C301铜基催化剂甲醇合成反应动力学(Ⅳ)——圆柱状催化剂平行反应效率因子二维模型的正交配置解

以一氧化碳和二氧化碳平行加氢反应作为铜基催化剂上甲醇含成的关键反应,按二维模型计算了圆柱状C301铜基催化剂上这两个反应的效率因子.将效率因子的模型计算值与实验测定值进行比较,表明正交配置法中计算平行反应效率因子的有效、准确的方法.     

C301铜基催化剂甲醇合成反应动力学(Ⅳ)——圆柱状催化剂平行反应效率因子二维模型的正交配置解

以一氧化碳和二氧化碳平行加氢反应作为铜基催化剂上甲醇含成的关键反应,按二维模型计算了圆柱状C301铜基催化剂上这两个反应的效率因子.将效率因子的模型计算值与实验测定值进行比较,表明正交配置法中计算平行反应效率因子的有效、准确的方法.     

活性非均匀分布固体催化剂有效因子的正交配置计算

利用正交配置方法,对具有不同反应级数的不可逆反应系统中活性呈δ函数、均匀、直线、抛物线、幂函数分布的球形固体催化剂的有效因子做了计算。计算结果表明:该算法与其他多种算法比具有简单、迅速、精度高,且容易推广到复杂反应系统等优点,是工程上计算固体催化剂有效因子的实用方法。     

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.     

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.     

用加权余量法计算球形催化剂的有效因子

本文利用加权余量法计算了等温球形催化剂的有效因子,并对催化反应n=1,2的两种情况与其它简化法进行了比较.文中取Dirac函数作为权函数,形式简单,在袖珍计算器上就能完成计算.其结果:当n=1时,与解析解非常接近;当n=2时,优于其它三种简化解法,很接近数值解.     

C207铜基催化剂常压甲醇分解反应动力学(Ⅱ)催化剂效率因子正交配置解

在内循环无梯度反应器中常压下测定了工业颗粒C207催化剂甲醇分解反应宏观速率,测定了催化剂孔径分布和曲节因子,获得了催化剂效率因子的实测值。探讨了计算催化剂效率因子的甲醇单组分模型和多组分模型的正交配置解,颗粒催化剂存在中心平衡死区。在相同反应条件下,催化剂效率因子模型计算值与实测值的相对误差的绝对值的平均值在11%以内,结果表明计算模型是可行的。     

甲醇合成铜基催化剂硫化氢中毒研究(Ⅱ)——表面中毒催化剂效率因子

在常压下内循环无梯度反应器中测定了工业颗粒C207铜基化剂在入口硫化氢含量7.19×10~(-4)通硫化氢4、8、12h后甲醇分解反应宏观速率,测定了催化剂孔径分布和曲折因子.由俄歇电子能谱测定获得,通H_2S 4h未中毒比半径x_c为0.938,通H_2S 8h为0.916,通H_2S 12h为0.896,与由本征失活动力学获得的计算值相符合.探讨了计算表面中毒催化剂效率因子的甲醇单组分模型和多组分模型的正交配置解,解决了颗粒催化剂存在表面中毒和中心平衡死区的效率因子的求解问题,中毒催化剂效率因子的实验值与模型计算值的相对误差,其绝对值的平均值在11%以内,表明表面中毒催化剂效率因子的计算模型是可行的.     

多孔催化剂效率因子的多组分扩散模型(VI)近似解析法求解二维模型

着眼于直接计算圆柱状催化剂效率因子的二维模型,进行了两方面的工作：发展合适的近似解析法并检验该方法的可靠性．在近似解析法中,以多项式关联效率因子和Thiele模数（φ）,并结合二维问题的特征,选择（1／tanh∮-1／φ）／φ为多项式元素．通过极端情况下二维反应-扩散方程的求解,提供了使用该方法所需参数的实际数值．在一级可逆反应、变换反应和催化剂表面中毒的甲醇分解反应3种场合下考察本文所提出的近似解析法,所得结果表明：该方法不仅计算过程极其简单,而且结果可靠,其计算精度与有限元法和正交配置法相当．该方法对表面中毒情况的计算同样适应．     

催化剂球化对内表面利用率的影响——非一级反应

本文提出了气固相非一级不可逆反应所用催化剂球化后对内表面利用率的通用计算方法。计算中分别将两端封闭的园柱体和周边封闭的园形薄片,在等温催化过程中和球体状催化剂的内表面利用率相比较,发现在同一 Thiele 模数时,它们之间的差异略大于一级不可逆反应。工业气固相催化反应所用催化剂形状不一,为了方便,需对各种不同形状催化剂的内表面利用率进行通用计算。有关文献报导,当一级不可逆反应时,计算了薄片和无限长园柱形催化剂的内表面利用率,并与等比外表面积的球形颗粒进行比较。解析解计算的结果,发现当Thielc 模数很大或很小时。三者不同形状催化剂的内表面利用率几乎相同,只在中间范围内才有差异,但仍很接近。因此,认为对于一级不可逆反应,不同形状催化剂内表面利用率均可按与颗粒具有相等比外表面积的球体来计算,但对非一级不可逆反应的适用性未有论及。本文同样以上述二种非球形催化剂,采用球化的方法与球形催化剂的等温双组分非一级不可逆反应的内表面利用率进行了计算,以了解球化方法在非一级不可逆反应中的适用性。     

伴有二级不可逆反应的非牛顿幂律流体薄膜流中化学吸收的研究

本文对伴有二级不可逆反应的非牛顿幂律流体降膜流中的吸收过程进行了研究,提出扩散反应方程和它的解,并得到实验验证.     

Effectiveness factor and selectivity estimation for a parallel reaction system

The case of double parallel reaction scheme taking place in a porous catalytic pellet is analyzed. Effectiveness factor expressions for both reactions are derived after matching asymptotic solutions strictly valid for small and large values of the Thiele moduli.It is assumed that the kinetics of both reactions follow a general irreversible power law model, that isothermal conditions prevail and that external mApproximate results in terms of effectiveness factors compare fairly well with exact results obtained by numerical integration of the differential equa     

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.     

Analysis of non-isothermal catalytic reactions. Limiting effect of non-key component

An improved method for predicting effectiveness factors for pseudo first order catalytic reactions with limiting non-key reactant has been derived. The method takes account of intraparticle temperature and concentration profiles in addition to interphase effects and solution of the system equations is obtained using the orthogonal collocation technique which is simple and involves only algebraic equations. The depth of penetration of reactant is also determined by this method. The results are discussed and compared with earliler work.     

Enhancement factors for gas-absorption with second-order irreversible chemical reaction

A relatively simple and explicit mathematical expression has been developed for estimating the enhancement factors for mass transfer accompanied by a second-order irreversible chemical reaction. The development is based on asymptotic characteristics, i.e., limiting solutions, for second-order enhancement factors. The resulting mathematical relation and other approximate analytical formulations previously presented in the literature have been critically compared with a numerical solution for the diffusion-reaction process based on film theory.     

A novel analytical second-order sensitivity calculation approach using the finite element method for chemical engineering problems

This paper presents an effective orthogonal collocation approach to approximate dynamic optimization problems into nonlinear programming problems, where the resulting problems can then be usually solved by first-order sensitivity based algorithms. However, the results obtained fail to satisfy the timeliness and accuracy requirements of some dynamic optimization problems. A novel collocation approach with second-order sensitivity information is therefore first proposed to improve the efficiency of the method. The resulting nonlinear programming problem is obtained through the orthogonal collocation on finite element combined with a single shooting approach. Three benchmark optimal control problems are considered to demonstrate the performance of the presented approach. Comparisons among the proposed approach, the BFGS method, and other literature solutions are also carried out in detail. Numerical results validate the effectiveness of the proposed method and the time saving benefit.     

A LINEAR APPROXIMATION METHOD TO EVALUATE ISOTHERMAL EFFECTIVENESS FACTORS

A linear approximation method to estimate effectiveness factors for isothermal catalytic pellets has been developed. The method is based on the Taylor series expansion of the reaction rate expression above the surface particle concentration for the key component. The application of the method to reaction systems with nonlinear kinetics yields simple analytic expressions for the effectiveness factor equivalent to that found for first order irreversible reaction. The effectiveness factor expressions obtained depend of one parameter analogous to the Thiele modulus. In this work we report the results obtained for a Monod type kinetic equation. The effectiveness factors predicted are compared with those obtained from the numerical solution of the exact boundary value problem. The error is negligible at low Thiele moduli and as this parameter is increased the error grows, reaching an asymptotic value at high Thiele moduli. For the example presented, the error is below 10%. The available results indicate that nonlinear cases such as Langmuir-Hinshelwood type of equations can be treated successfully using the method developed.     

CHEMICAL REACTIONS WITH MOLE CHANGES IN HETEROPOROUS CATALYSTS-PART II

In this short communication, the modified dusty-gas model^1-3 is used to describe the mass fluxes and to estimate the effectiveness factors in the transition regime of second order irreversible reactions with mole changes in heteroporous media. The results of this note show that the effectiveness factors predicted by the dusty-gas model are larger (up to about 30% for the systems examined) than those estimated by the modified dusty-gas model which accounts for the effects the pore-size and tortuosity distributions have on the mass fluxes in industrial heteroporous catalysts.     

Enhancement factors for gas absorption with reversible reaction

An approximate analytical expression is derived for the enhancement factor for absorption with a reversible chemical reaction which is second-order in each direction, with corresponding stoichiometry and equal diffusivities of reactants, using the Danckwerts model of mass transfer. The result agrees with simpler limiting expressions for the enhancement factors for irreversible reactions, reactions slow enough to give negligible depletion of reactants, and instantaneous reactions. The result agrees satisfactorily with the available corresponding data for numerical solutions of the differential equations for the Higbie model, with the exception of one case, where the deviation is probably due to an error in the numerical solution, or its graphical representation. No numerical solutions are available for comparison when concentrations of solute and reaction products in the bulk of the liquid are appreciable. The method seems applicable also to more complex kinetics.