A mathematical model for pyrolysis of a solid particle: Effects of the lewis number

A transient analysis of a fluid-solid pyrolysis system in which a solid is pytolyzed to form a fluid product and a solid product is presented. The analysis, based on utilization of the so-called volume reaction model, takes into account the simultaneous heat and mass transfer phenomena in the particle being pyrolyzed. Variations of physical parameters with respect to temperature and/or solid concentration are not neglected. Effects of the Lewis number on the solid conversion, the fluid and solid concentration distributions, and the temperature profile in the particle are examined. The results are graphically presented and interpreted.     

A THEORETICAL INVESTIGATION OF THE EFFECTS OF VARIABLE POROSITY AND DIFFUSIVITY ON THE MANUFACTURE OF REACTION-BONDED SILICON NITRIDE

Transient behaviour of the exothermic, irreversible silicon-nitrogen reaction has been simulated using a particle-pellet model which incorporates a sharp 'cut-of T reaction into the moving reaction zone in the heat mass transfer Held. Variations of certain physical parameters connected with the micro-structural changes during reaction, with respect to temperature and/or solid concentration are taken into account. The solution procedures to the resulting system or equations are based on an explicit finite difference scheme. Effects of the Thiele modulus and Biot number for heat transfer on the solid conversion and fluid concentration are examined, together with the effect of a zero heat of reaction on the temperature profiles in the compact. The results are graphically presented and interpreted.     

A finite element solution of coupled heat and mass transfer with chemical reaction

A finite element method is presented for solving the coupled non-linear parabolic differential equations describing transient transport of heat and mass in chemically reacting systems. The method appears to be a useful approximation for a wide variety of problems. Typical numerical results are reported for non isothermal catalytic solid—fluid reactions. Applications to other fields such as absorption accompanied by reaction and non-catalytic solid—fluid reaction models are also formulated.     

环己酮肟Beckmann重排制己内酰胺的研究进展

环己酮肟Beckmann重排制己内酰胺是重要的工业过程。本文较详细地介绍了不使用浓硫酸催化的反应，主要有气固相反应、固液相反应、离子液体系及超临界水条件下的反应。研究表明：气固相反应中，副产物较多，催化剂易失活，使用寿命短；固液相反应条件温和，且副产物少；离子液体系和超临界水条件下的Beckmann反应中，可避免使用有机溶剂，且反应副产物少。     

非热平衡多孔介质内反应与传热传质耦合过程

采用局部热不平衡假设,对发生强吸热化学反应的多孔介质体系建立了反应与传热、传质耦合问题的数学模型,采用Ergun-Forchheimer-Brinkman方程描述多孔介质中的流体流动.运用交替方向隐式(ADI)方法对模型离散求解,并采用文献中的实验数据对模型进行验证.计算了不同条件下颗粒物料层内气体和固体骨架的温度场、产物气体浓度场以及固体转化率分布,以得到多孔介质体系内固有化学反应时的传热、传质规律.结果表明,不能忽略固体骨架与流体间的温度差.入口渗流速度、入口气体温度以及固体颗粒尺寸是影响系统反应特性的重要参数.研究结果对具有强吸热反应的固定床反应器的设计和运行具有一定的参考作用.     

Temperature differences between phases in a moving bed reactor

Pseudo-homogeneous models of packed bed reactors assume equal temperatures and concentrations (or chemical potentials) for the solid and the fluid phases and are simpler than heterogeneous models. An analysis is presented for the degree of temperature departure between these two models under plug flow conditions with no axial dispersion. Fixed bed, cocurrent and countercurrent flow reactors are considered. The analysis yields two important parameters: α, the ratio of solid to gas thermal capacitances, and β, which is closely related to the number of interphase heat transferase units. In most industrial reactors, where β is greater than 50, the average temperature difference between phases is small, except for countercurrent reactors where gas and solid heat capacitances are nearly equal. Within this range of α, temperature differences can persist through the reactor, even with large values of β. The maximum temperature difference between phases is attained when the reaction heat effect is released in the worst case of a localized pulse in the reactor stream with the smaller thermal capacitance. These temperature difference measures can be used to estimate the validity of a pseudo-homogeneous model. This analysis is easily extended to concentration differences between phases.     

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.     

Transient diffusional interactions between solid bodies and isolated fluids

A generalized Sturm-Liouville approach is used to provide an efficient solution procedure for the problem of one-dimensional diffusion accompanied by an irreversible first-order reaction in a body suddenly immersed in an isolated volume of moderately stirred fluid. Specific results are presented for the slab, solid and hollow cylinders, and the sphere. The non-reactive, non-adiabatic calorimeter problem is solved by reduction to a closely related adiabatic problem with first-order heat generation in the body, the solution to which is contained in the earlier developments of the paper.     

A computer model for the regenerative bed

The transient behavior of a packed bed of uniform spheres is considered, where heat (or mass) transfer inside the sphere is described by a linear parabolic second order partial differential equation — the standard diffusivity equation. One dimenisonal plug flow is assumed; hence, the fluid behavior is given by a set of first order partial differential equations, with bed axial position and time as the independent variables. The existence of chemical reaction in the fluid makes these equations non-linear. The two systems of equations describing the solid and the gas are coupled by the equations for heat (or mass) transfer at the surface. Numerical methods for solving both the linear (no reaction) and non-linear (with reaction) cases are presented. In the former, the implicit Crank-Nicholson method is used; in the latter the two systems of equations are first decoupled and then solved separately.     

Numerical study of polyethylene burning in counterflow: Effect of pyrolysis kinetics and composition of pyrolysis products

The burning behavior of polyethylene in the counterflow of oxidizing air has been studied numerically with a coupled model describing feedback heat and mass transfer between gas‐phase flame and polymeric solid fuel. A 2‐dimensional elliptic equation in axisymmetric formulation (revealing the cylindrical shape of the polymer sample used in the experiment) has been employed to simulate heat transfer in solid fuel, and a set of 1‐dimensional hyperbolic equations has been used to determine the solid‐to‐gas conversion degree of the pyrolysis reaction. Four sets of products compositions and two modifications for the kinetic parameters of solid fuel pyrolysis reaction have been taken into account. Gas‐phase formulation is presented by set of 1‐dimensional conservation equations for multi‐component flow with detailed kinetic mechanism of combustion. The profiles of temperature and species concentrations in the flame zone have been calculated and compared with the results of experimental study of combustion of ultrahigh molecular weight polyethylene. Higher hydrocarbon composition (dodecane) has been found to show the best agreement between the temperature and species concentration profiles with the measurements, especially for the low‐level mass fractions of the by‐product components—propylene, butadiene, and benzene.     

An analytical solution for the transient response in a diffusion cell of the Wicke-Kallenbach type

An analytical solution is developed for the problem of transient diffusion and first order reaction in a solid flanked by two well mixed fluid compartments. This solution is necessary and useful in describing unsteady-state measurements in a Wicke-Kallenbach diffusion cell or reaction studies in a single pellet reactor. It is shown that a proper choice of an inner product vector space, following the methodology developed by Ramkrishna and Amundson [14, 15], leads readily to the desired solution and guarantees its completeness. This solution is valid for the equivalent heat transfer problem also.     

有内热源的多孔层中自然对流的稳定性分析

采用局部非热平衡模型, 通过数值法和Garlerkin近似法, 分析存在均匀内热源和边界浓度梯度时, 有效热导率比、流体和固相间的传热系数、浓度梯度的大小以及内热源在流体与固相内的分布情况对水平多孔层中临界内热源Rayleigh数的影响, 来研究相关参数对自然对流的稳定性的影响, 并得到临界内热源Rayleigh数的表达式。结果表明, 浓度Rayleigh数的增加可以促进自然对流的形成;内热源为正时, 自然对流的形成区域主要位于上半区域;内热源为负时, 自然对流的形成区域位于下半区域, 内热源总是促进自然对流的发生;有效热导率比、流体和固相间的内部传热系数、内热源在流体与固相内的分布情况相互耦合, 影响自然对流的稳定性, 这种影响取决于各参数的范围。     

UNSTEADY FLUID AND HEAT FLOW INDUCED BY A STRETCHING SHEET WITH MASS TRANSFER AND CHEMICAL REACTION

The effect of chemical reaction on the flow, heat, and mass transfer within a viscous fluid on an unsteady stretching sheet is examined. The stretching rate, temperature and concentration of the sheet, and the chemical reaction rate are assumed to vary with time. The time-dependent boundary layer equations governing the flow are reduced through a convenient similarity transformation to a set of ordinary differential equations, which are numerically solved by applying the fourth-order Runge-Kutta-Fehlberg scheme with the shooting technique. Results for the velocity, temperature, and concentration distributions as well as the wall temperature and concentration gradients are presented graphically for various values of the unsteadiness parameter A, Prandtl number Pr, Schmidt number Sc, and chemical reaction parameter γ.     

Revisiting shrinking particle and product layer models for fluid-solid reactions - From ideal surfaces to real surfaces

A general model based on an arbitrary geometry was developed for reactive solid particles which have surface defects and porosity. The model equations comprising intrinsic kinetics as well as mass transfer effects through the product layer and the fluid film surrounding the solid particle were derived for shrinking particle and product layer models. From the model equations, the fluid (gas or liquid) concentrations at the reaction surface can be calculated and the change of the solid phase can be predicted. The approach was illustrated with monodisperse particle distributions in batch reactors. Complex kinetics as well as simpler special cases were treated. In general, the model predicts a higher reaction order with respect to the solid component than the previous ideal models, which assume slab, cylindrical or spherical geometries for solid particles.     

A study on deviation of noncatalytic gas-solid reaction models due to heat effects and changing of solid structure

In this study a common type noncatalytic gas-solid reaction is modeled based on some well-known, previously presented mathematical models, including grain, modified grain and additive reaction times models. In order to approach more realistic models, the heat effects and the changing of solid structure effects are considered in the above named mathematical models. The governing equations are developed and solved numerically. Then, the predicted results are compared with available experimental data presented for some important industrial gas-solid reactions. The results reveal shortage of the simplifying assumptions of the referred models to predict solid conversion, as a result of neglecting heat effects and structural changes of solid reactant. In this study, for the first time, the process of the change in the different reaction controlling steps is considered during the reaction time. The results also show that the main rate-limiting resistances convert to each other during the reaction progress. It reveals that the undesirable heat and structural changing effects decrease with decreasing the particle diameter, increasing the convective heat transfer coefficient, and taking appropriate gas temperature. This study shows that considering heat effects and changing of solid structure improve the abilities of previous mathematical models to predict the behavior of noncatalytic gas-solid reactions.     

流化床的强化传热途径探讨

分析了直接法合成甲基氯硅烷的反应特点及反应器内流化床的传热过程。分别介绍了主要传热途径:管内强化传热和管外强化传热。着重提出了改进流化床横向构件的安装方式的建议,即在垂直管束间附着一些随流化床内气流浮动的桨式或梅花形内件,增加床内气固相接触的机会,以改善流化质量。     

Encapsulated nano-heat-sinks for thermal management of heterogeneous chemical reactions

This paper describes a new way to control temperatures of heterogeneous exothermic reactions such as heterogeneous catalytic reaction and polymerization by using encapsulated nanoparticles of phase change materials as thermally functional additives. Silica-encapsulated indium nanoparticles and silica encapsulated paraffin nanoparticles are used to absorb heat released in catalytic reaction and to mitigate gel effect of polymerization, respectively. The local hot spots that are induced by non-homogenous catalyst packing, reactant concentration fluctuation, and abrupt change of polymerization rate lead to solid to liquid phase change of nanoparticle cores so as to avoid thermal runaway by converting energies from exothermic reactions to latent heat of fusion. By quenching local hot spots at initial stage, reaction rates do not rise significantly because the thermal energy produced in reaction is isothermally removed. Nanoparticles of phase change materials will open a new dimension for thermal management of exothermic reactions to quench local hot spots, prevent thermal runaway of reaction, and change product distribution.     

FCC提升管反应器中终止剂注入对裂化反应的影响

通过对催化裂化提升管注入终止剂前后的工况进行数值模拟,研究了终止剂注入对提升管内速度分布、催化剂颗粒浓度分布、温度分布以及组分浓度分布的影响,考察了不同注入量以及注入高度的终止剂在提升管内的作用区域及其对裂化反应的影响。研究表明,终止剂的注入大幅提升了提升管内的油气速度,降低了催化剂浓度、油气和催化剂的温度,使得提升管内原料的裂化程度降低,二次反应减少。且不同注入量和注入高度的作用区域不同,对裂化反应的影响不同,应根据实际工况进行分析。     

MHD MIXED-CONVECTION INTERACTION WITH THERMAL RADIATION AND nTH ORDER CHEMICAL REACTION PAST A VERTICAL POROUS PLATE EMBEDDED IN A POROUS MEDIUM

This article investigates the hydromagnetic mixed convection heat and mass transfer flow of an incompressible Boussinesq fluid past a vertical porous plate with constant heat flux in the presence of radiative heat transfer in an optically thin environment, viscous dissipation, and an nth order homogeneous chemical reaction between the fluid and the diffusing species. The dimensionless governing equations for this investigation are solved numerically by the fourth-order Runge-Kutta integration scheme along with shooting technique. Numerical data for the local skin-friction coefficient, the plate surface temperature, and the local Sherwood number have been tabulated for various values of parametric conditions. Graphical results for velocity, temperature, and concentration profiles based on the numerical solutions are presented and discussed.     

蒸汽发生器传热管双向流固耦合数值分析

以大亚湾核电站蒸汽发生器为原型,考虑一、二次侧流体的共同作用,进行蒸汽发生器传热管双向流固耦合数值模拟。计算结果表明：所采用的双向流固耦合方法能较好地捕捉到蒸汽发生器传热管的位移变化规律,传热管中心截面的位移最大,且平衡时向第3象限偏移,由于流体弹性不稳定性的影响,X、Y方向的位移大小并不相等。沿传热管高度方向应力关于中心截面（0.5 m）对称分布,固定端附近由于固定约束的作用产生应力集中应力最大。不同截面上应力沿圆周方向的分布规律相似,受传热管位移的影响关于20°和200°所连的直线对称分布,在20°和200°附近出现应力极值。蒸汽发生器传热管双向流固耦合方法可为蒸汽发生器安全运行提供理论参考。