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Fluidized-solids reactors with continuous solids feed - I: Residence time of particles in fluidized beds

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Abstract

The distribution of residence times of solid particles is examined in fluidized beds at steady state with continuous feed and discharge of solids, both for beds consisting of a single particle size and for beds consisting of a wide spectrum of particle sizes. The mean age (residence time in bed) of particles of a given size in the overflow and carryover streams is found in all cases to be given by {A figure is presented} where F 1 is the mass flow rate of overflow stream, W is the weight of solids in the bed, ψ is the ratio of the size distribution function of overflow particles to that within the bed and κ{script} is the elutriation velocity constant of particles whose mean age is being considered. The constant ψ is a measure of the degree of vertical segregation of particles within the bed. In most practical situation the bed may be considered to be not segregated, in which case ψ can be taken to be unity. For significant carryover of solids the elutriation velocity constant κ controls in determining the average length of stay of particles in the fluidized bed. In all cases the mean age of particles of a given size is the same in both the overflow and carryover streams.

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... For a BFB, the mean residence time (MRT) of particles is usually much shorter than the time needed for them to mix after being fed in. Yagi and Kunii (1961) assumed the fluidized flow to be completely mixed and proposed the RTD function E(t) of a BFB to be ...
... As shown by their results illustrated in Fig. 1, close agreement between theory and experiment justified the assumption of complete mixing for the particles in the BFB. The present simulation was conducted in accordance with the procedures of Yagi and Kunii (1961). A schematic of the BFB is displayed in Fig. 2, and detailed simulation parameters are given in Table 2. ...
... Wei, Lu, and Wei, (2013) Water/quartz sands CFD The feeding method had an effect on the RTD, and there was a nonlinear relationship between feeding rate and RTD. (1) conducted by Yagi and Kunii (1961). ...
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The residence time distribution (RTD) of solids and the fluidized structure of a bubbling fluidized bed were investigated numerically using computational fluid dynamics simulations coupled with the modified structure-based drag model. A general comparison of the simulated results with theoretical values shows reasonable agreement. As the mean residence time is increased, the RTD initial peak intensity decreases and the RTD curve tail extends farther. Numerous small peaks on the RTD curve are induced by the back-mixing and aggregation of particles, which attests to the non-uniform flow structure of the bubbling fluidized bed. The low value of t50 results in poor contact between phases, and the complete exit age of the overflow particles is much longer for back-mixed solids and those caught in dead regions. The formation of a gulf-stream flow and back-mixing for solids induces an even wider spread of RTD.
... 9,10 Naturally, a 0.5−4 nm thick oxide shell quickly forms on the surface when bare ANPs are exposed to oxygen to generate a core−shell structure, which makes the surface reaction dynamics complicated and the morphological changes (cracks and broken) of the particles hard to predict. The well-known idealized "shrinking core" model, 11,12 whereby a reaction front moves inward separating an unreacted core with a completely oxidized shell, was initially used to describe ANP oxidation. Under the assumption of the "shrinking core" model, the oxidation rates observed in Park's experiments 13 were found to be consistent with a mass diffusion-controlled rate-limiting step, other than the chemical reaction-controlled step. ...
... As oxidation proceeds, the oxide shell gradually thickens until the total particle is oxidized, which is similar to the situation described by the shrink-core model. 11,12 While for C8S1, at oxygen pressure of 10 and 15 atm, the morphology of ANPs undergoes huge change, exhibiting the destruction of the oxide shell and dispersion of core Al into the ambient gas, which is totally different from the cases under lower oxygen concentration. As shown in Figure 3c,d, for C8S1 at 10 and 15 atm, small holes appear on the surface of the particle and gradually grows. ...
... The experimental methods that have provided the most direct measurement of particle RTDs have relied on measurements of the exit times of distinctive particles (e.g., particles with some distinctive physical characteristic such as color, size, or chemical composition that can be readily detected) after they have been injected as pulses into experimental bubbling or circulating fluidized beds. Typically, the particles that were measured have been classified either as Geldart A or B type, which characterizes the flow patterns they tend to exhibit [Geldart (1973), Kunii and Levenspiel (1991)]. 1 Some of the most relevant articles on these experiments include: Yagi and Kunii (1961a), Helmrich et al (1986), Berruti et al (1988), Ambler et al (1990), Smolders and Baeyens (2000), Harris et al (2003a&b), Bhusarapu et al (2004), andAndreux et al (2008). All of these studies have reported some common features in the observed RTDs: ...
... Many of the general modeling approaches developed for chemical reactors have been adapted for modeling particle RTDs in bubbling and circulating beds. Some relevant articles in the literature that discuss RTD modeling in this context include the following: Yagi and Kunii (1961a), Verloop et al (1968), Berruti et al (1988), Ambler et al (1990), Smolders and Baeyens (2000), Harris et al (2002), Bhusarapu et al (2004), and Andreux et al (2008). As with the modeling approaches used for the more general problem in chemical reactors, particle RTD models for bubbling and fluidized beds have adopted one of three basic approaches, listed below in increasing order of complexity: ...
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... In the case of a chemical reaction of a fluid on a reactive solid, the properties of the solid can be a major point of consideration, because the global kinetics of the reaction can greatly depend on the morphology of the solid (size, shape, porosity rate, etc.). As reported in the literature among fluidparticle reaction theories [24][25][26][27], one model (and several variants) has been successfully used: the Shrinking Core Model (SCM), originally developed by Yagi and Kunii [24,25]. On the scale of one particle (Fig. 6), this model suggests that the chemical reaction first occurs at the outer skin of the particle and then moves into the solid, leaving behind a completely converted and inert solid, commonly called "ash". ...
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Corrosion is a key issue for operators in the oil and gas industry since production fluids contain some water and both CO2 and H2S acid gases. In this context, this paper illustrates the development of a reactive barrier polymer against corrosion by H2S of offshore flexible pipes. The role of this reactive material, called anti-H2S material, is to avoid H2S reaching the structural steel layers of the flexible pipe during the whole service life of the structure, usually 20 years, and hence to place the steel layers in a sweet service environment. Placed between the existing pressure sheath and the steel layers, the anti-H2S material has the ability to neutralize H2S during its diffusion within the material. The neutralization is ensured by an irreversible chemical reaction on reactive components that are dispersed in the material. The raw material selection is based on both accurate requirements for their use in a flexible pipe and expected performances in a sour service environment over a long period of time. Some laboratory qualifications and experimental techniques are used to qualify the behavior of the material and build the material database. A dedicated multiphysics model is developed based on the coupling of permeation mechanisms and gas-solid reactions. Qualification of both the material and the model is performed thanks to middle-scale and full-scale tests conducted in representative sour service conditions.
... In all these cases, the consumption or ''reaction'' occurs on the surface of the solid (core-shell interface). Yagi and Kunii (1955) proposed the shrinking unreacted core model [9][10][11], which explains the behavior of irreversible non-catalytic reactions and a constant size, assuming that the unreacted solid is impermeable to the reactant fluid because it is densely packed, while the solid product layer is quite porous and, thus, reagents and fluid products can diffuse through the shell. There are many reports of systems that behave like the Yagi model and different modifications to this model have been proposed. ...
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Modeling of the bioleaching process applied to the system silver‐manganese (Ag‐Mn) was carried out. The two‐moving‐fronts model was used to describe the main stages of the process. Bioleaching involves a catalytic process carried out by bacteria to dissolve the mineral ores. Initially, the bacteria interact with the mineral to dissolve manganese, leading to the precipitation of silver. The Ag‐Mn compound is dissolved by the bacteria in two stages. First, the bacteria dissolve the manganese and form a biofilm composed mostly of exopolysaccharides. In the second stage, the biofilm is consumed by the bacteria, ending up in dissolved manganese and silver precipitation. At 48 h, the viscosity of the pulp reaches a maximum attributed to the maximum concentration of extracellular polysaccharides in the medium. Predictions describe the basic issues of the bioleaching process in this system.
... In a study by Yagi and Kunii [9], the effective thermal conductivity of a packed bed under static fluid 0 [W/m/K] was assumed to be 1.31 W/m/K. ...
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... To this end, understanding of the dominant controlling mechanism(s) is key to set up the governing and constitutive equations in a predictive model. The shrinking core model (SCM), developed by Yagi and Kunii [23,24], has been effectively applied to many gas-solid and liquid-solid reactive cases where mass transfer, heat transfer and reaction kinetics are interplaying factors in the process [25,26]. By establishing an analogy between reaction and extraction kinetics, the SCM was deployed in this study to capture the real-time changes of the particles. ...
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The olive oil industry generates enormous amounts of olive stones each year, which have the potential to be used as a biofuel but have high oil content, which negatively impacts the combustion process. In addition, olive stones contain high-value antioxidants, and their exploitation can provide additional revenues for the biofuel industry. In this work, we report the effect of different extraction solvents on the extraction of antioxidants and their activity. In addition, in vitro gastrointestinal digestion was used to evaluate the content and antioxidant activity of the olive stone extracts after gastrointestinal digestion. The extracts obtained by aqueous ethanol solvent (50% vol) exhibited the highest antioxidant activity with the DPPH IC50 of 1.27 mg mL⁻¹ and ferric reducing antioxidant power (FRAP) of 6.33 mg AAE g⁻¹. After in vitro digestion composed of gastric and intestinal processes, the antioxidant activity of olive stones decreased: DPPH IC50 value increased three times (a higher value of IC50 indicates lower antioxidant activity) and FRAP decreased almost five times with respect to the values obtained for original extracts. Furthermore, both phenomenological and shrinking core models were used to fit experimental oil extraction kinetics data and showed good agreement. Thermodynamic analysis showed that the extraction process is endothermic and irreversible while spontaneous and thermodynamically favourable for all conditions except for oil extraction from olive stones of 3.10 mm particle size at 20 °C. The calculated value for temperature coefficient is in good agreement with the previously reported values for the oil extraction from similar biomass.
... Yagi and Kunii first established the shrinking ore model of spherical particles without changing the particle size [30,31]. The process was as follows: (a) H + ion diffuse to the suface of the solid through the bulk solution surrounding the particle; (b) H + ion diffuse to the surface of unreacted core through the ash layer; (c) The reaction of H + ion with solid on the reaction interface of the unreacted core; (d) The soluble resultants diffuse to the surface of the solid through the ash layer back; (e) Soluble component diffuse to solution from solid surface through boundary layer. ...
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... The interface would become smaller and smaller throughout the hydrolysis reaction process. The shrinking core model was used to describe this typical kind of general non-catalytic gas-solid reaction (Yagi and Kunii, 1961). The characteristic of shrinking core model was that the reaction only occurred at the interface between the solid product layer and the unreacted core, and the interface gradually shrunk towards the center of the unreacted core (Stefan et al., 2016). ...
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... Three resistances to reaction can be distinguished namely, film diffusion, ash diffusion and reaction controlled (surface area controlled). The rate-controlling step is determined by the highest resistance of these three [21][22][23]. ...
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... This model was first developed by Yagi andKunii [1955, 1961], who visualized five steps occurring in succession during reaction (see Figure 1). ...
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Conference Paper
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The main objective of the SOLPART H2020 project is to develop, at a pilot scale (30-50 kW), a high temperature (800-1000°C) 24h/day solar process suitable for particle treatment in energy intensive non-metallic minerals’ industries. Calcium carbonate decomposition (Calcination reaction: CaCO3= CaO + CO2) is the most representative and most endothermal reaction in this type of application of solar process heat for industry. This paper presents the context, the particle to be treated, the reaction thermodynamics and kinetics, the mass and energy balances and the solar reactor technology currently under development.
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For non-catalytic gas–solid reaction, it is desirable to match the mean residence time (MRT) of particles and complete conversion time (tc) in a fluidized bed. In this study, the MRT differences (MRT ratios) between the coarse particles and the fine particles were investigated in a continuous fluidized bed with a side exit by varying the superficial gas velocity, feed composition and particle size ratio. The results show that the MRT ratio increases firstly and then decreases with increasing the gas velocity. By controlling the gas velocity and the feed composition of coarse particles, the MRT ratio can be modulated from 1.8 to 10.5 at the gas velocity of 1.0 m/s for the binary mixture with the size ratio of 2.2. The MRT ratio can reach to ~ 12 at the gas velocity of 1.2 m/s for the particles size ratio of 3.3. The present study has endeavored to obtain fundamental data for an effective plant operation to meet the need of synchronously complete conversion of particles with different sizes during the film diffusion controlling reaction.
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Chapter
Kapitel 8 widmet sich den mehrphasigen Reaktionssystemen, nämlich den heterogen katalysierten, den Fluid-Fest- sowie den Fluid-Fluid-Reaktionen. Zunächst wird in die Bilanzierung mehrphasiger Reaktionssysteme eingeführt und gezeigt, wie Stoff- und Wärmeübergang kinetisch zu berücksichtigen sind (Makrokinetik) und wie mit Hilfe des Wirkungsgradkonzeptes Vereinfachungen der Bilanzgleichungen vorgenommen werden können. Heterogen katalysierte Reaktionen werden umfassend hinsichtlich der kinetischen Relevanz auftretender Stoff- und Wärmetransportlimitierungen diskutiert und anschließend wird ausführlich auf die Auslegung isothermer, adiabater und polytroper Festbettreaktoren eingegangen. Die Auslegung von Wirbelschichtreaktoren wird ebenfalls behandelt und verschiedene Reaktormodelle vorgestellt. Bei den Fluid-Fest- und Fluid-Fluid-Reaktionen wird insbesondere die Auswirkung von Stofftransportlimitierungen auf die Kinetik diskutiert und jeweils die Reaktorauslegung erläutert.
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A study of the kinetics of the dissolution of a Nigerian columbite in hydrofluoric acid has been examined and an investigation on the quantitative leaching of the mineral was also carried out. The effects of some parameters such as acid concentration, contact time and temperature were investigated. Elemental analysis of the ore was done using Particle-induced X-ray Emission (PIXE) spectroscopy with 2.5 MeV protons and this showed the major elements in the ore to be Si (8.82 %), Fe (10.74 %), Mn (4.72 %), Ta (6.80 %),Nb (28.90 %) and W(2.61%), with K, Ni, Zn, Sr and Y occurring in traces. Experimental results indicate that the dissolution rate is chemical reaction controlled, with reaction order of 0.57. Dissolution of over 90 % of the columbite was achieved in 5 h, using 20 M HF at 90 oC with 100 μm particle sizes. Activation energy, Ea of 15.70 KJ.mole-1 was obtained for the process
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The thermal. decomposition of pyrite concentrate-into-sulphur and synthetic pyrrhotite was investigated in bench and semi-pilot scale fluidized bed reactors fired with methane or fuel oil. The pyrite was decomposed in a bed of coarse sand and the product pyrrhotite was carried over with the fluidizing gases and separated in hot cyclones. The effects of fuel/air ratio, reactor temperature, superficial gas velocity, particle size and feed rate on the elimination of labile-sulphur were studied. Conversion was enhanced by slightly reducing atmospheres, low feed rates, high gas velocities and reaction temperature (in the range 740° to 830°C). Elutriation rates of pyrrhotite particles from the fluidized bed were measured and mean residence times determined as a function of particle size and superficial gas velocity. Conversion rates are considered with regard to possible rate-controlling steps in the thermal decomposition of pyrite.
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When the reaction is controlled by the diffusion through liquid, the dissolution process of mono-sized particles was predicted based on the shrinking core model. The changing of particle's diameter satisfied the square-line law. Based on the dissolution of mono-sized particles, the model of solids overall conversion has been established, and the correlation between micro and macro model of mono-sized particle and particle groups has been obtained. The correlation model was verified by the dissolution experiment of limestone with different temperature and concentration of hydrogen iron. And the results of model are well agree with the experimental results. This correlation model has a significant for improving the liquid-solid reaction theory system and back deriving micro chemical reaction parameters from the macro experimental data.
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Using different polypropylene powders, the residence time distribution was determined by pulse trace method in the cold model experimental apparatus of a horizontal stirred bed reactor (HSBR) equipped with different kinds of stirring paddles. The experimental data were simulated with multi-level model of the whole mixed reactor in series and two-parameter model, respectively. The results demonstrate that the back-mixing degree of leaf blade agitator was the maximum and most close to a fully back-mixed flow; the back-mixing degree of T-type agitator was the minimum, and most close to the plug flow.
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In this study, the gas formation of anaerobic digestion was analyzed by the shrinking core model. This model is based on the mass transport equations. The experiments were carried out with hydrothermal treated wheat straw. Additionally a control group of untreated wheat straw was examined.With untreated straw the beginning of microbiological growth was limited by convection through the surrounding fluid film. With further incubation time the bacteria formed a biofilm. Diffusion through this layer limited the degradation.A short hydrothermal treatment decreased the convection-limited phase.The gas yield of the straw was 0.54dm3 (0°C, 1atm) per gram volatile solid. The pretreated straw yielded in 0.51dm3 (0°C, 1atm) per gram volatile solids with the same mean content of methane (49vol%) and carbon dioxide (51vol%).
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Rotary reactors or rotary kilns are the reactors facilitating the chemical reaction between the gas and solid phases usually at high temperatures. This book, which is written by an expert in the field, describes the principles of the rotary reactor and the mode of its operation. These reactors are widely used in various chemical process industries (food, pharmaceuticals) and metallurgical industries. The book defines the physiochemical aspects of the rotart reactors and provides theoretical equations of their operation. The first part of this book presents the fundamentals; solid movement, conversion of solids, and heat transfer. The middle part of the book applies these equations to a variety of processes which have been developed so far, and shows how they are used. In its last part, conceptual designs of novel rotary reactors are proposed, which performance characteristics are predicted on the basis of above equations, especially, in gasification of solid wastes. - Defines the rotary reactors and their mode of operation. - Defines all operating parameters and gives equations to predict the operation of rotary reactors under various conditions. - Includes a number of practical examples from various industrial applications (metallurgical waste treatment etc)..
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The kinetics and thermal characteristics of oil shale semi-coke and sawdust, including their blends, during co-combustion were investigated using a non-isothermal thermogravimetric analyzer (TGA). The ratio of semicoke to sawdust in the blends by mass was set as 10:0, 9:1, 8:2, 7:3, 6:4, 5:5 and 0:10. The combustion performance of samples improved significantly with increasing sawdust proportion in the mixture and rising heating rate. The kinetic analysis demonstrated that the distributed activation energy model (DAEM) could well describe the value of apparent activation energy at different fixed conversion values. Gaseous emission analysis by using the coupled Fourier transform infrared spectroscopy (FTIR) demonstrated that organic compounds were produced by the pyrolysis of sawdust, while inorganic compounds were generated during the whole combustion process. Most of the inorganic compounds were CO2 and CO. Seldom SO2 and NOx were released at the initial stage. The results obtained indicated that the blends may improve the combustion performance of oil shale semi-coke and sawdust.
Chapter
This chapter discusses binder burnout. The polymers that are used to give strength to a ceramic green body when the green body is dry must be burned out before sintering because they would decompose in an uncontrolled manner at sintering temperatures, giving off huge volumes of gas at high pressure that will cause the green body to crack. Binder burnout is performed at temperatures between 300 and 700oC—much below the temperatures used for sintering. During binder burnout, the polymer undergoes a controlled thermal decomposition reaction that can take several forms. In general, thermal decomposition of polymers form both volatile and solid residues as products of the reaction. The solid residues react further at higher temperatures to give subsequent volatile products and other solid residues. The kinetics of binder burnout is discussed in terms of the thermal decomposition reaction kinetics, as well as the kinetics of mass transfer for the volatiles and the heat transfer required to supply the heat of reaction.
Thesis
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This thesis aims to extend existing insights on micro-structural development of cement / gypsum-based materials during hydration, usage and fire using cellular automata, experiments and mathematical models in order to further understand and optimize these cement/gypsum-based materials. The main findings in this thesis are the following; • Cellular automata systems can be applied for regular and random packing of digitized spheres. • A hybrid model, combining chemical reaction controlled and diffussion controlled models has been successfully introduced and tested. • CEMHYD3D has been successfully modified for multi-cycle and multiscale modelling of ordinary Portland cement with a particle size distribution. • Ultrasonic sound measurements can be applied for determining the hydration curve of calcium sulphate based materials. • The thermal conductivity of gypsum plasterboard at room and elevated temperature can be modelled using a three-phase model. • A combination of slag cement, calcium sulpahte hemihydrate and quicklime can be applied fot the stabilization and solidfication of contaminated soil.
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A shrinking core model is presented for the galvanostatic discharge of a metal hydride particle. A quantitative criterion for when the shrinking core can be completely neglected or approximated by a pseudosteady-state solution is presented. The effect of shrinking of the core on the discharge behavior of a metal hydride particle is also studied.
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Simi-dry flue gas desulfurization (FGD) in a pilot circulating fluidized bed (CFB) reactor was studied by the CFD method. Heterogeneous hydrodynamics and desulfurization reaction were simulated in a three-dimensional domain of the CFB riser. Euler-Euler approach was adopted and the O-S drag model was utilized for the unsteady gas-solid two-phase flow, which achieved the typical core-annulus structure of both the particle concentration and the particle velocity. The collision coefficient (e) was selected by comparing with the experimental data of the solid volume fraction. The desulfurization was described by the continuous conversion model and the liquid film thickness equation for interphase mass transport was modified to avoid “divided by zero”. Detailed analysis figured out that the water mass fraction in the particle phase played a significant role in the desulfurization. The sorbent dissolving might be a controlling step when the water mass fraction was very small, and should be taken into consideration rather than neglected. Operating parameters were discussed for their impact on the desulfurization efficiency. Computational results showed that the jet water flow rate was the most significant parameter as the circulating solid mass flow rate followed closely behind, suggesting that uniform water jetting will be the most improving method.
Conference Paper
The presence or absence of gas phase species during combustion of aluminum nano- particles (n-Al) is a crucial observable in evaluating competing theories such as a diffusive oxidation mechanism and the melt dispersion mechanism. Absorption spectroscopy is used to probe the ground state of Aluminum monoxide (AlO) and Al vapor in order to quantify the amount of Al and AlO present under conditions where these species were not observed in emission previously. Absorption measurements were made during combustion of nano-aluminum and micron- sized aluminum in a heterogeneous shock tube. AlO was detected in absorption at temperatures as low as 2000 K in n-Al combustion, slightly below the limit seen in micro-Al combustion. Al vapor was detected during n-Al combustion at temperatures as low as 1500 K, significantly lower than in micro-Al combustion. A comparison with n-Al in an inert environment did not show Al vapor at temperatures below 2300 K, suggesting a nearly pristine oxide coat that inhibits the production of Al vapor in appreciable quantities without reaction. However, at these temperatures, we would have been able to detect Al vapor from equilibrium partial pressures if Al is present at the surface of a particle. These results are contrary to predictions of the melt dispersion mechanism, which should result in the generation of aluminum vapor from high energy Al clusters produced from n-Al particles that spallate from mechanical stresses under rapid heating regardless of bath gas. These results further indicate a gas phase component of n-Al combustion is observed in temperatures as low as 1500 K.
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Two competing models for nanoaluminum combustion, the shrinking-core model and the melt dispersion mechanism, make very different predictions about the flame structure of burning nanoparticles. In this work, we test specifically the differing predictions of gas-phase structure surrounding the particle using the UIUC heterogeneous shock tube and absorption spectroscopy. AlO features are seen in burning nanoaluminum at ambient temperatures above 2000 K, while strong Al absorption features persist in burning nanoaluminum in ambient temperatures as low as 1500 K. Implications of these results in terms of the two competing mechanisms will be discussed.
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Bubbling fluidisation remains important in energy systems and is currently of interest because of chemical-looping approaches for separating CO2 from flue gases. For example, in chemical looping combustion the conveying medium for oxygen, the 'oxygen carrier', is a particulate solid circulated between reducing and oxidising reactors, facilitated by fluidisation. The processes undertaken in the reactors require intimate mixing and heat transfer amongst the various solids and gases, obtainable only in a fluidised bed. At the laboratory scale, it is often necessary to evaluate the kinetics of the reaction of oxygen carrier particles with fuels; realistically, this can only be undertaken in laboratory-scale fluidised beds. This chapter reviews the fundamentals underpinning the design and scale-up of bubbling fluidised systems.
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Bei der Gewinnung und Veredelung von Stoffen aus natürlichen Ressourcen finden Umsetzungen zwischen gemahlenen Rohstoffen und fluiden Medien (Gase, Flüssigkeiten) statt. Ausgangsmaterialien sind mineralische und fossile Stoffe, wie Erze und Kohlen, sowie Nachwachsende Rohstoffe. In den Modellvorstellungen schrumpfen die Ausgangspartikel während der Reaktion. Das Design gebildeter Partikel hängt u. a. von der Qualität, weiteren Vorbehandlungen und den dispersen Eigenschaften der Rohstoffe ab. Läuft der Prozess über eine Schmelze, so kann das Produktdesign durch Reinigung, Zusätze und Formgebung eingestellt werden. Anderenfalls weisen Partikel aus pulvrigen, granularen oder fasrigen Ausgangsstoffen nach der Umsetzung zwar eine völlig andere Chemie auf, behalten aber weitgehend die Größe und Form des Ausgangsmaterials bei. Für ein weitergehendes Produktdesign sind nachgeschaltete Prozesse erforderlich. During the recovery and processing of materials from natural resources reactions between ground raw materials and fluid media take place. Starting materials are mineral and fossil substances, e.g., ore and coal, and renewable resources. In the physical model the particles shrink during the reaction. The design of the formed particles depends on the deposit, type and quantity of impurities, on further pre-treatments and the disperse properties of raw materials. Molten materials can be purified, doped and shaped. Otherwise, particles formed from powders, granular or fibrous materials show a completely different chemistry after the reaction, but largely kept size and shape of the starting material. Others disperse properties such as bulk density, density and flow properties, are changing by the reaction. For additional product design (cleaning, shaping) downstream processes are required.
Article
The ignition behaviour of sodium droplets in the atmospheric air has been studied numerically with two available models of pre-ignition stage combustion. Surface reaction is very important in the pre-ignition stage, and the different reaction rate-controlling processes involved in this stage are explained using the shrinking core model. The droplet ignition behaviour is studied by considering the energy balance at the droplet surface in terms of rate of heat generation from the surface oxidation reaction and rate of heat loss to the ambient air. Ignition delay times are evaluated numerically using the two pre-ignition models with different ranges of values to the main parameters that can affect the ignition behaviour of the sodium droplets. Based on these results, the relative capability of the models has been brought out in predicting the droplet ignition behaviour, so that the better model could be chosen for the sodium spray fire analysis code being developed. Analysis results show that the reaction kinetics limited pre-ignition model predicts the limit of ignitability for sodium droplets under different initial and convective conditions, whereas the mass transfer limited pre-ignition model predicts this only under very low oxygen concentrations.
Article
The sodium manganese ferrite thermochemical cycle for hydrogen production by water splitting can successfully operate in a relatively low temperature range (1023–1073 K) and has a high potential for coupling with the solar source using conventional structural materials. With the aim of implementing the cycle in a solar reactor, the hydrogen evolution rate from the reactive mixture measured in laboratory apparatus has been modeled by using a shrinking-core model. Such a model proved to adequately describe the rate of hydrogen production in the studied temperature and water concentration range. The model was extended to predict the behavior of the reactive mixture subjected to different experimental conditions.
Article
It is shown that the pseudo steady state approximation in the application of the shrinking core model to liquid—solid reactions is valid even when the ratio of liquid reactant concentration to molar density of the solid is high. In this case the pseudo steady state approximation neglects both the accumulation term and the convective mass transfer term in the mass balance. The respective errors thus introduced have different signs and largely cancel each other. It is also shown that the experimental analysis of liquid—solid reactions can be simplified by a suitable design of batchwise experiments, which also increases the accuracy in parameter estimation.
Article
The effect of high concentrations of sodium carbonate in soda ash digestion of scheelite concentrates has been studied by analysing the temperature profile through the calcium carbonate ash layer, and using a calcium sequestering agent (EDTA) in the leaching system. A mechanism based on the principles of the adsorption phenomena involved is described to justify the probable presence of a double compound of sodium and calcium carbonates blocking the calcite pores.
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