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Fluidized-solids reactors with continuous solids feed—III
Abstract
Experimental data from gas-solid fluidized reactor systems are analysed on the basis of the theoretical treatment of Parts I and II. The following systems are treated: 1.Roasting of pyrrhotite and zinc blende particles with uniform size.2.Roasting of zinc blende concentrate with wide distribution of size.3.Distillation of sulphur with two-stage fluidized reactor.4.Nitrogenation of calcium carbide.Close agreement between theory and experiment is obtained.RésuméEn se basant sur la théorie présentée dans les parties I et II de cet article, les auteurs analysent les données experimentales pour des réacteurs gaz-solide à lit fluidisé.Le systèmes suivants ont été étudiés: 1.Grillage de particules de pyrrholine et de blende de taille uniforme;2.Grillage de blende concentrée avec large distribution de dimensions;3.Distillation de sulfures dans des réacteurs fluidisés à deux étages;4.Fixation d'azote sur le carbure de calcium.Il y a bon accord entre les expériences et la théorie.ZusammenfassungExperimentelle Daten eines Gas-Feststoff-Wirbelschicht-Reaktors wurden auf Grund der theoretischen Ableitung des 1 und 2 Teiles dieser Arbeit untersucht. Dabei wurden folgende Systeme behandelt: 1.Röstung von Magnetkies und Zinkblende gleicher Korngrösse.2.Röstung von Zinkblende-Konzentraten mit grossen Kornspektrum.3.Destillation von Schwefel in einem 2-Stufen-Wirbleschicht-Reaktor.4.Kalkstickstoffbildung aus Karbid.Dabei wurde gute Übereinstimmung zwischen Theorie und Experiment erzielt.
... For more realistic particles with a wide-size distribution, there exists not only the back-mixing problem, but also that the time required for the complete reaction of the wide-size particles does not match the particles' residence time [6,8]. For instance, for the gas-solid reaction under the chemical reaction control, the external diffusion control, and the internal diffusion control, the time required for the complete conversion of the particles is proportional to the , , and , respectively [6,9,10], ...
... Fig. 4(a) shows the results of regulating the MRT ratio of coarse and fine particles in the fluidized bed with an elutriation pipe or a horizontal pipe, where , , and represents the 1th, 1.5th, and 2th power of their diameter ratio, respectively. According to the unreacted shrinking core model [6,9,10], when the reaction rate of both coarse and fine particles is controlled by the same control mechanism, the time required for the complete conversion depends theoretically on the particle size ratio of coarse and fine particles. For instance, for the gas-solid reaction of the chemical reaction control, the external diffusion control, and the internal diffusion control, the time required for the complete conversion of the particles is proportional to , , and , respectively. ...
How to simultaneously regulate the residence time of polydisperse particles and completely inhibit particle backmixing remains a challenge of fluidization technology. In this study, it is shown that adding elutriation pipe into multiple-chamber fluidized beds to strengthen particle elutriation and entrainment is an effective measure. Coarse-grained CFD-DEM simulation results show that the addition of the elutriation pipe can completely inhibit the particle backmixing between adjacent chambers, and the mean residence time (MRT) ratio of coarse and fine particles can be regulated to be larger than their diameter ratio. Furthermore, a study on the numbered-up multiple-chamber fluidized beds find that (i) the MRT ratio of coarse and fine particles can be larger than the 1.5th power of their diameter ratio with full suppression of particle backmixing between adjacent chambers; (ii) the MRT of each size of particles is a linear function of chamber number, whereas the MRT ratio approaches an asymptotic value. The results are of guiding significance for improving the overall conversion rate of polydisperse particles.
... Besides, it has been also studied experimentally and examined industrially by many researchers (Adhia, 1969;Natesan and Philbrook, 1970;Queiroz et al., 2005), thus the roasting of ZnS is adopted to verify the correctness of CFD simulation method established in this paper. Fig. 2 shows the experimental FBR for the roasting of ZnS particles by air (Yagi et al. 1961), along with the corresponding 3D computational mesh. The detailed physical properties of the solid and gaseous reactants are listed in Table 1. ...
... The solid residence time and reaction temperature are the two key parameters that affect the performance of the continuous FBR. Yagi experimentally determined that the time required for the complete conversion (h) of ZnS particles at 700 and 800°C was 20.0 and 3.8 min, respectively (Yagi and Kunii, 1961). Fig. 4 shows that the simulated X À s reach the steady state around 30.0 and 5.0 min, which are longer than the corresponding h for the solid back-mixing and wide RTD in the continuous FBR. ...
Non-catalytic fluidized bed reactors (FBRs) have been utilized in various industries. In this study, a computational fluid dynamics (CFD) model, involving a combination of transport processes, intrinsic kinetics, and flow structure, is established and validated to investigate the continuous gas-solid reaction. The simulated results indicate that the solid conversion rate is determined by the solid reaction rate and the mass flow rate. Traditional interphase transfer models have been proven to overestimate the momentum and mass transfer coefficients, and cause deviations in the predicted results. The gas-solid reaction rate, obtained from the structure-based model, depends on reaction time and bed position owing to the variations in the overall reaction rate constant and the non-uniform gas-solid flow structure. The period longer than twice the time required for complete conversion of particle has little effect on the solid conversion process, because of the higher internal diffusion resistance and the wider residence time distribution of particles. The mass transfer during the bubble phase also contributes to the reaction process. Therefore, this study provides a methodology for the CFD simulation of continuous non-catalytic FBRs.
... The raw materials used in the fluidized bed magnetizing roasting process normally have a wide particle size distribution (Zhu and Li, 2014). Studies on the reaction kinetics of iron oxide reduction (Yagi and Kunii, 1961;Hou et al., 2012Hou et al., , 2015 have concluded that the complete conversion time of a particle is highly dependent on its size, and it takes tens of minutes to fulfil the reduction of iron oxide for most iron ores from China. Furthermore, the reduction of iron oxide is a sequential reaction process, likely according to the sequence of Fe 2 O 3 → Fe 3 O 4 → FeO → Fe, in which the desirable product (Fe 3 O 4 ) is an intermediate. ...
... It is unfortunately not possible to quantitatively evaluate this point yet, since only the bed hydrodynamics is simulated, no chemical reactions are involved in the simulations. It however still possible to offer insight into the system: according to the study of Yagi and Kunii (1961), if the particle conversion is limited by chemical reactions which is most likely occurred in the conversion of fine particles, the complete conversion time of a particle is scaled as d p , and if the internal diffusion is the limiting step which is most likely occurred in the reaction of coarse particles, the complete conversion time is scaled as d 2 ...
Residence time distribution of particles is a critical parameter for proper design of gas-solid fluidized beds, especially in many non-catalytic solid conversion processes where it is highly desirable to match the residence time of a particle and its complete conversion time to achieve the synchronized conversion of particles of different sizes. However, the requisite of considering particle polydispersity and the long residence time of particles required by reaction kinetics together pose a great challenge to the computational fluid dynamics study of such systems. To this end, a GPU-based, massively parallel coarse-grained CFD-DEM method-the EMMS-DPM method (Lu et al., 2014) was extended to simulate the residence time distribution of polydisperse particles in a continuously operated multiple-chamber fluidized bed with a calculation of physical time of up to one hour. It was shown that the experimentally measured pressure drop of the bed or the solid holdup can be predicted reasonably well by the ad hoc drag models of non-spherical and polydisperse particles proposed in present study; the residence time distribution of particles of whole system can also be predicted correctly; and finally, the ratio of the mean residence time of coarse particles to that of fine particles is about three, which is insufficient to achieve the synchronized conversion of particles of different sizes according to an ideally theoretical analysis, great effort is needed to get a better match between the residence time and the compete conversion time of particles.
... In fluidized bed reactors, different size particles require different residence times to achieve complete conversion. For instance, for the reactions with limiting by chemical reaction or by the internal diffusion, the time for a particle to a complete conversion is proportional or quadratically proportional to the particle size d p , respectively [4]. However, in a conventional fluidized bed, it is difficult to match the residence times of the different size particles with their respective complete conversion times, especially when a wide size distribution (WSD) is encountered. ...
... It is ideal that the MRT of particles in each size is identical to their τ. According to the shrinking core model [4], τ is proportional to the particle diameter under the reaction control with a first order. Fig. 5 shows the MRT and the complete conversion time for the different size particles at the fluidization number of 23. ...
For non-catalytic gas-solid reactions, it is desirable to match the mean residence time (MRT) of a particle and its complete conversion time (τ) in fluidized beds. In this study, the MRTs of the particles with wide size distribution (WSD) were characterized and tuned in a continuous fluidized bed by varying the gas velocity and by the introduction of baffle. For the WSD particles with maximum diameter ratio of 4, the MRT ratio of the coarse to the fine particles increases from the 1.1 up to 1.7 with only changing the gas velocity. By introducing baffles into the fluidized bed under a relatively high gas velocity, the MRT difference for the different size particles becomes more prominent. With four layers of baffle, the MRT ratio of the coarse to the fine particles can reach 5.5. This study provides a new way to adjust the MRT difference for particles with WSD.
... 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. ...
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.
... 。实验方面， 白 书培等 [12] 发现在气速、 粒径、 床高、 颗粒流量等操作 条件中， 气速是影响停留时间分布的主要因素， 随 着气速的增加， 颗粒在床内的混合加剧， 气速达到 一定值时， RTD 曲线出现多峰。但高巍等 [13] 认为颗 粒流率、 床高、 粒径分布是影响颗粒 RTD 的主要因 素， 气速则是次要因素。颗粒进料流率也是影响颗 粒 RTD 的重要因素， 流率越大， 颗粒停留时间越短， 颗粒流动向平推流靠近 [13] 。Matheson 等 [14] 发现相比 粗颗粒， 细颗粒在床内的混合程度更强， 粗颗粒停 留时间分布更趋于平推流 [13] 。不同粒径颗粒在流化 床中停留时间存在差异， 随着颗粒粒径的增加， 颗 粒平均停留时间增长 [15] ， 同一流化床内粗颗粒比细 颗粒停留时间更长 [16] 。Yagi 等 [17] [39] ， 采用 基于 GPU 大规模并行的粗粒化 CFD-DEM 方法 [40] ...
Scale-up of fluidized bed is a great challenge in chemical engineering. In order to explore the particle flow behavior and residence time distribution characteristics of the continuously operated polydisperse fluidized bed during the scale-up process, a large-scale parallel GPU-based coarse-grained CFD-DEM method coupled with a polydisperse and non-spherical particle drag model was used. Long-term particle residence time simulations were carried out in a continuously operated three-dimensional fluidized bed. Through the simulation of fluidized beds of different sizes (lengths), it is found that the mean residence time (MRT) of particles of different sizes has a linear relationship with the length of the fluidized bed. This relationship can be used to predict the particle MRT of larger fluidized beds. As the length of the fluidized bed increases, the difference in MRT of particles with different sizes becomes larger, indicating that the increase in the length of the fluidized bed has a certain ability to regulate the residence time of particles with different sizes.
... 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]. ...
Cellular automata are frequently used to model chemical reactions and processes. In this paper, a direct relation is established between chemical kinetic models for surface and diffusion controlled reactions and cellular automata parameters. The considered particles are allowed to have growing/shrinking sizes, caused by the difference in the volume of the consumed reactant and the formed reaction product. From the moment a minimum diffusion layer thickness is obtained, the cellular automata approach can be applied to study the diffusion (ash layer) controlled model for both cases. In order to be able to also describe the reaction before this minimum diffusion layer thickness is formed, chemical reaction controlled and diffusion controlled models are combined here. Applying this hybrid model, a closed-form relation is found between the cellular automata parameters (particle size, reaction probability) and the fundamental kinetics of surface (β1) and diffusion (β2) controlled reactions.
... This model was first proposed in the seminal work by Crank (Crank, 1957(Crank, , 1975. When applied to sorbent spherical beads, it is an example of the well-known so-called "shrinking unreacted core" model (Yagi and Kunii, 1961;Ruthven, 1984;Levenspiel, 1999;Leyva-Ramos et al., 2010, 2012 in which adsorption of the diffusing solute progressively builds up an ash shell of reacted material at the periphery of the bead and leaves an unreacted core at the centre, that shrinks in the course of time. The model introduced by Crank was solved in the case of a very large (virtually infinite) amount of solute, in which the external solution concentration could be taken as constant (Crank, 1957(Crank, , 1975Ruthven, 1984;Levenspiel, 1999). ...
The most popular formula used in the literature about liquid/solid adsorption kinetics to describe diffusion-controlled processes is the intraparticle diffusion (IPD) equation. However, this formula was introduced originally for pure diffusion. It does not account explicitly for the effect of adsorption (except in the limit of very low adsorbate concentration). In this work, the problem of diffusion-controlled kinetics is studied by using a diffusion-adsorption model which should hold when the solute concentration in the external solution is sufficiently high. The case of a finite amount of solute initially in the stirred batch adsorber is solved analytically. For short times, the formula for the uptake turns out to have the same form vs. time as the IPD equation. However, it also predicts a decrease of the fractional uptake with the initial bulk concentration, as observed in the literature, and it shows that the IPD diffusion coefficient is a lumped parameter depending on the experimental conditions. These theoretical results are used for a discussion of the IPD equation and for descriptions of experimental results taken from the literature. © 2016, Universidad Autonoma Metropolitana Iztapalapa. All rights reserved.
... In eq 11, R ash = R 2 ρ T/(6 e ) accounts for the resistance to diffusion of water through the ash layer, and its value depends on the initial dimensions of the grain and the diffusivity of the gas through the solid product. Accounting for both the surface reaction kinetics and the resistance to diffusion in the product layer, the following relation is obtained: 18,19 ...
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.
... Yagi and Kunii [31][32][33] distinguish five steps occur during reaction succession; ...
A direct link between the chemical reaction controlled (shrinking core) model and cellular automata, to study the dissolution of particles, is derived in this paper. Previous research on first and second order reactions is based on the concentration of the reactant. The present paper describes the reaction kinetics based on particles and takes into account the shape and specific surface of these particles.
As a vehicle for the present study of cellular automata, a simplified version of the CEMHYD3D model is used. During the research it was found that during the dissolution of particles, additional reactive surface was created due to the dissolution of voxels in the middle of the top-surfaces. Therefore a modification of the dissolution routine within CEMHYD3D was introduced. This modification introduced the preference of the system to dissolve voxels on the outside of the particles rather than the middle of the top-surfaces of the particles. In this way the increase of reactive surface is prohibited and a spherical shape maintained.
Using this modification, it is proven that the dissolution of digitized particle can be describe based on the chemical reaction controlled system. Based on 165 simulations a general linear relation between cycles and time was derived. The derived model can describe the reaction sufficient up to 99.9%. Therefore it can be concluded that the single ‘cellular automata’ particle unambiguously related to the chemical controlled reactions.
... The film-pore diffusion model (FPDM) of interest in this work was proposed by Spahn and Schlünder (1975) and Brauch and Schlünder (1975), based on the unreacted core theory (Levenspiel, 1999;Yagi and Kunii, 1961). This model describes the occurrence of adsorption by external film mass transfer (which may be negligible), followed by intra-particle pore diffusion to the adsorption sites where solute molecules (adsorbate) are taken up. ...
Mathematical models for a batch process were developed to predict concentration distributions for an active ingredient (yancomycin) adsorption on a representative hydrophobic-molecule adsorbent, using differently diluted crude fermentation broth with cells as the feedstock. The kinetic parameters were estimated using the maximization of the coefficient of determination by a heuristic algorithm. The parameters were estimated for each fermentation broth concentration using four concentration distributions at initial vancomycin concentrations of 4.96, 1.17, 2.78, and 5.54 g l(-1). In sequence, the models and their parameters were validated for fermentation broth concentrations of 0, 20, 50, and 100% (v/v) by calculating the coefficient of determination for each concentration distribution at the corresponding initial concentration. The applicability of the validated models for process optimization was investigated by using the models as process simulators to optimize the two process efficiencies.
A mesoscale model based on the lattice gas cellular automata (LGCA) is proposed for heterogeneous reaction in porous media. This model features an entirely discretized reaction system, including discrete space, time, gas phases, and solid particle. To describe gas diffusion at solid nodes and gas–solid heterogeneous reaction on the phase boundary, two local probabilities are proposed, which are verified by the analytical solutions for gas diffusion and gas–solid reaction problems. This model was then applied to the hydrogen reduction of porous Fe3O4. The effects of the porosity, reaction rate constant (kl), and initial H2 concentration on the reduction were analyzed. The results indicate that the reaction rate increased with increasing porosity, kl, and H2 concentration. The solid product Fe was randomly distributed on the framework of Fe3O4 at smaller kl and concentrated around the unreacted Fe3O4 at higher kl, which is consistent with our experimental results.
Hydrophilic nanosized minerals exposed to air moisture host thin water films that are key drivers of reactions of interest in nature and technology. Water films can trigger irreversible mineralogical transformations, and control chemical fluxes across networks of aggregated nanomaterials. Using X-ray diffraction, vibrational spectroscopy, electron microscopy, and (micro)gravimetry, we tracked water film-driven transformations of periclase (MgO) nanocubes to brucite (Mg(OH)2) nanosheets. We show that three monolayer-thick water films first triggered the nucleation-limited growth of brucite, and that water film loadings continuously increased as newly-formed brucite nanosheets captured air moisture. Small (8 nm-wide) nanocubes were completely converted to brucite under this regime while growth on larger (32 nm-wide) nanocubes transitioned to a diffusion-limited regime when (∼0.9 nm-thick) brucite nanocoatings began hampering the flux of reactive species. We also show that intra- and inter-particle microporosity hosted a hydration network that sustained GPa-level crystallization pressures, compressing interlayer brucite spacing during growth. This was prevalent in aggregated 8 nm wide nanocubes, which formed a maze-like network of slit-shaped pores. By resolving the impact of nanocube size and microporosity on reaction yields and crystallization pressures, this work provides new insight into the study of mineralogical transformations induced by nanometric water films. Our findings can be applied to structurally related minerals important to nature and technology, as well as to advance ideas on crystal growth under nanoconfinement.
The promotion effect of pre-oxidation on reduction of ilmenite was revealed from the view of pore formation. The result shows that the enhancement of pre-oxidation on reduction of ilmenite ore is attributed to the formation of porous structure during the reduction process. Reduction of ilmenite is inhibited by iron-rutile topology structure formed on the particle surface. By contrast, porous structure ilmenite is regenerated during the ferric-to-ferrous reduction stage of the pre-oxidized ilmenite with dominant reduction rate over diffusion rate of produced ferrous ω ≥ 33.2 mol/m⁴. The newly formed porous structure ilmenite enlarges particle surface area with facilitated gas-solid contact, thus it is responsible for the enhancement of the reduction of pre-oxidized ilmenite. A novel formation mechanism of porous structure is also proposed based on the competition and coordination between the reduction rate and diffusion rate determined by reduction potential and temperature.
The reduction of wüstite (FeO) is the most difficult step in the multi-step of iron oxides, and the basic characteristics of the hydrogen reduction of FeO are particularly important for the low-carbon development in metallurgy. In this work, the hydrogen reduction of pure FeO pellets was studied numerically by a 2D mesoscale method, which was further developed based on the lattice gas model. The method employed the directional probability and reaction probability to describe gas diffusion and reaction, respectively. The method was firstly validated by comparing with experiments reported by Usui et al. Then, the influence of reaction temperature, particle size, and porosity on the hydrogen reduction of FeO was conducted. The results demonstrated that the reaction rate increased with increasing temperature, increasing porosity, and decreasing particle size. The reaction mechanism depended on FeO pellet radius and porosity, it was boundary reaction at smaller radius (80 μm) or smaller porosity (0.210).
Exploitation and utilization of mineral resources have played a vital role in China’s rapid economic developments. Although the history of mineral processing is quite long, technologies in this field have varied with the changes of market demands. This is particularly the case for minerals whose high-grade deposits are depleting. The aim of this review is to present our recent efforts on developing new routes for the utilization of low-grade minerals, such as iron ores and brine-containing lithium. The emphasis on the two minerals lies in the fact that iron plays a vital role in modern-day civilization and lithium is a key component in electric vehicles for transportation. Furthermore, the utilization of magnesium chloride reserves, one of the largest wastes in western China, as raw materials for fabrication of functional materials is also included in this review.
Multi-baffle fluidized beds are recognized as efficient for controlling the difference in the mean residence time (MRT) of particles with a wide size distribution (WSD). Modeling the MRT of the particles of the each size is of great importance in the design of baffled fluidized beds for various applications. An analogy to the gas-liquid distillation model, based on the relative elutriation degree, was proposed herein for predicting the MRT of the particles of each size. The model was validated by comparison of the predicted and measured composition of the particles of each size in baffle-free and baffled fluidized beds. Moreover, the effects of the gas velocity, number of baffles, and baffle structure on the difference in the MRT for the WSD particles were investigated by applying the proposed model.
The decomposition kinetics of low grade coals was studied and compared with the kinetics of higher grade coals using thermogravimetric analysis. The effect of atmospheres (air, O2 and N2) on coal decomposition kinetics was also investigated. Experiments were carried out under non-isothermal conditions from room temperature to 950 °C at a heating rate of 10 °C/min. Three kinetic models—multiple linear regression equation, unreacted shrinking core and continuous reaction—were used to determine the kinetic parameters of coal decomposition. From the kinetic parameters determined through the multiple linear regression equation, coal type and the atmosphere had an effect on coal decomposition kinetics. Also, there was some variation in the kinetic parameters of coal decomposition determined by the chosen kinetic models. However, the model employing multiple linear regressions yielded consistent results with respect to theoretical background. Under air, the order of the secondary decomposition of coal samples was found to be 0.88, 1.33, 1.69 and 1.52 for samples A, B, C and D, respectively. The order of the secondary decomposition of coal samples when operated under O2 was 1.09, 1.45, 2.36 and 1.81 for samples A, B, C and D, respectively. Under N2, the order of the secondary decomposition of coal samples was 0.72, 0.79, 1.15 and 1.02 for samples A, B, C and D, respectively.
The oxidation kinetics of U3O8 powder to ε-UO3 in an NO2 environment was measured by in situ x-ray diffraction (XRD). Experiments were performed at temperatures of 195, 210, 235, and 250 °C using a custom designed and fabricated sample isolation stage. Data were refined to quantify phase fractions using a newly proposed structure for the ε-UO3 polymorph. The kinetics data were modeled using a shrinking core approach. A proposed two-step reaction process is presented based on the developed models.
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
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.
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.
This paper treats the behavior of solids which circulate between two environments, both in mixed flow. In the reactor the solid react and remove a component from the gas stream, in the regenator another reaction takes place releasing the captured material and restoring the solid to its initial state. Shrinking core kinetics is assumed in which case the particles will have a varying number of concentric rings of product. We related the mean composition of the solid stream with the system parameters (flow rate of solid and size of units) and the particle kinetics, and present the results in the form design charts.
A comparative assessment of the attrition phenomena occurring in fluidized beds, pneumatic pipelines, and spouted beds has been made using the distributed fracture model. The controlling mechanisms responsible for attrition in these systems have been identified. The model is shown to correctly predict the interrelationship between the fraction of feed attriting and the distribution of sizes produced on attrition. A simple method is developed to estimate attrition in continuous fluidized and spouted beds. An analytical expression is also derived to calculate the size distribution of the product fines when the feed follows a specific distribution equation.
The development of injectable bone cements requires a detailed understanding of the reactivity of tricalcium phosphate (TCP)-based cements. The present study systematically investigates a broad set of materials with varying particle size, crystal phase and degree of crystallinity prepared by solid state reaction or flame spray synthesis and sintering. Amorphous TCP nanoparticles of 13, 19 and 40 nm particle diameter were highly reactive and set to calcium deficient hydroxyapatite (CDHA) within minutes. A pronounced increase in reactivity was observed for smaller nanoparticles while the total energy release during setting was constant. The use of α- or β-TCP as starting material confirmed the importance of phase composition in determining cement reactivity. These crystalline phases were much less reactive or even inactive and showed a pronounced influence of the preparation method. The experimentally measured kinetics was used to formulate a physical model of the cement setting reaction based on the shrinking core model. This detailed theoretical understanding of the cement setting processes can now assist the development of injectable cements for minimally invasive orthopedic surgery.
Initial rates were measured for the reduction of single pellets of nickel oxide with carbon monoxide at atmospheric pressure and temperatures from 566 to 796°C. The nickel oxide pellets were porous (ϵ0 = 0.032 − 0.35) and intrapellet diffusion retarded the rate so that the shrinking core model was not applicable. Effective diffusivities for the lower porosity pellets were very small, corresponding to tortuosity factors of about 180 for ϵ0 = 0.032 and 92 for ϵ0 = 0.062.
The reaction appeared to be first order in carbon monoxide. Rate constants, based upon the intraparticle area, indicated an activation energy of 47 kcal/g.-mole over the temperature range 566 to 682°C. At higher temperatures the rate was constant. These results, while not conclusive, are in agreement with a reaction sequence consisting of formation of nuclei of nickel atoms in the nickel oxide surface, rapid adsorption of carbon monoxide at the nickel-nickel oxide interface, migration of the adsorbed carbon monoxide to the adjacent lattice, and a slow reaction to extract oxygen from the lattice.
Steady-state behavior of a non-adiabatic gas-liquid CSTR is classified applying a second-order reaction model without any limitation on the reaction regime. Uniqueness and multiplicity regions are determined in the parameter space of reactivity versus liquid residence time, with the ignition and extinction points explicitly shown. An isola with five steady states is found possible for the adiabatic reactor; however, even a small heat loss reduces the number of steady states to three.
A reactor model is presented to calculate the sulfur retention and SO2 emission of a fluidized-bed coal combustor with absorption of SO2 by limestone or dolomite. It is based on the two-phase theory of fluidization and a two parameter simplified rate expression for the sulfation reaction. Both parameters can be determined by experimental reaction rate measurements. In the overall reactor model, an average size is assumed for all the stone particles in the bed. Sulfur retention is found to be dependent on only three dimensionless parameters. Comparisons with experimental measurements indicated that the model predicts satisfactorily the dependence of sulfur retention on the Ca/S ratio, sulfur content of the coal, excess air, gas residence time, and sorbent type.
Kinetics of oxidation of ZnS particles in a batch-type fluidized bed were studied at temperatures between 800 and 910°C. A
two-phase model was employed for the fluidized bed, and the partial pressure of oxygen and the gas-film mass transfer coefficient
on the particle surface were separately evaluated in gas bubbles and in the emulsion phase. The calculated fractional reaction
coincided well with the experimental results. The difference in O2 partial pressure between gas bubbles and emulsion phase was found to be fairly large especially under the vigorous fluidizing
condition. Furthermore, it was shown from the mathematical model that the reaction of ZnS particles in the gas bubbles is
negligible because of the extremely low solid concentration and that the overall rate of reaction in the emulsion phase is
virtually controlled by the rate of gas-film mass transfer at higher temperature. The resistance of interfacial reaction within
the particle also becomes significant when the temperature is lowered.
This paper develops general equations in terms of mass balances to relate the particle size distributions and flow rates of feed and outflow streams in fluidized beds. These equations take into account the size distribution of feed solids, arbitrary particle growth or shrinkage within the bed, and the effect of elutriation of fines on the properties of both outflow and carryover streams.Practical calculation procedures are outlined. The equations are also applied directly to a circulation system where particles grow in one unit and shrink in the other to yield the conditions for stable operations.
The sorption of acid dyes from aqueous effluents onto activated carbon has been studied. The effects of initial dye concentration and activated carbon mass on the rate of Acid Blue 80 and Acid Yellow 117 removal have been investigated. Three mass transport models based on film and pore diffusion control have been applied to model the experimental concentration decay curves. The models are compared on the basis of the solid-phase loading capacity using various assumptions since the assignment of an appropriate solid-phase loading has been the subject of several papers on this topic and no comparisons have been provided on the effectiveness of each approach. The equilibrium solid-phase concentration is assumed: (i) incorporating a time-dependent solid-phase concentration Ye,t, (ii) equal to the intersection point of the equilibrium isotherm and the operating line and (iii) the point on the equilibrium isotherm where the liquid-phase concentration equals the initial concentration in the film–pore diffusion model.
Zinc blend concentrate with considerably wide distribution of size was roasted in the fluidized bed. The results of roasting were almost satisfactory and they were analysed with the preceding theory which could explain the several new phenomena recognized in this experiments and made clear the mechanism of roasting in the fluidized bed.
A mechanism of heat transfer from a tube wall to fluid flowing in a packed bed is proposed whereby : (1) a mass of fluid is thrown against the wall ; (2) the fluid at the wall assumes the wall temperature and transfer occurs inward ; (3) this mass of fluid moves away from the wall and is replaced by new fluid. On the basis of this mechanism the following equation was derived using order of magnitude considerations : This expression is compared with data on wall film coefficients for cylindrical packings. Good agreement is obtained. However, no such agreement is obtained for spherical packing. The explanation for this difference proposed by Plautz [3] is subscribed to.RésuméPour le transfert de la chaleur entre la paroi d'un tube et un fluide en mouvement, dans un lit poreux, l'auteur fait les hypothèses suivantes : 1.Une masse de fluide rencontre la paroi.2.Le fluide, au contact de la paroi, prend sa température et un transfert s'établit vers l'intérieur.3.Cette masse de fluide quitte la paroi et est remplacée par une autre.Sur la base de ce mécanisme et en tenant compte de ces considérations par ordre d'importance, il obtient l'équation ci-dessus qu'il compare aux valeurs expérimentales des coefficients de “film le long de la paroi” pour des garnissages cylindriques. L'accord est bon, mais pour des garnissages sphériques, l'accord est moins satisfaisant. L'auteur accepte l'explication de cette différence proposée par Palutz.
When a fluid flows through a vessel at a constant rate, either “piston-flow” or perfect mixing is usually assumed. In practice many systems do not conform to either of these assumptions, so that calculations based on them may be inaccurate. It is explained how distribution-functions for residence-times can be defined and measured for actual systems. Open and packed tubes are discussed as systems about which predictions can be made. The use of the distribution-functions is illustrated by showing how they can be used to calculate the efficiencies of reactors and blenders. It is shown how models may be used to predict the distribution of residence-times in large systems.RésuméQuand, dans un récipient, on introduit, à vitesse constante, un fluide donné, on suppose généralement soit un mélange parfait, soit un “écoulement frontal parfait.” En pratique, de nombreux systèmes s'écartent de l'une ou l'autre de ces hypothèses simplificatrices et les calculs qui en résultent sont plus ou moins inexacts. L'auteur expose, pour des systèmes réels, comment l'on peut définir et mesurer des fonctions de distribution pour la “durée de séjour”: ceci peut s'appliquer à des tubes vides ou munis de garnissages. Par emploi de ces fonctions de distribution, l'auteur montre comment on peut calculer l'efficacité des réacteurs ou des mélangeurs. Des modèles peuvent être utilisés pour prévoir la répartition des “durées de séjour” dans des systèmes de grandes dimensions.
According to the concept of two-phase fluidization, a part of the gas in a fluidized reactor passes through the uniform dispersed solid-gas phase in the form of bubbles, channels, and slugs. Material transport by mixing or diffusion takes place at the phase boundaries. A mass transfer coefficient between the two phases may be used to evaluate the effectiveness of contact between the gas and solid. The reaction rate for the catalytic decomposition of nitrous oxide was determined in a fluidized bed of impregnated alumina particles and compared with the corresponding rate in a fixed bed. Simultaneous rate equations were established based on the assumption that the continuous phase is either completely unmixed or uniformly mixed, and the discontinuous phase passes without mixing. The effects of the velocity of the gas, the particle size, and the bed depth on the transfer coefficient were investigated. Applications to heat transfer in fluidized beds and equipment design are discussed.