Rate-controlling Process Research Articles

Model development and validation of hydrogen transport through supported palladium membranes

Abstract Porous matrices are often used to provide structural support to thin Pd-based metallic membranes in H2 separation applications. Optimizing such composite membranes requires detailed understanding of all possible rate-controlling processes including surface and bulk processes in the metal and diffusion of gases through the porous media. In the work described in this paper, we fabricate a composite membrane by depositing a thin (∼5–6 μm) Pd film on a porous α-Al2O3 tube and then measure the H2 permeance of this composite membrane over a range of operating conditions. The rate-controlling processes for the H2 permeation are evaluated with a computational model which combines a detailed thermo-kinetic Pd–H2 interaction model and a porous media transport model. The Pd–H2 thermo-kinetic model is validated against literature data, and the porous media transport model is independently calibrated using experimental measurements. The combined composite membrane model gives good agreement with experiments over a large range of temperatures (250–450 °C) and H2 partial pressures (100–385 kPa). This validated model is then used to analyze the importance of design parameters such as Pd thickness and support micro-structure on H2 flux through the membrane. These parametric studies will also aid in assessing trade-offs between membrane structural robustness and overall performance.

Experimental and Modeling Study of the Transport of Chromium Acetate Solutions Through Carbonate Rocks

Summary Gelled polymer systems are applied to oil reservoirs to reduce water production and to increase sweep efficiencies in recovery processes. A common system consists of hydrolyzed polyacrylamide with a chromium (III) crosslinker. Transport of these chemicals through the reservoir rock is essential for a successful treatment. In carbonate reservoirs, dissolution of the carbonate raises the pH of the gelant to levels where chromium precipitates, robbing the gelant of crosslinker. The transport of chromium acetate solutions through dolomite rock material was studied by injecting various solutions through short cores and measuring Cr, Mg, and Ca concentrations and pH in the effluent. Chromium retention in the cores caused by precipitation was a rate-controlled process. A mathematical model was developed that described convection, dispersion, kinetic reactions of carbonate dissolution and chromium precipitation, and chemical equilibrium for reactions between aqueous components. Experimental data from this work and taken from literature were simulated by the model. One rate equation with one set of parameters described the steady-state values of chromium concentration exiting the cores after the breakthrough of the injected solutions.

Optimization of Secondary-Air Addition in a Continuous One-Dimensional Spray Combustor

A framework is established for optimal control of continuous combustors using the sequential linear quadratic algorithm. An analysis is presented for liquid-fuel vaporization and burning in a continuous combustor with secondary-air addition at downstream locations. A steady one-dimensional flow is portrayed and a system of nonlinear ordinary differential equations is established. Three combustion models are presented with different rate-controlling processes: vaporization, vaporization-mixing, and vaporization-mixing-reaction. The models have a sufficient number of characteristic times and sufficient nonlinearity to provide a challenge to an optimization procedure. The proposed method yields an optimal distribution of secondary-air addition.

Kinetics of reactive diffusion between Ta and Cu–9.3Sn–0.3Ti alloy

Tantalum is used as a diffusion barrier in the superconducting Nb3Sn composite-wire manufactured by the bronze method. In order to examine the consumption behavior of the Ta barrier during annealing in the bronze method, the kinetics of the reactive diffusion between Ta and a bronze was experimentally observed using sandwich diffusion couples composed of Ta and a Cu–9.3Sn–0.3Ti alloy. The (Cu–Sn–Ti)/Ta/(Cu–Sn–Ti) diffusion couples were isothermally annealed at temperatures of T = 973–1053 K for various times up to t = 1462 h. Owing to annealing, Ta9Sn is formed as a uniform layer at the initial (Cu–Sn–Ti)/Ta interface in the diffusion couple, and gradually grows mainly toward Ta. The mean thickness of the Ta9Sn layer is proportional to a power function of the annealing time. However, the exponent of the power function is equal to unity at t tc. Thus, the transition of the rate-controlling process for the growth of Ta9Sn occurs at t = tc. The critical annealing time tc takes values of 1.83 × 106, 4.63 × 105, and 5.98 × 105 s at T = 973, 1023, and 1053 K, respectively. The growth of Ta9Sn is controlled by the interface reaction at the migrating Ta9Sn/Ta interface in the early stages with t tc. Due to the transition of the rate-controlling process, the growth rate is always much smaller for Ta9Sn than for Nb3Sn. As a result, Ta works as an effective barrier against the diffusion of Sn from the bronze to the Cu stabilizer in the superconducting Nb3Sn composite-wire.

Grain growth systematics for forsterite ± enstatite aggregates: Effect of lithology on grain size in the upper mantle

Grain growth kinetics of forsterite (Fo) and enstatite (En) in fine grain aggregates of Fo ± En are examined as a function of volume fraction of En ( f En = 0.00 to 0.42). Growth rates fit d n ∝ k · t ( d: mean grain diameter; n: grain growth exponent; k: growth constant; t: time), where n ∼ 5 for both forsterite and enstatite grains in the enstatite-bearing samples. A negative correlation between k Fo and f En can be expressed as k Fo ≈ 0.06 exp [30 f En ( f En − 1.1)], whereas k En takes almost constant values for different f En. In addition, the ratio of d Fo/ d En is almost constant during grain growth, and its value becomes smaller with increasing f En, such that d Fo/ d En ≈ 0.74/ f En 0.59. Our obtained grain growth parameters and the microstructural characteristics in experimental and natural samples all indicate that the rate-controlling process for grain growth in both experiments and in nature is grain boundary diffusion of Si through grain boundaries of olivine. Thus, we are able to propose a semi-empirical relationship of d Ave / d dun ≈ { exp [ 30 f px ⋅ ( f px − 1.1 ) ] } 1 5 ⋅ ( 1 + 1.35 f px 1.59 − f px ) ( d Ave: average grain size in the rock; d dun: average grain size in dunite; f px: fraction of pyroxenes), which can predict how lithology affects grain size in the upper mantle. Grain size in lherzolite (pyroxenes content of 40%) can be ∼ 4 times smaller than that in dunite (pyroxenes content of 5%). Such grain size reduction through change in lithology can significantly affect viscosity of mantle deformation via grain-size sensitive creep.

Molecular Electrochemistry and Redox Catalysis in Ionic Liquids

The reductive electrochemistry of substituted benzophenones in [Bmpy][NTf2] and [Bmim][NTf2] ionic liquids is presented where electrochemistry in [Bmpy] medium results in reversible formation of the radical anion and the dianion species indicating that neither protonation nor ion pairing occurs; whereas in [Bmim], its protic nature results in radical anion protonation leading to an ECE or a DISP1 post electron transfer process and thus irreversibility. The mediated oxidation of alcohols by TEMPO is also presented along with a mechanism / kinetic model involving a rate-controlling pre-equilibrium process which generated the electroactive alcoholate species. The ability of electrochemistry to inform us about the physiochemical nature of ionic liquids, as well as ionic liquids' ability to facilitate and enable electrochemistry, is also discussed.

Spontaneous and Forced Imbibition of Aqueous Wettability Altering Surfactant Solution into an Initially Oil-Wet Capillary

Unforced invasion of wettability-altering aqueous surfactant solutions into an initially oil-filled oil-wet capillary tube has been observed to take place very slowly, and because this system is an analogue for certain methods of improved oil recovery from naturally fractured oil-wet reservoirs, it is important to identify the rate-controlling processes. We used a model for the process published by Tiberg et al. ( Tiberg , F. , Zhmud , B. , Hallstensson , K. and Von Bahr , M. Phys. Chem. Chem. Phys. 2000 , 2 , 5189 - 5196 ) and modified it for forced imbibitions. We show that when applied pressure differences are not too large invasion rates are controlled at large times by the value of the bulk diffusion coefficient for surfactant in the aqueous phase and at early times by the resistance to transfer of surfactant from the oil-water meniscus onto the walls of the capillary. For realistic values of the bulk diffusion coefficient, invasion rates are indeed slow, as observed. The model also predicts that the oil-water-solid contact angle during unforced displacement is close to pi/2, and so, the displacement occurs in a state of near-neutral wettability with the rate of invasion controlled by the rate of surfactant diffusion rather than a balance between capillary forces and viscous resistance. Under forced conditions, the meniscus moves faster, but the same kinds of dynamical balances between the various processes as were found in the spontaneous case operate. Once the capillary threshold pressure for entry into the initial oil-wet tube is exceeded, the effect of pressure on velocity becomes more significant, there is not sufficient time for the surfactant molecules to transfer in great quantity from the meniscus to the solid surface, and wettability alteration is then no longer important.

Phosphate desorption kinetics from goethite as induced by arsenate

The kinetics of the arsenate-induced desorption of phosphate from goethite has been studied with a batch reactor system and ATR-FTIR spectroscopy. The effects of arsenate concentration, adsorbed phosphate, pH and temperature between 10 and 45 °C were investigated. Arsenate is able to promote phosphate desorption because both oxoanions compete for the same surface sites of goethite. The desorption occurs in two steps: a fast step that takes place in less than 5 min and a slow step that lasts several hours. In the slow step, arsenate ions exchange adsorbed phosphate ions in a 1:1 stoichiometry. The reaction is first order with respect to arsenate concentration and is independent of adsorbed phosphate under the experimental conditions of this work. The rate law is then r = k r [ As], where r is the desorption rate, k r is the rate constant and [ As] is the arsenate concentration in solution. The values of k r at pH 7 are 1.87 × 10 −5 L m −2 min −1 at 25 °C and 7.95 × 10 −5 L m −2 min −1 at 45 °C. The apparent activation energy of the desorption process is 51 kJ mol −1. Data suggest that the rate-controlling process is intraparticle diffusion of As species, probably As diffusion in pores. ATR-FTIR spectroscopy suggests that adsorbed phosphate species at pH 7 are mainly bidentate inner-sphere surface complexes. The identity of these complexes does not change during desorption, and there is no evidence for the formation of intermediate species during the reaction.

Present status and strategy of reel-to-reel TFA-MOD process for coated conductors

On the research and development of a reel-to-reel TFA-MOD (Metal Organic Deposition using Trifluoro-acetates) process, a present status is reviewed and its future strategy is addressed. As a base of the study, the 90 m long tape with uniform I c distribution of the 300 A/cm-width level was obtained on the CeO 2 buffered IBAD-Gd 2Zr 2O 7/Hastelloy C276 substrate. The tape has the 56 m region with the end-to-end I c value of 250 A, which corresponds to maximum product of I c × L of 14,000 Am. Based on the results, several directions on R&D have been studied such as “higher I c ”, “higher I c – B”, “higher production rate both in coating/calcinations and crystallization steps” and lower cost buffer/substrate”. Then, an extremely high I c value of 735 A/cm-width was achieved in a short tape by the compositional control (e.g. Ba-deficient), in the starting solutions. On the efforts for achieving higher I c – B properties, high I c values of 115 and 35 A/cm-width under the magnetic fields of 1 and 3 T were obtained by the RE mixture of Y and Gd in REBCO, addition of Zr and a growth rate control process. On the other hand, the production rate for the coating/calcinations process was improved by development of new starting solutions, which uses F-free Y salt instead of TFA salt of Y. The high J c value of 1.9 MA/cm 2 was confirmed using the precursor films fabricated at a high traveling rate of 10 m/h. Concerning a higher rate in the crystallization step, the multi-turning system with a vertical gas flow system was developed. The validity of the concept was confirmed using 2-turn parts of the furnace. The high I c value of 250 A/cm-width was realized in the 5 m tape crystallized with a traveling rate of 3 m/h, which is equivalent to 15 m/h for usage of entire area of the furnace of 10-turns. Furthermore, in order to achieve the lower cost, the architecture of the coated conductor with a low cost buffer/substrate system has been developed. An IBAD buffered substrate using IBAD-MgO layer (CeO 2/LMO/IBAD-MgO/Hastelloy C276) was developed and a high production rate of 24 m/h was realized for IBAD-MgO layer using a small ion gun system with the area of 6 × 22 cm 2. The grain texturing of the substrate was reached the Δ ϕ value of 4° in the CeO 2 layer. This substrate was applied to the above mentioned multi-turning crystallization furnace for TFA-MOD process. Then, a 5 m long tape with 260 A/cm-width (@77 K. s.f.) was achieved. According to the TFA-MOD process in the above achievements, the prospects of each issue for the future stage were independently confirmed. Consequently, R&D combining the above-mentioned achievements for longer tapes are expected in the next stage.

Thermokinetic modeling and parameter estimation for hydrogen permeation through Pd0.77Ag0.23 membranes

Optimizing thin-film Pd-alloy membranes for H2 purification requires detailed understanding of all possible rate-controlling processes including surface adsorption, solution into the bulk metal, bulk diffusion, dissolution, and desorption. H2 permeation through Pd0.77Ag0.23 alloy is analyzed by extending pure Pd diffusion models in the literature with a microkinetic model for surface and bulk reactions between H2 and the alloy. Experimental data and first principles studies from literature are used to estimate and critically modify model parameters. Model results compare extremely well with literature over a broad range of membrane thicknesses (1–20 μm) and operating conditions. The importance of surface processes increase with decreased film thicknesses (below 10 μm) characteristic of recent advances in membrane technology. Previously observed enhancement of H2 flux after heat treatment in air is explained by increased surface area. Sensitivity of H2 flux to various thermokinetic parameters provides further insight as to when different processes are rate-controlling.

Transition of rate-controlling process for reactive diffusion between Ta and bronze in superconductor

The reactive diffusion between Ta and a bronze was experimentally examined using sandwich diffusion couples consisting of Ta and a Cu-9.3Sn-0.3Ti alloy. The diffusion couples were isothermally annealed at a temperature of T = 1053 K for various times up to t = 1200 h. During annealing, a layer of Ta9Sn is formed at the interface in the diffusion couple. The mean thickness of the Ta9Sn layer increases in proportion to a power function of the annealing time. The exponent of the power function is equal to unity at t < 167 h but smaller than 0.5 at t > 167 h. This means that the transition of rate-controlling process occurs at t = 167 h. For the reactive diffusion between Ta and the bronze at T = 1053 K, the growth of Ta9Sn is controlled by the interface reaction at t < 167 h but by the volume and boundary diffusion at t > 167 h.

On the delamination of FeCrAl ODS alloys

Tensile specimens have been tested at room temperature, finding clear delamination in the rolling direction but only incipient delamination in the transverse direction. Delamination is found to be a strain rate-controlled process whose morphology depends on the material's processing history, suggesting that its cause may be embrittlement induced by hydrogen occluded during processing. Delamination has only a small influence on mechanical properties in the rolling direction, but in the transverse direction a loss of ductility is detected particularly for aged specimens.

On the strength and stress-relaxation response of fine-grain Cu–42.2 at.%Zn–0.6 at.%Pb alloy polycrystals

Tensile tests were performed at room temperature to measure the strength and stress-relaxation response of Cu–42.2 at.%Zn–0.6 at.%Pb polycrystals of grain size 5, 7, 9 and 11 μm. The values of the strength parameters, namely yield stress, ultimate tensile strength and fracture stress, were found to decrease with the increase in grain size in accordance with the Hall–Petch law, whereas the ductility decreased with the reduction in grain size. The stress-relaxation response studied at constant strain was logarithmic in nature. For a given initial stress level σ o, from which relaxation at constant strain was allowed to start, both the amount of stress relaxed, Δ σ( t) = σ o − σ( t), and the magnitude of the stress-relaxation rate, s = [d(Δ σ)/d ln( t)], increased with the increase in grain size. However, the stress-sensitivity of relaxation rate, d s/d σ o, was independent of the grain size. The intrinsic height of the energy barrier, U o, to the movement of relaxing dislocations was found to be 5.3 eV, which points to dislocation intersection as the rate-controlling process of stress-relaxation. A comparison of the available data for copper and Cu–Zn alloy system over a wide range of solute concentration shows that stress-relaxation response is sensitive to the alloy microstructure, e.g. mode of spatial distribution of solute atoms, dispersion of second-phase particles, etc.

Morphology of Compounds Formed by Isothermal Reactive Diffusion between Solid Fe and Liquid Al

The morphology of the compounds formed by the reactive diffusion between solid Fe and liquid Al was experimentally observed using Fe/Al diffusion couples. The diffusion couples were prepared by an isothermal bonding technique and then immediately annealed at temperatures of T=973, 1023 and 1073 K for various times up to t=2.4×103 s. At these temperatures, Fe is solid, but Al is liquid. During annealing, a compound region consisting of Fe2Al5 and FeAl3 is formed at the Fe/Al interface in the diffusion couple and grows towards the Fe solid specimen. However, FeAl2 and FeAl were not detected clearly. The thickness is much smaller for FeAl3 than for Fe2Al5, and thus the compound region is mainly composed of Fe2Al5. At T=973–1073 K, FeAl3 is produced as a rather uniform thin layer. On the other hand, the Fe2Al5 region shows the irregular tongue-like morphology at T=973–1023 K but the uniform layer morphology at T=1073 K. The irregularity of the Fe2Al5 region is attributed to the anisotropy for the interdiffusion coefficient of Fe2Al5. The temperature dependence of the irregularity implies that the anisotropy is large at T=973–1023 K but small at T=1073 K. The mean thickness of the compound region is proportional to a power function of the annealing time. Although the activation enthalpy of the proportionality coefficient is evaluated with an Arrhenius equation, the morphology of the Fe2Al5 region varies depending on the annealing temperature. In such a case, the rate-controlling process for the growth of the compound region cannot be readily estimated from the activation enthalpy.

Mechanical properties versus temperature relation of individual phases in Sn–3.0Ag–0.5Cu lead-free solder alloy

The non-homogeneous Sn–3.0Ag–0.5Cu (SAC305) lead-free solder alloy consists of Sn-rich (β-Sn) and eutectic phases. The mechanical properties of these individual phases were demonstrated to be a function of the temperature. The nanoindentation methodology was utilized to examine the mechanical properties at 60 °C, 80 °C, 110 °C, 130 °C, and 150 °C, respectively. It was found that for both Sn-rich phase and eutectic phase, the hardness and Young’s modulus exhibited the dependence on the temperature. Moreover, the creep deformation which occurred at the dwell time of sustained loading was quite sensitive to the prescribed temperature. Basically, the higher temperature resulted in a larger creep deformation. This in turn caused the variable strain rate sensitivity of the individual phases, which was extracted by Mayo–Nix approach. The Sn-rich phase showed larger creep deformation than that of eutectic phase. However, a greater strain rate sensitivity index value was obtained for eutectic phase at the temperature regime (25–130 °C). The derived activity energy implied that for both β-Sn and eutectic phases two rate-controlling processes took place during the creep deformation, in which the transition temperature is around 130 °C.

Use of pervaporation to separate butanol from dilute aqueous solutions: Effects of operating conditions and concentration polarization

This study deals with the separation of n-butanol from aqueous solutions by pervaporation. The effects of feed concentration, temperature, and membrane thickness on the separation performance were investigated. Over the low feed butanol concentration range (0.03–0.4 wt%) studied, the butanol flux was shown to increase proportionally with an increase in the feed butanol concentration, whereas the water flux was relatively constant. An increase in temperature increased both the butanol and water fluxes, and the increase in butanol flux was more pronounced than water flux, resulting in an increase in separation factor. While the permeation flux could be enhanced by reducing the membrane thickness as expected for all rate-controlled processes, the separation factor was compromised when the membrane became thinner. The effect of membrane thickness on the separation performance was analyzed taking into account the boundary layer effect. This could not be fully attributed to the concentration polarization, which was found not significant enough to dominate the mass transport. A variation in the membrane thickness would vary the local concentration of permeant inside the membrane, thereby affecting the permeation of butanol and water differently. Thus, caution should be exercised in using permeation flux normalized by a given thickness to predict the separation performance of a membrane with a different thickness because the membrane selectivity can be affected by the membrane thickness even in the absence of boundary layer effect.

Evaluation of kinetic parameters for the thermal decomposition of gamma-irradiated anhydrous lanthanum nitrate

The thermal decomposition of gamma-irradiated anhydrous lanthanum nitrate was studied by dynamic thermogravimetry. The decomposition proceeds via three consecutive stages characterized by different activation energies. The reaction order, activation energy, frequency factor and entropy of activation were calculated using the Coats–Redfern, Freeman–Carroll and Horowitz–Metzger methods and were compared with those of the unirradiated salt. Irradiation enhances the decomposition and the effect increases with the irradiation dose. The activation energies of all the three stages decrease on irradiation. The mechanism of the decomposition of unirradiated and irradiated anhydrous lanthanum nitrate follows the Mampel model equation,−ln(1−α) for g(α), and the rate-controlling process is random nucleation with the formation of a nucleus on every particle.

Non-porous magnetic micro-particles: Comparison to porous enzyme carriers for a diffusion rate-controlled enzymatic conversion

In this study the kinetics of conversion of a low-soluble substrate by an immobilized enzyme was investigated with respect to the diffusion limitation within porous and non-porous carriers. Non-porous micro-magnetic beads in comparison to conventional porous supports like Eupergit and Sepharose were tested. Due to their small diameters and their magnetic properties, micro-magnetic beads are especially applicable in diffusion rate-controlled processes in biological suspensions. The enzymatic reaction studied was the conversion of emulsified dirhamnolipid by immobilized Naringinase from Penicillium decumbens to monorhamnolipid and l-rhamnose. Taking into account mass transfer phenomena, the variation of the reaction effectiveness factor with increasing enzyme loading was estimated and compared with experimental efficiencies utilizing different enzyme loaded immobilized preparations. For comparison, carrier activities were also determined with the model substrate p-nitro-phenyl-rhamnoside. Intrinsic enzyme activities were thereby evaluated for porous supports. Highest specific activities were obtained with the micro-magnetic beads. These non-porous micro-beads demonstrated to be the most suitable carrier for bioconversion of a low-soluble substrate like rhamnolipids, where mass diffusional resistances in the three-phase reaction process are completely overcome. However, the smaller particle surface available limited the specific activity obtained at high protein loadings.

Growth rate of Nb3Sn for reactive diffusion between Nb and Cu–9.3Sn–0.3Ti alloy

In order to examine experimentally the growth behavior of Nb3Sn during reactive diffusion between Nb and a bronze with the α + β two-phase microstructure, a sandwich (Cu–Sn–Ti)/Nb/(Cu–Sn–Ti) diffusion couple was prepared from pure Nb and a ternary Cu–Sn–Ti alloy with concentrations of 9.3 at.% Sn and 0.3 at.% Ti by a diffusion bonding technique. Here, α is the primary solid-solution phase of Cu with the face-centered cubic structure, and β is the intermediate phase with the body-centered cubic structure. The diffusion couple was isothermally annealed at temperatures between T = 923 and 1,053 K for various times up to 843 h. Owing to annealing, the Nb3Sn layer is formed along each (Cu–Sn–Ti)/Nb interface in the diffusion couple, and grows mainly into Nb. Hence, the migration of the Nb3Sn/Nb interface governs the growth of the Nb3Sn layer. The mean thickness of the Nb3Sn layer is proportional to a power function of the annealing time. The exponent of the power function is close to unity at T = 923 K, but takes values of 0.8–0.7 at T = 973–1,053 K. Consequently, the interface reaction at the migrating Nb3Sn/Nb interface is the rate-controlling process for the growth of the Nb3Sn layer at T = 923 K, and the interdiffusion across the Nb3Sn layer as well as the interface reaction contributes to the rate-controlling process at T = 973–1,053 K. Except the effect of Ti, the growth rate of the Nb3Sn layer is predominantly determined by the activity of Sn in the bronze and thus the concentration of Sn in the α phase. As a result, the growth rate is hardly affected by the volume fraction of the β phase, though the final amount of the Nb3Sn layer may depend on the volume fraction.

Reaction of Sn to Nanocrystalline Surface Layer of Cu by Near Surface Severe Plastic Deformation

The near surface ultrafine grains (NSUFG) layer with grain sizes of about 35nm to 200nm from surface to about 10 μm was prepared in the OFHC-Cu sheet with coarse grains size of about 7.2 μ m (CG-Cu) by Near Surface Sever Plastic Deformation method. The solid reactions of Sn to NSUFG layer and CG-Cu were basically investigated at 379K to 493K for 1x10 3 to 6x10 6 s. The Cu 6 Sn 5 (η) and Cu 3 Sn (e) layers were formed between Cu and Sn. The thickness of the e layer in NSUFG-Cu/Sn was similar to that in CG-Cu/Sn one, while the thickness of the η layer in NSUFG-Cu/Sn reaction was about two times thicker than that in CG-Cu/Sn one. This enhancement of the η layer growth in NSUFG-Cu/Sn reaction was due to the large supply of Cu atoms to the reaction layer by the grain boundary diffusion in the NSUFG-Cu. The rate-controlling processes of layer growth were boundary diffusion mechanism in reaction layer at lower temperatures in shorter annealing time, and volume diffusion mechanism at higher temperatures in longer annealing times.