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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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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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This study aims to develop a mathematical model that can explain the regeneration process mechanism of the aluminum which is in the packaging of food bricks (the Pet-Al residue Rsd(Pet-Al) is a laminated foil residue made from polyethylene and aluminum foil) as a raw material in alkaline solution and evaluate that model based on the experimental data. In fact, the literature shows that a symmetrical diffusion of the reagent occurs through the two sides of large bare surfaces, this is true when both surfaces of the solid are naked. In our case, the Pet-Al residue suggests another mode of attack seeing that both of aluminium surfaces are covered with polyethylene. For that, a new Edge Shrinking model called “Aymen Edge Model” was invented. The process mechanism that occurs involves the reactant diffusion step and the chemical reactions step; those steps run simultaneously. The concentration of free hydroxyls OH⁻ in the solution compared to the reference solution, [OH-]solution - [OH-]reference = f(t), gives an idea of the different stages observed during of the consumed hydroxyls evolution. The SEM micrographs resulting, after a basic treatment, with concentration from 1M to 10M at a temperature ranging from 20 to 80 °C, proves that the attack is done by the edges and also confirm the obtaining salts.
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This paper reports on experiments conducted with a cold flow model utilized for the investigation of the particle residence time distribution and mixing characteristics in a bubbling fluidized bed with continuous solids exchange. The investigated system is of a rectangular cross section (0.4 × 0.2 m) with a bed height of 0.17 m. A measurement device based on an alternating current bridge circuitry coupled with lock-in amplifier technology was built in the scope of quantifying the solids residence time distribution, whereby a pulse-injected ferromagnetic tracer creates the input signal. The implementation of a profound mathematical routine ensures the reproducible calculation of the particles mean residence time and characteristic values describing particle mixing phenomena. Therefore, the E-curve was modeled by mathematical convolution of the exit age distributions available for an ideally mixed continuous stirred tank reactor and a plug flow reactor with axial dispersion. It is shown that the in-bed mixing is highly dependent on the fluidization rate as well as on the solids circulation rate. Albeit the lowest superficial gas velocity equals a fluidization number of 4.7, the formation of dead spaces and short-circuit flows was observed under these conditions. Axial dispersion coefficients in the range of 5·10-3 to 7·10-1 m² s⁻¹ were obtained.
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Anthropogenic climate change is amongst the greatest of challenges to human civilization. A key area that will play a large role in mitigating its effects are clean fossil fuel applications. Clean coal combustion can be achieved with an oxygen-fired pressurized fluidized bed combustor incorporating carbon capture and storage. In relation to pressurized fluidization processes, understanding the influence of pressure on fluidized bed hydrodynamics and, in turn, their effect on parameters including fuel residence time is essential. For the combustor under consideration here, a fraction of the heat exchanger boiler tubes are submerged in the fluidized bed such that the effect of the horizontal tube bundle on the fuel residence time is of great importance. The main focus of the present work was to evaluate the impact of gas velocity, pressure, presence or absence of a horizontal tube bundle and fuel feed rate on the average fuel residence time in a dense gas-solid fluidized bed. Experiments were conducted under cold flow conditions in a pressurized fluidized bed with an inner diameter of 0.15 m. The fluidization material was large glass beads (1.0 mm in diameter) while fuel particles were simulated with smaller glass beads (64 and 83 μm in Sauter mean diameter) that were susceptible to entrainment. Operating pressures and superficial gas velocities were maintained between 101.3 and 1200 kPa and 1.5 and 3.2 Umf, respectively. To simulate continuous fuel injection, experiments were conducted with the fuel surrogate particles being continuously fed to the fluidized bed of large particles over a desired period of time. Downstream, entrained particles were captured to determine the average entrainment rate and average mass of fuel particles inside the fluidized bed at steady state, which yielded the average fuel residence time. The combination of elevated pressure with the tube bundle present was found to have the most influential impact when compared to base conditions of atmospheric pressure and with no tube bundle present. It was found to enhance gas bubble break up and reduce the average gas bubble size substantially. In turn, this increased the average residence time of 83 μm particles by nearly three-fold in comparison to the case of atmospheric pressure with no tube bundle present. The effect of gas velocity on particle residence time was not found to be statistically significant under the range tested. Similarly, the effect of increasing fuel feed rate by 50% had no statistically significant impact.
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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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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.
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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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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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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.
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A prototype horizontal pulsed fluidized bed (HPFB) has been built for continuous biomass torrefaction in our lab. Solids residence time distribution (RTD) of hemlock sawdust in the HPFB reactor was measured to study particle transport and mixing using a pulse injection of particle tracer. Effects of weir height, gas pulsation frequency, solids feed rate and gas velocity were investigated. A modified axial dispersion model was adopted to fit the experimental RTD curves, where horizontal dispersion coefficients were obtained. It is found that horizontal dispersion coefficients were slightly higher in the deeper bed. In the shallow bed, horizontal dispersion coefficients increased with increasing solids feed rate. The solids mixing intensity also found to increase with increasing the gas velocity. Horizontal solids dispersion coefficients obtained in the HPFB were significantly smaller than values calculated by literature correlations. A correlation in the shallow HPFB was established based on our experimental data.
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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