MODELING OF THREE PHASE NONCATALYTIC BUBBLE COLUMN REACTORS

Mathematical models have been developed for the design of bubble column slurry reactors wherein the particles with nonuniform distribution of solid reactant take part in the reaction and follow the shrinking core model. The cases of external mass transfer control, ash layer diffusion control and chemical reaction control have been analyzed using solid distribution functions presented by Dudukovic (1984). It was found that the nonuniformity of solid reactant can strongly affect the reactor performance. Correction factors for modifying the performance charts of Joshi el al. (1981) who considered only uniform solid reactant distribution are presented for design and scale-up purposes.     

MODELING OF THREE PHASE NONCATALYTIC BUBBLE COLUMN REACTORS

Mathematical models have been developed for the design of bubble column slurry reactors wherein the particles with nonuniform distribution of solid reactant take part in the reaction and follow the shrinking core model. The cases of external mass transfer control, ash layer diffusion control and chemical reaction control have been analyzed using solid distribution functions presented by Dudukovic (1984). It was found that the nonuniformity of solid reactant can strongly affect the reactor performance. Correction factors for modifying the performance charts of Joshi el al. (1981) who considered only uniform solid reactant distribution are presented for design and scale-up purposes.     

A zone model for reactions of solid particles with strongly adsorbing species

A new zone model for reaction of solid particles with zeroth order reaction with respect to the fluid reactant and first order with respect to solid reactant has been proposed and analytical solutions for conversion and effectiveness factor obtained. The effect of Biot number and Thiele modulus on model predictions is investigated. Comparison of the model to other models for fluid solid reactions is presented together with the method for model discrimination. The model predicts conversion time behaviors encountered in practice.     

Modeling the reaction of gaseous HCl with CaO in fluidized bed

An integrated mathematical model is developed to evaluate the performance of the reaction of gaseous HCl and CaO in fluidized bed. The model considers initial pore size distribution of solid reactant, pore structure change and attrition caused by particles movement. Bethe network is used to describe the pore space topology, and the percolation theory is used to determine the accessible reaction surface area of the sorbent particles and the effective diffusion coefficient of gaseous HCl. This model prediction accounts for the diffusion of HCl in shrinking pore space as well as in product layer, and clearly demonstrates the increasing diffusion resistance and the isolation of partially reacted pores causing incomplete conversion of solid. The model shows excellent agreement with the experimental data.     

Direct production of crystalline boric acid through heterogeneous reaction of solid borax with propionic acid: Operation and simulation

The production of boric acid through reaction of borax crystals with propionic acid was investigated in batch mode. It was found that the product boric acid precipitates on the solid borax reactant. An increase in the coefficient of variation of feed crystals resulted in an increase in the time of completion of the reaction. A sharp interface model with variable bulk fluid concentration of liquid reactant was developed for simulation of the process. The analytical solution of the series of rate equations involving liquid film, solid boric acid layer and chemical reaction resistances was obtained, and a new method for simultaneous determination of kinetic parameters was established. The chemical reaction and diffusion through the solid layer of boric acid were the rate controlling mechanisms. A numerical algorithm was also developed for predicting the fractional conversion of multisize borax crystals using the mono size kinetic parameters determined according to the proposed analytical method.     

Effectiveness factors for solid-catalyzed gas-solid reactions

Effectiveness factors are given for gas-solid reactions catalyzed by a solid catalyst. Since the gasification of the solid reactant takes place at the catalyst-solid reactant interface, the gaseous reactant has to diffuse to the interface. As conversion proceeds, the thickness of the catalyst layer increases causing the effectiveness factor to decrease. Effectiveness factors obtained for the surface reaction show heavier dependence on the order of reaction and the Thiele modulus when compared with the effectiveness factors for the solid-catalyzed gas reactions. For the general case of gaseous reactant consumed by both surface and volume reaction, two Thiele moduli are required and the effectiveness factor decreases exponentially with increasing conversion. The effectiveness factor calculated from literature data on catalytic hydrogasification of coal is given to illustrate this dependence on conversion.     

A mathematical model for pyrolysis of a solid particle — effects of the heat of reaction

A transient analysis of the effects of the heat of reaction in a solid pyrolysis system is presented. Two cases, one characterizing the heat-transfer-controlled reaction and the other self-sustaining reaction, are analyzed. To carry out the numerical simulation, utilization is made of the volume reaction model which takes into account the simultaneous heat and mass transfer phenomena, and the method of line which utilizes the second order centered finite difference scheme for the spatial discretization. Effects of the heat of reaction on the solid conversion, solid reactant, and fluid product concentration profiles, temperature distribution, enthalpy, and average fluid product concentration in the particle are examined. The results are graphically presented and interpreted.     

A new model for thermal volatilization of solid particles undergoing fast pyrolysis

A new model is proposed for representing the thermal volatilization of solid particles under the conditions of fast pyrolysis. The solid, initially at low temperature, is suddenly immersed into a high-temperature medium where it decomposes to gaseous products, the external surface of the particle being exposed to a high heat flux from the medium. As heat penetrates into the solid by conduction, the decomposition reaction occurs at a rate which increases with temperature. Equations for simultaneous heat and mass balances are derived and numerically solved, yielding the internal temperature profile and the rate of shrinkage of the particle, from which the time for total consumption is easily deduced. It is shown that the regime of volatilization depends on two parameters: a thermal Thiele and a thermal Biot modulus. The ablation regime is achieved if both M and B are large (⪢ 100). In this regime, the shrinking velocity is constant and the reaction takes place only in a thin layer at the solid surface.     

连续多级串联完全混合槽中固体颗粒反应产率计算方法

本文针对级内颗粒完全混合一级间无颗粒返混的多级反应器,探讨了按停留时间分布计算固体颗粒反应率的方法。首先分析了用δ（0）函数示踪法与多元独立随机变量和的分布密度函数法求颗粒停留时间分布的特点;应用后一种方法推得了计算颗粒反应产率的一般公式。从固体颗粒固相反应物浓度分布密度函数也可以推得此公式。在此基础上对一类特殊的反应速度方程,解析求出了直接计算任何一级反应产率的通式;对求解计算通式困难的反应速度方程,论证了两种逐级计算方法:以反应时间作计算参量及以颗粒固相反应物浓度作计算参量。     

Mathematical modelling of gas-solid reactions with solid product

Random pore structural models, that can be used with any type of pore size distribution, are developed for the study of gas-solid reactions with solid product under reaction conditions controlled by kinetics and diffusion in the product layer. An intraparticle diffusion and reaction model is also developed and used, along with the structural models, to study the transient behaviour of solid particles reacting under significant intraparticle diffusional limitations. Simulation results for the limestone-SO₂ system show that the transient behaviour of the reacting particles is strongly influenced by the type of the pore size distribution. Various pore structures characterized by the same values of internal surface area and porosity can lead to completely different reaction trajectories. The predictions of the mathematical models compare well with experimental data from the literature.     

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.     

A structural model for gas solid reactions with a moving boundary—VI: The effect of grain size distribution on the conversion of porous solids

A distributed model is proposed for a first order, irreversible reaction between a porous solid and a gas in which allowance is made for a grain size distribution in the reactant solid matrix. By using approximate algebraic relationships between conversion and time, adopted from the grain model, solutions were generated for various types of grain size distribution. It was found that in general the plots of conversion against time for a grain size distribution differed from those computed for a single mean grain size. Only for closely sized grains or for a log normal grain size distribution was this difference relatively small. Thus the effect of grain size distribution is thought to be of importance in both the interpretation of experimental data in terms of the grain model and in procedures used for deducing kinetic parameters from experimental measurements.     

垃圾焚烧炉对流受热面烧结积灰生长特性

使用扫描电子显微镜、X射线荧光光谱仪、激光粒度分析仪等分析手段,对流化床垃圾焚烧炉对流受热面的松散性浮灰和烧结性积灰的微观结构和组成成分等进行研究。结果表明,省煤器浮灰中大部分颗粒保持着独立的形态,而对流管束浮灰存在烧结现象;绝大部分的浮灰粒径位于0～100μm;省煤器浮灰的灰熔点低于对流管束浮灰熔点80℃左右;对流管束浮灰和省煤器浮灰在成分组成上差别不大,浮灰中的主要元素均为Ca、Si、Al和S,但对流管束浮灰中Ca和S的含量高于省煤器浮灰。各层积灰中Ca和S的含量较高,主要物相为CaSO₄。对流管束积灰中Ca和S含量高于省煤器积灰;对流管束和省煤器积灰中Al和Si的含量远低于浮灰中的相应含量。从积灰内层到外层Ca和S的含量逐渐减少,而Al和Si的含量逐渐增加;积灰内层K、Na、Fe和Cl的含量高于其他层。     

Volume reaction model for pyrolysis of a single solid particle accompanied by a complex reaction

A fairly general model is proposed for the pyrolysis of a single solid particle accompanied by consecutive reactions. The model not only takes into consideration the transient heat transfer, mass transfer, and chemical reaction simultaneously but also the functional dependencies of various parameters on the variation of the solids concentration and temperature in the particle. The effects of the heat of reaction, Thiele modulus, and rate of reaction on the solids reactant conversion, concentration profiles and temperature profiles are analyzed and graphically presented.     

Convective heat transfer and solid conversion of reacting particles in a copper(II) chloride fluidized bed

This paper develops a predictive model of convective heat transfer and conversion of cupric chloride particles in a fluidized bed reactor of a copper–chlorine (Cu–Cl) cycle of thermochemical hydrogen production. The hydrolysis reaction of particles in the fluidized bed is endothermic and it requires excess steam for complete conversion of cupric chloride solid. The excess steam supply may be used for partial heat supply to the endothermic reaction, and also to avoid defluidization in the bed. To avoid defluidization, the change of gas flow in the bed due to the reaction should be minimized at a given operating condition. The model predicts the maximum possible steam inlet temperature, steam conversion, amount of partial heat supply, and also gas flow rates through the bed to avoid defluidization. The new model presents significant new insight by analyzing the hydrodynamic and mass transport processes, considering the equilibrium limitation on the conversion of cupric chloride solid. The model results indicate that the chemical reaction requires a high mole ratio of steam for complete conversion of cupric chloride particles. The maximum steam conversion is limited by temperature, pressure, and the presence of hydrogen chloride gas. The maximum conversion of steam at 400 °C is 3.75% and it requires excess steam of 12.8 moles per unit mole of cupric chloride solid for complete conversion of solid. The heat supply by steam for the reaction, as well as raising the solid feed to the reaction temperature, varies with reaction temperature. The paper also adds significant new insight by analyzing the steam flow requirement in terms of temperature, conversion rate, and quality of fluidization. Additional new results are presented and applications discussed for the Cu–Cl cycle of nuclear hydrogen production.     

A grain size distribution model for non-catalytic gassolid reactions

A new model to describe the non-catalytic conversion of a solid by a reactant gas is proposed. This so-called grain size distribution (GSD) model presumes the porous particle to be a collection of grains of various sizes. The size distribution of the grains is derived from mercury porosimetry measurements. The measured pore size distribution is converted into a grain size distribution through a so-called pore-tosphere factor whose value is also derived from the porosimetry measurements. The grains are divided into a number of size classes. For each class the conversion rate is calculated either according to the shrinking core model, involving core reaction and product layer diffusion as rate-determining steps or according to a new model in which some reaction at the grain surface is assumed to be limiting. The GSD model accounts for the phenomenon of pore blocking by calculating the maximum attainable conversion degree for each size class. In order to verify the model, two types of precalcined limestone particles with quite different microstructures were sulphided as well as sulphated. Furthermore, a single sample of sulphided dolomite was regenerated with a mixture of carbon dioxide and steam. For each reaction good agreement was attained between measured and simulated conversion vs. time behaviour.     

Thermodynamic analysis of carbon dioxide reforming of methane in view of solid carbon formation

A thermodynamic equilibrium analysis on the multi-reaction system for carbon dioxide reforming of methane in view of carbon formation was performed with Aspen plus based on direct minimization of Gibbs free energy method. The effects of CO₂/CH₄ ratio (0.5-3), reaction temperature (573-1473 K) and pressure (1-25 atm) on equilibrium conversions, product compositions and solid carbon were studied. Numerical analysis revealed that the optimal working conditions for syngas production in Fischer-Tropsch synthesis were at temperatures higher than 1173 K for CO₂/CH₄ ratio being 1 at which about 4 mol of syngas (H₂/CO = 1) could be produced from 2 mol of reactants with negligible amount of carbon formation. Although temperatures above 973 K had suppressed the carbon formation, the moles of water formed increased especially at higher CO₂/CH₄ ratios (being 2 and 3). The increment could be attributed to RWGS reaction attested by the enhanced number of CO moles, declined H₂ moles and gradual increment of CO₂ conversion. The simulated reactant conversions and product distribution were compared with experimental results in the literatures to study the differences between the real behavior and thermodynamic equilibrium profile of CO₂ reforming of methane. The potential of producing decent yields of ethylene, ethane, methanol and dimethyl ether seemed to depend on active and selective catalysts. Higher pressures suppressed the effect of temperature on reactant conversion, augmented carbon deposition and decreased CO and H₂ production due to methane decomposition and CO disproportionation reactions. Analysis of oxidative CO₂ reforming of methane with equal amount of CH₄ and CO₂ revealed reactant conversions and syngas yields above 90% corresponded to the optimal operating temperature and feed ratio of 1073 K and CO₂:CH₄:O₂ = 1:1:0.1, respectively. The H₂/CO ratio was maintained at unity while water formation was minimized and solid carbon eliminated.     

Critical evaluation of coupling particle size distribution with the shrinking core model

The shrinking core model (SCM) is widely used to model fluid-solid reactions such as the leaching of metals from minerals. In most cases, however, the particle size distribution (PSD) of the solid material was disregarded. In this paper the erroneous shift in the control regime when neglecting PSD was quantified and the dependence of the shift on the coefficients of variation (CV) and the type of PSD was analysed. By coupling the SCM with a Gamma PSD, it was found that neglecting the PSD would shift the control regime from chemical reaction to inert/ash layer diffusion, when the CV was between 0.7 and 1.2. For a system controlled by liquid film diffusion, neglect of the PSD, would shift the control regime to chemical reaction when CV is between 0.3 and 0.7 or to inert/ash layer diffusion when CV is greater (0.9-1.5). It was therefore postulated that some researchers had unknowingly made invalid conclusions about the control regime due to the neglect of PSD. However, an inert/ash layer diffusion-controlled process was insensitive to the neglect of PSD. When CV<0.3, neglect of the PSD would not cause any erroneous shifts, irrespective of the control regime. Experimental data confirmed the observation. For a given CV, the deviation in the fraction reacted from the mono-PSD increases with CV and decreases with time. The maximum deviation, which occurs at the beginning, is about 10% with a gamma PSD of CV=0.3. The percent deviation is dependent of the type of PSDs. Gamma PSD gives the lowest deviation while Gaudin-Schuhmann results in the largest deviation (maxi. ∼19%, with CV=0.3) in the first half of dissolution process. Log-normal distribution gives a larger deviation than gamma but quickly approaches the latter with time. The deviation for Rosin-Rammler is between log-normal and Gaudin-Schuhmann. For systems with CV less than 0.3, the SCM can be fairly used without considering PSD. When CV is greater than 0.3, particularly in the early stage of a dissolution process with a PSD other than gamma, PSD should be included to avoid substantial errors.     

水对前驱物催化合成二噁英的影响

The effect of water on the formation of polychlorinated dibenzo-p-dioxins（PCDDs）and dibenzofurans（PCDFs）from precursor was investigated by the experiments with a fixed-bed reactor：the reactant mixture with different moisture of 123-TrCB and CuCl₂ for metal-catalyzed formation,that of 123-TrCB and fly ash for surface-catalyzed formation. The experimental results show that the water has the following effects：first,suppressing the formation of PCDD/Fs as less its yield;second,inhibiting chlorination reaction as lower chlorination degree;third,having different effect on PCDDs and PCDFs as lower ratio of PCDFs/PCDDs.The explanations might be the competitive adsorption of water vapor with TrCB on active sites of the fly ash and the catalysis of copper was weakened chloride because of its oxidative conversion to copper oxide.     

Modelling of non-catalytic gas—solid reactions—I. Transient analysis of the particle—pellet model

A transient analysis of the problem of non-catalytic gas—solid reaction based on the particle—pellet model, which considers the particulate nature of the pellet and includes the external transport resistances, is presented. The method of solution of the resulting non-linear partial differential equations is based on the orthogonal collocation technique. The transient model has been compared with the pseudo-steady analysis of the problem. The effect of various parameters on the temperature profiles in the pellet and the conversion of the solid reactant has been discussed.