Corrosion of ceramics in halogen-containing atmospheres

Most single component oxide ceramics undergo active corrosion in halogen-containing gases such as HCl to form gaseous corrosion products only. At high temperatures, such corrosion reactions are controlled by gaseous diffusion of the product gases away from the solid surface. As a result, the reaction kinetics and the corrosion rate can be predicted if the thermodynamics of the reaction are known. Similar behaviour is expected for nitride ceramics. However, several multicomponent oxides, typified by NiAl₂O₄, and carbides may react to form a porous solid product layer through which diffusion takes place and controls the corrosion rate. Nevertheless, even in these cases, if gaseous diffusion still controls, the rate of corrosion can be modeled and predicted.     

A new approach to the kinetic modeling of the reaction of gaseous HCl with solid lime at low temperatures

The chemical reaction between gaseous HCl and solid Ca(OH)₂ has several applications, namely in the dry scrubbing of acid gases. The behavior of this reacting system in a laboratory-scale tubular reactor was simulated using the ‘grain model’ for the solid phase and a cascade of CSTRs for the gaseous phase. This model was applied to experimental data obtained in a previous study, at low temperatures (50-130°C) and high humidity level. The results show that the diffusion of the gaseous reactant through the product solid layer is the rate-limiting step for this reaction. In the first reacting moments, when no solid product has yet been formed, the reaction is limited by the total consumption of the gaseous reactant, indicating a very fast chemical reaction . These results were compared with those obtained by two other models used to describe the behavior of the gaseous phase: the ‘differential reactor model’ and the ‘average concentration model’. We show that the differential reactor model, which has been largely applied in published works about this and other similar reacting systems, is not adequate for modeling the reaction process, particularly in its initial phase.     

A general model for the simulaiton of multi-component adsorption from a finite bath

General equations are presented to describe multi-component adsorption from a finite bath onto adsorbent particles. External film resistance and diffusional resistance within the particle are both included. Transport within the particle can be by pore or solid diffusion or both.Orthogonal collocation was used to solve the equations for two component adsorption onto uniform spherical particles for the two cases of pore and solid diffusion. In certain circumstances, the concentration profiles within the particles can show a displacement effect.By superposition of model predictions onto experimental results of Balzli [18] estimates were made of pore and solid diffusion within carbon particles. In one case studied, the estimated values of solid diffusivities were less sensitive to changes in the initial bath concentrations than the pore diffusivities.     

Direct formation of particles from drops by chemical reaction with gases

The factors which influence the direct formation of solid particles by reaction of sprays with gaseous media were investigated by studying the reaction of single macro-drops of orthophosphoric acid with gaseous ammonia. The composition, temperature and physical nature of the drops were measured or recorded as the reaction proceeded. The controlling resistance for mass-transfer was found to exist within the drop and a diffusion model adequately described the uptake of ammonia for the conditions studied. The maximum uptake of ammonia increased with delay in formation of a permanent solid phase. This delay was increased or altered by (i) reduction in acid concentration, (ii) addition of sulfuric acid, (iii) cyclic exposure of the drop to the gas, and (iv) humidification of the gas.     

Pore network model for catalytic dehydration of methanol at particle level

γ‐Alumina is used as a catalyst for converting methanol to dimethyl ether. The process takes place in a packed or fluidized bed reactor consisting of microporous particles with distributed pore sizes and interconnectivities. The efficiency of the process is, however, significantly affected by the pore space structure of the particles. All the previous attempts for modeling this phenomenon have used continuum formulation of the problem based on classical equations of mass transport and reaction, without any regards for the effect of pore space morphology. In this article, we study the catalyst's performance by developing a network model for the pore space, with distributed pore sizes and interconnectivities. The network model is used to study the effect of several parameters such as pore space morphology, concentration, and temperature on catalyst's effectiveness factor. The results will be used for reactor simulations. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Calculation of the gasification of cokes of high-ash coals on the basis of the model of randomly porous media

A mathematical model is constructed to describe the dynamics of the pore structure of cokes of high-ash coals with allowance for the fact that the different parts of the internal volume of the structure are not equally accessible to the gaseous reactant. The model accounts for the increase in the area of the pore structure due to the removal of organic material, coalescence of pores, and opening of the interior volumes of the sample in the course of conversion. In the examination of heat- and mass-transfer processes inside the particles, attention is given to the thermal effect of the reaction along with diffusion resistance in the mineral component and the layer of reaction products — which decreases the cross section of the transport pores. The results of the calculations are compared with experimental data on the gasification of culm in gaseous carbon dioxide.Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 28, No. 2, pp. 58–65, March–April, 1992.     

Carbon dioxide capture with dolomite: A model for gas-solid reaction within the grains of a particulate sorbent

This work describes a mathematical model for a gas-solid reaction taking place within reactant particles made up of very small spherical grains, which grow during the reaction process due to solid product formation around the grain inner core, so that the particle void-fraction is reduced as the reaction proceeds. The structural changes in the spherical grains are taken into account in the proposed model by the inclusion of a variable diffusion coefficient of the gaseous reactant through the developing product layer. This progressively increasing transport resistance leads to a marked reduction in both reaction rate and sorbent capacity, as observed in practice in the carbonation of calcined dolomite, a process of importance in hydrogen production by means of coal or biomass gasification.     

Reaction mechanism of a single calcium hydroxide particle with humidified HCl

The reaction of HCl with Ca(OH)₂ is investigated at industrially relevant conditions of 10% relative humidity, 250 ppm or less HCl in nitrogen and a temperature of 100 °C. A particle model is used where an interface step and diffusion in pores as well as in solid state are taken into account. The textural parameters of the model are based on data of commercially available Ca(OH)₂. Most importantly Ca(OH)₂ single crystals are exposed to HCl containing gas to independently determine the product layer diffusion coefficient. A comparison between model simulations and single-particle (SP) experiments that are performed by means of an ultrasonic levitator (i.e., a particle is held against gravity without neighbouring surfaces) reveals that the overall reaction is solely governed by pore diffusion since the interface step is reaching equilibrium almost instantly and solid-state diffusion in conjunction with mean pore wall thickness is fast at . Elementary analyses of Cl across the cross-sections of the SP show significant local textural and chemical variability that cannot be fully explained yet.     

Theoretical Model of Phosphorus Incorporation in Silica in Modified Chemical Vapor Deposition

Based on experiment, a theoretical model is developed of phosphorus incorporation in modified chemical vapor deposition. In the glass formation stage of this process, gas-phase reaction of silicon tetrachloride and phosphorus oxychloride generates submicrometer particles of phosphorus-doped silica. These particles deposit in a thin porous soot layer which is then viscously sintered. Equations for thermal and dopant transport through the soot voids and particles during sintering predict that gradients in each layer are due to inhibited diffusion of dopant through the gaseous voids of the soot, not to gas-phase gradients. Thermal gradients create variations in gas and solid diffusion and dopant solubility which enhance concentration gradients. These results apply to viscous sintering of glasses produced by flame hydrolysis and sol-gel processes.     

二氧化硅气凝胶的气相热导率模型分析

气凝胶是一种超级隔热材料,具有极低的整体热导率。气凝胶的纳米多孔网络结构极大限制了气体分子热运动,使得气凝胶中的气相热导率低于自由气体的气相热导率。本文介绍并讨论了气凝胶气相热导率的基本理论和模型,考察了孔径尺度和气凝胶固相骨架对气相热导率的影响。结果表明,气凝胶气相热导率随气压和孔径的减小而迅速降低,随气凝胶密度的增大而降低。当压力极低时,气凝胶的气相热导率远低于常压下大空间的静止空气。气凝胶纳米固体网格对气相热导率存在重要影响,在(0.01～100)×10⁵ Pa的压力范围内影响尤其显著。     

Micrograin models of reacting porous solids with approximations to logarithmic solid conversion

Several experimental studies of gaseous reactions with porous solids at slow reaction rates, where pore diffusion is not rate controlling, have shown that the heterogeneous reaction rate decreases following an apparent logarithmic law. This is superficially analogous with a first order homogeneous batch reaction. In the present study a micrograin model for a porous reacting pellet is proposed and several micrograin size distribution are examined. It is shown that dimensionless rates calculated for the expected log-normal distribution of micrograins, within a wide range of size distribution standard deviations, approximates the logarithmic law within the usual experimental error. Normal distributions and Gates-Gaudin-Schuhmann distributions for the aggregation of micrograins constituting the porous solid pellet are also considered.     

Modelling of pore structure evolution during catalyst deactivation and comparison with experiment

Supercritical fluids are often proposed as a means of extending the lifetimes of heterogeneous catalysts that deactivate by deposition of solid carbonaceous deposits, often called ‘coke’. This is because the higher density of the supercritical state, compared to the gaseous state, permits the dissolution and removal of coke precursors and coke, before coke can build up and inhibit mass transfer. However, the impact of this process on the extension of catalyst lifetime achieved depends strongly upon the nature of the pore space of the catalyst support, as this dictates the rates of mass transport and the susceptibility of the pellet to pore blockage. In order to optimise the design for running a catalytic process under supercritical conditions, it is vital to be able to predict the interaction between mass transport rates and structural evolution. Previous work has neglected the full complexity of the void space of heterogeneous catalysts, but capturing this in the model is essential to fully understand the evolution of that void space during coking. In this work, a novel structural model that captures the key features of the void space that control mass transport and structural evolution has been employed. Simulations of various reaction schemes, capturing the important aspects of the real reaction pathways, coupled with mass transport, have enabled the prediction of the particular trajectories of structural evolution to be expected. These simulations have been compared with experimental observations of the structural evolution of a real catalyst under supercritical conditions. A comparison of simulation with experiment has enabled a validation of the structural model and particular reaction scheme used in the simulations.     

Modellierung isothermer Festbettadsorber

Modelling of isothermal fixed bed adsorbers . The effective adsorption velocity in porous solids is determined primarily by the adsorption equilibrium coupled with bulk diffusion, Knudsen diffusion, and surface diffusion in the particles. Adsorption and mass transport may follow different mechanisms for different combinations of gaseous (fluid) and solid phases and for different pore size distributions. For the industrially important cases models were developed and discussed for isothermal fixed bed adsorbers. The balances of the different models show different mathematical structures, so that different mathematical evaluation methods are necessary for determination of the breakthrough curve. Computed results of the models are discussed. The evaluation of the breakthrough curves is needed for parameter estimation from laboratory scale experiments and for the design of industrial adsorbers with known parameters.     

磷酸复杂系统液固相反应动力学(Ⅰ) 分形介质中的扩散与反应机理

采用随机过程理论导出了液相在固体颗粒分形介质中的扩散方程 ,得到了分形扩散系数与自由空间扩散系数的关系式 .同时研究了以磷酸与具有丰富内孔隙的磷矿颗粒为代表的液固两相反应的机理和动力学模型 .发现已反应完毕的区段与尚未反应的区段之间的反应界面不是一个面 ,而是一个过渡区段 ,这一反应区段将逐步向颗粒中心移动 .根据固相物质的分形结构与反应机理 ,导出了描述这一过程的理论模型 .     

LIQUID AND SOLID PHASE REACTION KINETICS OF PHOSPHORIC ACID COMPLEX SYSTEM(Ⅰ) DIFFUSION AND REACTION MECHANISM IN FRACTAL MEDIA

采用随机过程理论导出了液相在固体颗粒分形介质中的扩散方程 ,得到了分形扩散系数与自由空间扩散系数的关系式 .同时研究了以磷酸与具有丰富内孔隙的磷矿颗粒为代表的液固两相反应的机理和动力学模型 .发现已反应完毕的区段与尚未反应的区段之间的反应界面不是一个面 ,而是一个过渡区段 ,这一反应区段将逐步向颗粒中心移动 .根据固相物质的分形结构与反应机理 ,导出了描述这一过程的理论模型 .     

Passivity based control of reaction diffusion systems: Application to the vapor recovery reactor in carbothermic aluminum production

We develop a passivity based controller for a reaction diffusion system. The model used in the simulation study describes the vapor recovery reactor used in carbothermic aluminum reduction. It takes into account, non-catalytic gas–solid reactions, the moving bed of solid particles and the shrinkage of the unreacted particle core. The reaction diffusion system is solved using the finite element method. We use passivity based control to adjust the carbon feed and the heat input to achieve the required conversion and maintain the temperature along the reactor. The efficiency of the reactor is determined by calculating the extent of vapor recovery and the conversion of carbon particles. The sensitivity of different parameters such as solid flow rate and column height based on the reactor performance is also determined. We show that the control scheme based on the inventory balances performs well under various operating conditions.     

On the validity of the shrinking core model in noncatalytic gas solid reaction

By using a matched asymptotic expansion technique, the shrinking core model (SCM) used in non-catalytic gas solid reactions with general kinetic expression is rigorously justified in this paper as a special case of the homogeneous model when the reaction rate is much faster than that of diffusion. The time-pendent velocity of the moving reacted-unreacted interface is found to be proportional to the gas flux at that interface for all geometries of solid particles, and the thickness order of the reaction zone and also the degree of chemical reaction at the interface is discussed in this paper.     

PREDICTION OF A GAS-PARTICLE TURBULENT JET WITH THE FLUCTUATION-SPECTRUM-RANDOM-TRAJECTORY MODEL

A numerical treatment for determining the particle velocity and the trajectories in a two-phase flow is described herein and this new fluctuation-spectrum-random-trajectory (FSRT) model is proposed to account for the turbulent diffusion of particles. It is predicted for the flow of a turbulent axisymmetric gaseous jet laden with spherical solid particles of nonuniform size. The particle velocity and the concentration field are obtained by the revised volume average method. The predictions are compared with experiment.     

攀西高锰稀土矿泥盐酸浸取稀土动力学

采用盐酸浸取攀西高锰稀土矿泥,考察了浸取反应温度、矿石粒度及盐酸浓度对浸取速率的影响. 结果表明,当盐酸浓度为2 mol/L时,浸取过程符合缩核模型,表观活化能为9.59 kJ/mol,属内扩散控制,宏观动力学方程为：K=(4.15?10–4)/r02 · exp(9590/RT); 当盐酸浓度大于2 mol/L时,矿石中的锰被大量浸出,其结构被破坏,浸取过程为混合控制.