氨合成及中温变换催化剂内表面利用率计算的数值解

催化剂颗粒内反应组分的传质过程,对于许多工业生产条件下气——固相催化反应速率的影响不容忽视。颗粒催化剂内表面利用率(或效率因子)的计算是计算宏观催化反应速率的主要组成部分。如果处于等温状况的球状或平板状催化剂上进行的反应是一级反应,则表征催化剂内反应组分浓度分布的微分方程是二阶线性齐次常微分方程,有解析解,内表面利用率从而可以迅速求得。如果反应不是一级反应,例如氨合成、一氧化碳中温变换等催化反应以幂函数形式表示的动力学方程,则浓度分布方程是非线性常微分方程,无解析解。在此情况下,常用的方法是将动力学方程简化为一级反应而求得近似解。本文采用的方法是将二阶非线性常微分方程转换成一阶常微分方程组,在电子计算机上用打靶法求解此微分方程组的边值,从而求得催化剂内反应组分的浓度分布及内表面利用率的数值解,并按照典型的工业生产条件,将数值解及近似解的计算结果进行了比较。     

多孔催化剂效率因子的多组分扩散模型(Ⅴ) 表面中毒并伴有平衡死区圆柱状催化剂效率因子的有限元求解

针对表面中毒并伴有平衡死区二维圆柱状催化剂的反应-扩散偏微分方程组的特殊性,引入有限元方法求解该类问题,建立了求解步骤。实际计算所得效率因子与实验值对照表明,本法结果准确,过程简单,容易推广应用于各种相类似的体系。     

多孔催化剂效率因子的多组分扩散模型(Ⅴ) 表面中毒并伴有平衡死区圆柱状催化剂效率因子的有限元求解

针对表面中毒并伴有平衡死区二维圆柱状催化剂的反应-扩散偏微分方程组的特殊性,引入有限元方法求解该类问题,建立了求解步骤。实际计算所得效率因子与实验值对照表明,本法结果准确,过程简单,容易推广应用于各种相类似的体系。     

假瞬态洁求解中温变换B109催化剂效率因子

建立了描述工业催化剂粒内浓度和温度分布的扩散数学模型.借助假瞬态法,提出了非等温扩散模型的有效解法.本文对16组宏观实验速率,获得了各组分的浓度和温度分布,及中温变换B109催化剂效率因子的数值解.采用该法能在不修改边界条件的情况下,求解催化剂颗粒内存在“死区”的定解问题.计算结果合理,计算速度快.     

假瞬态洁求解中温变换B109催化剂效率因子

建立了描述工业催化剂粒内浓度和温度分布的扩散数学模型.借助假瞬态法,提出了非等温扩散模型的有效解法.本文对16组宏观实验速率,获得了各组分的浓度和温度分布,及中温变换B109催化剂效率因子的数值解.采用该法能在不修改边界条件的情况下,求解催化剂颗粒内存在“死区”的定解问题.计算结果合理,计算速度快.     

S101型钒催化剂内表面利用率的多组分扩散模型

根据颗粒催化剂内多组分分子扩散与努森扩散联合过程的特征,提出了计算二氧化硫催化氧化S101型钒催化剂内表面利用率的多组分扩散模型及求解方法。该模型解决了本征动力学方程为双曲型时、以及催化剂颗粒内部存在“死区”时内表面利用率的计算。文中列举了计算实例。     

不规则形状A301氨合成催化剂内扩散有效因子

对于不规则形状A301氨合成催化剂,测定了其形状系数和球化的当量直径及高压下本征动力学方程,用SPSR法测定了不规则催化剂颗粒的曲折因子,根据多组分单一反应等温球形A301氨合成催化剂内反应-扩散-维模型,用正交配置法结合解非线性方程组的Broyden拟牛顿法求解了模型,获得了催化剂粒内各组分的浓度分布和催化剂的内扩散有效因子.利用所测得的高压下A301催化剂的总体速率对模型进行了检验,模型计算值和实验值吻合,表明球化模型和所得当量直径、曲折因子等模型参数可用于描述A30l催化剂内的反应-扩散过程及工程设计计算.     

多孔催化剂效率因子的多组分扩散模型 (Ⅱ)B109中温变换催化剂的效率因子

按照本文(Ⅰ)中提出的多孔催化剂效率因子的多组分扩散模型及其数值计算方法,本报计算了B109中温变换催化剂的效率因子,并与实验测定值进行了比较.测试了B109变换催化剂的孔隙率、孔径分布、曲节因子和常压下的本征动力学,并在内循环无梯度反应器中测试了常压下φ9.8×8.3mm圆柱状颗粒B109催化剂于各种气体组成和温度条件下只计入内扩散过程的宏观反应速率.由此获得十六种情况下效率因子的实验观察值为0.142至0.455,相同反应条件下模型预计值与实验观察值的相对误差为-0.25至0.06.比较的结果令人满意.     

硫中毒状态下B108中变催化剂效率因子的研究

硫中毒状态下铁铬系变换催化剂效率因子的研究,迄今尚未见报道。本文根据水煤气变换反应的特点,以均匀中毒假设为前提,建立多组分扩散模型描述稳态情形下,500ppm 硫化氢气相浓度时各反应组分在等温原粒度催化剂中的浓度分布。所有6个实验条件下的效率因子计算机求解结果表明,模型与实验值符合良好。从浓度分布和死区两方面解释了相同条件下,宏观反应速率受硫化氢影响较本征速率小38.30%的原因。研究表明,采用的实验手段是可行的,所建立的模型可用于工业过程的分析。     

外齿轮形颗粒催化剂上乙烯催化氧化的反应工程计算

针对乙烯氧化制环氧乙烷反应体系,对外齿轮异形催化剂建立三维反应-传质-传热模型。有效扩散系数和有效热导率均为待求解浓度场和温度场的函数,使得偏微分方程组模型为强非线性。采用有限元算法求解,并对模型有效性进行验证,定量研究了催化剂几何比外表面积和内扩散效率因子的关系。计算结果表明,几何比外表面积为1862 m2·m-3的外齿轮催化剂内扩散效率因子为0.1804,而几何比外表面积为924 m2·m-3的圆柱形催化剂内扩散效率因子为0.0993。对单个催化剂颗粒反应-传递现象的研究能定量指导催化剂设计,并为耦合反应器流体力学和催化剂反应传递现象多尺度模拟计算奠定基础。     

计算多孔催化剂有效因子的区域分割法

提出了计算多孔催化剂颗粒有效因子的区域分割法,将整个一维区间划分为几个子区间,然后在每个子区间内用一点配置法求解非线性扩散-反应问题.采用区域分割法,针对三种不同形状的催化剂颗粒,对幂函数型动力学方程和双曲型动力学方程进行了大量的计算.所得的计算结果与正交配置解吻合.区域分割法的优点是使用简便、计算快速.采用区域分割法还可以计算催化剂颗粒死区半径,所得计算结果合理.     

Calcul du profil de concentration et du facteur d'efficacite lors d'une reaction avec changement de volume

The influence of the stoichiometry of a reactive system involving a large number of components on the effectiveness factor of a catalyst has been studied. An adequate change of variables reduces the problem to solving a set of two non linear first-order differential equations describing the diffusion of a single component in the pores of the catalyst. The method is applied, as an example, to the oxidation of sulfur dioxide, in order to estimate errors predicted by the constant volume hypothesis, as functions of catalyst particle size, degree of conversion, and initial concentrations.     

CATALYST EFFECTIVENESS FOR MULTICOMPONENT REACTIONS WITH CONCENTRATION-DEPENDENT DIFFUSIVITIES

The diffusion coefficient,D_i has been formulated of the reacting species in the transition region of diffusion for a stoichiometricly simple isothermal reaction in a porous catalyst and its concentration dependence has been determined. The concentration dependence of D_i incorporated into the mass balance of the catalyst pellet introduces a new parameter, A (Eq. 11). The effect is demonstrated of this parameter on predicted values of effectiveness factors for three kinetic equations of the Langmuir-Hinshelwood type (Eq. 36-38). If the effectiveness factor is a monotonously decreasing function of the Thiele Modulus, or if the concentration dependence of D_i is not too strong, the effectiveness factor can be predicted from the solution of mass balance with concentration independent diffusivity. This prediction can be improved by using a mean diffusion coefficient D_i.     

Effectiveness factor of a catalytic sphere in particle assemblage approached with a cell model

The cell model approach was extended to the catalytic reaction over a spherical catalyst pellet and the effects of several parameters on the effectiveness factor were investigated via numerical simulation. The proposed mathematical model consisted of the partial differential equations for gas reactant flow in the external gas phase around a catalyst sphere, mass transport in the gas phase, and two-dimensional diffusion-reaction in the catalytic sphere. Numerical simulation in the orthogonal boundary fitted reference frame demonstrated the decrease in effectiveness factor of a catalyst sphere due to the external mass transfer resistance and inter-particle hydrodynamic interaction. It was observed that the voidage of the particle assemblage shows more recognized influence than the Peclet and Reynolds numbers of particles and the azimuthal diffusion of reactant inside the particle was negligible. On this basis, a simplified set of cell model equations for catalytic reaction in particle assemblages were proposed. An example of optimizing search indicated the present model may be used to detect the most strong influence on catalytic reaction in particle assemblage over the practical ranges of operating and designing parameters to avoid excessive loss in the effectiveness factor.     

Dead zones in porous catalysts: Concentration profiles and efficiency factors

This paper examines the conditions under which a dead zone, or a portion of the catalyst devoid of reactant, can form in a porous catalyst in which simultaneous reaction and diffusion are occurring. The condition that allows for the existence of a dead zone is defined by a critical Thiele modulus. When the Thiele modulus – the ratio of chemical reaction to diffusion – is greater than the critical Thiele modulus, a dead zone exists. This dead zone can be mathematically defined by a change of boundary conditions. We examine nth order reactions in isothermal infinite slabs, infinite cylinders, and spheres. In addition, we provide analytical concentration profiles and efficiency factors for zero-order reactions in non-isothermal infinite slabs (in the so-called low beta approximation). We also discuss some common errors and misconceptions associated with this phenomenon.     

APPROXIMATE EFFECTIVENESS FACTOR ESTIMATION FOR WAVE SHELL CATALYST

The estimation of effectiveness factor for the case of wave shell catalyst is attempted through an approximated procedure developed by the authors for other kind of catalytic pellets. It is shown that the approximate scheme can be used even with this kind of important catalysts and that the results so obtained are very accurate. The analysis is only restricted to the case of single reaction although it can be used even for those cases where non-isothermal conditions could prevail. The estimation avoid the solution of the governing mass and heat balance differential equations by numerical procedures. Finally a set of algebraic equations must be solved through an iterative scheme which is illustrated for the case of isothermal systems.     

The design of catalyst pellets

Because of the limitations of the effectiveness factor concept to few simple types of complex reactions and independent diffusion coefficients, it is necessary to solve the balance equations individually for each component in the general case. Therefore the characteristic equations for a catalyst pellet design were generalized for any type of complex kinetic model with regard of the multicomponent diffusion relations. In order to supply the necessary parameter values, conventional models for the physical properties of the catalyst are used. The whole modelling served as a basis of a computer program for several purposes: The control of transport limitations, the evaluation of the pseudohomoheneous production rates and the optimization of the physical properties of the catalysts. The importance of an appropriate catalyst pellet design and the application of the computer program is demonstrated by several examples.