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As an illustration of the potential utility of optimal-control theory, we determine the time-varying electrode potential which maximizes the desired product produced from a coupled, chemical-electrochemical reaction sequence occurring in a well-mixed batch reactor for a specified reaction time. The reactant is electrochemically reduced to a stable intermediate which is itself a reactant for two competing parallel reactions: a homogeneous chemical decomposition to the desired product, or a further electrochemical reduction to an undesired product. If the transfer coefficient of the first reaction is greater than that of the second, then chattering control, in which the potential switches at an infinite frequency between two limits, is optimal. If the transfer coefficients have the opposite relationship, then a continuous, time-varying potential is optimal. We compare the results of applying the optimal, chattering-potential control with those resulting from the best continuous and steady controls. Improved selectivity results from a chattering control and may be effected even in the presence of significant mass-transfer resistance. Since an infinite-frequency control cannot be actually implemented, we discuss how a high-frequency, rectangular waveform can be determined which results in essentially the same product distribution as a chattering control. A qualitative, simple-to-apply method to determine whether selectivity enhancement is attainable using chattering controls is also illustrated. 相似文献
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Joel F. Moxley 《Chemical engineering science》2003,58(20):4705-4708
“Ignition/extinction” phenomena and steady-state multiplicity were discovered in an autohumidification polymer electrolyte membrane fuel cell. At steady state, the water produced by the fuel cell reaction is balanced by water removal by the flowing reactant gas streams. Ignition, corresponding to a high fuel cell current, arises from positive feedback between the water produced by the reaction and the transport of protons in the membrane. A critical level of membrane hydration is required for ignition; insufficient membrane hydration will extinguish the fuel cell current. This new autocatalytic mechanism has an interesting analogy to the autothermal reactor. 相似文献
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Currently available information on droplet coalescence and break-up rates in turbulent flows in mixing vessels can be used to control drop sizes in dispersed phase equipment. The effect of drop size distributions on the selectivity and productivity in multi-reaction systems is examined in this paper.
The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up.
The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed. 相似文献
The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up.
The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed. 相似文献
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提出了以双酚A、三氯氧磷和苯酚为原料合成双酚A双二苯基磷酸酯(BDP)。研究了原料配比、反应温度、反应时间等因素对产品质量和收率的影响,从而确定最佳的工艺条件:三氯氧磷、双酚A和苯酚的摩尔比为6:1:4.05,酰氯化反应温度为120℃,保温反应3.5小时,酯化反应阶段,120℃保温反应3小时,150℃保温反应3小时,产品收率为91.12%,BDP单体含量为83.68%。 相似文献
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提出了以间苯二酚、三氯氧磷和苯酚为原料合成四苯基间苯二酚二磷酸酯(RDP)。研究了原料配比、反应温度、反应时间等因素对产品质量和收率的影响,从而确定最佳的工艺条件:三氯氧磷、间苯二酚和苯酚的摩尔比为5:1:4.2,酰氯化反应温度为114℃,保温反应4小时,酯化反应阶段,120℃保温反应3小时,150℃保温反应3.5小时,产品收率为92.6%,RDP单体含量为72.5%。 相似文献
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In earlier work, we have observed discrepancies relating to the early hydration of calcium aluminate cement (CAC) when comparing data from heat flow calorimetry of CAC paste with results from mortar strength tests using the crushing method. Here, we investigated on this phenomenon and found that the sand which is used as a filler exerts a major influence on CAC hydration resulting in acceleration. Furthermore, in particular fine filler materials such as, for example, microsilica, fine limestone powder, and especially α- and γ-Al2O3 also produced a strong hydration accelerating effect which is dependent on their specific surface area. The mechanism underlying the acceleration is that under alkaline conditions their negative surface charge attracts calcium ions as was confirmed via inductively coupled plasma atomic emission measurements. Such a layer generates favourable conditions for the nucleation of CAC hydration products (C-A-H phases). The resulting crystalline hydrates which form on the surface of the filler particles submerged in CAC cement pore solution were visualized via SEM imaging. This way, specifically selected fillers can significantly accelerate CAC hydration and save precious lithium salts which are commonly used to boost the early strength of CAC. 相似文献
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Shivareddy Induri Sonali Sengupta Jayanta K. Basu 《Journal of Industrial and Engineering Chemistry》2010,16(3):467-473
The purpose of this work is to study the kinetics of the esterification of maleic anhydride with methanol to form dimethyl maleate in a batch reactor in the presence of H-Y zeolite as a catalyst. This is a series-parallel type multiple reaction where, the first reaction involves the formation of monomethyl maleate that further reacts with alcohol to form dimethyl maleate. Dimethyl maleate was found to be the only product in the reaction mixture. Temperature, speed of agitation, catalyst size, reactant mole ratio and catalyst loading have pronounced effect on the rate of the reaction. A homogeneous rate model and heterogeneous rate models have been derived and fitted with the experimental data. The activation energy was found to be 44.65 kJ/mol. 相似文献
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《Journal of the European Ceramic Society》1999,19(3):277-283
A physical model is presented that predicts the stress distribution created in a particle during its reaction with a surrounding reactant to form a uniform layer of reaction product on its surface, when the reaction involves a volume change. The results of the model are applied specifically to the case of silicon reacting with nitrogen to form Si3N4. The model predicts the generation of a high, tensile hydrostatic stress in the Si core as well as high tensile radial stress and compressive tangential stress in the nitride layer. Although the model is restricted to elastic deformation only and therefore predicts unrealistically high stresses in some cases, the results are anyway of relevance in the consideration of possible non-elastic processes such as creep and fracture and also in assessing the possible effect of stress on the reaction equilibrium. It is predicted that the nitride reaction layer would fracture during the nitridation process. A second model is also presented predicting the residual stresses arising during cooling of a partially reacted particle as a result of the difference in thermal expansion of the reactant core and the reaction product layer. In the case of the reaction of silicon to silicon nitride these thermal expansion mismatch stresses are significant but small compared to the stresses due to the chemical reaction. © 相似文献
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Paul Wencil Brown 《Journal of the American Ceramic Society》1993,76(12):2971-2976
Hydration reactions of C3 A and C4 AF with calcium sulfate hemihydrate and gypsum were investigated and the kinetics of the reactions compared. The rates of C3 A and C4 AF hydration, as determined by heat evolution, vary depending on whether the sulfate-containing reactant is gypsum or calcium sulfate hemihydrate. The following sequence of reactions involving C4 AF occurs when hemihydrate is the reactant: gypsum formation during the first hour, ettringite formation between 20 and 36 hours, and the conversion of ettringite to monosulfate over a period of about 12 hours. Monosulfate formation initiates prior to the complete consumption of gypsum. The onset of this conversion occurs at a shorter hydration time when hemihydrate is a reactant and the total amount of heat evolved is lower. The hydration reactions in saturated calcium hydroxide solution occur more slowly than those in water. Based on heat liberation, C4 AF reacts at a much higher rate than C3 A. Ettringite formation occurs during the first 8 to 9 days of C3 A hydration. Once the gypsum is consumed, ettringite converts to monosulfate during two additional days. Compared to gypsum, hemihydrate decreases the rates of hydration of both C3 A and C4 AF. The effects on the hydration characteristics of C4 AF are significant. The hydration of C3 A with gypsum in water, in saturated Ca(OH)2 solution, and in 0.3 M NaOH solution were compared. Heat evolution is the lowest for hydration in 0.3 M NaOH. The onset of monosulfate formation occurs prior to the complete reaction between gypsum and C3 A in the NaOH solution. 相似文献
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《Chemical engineering science》1987,42(1):53-61
The velocity profile in analytical form has been developed for the growing swirl in a rotating tube under stable laminar conditions by solving the equation of motion via perturbation treatments. The resultant mixing induced by fluid flow in the presence of molecular diffusion and chemical reactions has also been characterized. The results suggest that the rotational speed provides an additional degree of freedom with which to vary the level of reactant conversion and of product distribution for a consecutive-competitive reaction. 相似文献
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This paper focuses on the interactions that occur between cement phases during early hydration, especially between the hydration of alite and C3A-gypsum. This study shows that alite reaction is accelerated in the presence of gypsum. This acceleration was attributed to the interaction of gypsum with Aluminium ions present in alite. Three exothermic peaks attributable to the aluminate reaction could be observed in model cements instead of one in C3A-gypsum systems. The first corresponds to the C3A dissolution when the sulfate ions run out, but the product formed is ettringite. The second corresponds to the formation of calcium monosulfoaluminate, but the third could not be assigned to any specific reaction. The effect of alite/C3A ratio, the dispersion of the phases in the grains and the temperature were also investigated. With respect to temperature, it was found that the activation energy for the C3A-gypsum reaction was higher than that for alite. 相似文献
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The oxidation reaction kinetics of bitumen from Athabasca oil sands have been investigated in a flow-through fixed bed reactor using gas mixtures of various compositions. The system was modelled as an isothermal integral plug-flow reactor. The oxidation of bitumen was found to be first order with respect to oxygen concentration. Two models were examined to describe the kinetics of bitumen oxidation. In the first, the Athabasca bitumen is considered to be a single reactant and the oxidation reaction a single irreversible reaction. The activation energy for the overall reaction was found to be 80 kJ mol?1. This model is limited to calculating the overall conversion of oxygen. Because the fraction of oxygen reacting to form carbon monoxide and carbon dioxide increases with temperature, a more sophisticated model was proposed to take this into account. The second model assumes that the bitumen is a single reactant and that the oxidation of bitumen may be described by two simultaneous, parallel reactions, one producing oxygenated hydrocarbons and water, the other producing CO and CO2. The activation energy for the first reaction was found to be 67 kJ mol?1, and for the second, 145 kJ mol?1. This more sophisticated model explains the result that at higher temperatures more oxygen is consumed in the oxidation of carbon, because this reaction has a higher activation energy than the reaction leading to the production of oxygenated hydrocarbons and water. This model can also predict the composition of the product gases at various reaction conditions. 相似文献
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铬铁渣无害化处理与资源化利用主要集中在水泥建筑材料的应用上,但由于缺乏对铬铁渣水泥固化体固化、养护过程及其水化产物中水溶性Cr6+溶出规律和水化反应程度及水化产物的了解,从而限制了铬铁渣的资源化和规模化安全利用水平。以青海某厂铬铁渣为研究对象,对其水溶性Cr6+溶出规律及其水化产物做了研究。结果表明:水溶性Cr6+和Cr3+参与了水泥的水化反应,形成了稳定的水化产物,随着铬铁渣掺量的增加,水泥-铬铁渣复合胶凝材料水化过程中水溶性Cr6+量呈上升趋势,当掺量不大于15%时,水溶性Cr6+质量分数不超过0.000 19%,符合利用铬渣作水泥混合材的标准;铬铁渣作水泥混合材的最佳掺量是10%。 相似文献
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An important microstructural aspect of the early hydration of Portland cement (PC) is the formation of a shell of hydration products around cement grains. There is, at present, limited information on the mechanism of formation of the shell and of the chemistry of the phases that constitute the shells. Through the use of STEM imaging of early age hydrated cement pastes as early as 2 h, the present work shows that the shells correspond to the first C-S-H type product formed which has a distinct morphology compared to C-S-H formed later when the main reaction occurs (nucleation and growth stage at setting time). The shells form only around the silicate part of the grain and are not empty but filled with a fragile fibrous C-S-H which appears to have a lower (packing) density than the rest of the hydration products. The cement grains underneath the shells are seen to react unevenly and the hydration seems to follow a reaction front, leaving striations up to 1 µm deep on the grains. Over the long term, the original fragile product seems to densify and gives rise to the usual inner C-S-H. High resolution EDS chemical analysis and mappings were used to get insight into the chemistry associated with the formation of these early age products. The C/S ratio of all C-S-H (inner and outer shell) is the same (within the limits of the analysis accuracy) and evolves insignificantly over the first 24 h of hydration. High concentrations of sulfate are associated with the C-S-H formed during the early development of the microstructure, but these decrease later, the sulfate being mainly incorporated into ettringite. 相似文献
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K. M. Hanna R. L. Cook D. L. Kantro 《Journal of chemical technology and biotechnology (Oxford, Oxfordshire : 1986)》1970,20(11):341-345
The rate of hydration of dibarium silicate (Ba2SiO4) in paste form at room temperature was investigated. The uncombined barium hydroxide produced in the reaction, determined by a modified Franke method, was used as a measure of the extent of hydration. The linear relationship obtained between the uncombined barium hydroxide and the chemically combined water confirms that similar hydration products are formed at all stages of hydration, and either may be used as a measure of the degree of hydration. The rate of hydration of dibarium silicate was found to be lower than that of tricalcium aluminate, but higher than those of alite, tricalcium silicate and β-dicalcium silicate. The effect of water/solid ratio on the rate of hydration was also investigated. Dibarium silicate was completely hydrated after 30 days when it was mixed with a water/solid weight ratio > 0.7:1. 相似文献