a hydrogen-permeable membrane based on the concept of continuous stirred tank reactor (CSTR). However, when the hydrogen permeation rate is high to a certain extent, concentration polarization will appear in a membrane tube which results in the deviation of hydrogen permeation rate from Sieverts’ law. Under such a situation, the nature of mass transfer in a membrane tube is characterized by plug flow reactor (PFR) rather than CSTR. To figure out the feasibility of Sieverts’ law, a two-dimensional numerical method is developed to simulate the phenomena of concentration polarization for hydrogen permeation in a Pd-based membrane tube. Four important parameters affecting hydrogen permeation are taken into account; they include the pressure difference, H₂ molar fraction in the influence, Reynolds number and membrane permeance. The predictions indicate that increasing pressure difference or membrane permeance facilitates H₂ permeation rate; concentration polarization is thus triggered. Alternatively, when Reynolds number or H₂ molar fraction decreases along with a higher permeance, the deviation of PFR from CSTR grows, even though H₂ permeation rate declines. From the obtained results, it is concluded that the H₂ permeation rate can be predicted by Sieverts’ law if the H₂ permeation ratio is no larger than 30%.     

Momentum and heat transfer in the adsorbent of a waste-heat adsorption cooling system

This paper presents a numerical and experimental analysis of the coupled heat and mass transfer mechanisms in the adsorbent of a waste-heat adsorption cooling system. A new three-dimensional non-equilibrium model is developed and used to investigate the simultaneous transport of heat and mass. In the model, a linear driving force equation is used to account for mass-transfer resistance within the pallets (internal resistance), while Darcy's law is introduced to describe the adsorbate flows in the interparticle voids (external resistance). An experiment has been conducted to validate this model. The temperature, pressure, velocity and water uptake fields of the bed and their effects on system performance are discussed.     

Analysis of hydrogen diffusion coefficient during hydrogen permeation through pure niobium

The hydrogen solubility and the hydrogen permeability of pure niobium at high temperature are investigated in order to analyze the hydrogen diffusion coefficient during the hydrogen permeation. It is shown that the hydrogen dissolution reaction into niobium metal does not follow the Sieverts' law at the practical hydrogen permeation pressures. The hydrogen diffusion coefficient during the hydrogen permeation through pure niobium at high temperature is evaluated from the linear relationship between the normalized hydrogen flux, J·d, and the hydrogen concentration difference, ΔC. It is found that the hydrogen diffusion coefficient under the practical condition is much lower than the reported values measured for dilute hydrogen solid solutions. Surprisingly, the hydrogen diffusion is found to be faster in Pd–Ag alloy with fcc crystal structure than in pure niobium with bcc crystal structure at 773 K during the hydrogen permeation.     

Surface coating with a high resistance to hydrogen entry under high-pressure hydrogen-gas environment

Development of a surface coating with high resistance to hydrogen entry under a high-pressure hydrogen-gas environment is presented. Two aluminum-based coatings were developed on the basis of preliminary tests: two-layer (alumina/Fe–Al) and three-layer (alumina/aluminum/Fe–Al) coatings, deposited onto cylindrical and pipe (Type 304 austenitic stainless steel) surfaces by immersion into a specially blended molten aluminum alloy. The coated specimens were exposed to hydrogen gas at 10–100 MPa at 270 °C for 200 h. Specimen hydrogen content was measured by thermal desorption analysis; hydrogen distributions were analyzed by secondary ion mass spectroscopy. Both coatings showed high hydrogen-entry resistance at 10 MPa. However, resistance of the two-layer coating clearly decreased with an increase in pressure. In contrast, the three-layer coating showed excellent hydrogen-entry resistance at a wide pressure range (10–100 MPa), achieved by the combined effect of alumina, aluminum, and Fe–Al layers.     

Finite element-based simulation of a metal hydride-based hydrogen storage tank

In this paper, a novel 3D flexible tool for simulation of metal hydrides-based (LaNi₅) hydrogen storage tanks is presented. The model is Finite Element-Based and considers coupled heat and mass transfer resistance through a non-uniform pressure and temperature metal hydride reactor. The governing equations were implemented and solved using the COMSOL Multiphysics simulation environment. A cylindrical reactor with different cooling system designs was simulated. The shortest reactor fill time (15 min) was obtained for a cooling design configuration consisting of twelve inner cooling tubes and an external cooling jacket. Additional simulations demonstrated that an increase of the hydride thermal conductivity can further improve the reactor dynamic performance, provided that the absorbent bed is sufficiently permeable to hydrogen.     

Thermochemical hydrogen production with a copper–chlorine cycle,II: Flashing and drying of aqueous cupric chloride

This paper examines the evaporative drying of aqueous cupric chloride (CuCl₂) droplets in the copper–chlorine (Cu–Cl) thermochemical cycle of hydrogen production. An aqueous CuCl₂ stream exiting from an electrochemical cell is preheated to 150 °C, before entering a flash evaporator to produce solid CuCl₂(s). New innovations of heat recovery aim to develop alternatives that reduce costs and improve efficiency of the evaporation process for CuCl₂ particle production. The liquid phase flashes due to a sudden pressure drop. Analytical solutions are developed for the cupric chloride spraying and drying processes, including empirical correlations for heat and mass transfer, based on a single droplet of aqueous CuCl₂ solution. The study shows that considerable drying can be accomplished through differentials of humidity alone. It also shows that benefits of flashing the solution to enhance drying are relatively minor, compared to the rate of evaporative drying in the spray drying process.     

Hydrogen permeation and recovery from H2–N2 gas mixtures by Pd membranes with high permeance

Hydrogen separation from H₂–N₂ gas mixtures by means of high-permeance Pd membranes is an appropriate route to gain pure hydrogen for fuel cell applications. To figure out the mass transfer phenomena of H₂ in membrane tubes, H₂ permeation and recovery characteristics of two high-permeance Pd membranes are investigated. Four important factors influencing H₂ permeation, namely, the H₂ pressure difference, H₂ concentration, the flow rate at the exit of the retentate side, and membrane temperature, are taken into account. The experimental results suggest that decreasing H₂ concentration, flow rate, and temperature reduce the permeances of the membranes and H₂ recovery, even though the H₂ pressure difference is identical. The dimensionless permeance, a permeance ratio between H₂–N₂ gas mixture and pure H₂ as feed gases, is used to evaluate the extent of concentration polarization. Within the investigated ranges of the four factors, the dimensionless permeances of the two membranes are in the ranges of 0.022–0.206 and 0.042–0.359, respectively, revealing that the concentration polarization diminishes the permeance of the membranes down to the level within two orders of magnitude. Nevertheless, over 46% of H₂ is recovered.     

Theory,modelling and performance measurement of unitised regenerative fuel cells

Unitised Regenerative Fuel Cells (URFCs) based on Proton Exchange Membrane (PEM) technology provide a promising opportunity for reducing the cost of the hydrogen subsystem used in renewable-energy hydrogen systems for remote area power supply. A general theoretical relationship between cell potential and current density of a single-cell URFC operating in both fuel-cell and electrolyser modes is derived using the Butler–Volmer equation for both oxygen and hydrogen electrodes, and accounting for membrane resistance and mass transport losses. Modifying the standard Butler–Volmer equation with a denominator term containing two additional ‘saturation’ parameters to reflect mass transport constraints generates voltage–current curves that are much closer to experimentally obtained polarisation curves in both modes. The theoretical relationship is used to construct a computer model based on Excel and Visual Basic to generate voltage–current curves in both electrolyser and fuel cell modes for URFCs with a range of membrane electrode assembly characteristics. Hence the influence of key factors such as exchange current densities and charge transfer coefficients on cell performance is analysed. Experimental results for voltage–current curves from singe-cell URFCs with a number of different oxygen-side catalysts are reported, and compared to the theoretically modelled curves. Generally values have been found for exchange current densities, charge transfer coefficients, and saturation current densities that give a close fit between the empirical and theoretically generated curves. The values found conform well to expectations based on the catalyst loadings, in partial confirmation of the validity of the modelling approach. The model thus promises to be a useful tool in identifying electrodes with materials and structures, together with optimal catalyst types and loadings that will improve URFC performance.     

Impact of vacuum operation on hydrogen permeation through a palladium membrane tube

Palladium (Pd) membranes are characterized by their high permselectivity to hydrogen and easy operation, and are promising devises for separating hydrogen from hydrogen-rich gases. The membranes are normally operated with atmospheric pressure at the permeate side. Instead of this common operation, hydrogen permeation through a Pd membrane under vacuum operation at the permeate side is investigated and compared with that under normal operation. In this study, two membrane operating temperatures (320 and 380 °C), four H₂ partial pressure differences (2, 3, 4, and 5 atm) across the membrane, and four feed gases are considered. The results suggest that the vacuum operation can efficiently intensify the H₂ permeation rate. The improvement in H₂ permeation rate due to the vacuum operation can be increased up to 136%. The positive effect of the vacuum operation is especially pronounced when the gas mixtures are used as the feed gases, stemming from the effective attenuation of the concentration polarization. An increase in membrane temperature raises the H₂ permeation rate, but its influence in enhancing the H₂ permeation rate with the vacuum operation is not as significant as that without the vacuum one. It is found that the retardation effect of impurities on the mass transfer is always ranked as CO > CO₂ > N₂, regardless of with/without vacuum operation.     

Fixed bed membrane reactors for WGSR-based hydrogen production: Optimisation of modelling approaches and reactor performance

The production of high-purity hydrogen using the water–gas-shift reaction in both conventional fixed bed reactor and hydrogen perm-selective membrane reactor at low to medium scale is studied in this work by developing and comparing models with different complexity levels. A two-dimensional rigorous reactor model considering radial and axial variations of properties (including bed porosity), setting mass, energy and momentum differential balances, and nesting a rigorous model for mass transfer within the porous catalyst was considered as reference for comparison. Different simplifications of this model for taking into account mass-transfer effects within the catalyst pellet (Thiele modulus, evaluation of apparent kinetic constants, empirical correlation for effectiveness factors or just neglecting these effects) were tested, being observed that these effects are not negligible and that the first two approaches are accurate enough for taking into account mass transfer within catalyst pellets. Regarding to the reactor model, it was observed that one-dimensional models are not adequate, especially for the membrane reactor. Analogously, neglecting the momentum balances in the reactor (as made is most simulations reported in the literature) leads to important misspredictions in the behaviour of the membrane reactor performance. Finally, the influence of the main operation parameters (inlet temperature, pressure, space velocity, etc.) was studied using the detailed reactor model, concluding that space velocity and pressure are the most important parameters affecting reactor performance for membrane reactors.     

Performance investigation of a two-stage sorption hydrogen compressor

Metal hydrides (MH) are widely investigated for several thermodynamic applications; sorption hydrogen compressor (SHC) is one among them. In this study, the thermodynamic performance and heat – mass transfer behaviour of a two-stage sorption hydrogen compressor (TSSHC) are investigated with the employment of La_0·9Ce_0·1Ni₅ and MmNi_4.8Al_0.2 alloys in series. The hydrogen supply and the discharge temperatures are chosen as 20 °C and 80 °C, respectively. The thermodynamic performance data, i.e. compressor work and efficiency, are evaluated using the experimentally measured pressure-concentration-isotherm (PCI) and thermodynamic properties. In contrast, the heat and mass transfer behaviour is predicted by solving governing equations through the finite volume method (FVM). The numerical model is validated with experimental PCIs, and the results are in close agreement. The predicted cycle time is 75 min, comprising hydrogen supply, sensible heating and cooling, and hydrogen delivery. The TSSHC possessed a compression ratio of 9.5 and a cycle efficiency of 11.4% in which the hydrogen supply pressure is 9 bar using 0.5 kg of each alloy. Later, the influence of mass transfer on overall compressor work, heat input and efficiency is also presented.     

Current density effect on hydrogen permeation in PEM water electrolyzers

Hydrogen permeation is an important phenomena for PEM water electrolyzers, due to several reasons as safety issues and efficiency loss. The present contribution deals with the measurement of hydrogen volume fraction within the anode product gas during PEM water electrolysis for different temperatures and cathode pressures. High cathode pressures lead to high anode hydrogen volume fractions close to the lower explosion limit of hydrogen in oxygen, which are caused by increased hydrogen permeation. It is shown that the results of the hydrogen volume fraction measurements can be easily converted into hydrogen permeation rates. Additionally, the experimental obtained permeation data indicate that hydrogen permeation increases linear with increasing current density. The impact of current density on the hydrogen permeation is very strong in comparison to the effects of temperature and pressure e.g. a current density increase of 1 A/cm² can causes a permeation increase comparable to a cathode pressure increase of 20 bar. In the second part of this contribution different theories to explain this strong dependence on current density are discussed. The most probable explanation is that due to mass transfer limitations a supersaturation of dissolved gas within the catalyst ionomer film arises that causes the investigated increase in permeation.     

Hydrogen permeation properties of Pd-coated V89.8Cr10Y0.2 alloy membrane using WGS reaction gases

The influence of co-existing gases on the hydrogen permeation was studied through a Pd-coated V_89.8Cr₁₀Y_0.2 alloy membrane. Preliminary hydrogen permeation experiments have been confirmed that hydrogen flux was 6.26 ml/min/cm² for a Pd-coated V_89.8Cr₁₀Y_0.2 alloy membrane (thick: 0.5 mm) using pure hydrogen as feed gas. Also, the hydrogen permeation flux decreased with decrease of hydrogen partial pressure at constant pressure when H₂/CO₂ and H₂/CO₂/H₂S mixture applied as feed gas respectively and permeation fluxes were satisfied with Sievert's law in different feed conditions. It was found from XRD and SEM results after permeation test that the Pd-coated V_89.8Cr₁₀Y_0.2 alloy membrane had good stability and durability for various mixture feeding conditions.