An improved shooting method for computation of effectiveness factors in porous catalysts

When applied to compute the concentration profile and the effectiveness factor in a porous catalyst, the conventional shooting method requires that the concentration at the catalyst center y(0) must be greater than zero to yield a nontrivial solution. Since, for reactions with reaction orders less than one, y(0) can become zero in the solution when the Thiele modulus is large, the applicability of the conventional method is limited. In this study we propose an improved shooting method which is absent of such limitations and yet retains the merits of the conventional shooting method. The proposed method is shown to be robust, efficient in computation of the effectiveness factors. Not only a single steady state, but also multiple steady states, can easily be identified with the proposed method. A simple rule for stability of a state is also given in the method.     

An approximation method for the effectiveness factor in porous catalysts

An efficient method for computing approximate value of the effectiveness factor is presented. The method is developed for an arbitrary rate expression and for three representative catalyst shapes, namely, an infinite slab, an infinite cylinder and a sphere. In the method, two new asymptotic expansions for small and large Thiele moduli are developed and joined together at an intermediate value of the Thiele modulus, which can be calculated by a simple equation. The approximation is highly accurate for small and large Thiele moduli, and it has small or negligible errors for intermediate values of the Thiele modulus. As demonstrated with examples, the approximation method is fast, straightforward and is a dependable alternative to numerical methods for computing exact values of the effectiveness factor.     

Effectiveness factor approximations for multiple steady states in porous catalysts

The effectiveness factor is formally determined by solving a two-point boundary value problem, often numerically. To enhance the computational efficiency in simulations of large-scale reactor systems with porous catalysts, a simple approximation formula for the effectiveness factor is often used. For some reaction rate functions, however, the effectiveness factor as a function of Thiele modulus can show multiple values or sharp changes for a small change in the modulus. In this case, single-valued approximations of the effectiveness factor may give rise to large errors. Based on the two well-known asymptotes of the effectiveness factor for small and large Thiele moduli, we proposed equations for the approximation of the effectiveness factor for up to three multiple steady states and two catalyst geometries of an infinite slab and a sphere. The proposed equations were demonstrated to be useful in estimating the effectiveness factor, particularly for the stable steady states, and also in quickly estimating the Thiele modulus range where multiple effectiveness factors should be searched.     

Parametric dependence of solution multiplicity in reactive flashes

Necessary conditions for steady-state multiplicity in an isobaric reactive flash with constant split fraction are established. Multiplicity is caused by the interaction between separation and reaction in systems in which the activation energy and the gradient of boiling temperature with composition are sufficiently large. This interaction may cause the net reaction rate to decrease even with an increase in reactant mole fraction. Parametric studies and asymptotic arguments show that the ratio of the activation energy to the heat of vaporization must be greater than one for multiplicity to occur. Even when no vapor is generated, i.e. a CSTR whose liquid contents are at the boiling point, multiplicity can occur. Multiplicity is possible in endothermic systems as well as those with a small heat of reaction, which typically do not display multiplicity in the one phase CSTR. Several examples are considered, including the synthesis of ethylene glycol.     

溶胶-凝胶法制备催化剂的研究进展

溶胶 凝胶技术越来越广泛应用于催化剂制备过程,介绍了溶胶-凝胶法的机理、分类以及在催化剂制备中的应用与特点,分析归纳了溶胶 凝胶法制备催化剂过程中金属前驱体、水解、干燥方法和焙烧温度等因素对制得高分散、高比表面积和良好孔径的催化剂的影响。在制备催化剂的过程中,要合理调节和控制这些因素,才能制备高分散性、高纯度和高活性的催化剂。最新研究结果表明,用溶胶 凝胶法制得的催化剂组分更分散,改善晶格氧活性,对异丁烷转化率和氧化产物的选择性均有所改善。     

A novel kind of multiple steady states characteristics in the dividing wall column

In this article, one kind of multiple steady states(MSS) phenomenon was investigated for a dividing wall column(DWC). The four-section model constructed in Aspen Plus was employed to simulate two DWC cases: mixture of n-hexane, n-heptane and n-octane; system of methanol, ethanol and n-propanol. It can be seen that there is a range of vapor split ratio in which multiple solutions of reflux ratio exist for fixed DWC configuration with the same feed and product streams. The width and the curve shapes of the MSS region, and the number of solutions change with the liquid split ratio. This MSS phenomenon was further explained using the component recovery around the prefractionator and the component recycling flow inside the DWC. This MSS phenomenon is helpful for DWC design by knowing the probable existence of multiple solutions in advance.     

Prediction of the effective diffusion coefficient in random porous media using the finite element method

A finite-element-based method is presented for evaluating the effective gas diffusion coefficient of porous solids. Using this method, the 3-D micro-scale geometries of the porous solids are constructed under the ANSYS platform by the parametric code; the relation between effective gas diffusivity and micro-scale features of random-distributed porous solids is established. The results show that in random-distributed pore media, there is a percolation threshold ε _p, and this percolation threshold decreases with increasing coordination number of the pore network. The relationship between the effective diffusivity and porosity is strongly nonlinear when the porosity, ε, is less than a certain value ε _L ; for ε > ε _L , the relationship becomes quasi-linear. This dividing point ε _L decreases with increasing coordination number. The larger the coordination number of the pore network, the higher the effective gas diffusivity. Based on the simulation results and observations, a formula relating the effective diffusion coefficient with porosity is proposed.     

用改进的基团贡献法计算二元体系液相分子扩散系数

一种改进的用基团贡献原理计算二元体系液相分子扩散系数的方法,可用于大部分非理想液相体系。用150多个体系的1000多个实验点对此方法进行了验证,结果表明对于理想体系和无限稀释溶液的分子扩散系数,计算值与实验值平均相对误差不超过5%,对于大部分的非理想体系其平均相对误差小于10%。与原有的经验、半经验关联式相比,改进的方法具有更大的适用范围,能更准确地预测液相分子扩散系数。     

重质油在催化剂孔道内受限扩散及其关联模型研究进展

重质油分子结构复杂、尺寸较大且容易聚集形成缔合体,致使在加氢及催化裂化催化剂孔道内存在明显的扩散阻力,显著阻碍了反应物分子与催化剂孔道内部活性位的接触,导致反应速率与转化率明显低于轻质原料。因此,研究重油分子在催化剂孔道内扩散受阻情况可以为催化剂的设计优化提供信息与指导。尽管借助仪器或膜材料能获得溶质分子的扩散性能,但与反应条件下扩散规律差别较大,因此在实际反应体系下获得重油分子在催化剂孔道中的扩散传质具有重要的现实意义。综述采用反应动力学手段获得扩散传质数据并建立受限因子关联模型及其影响因素的研究进展,从反应物选择、反应条件及催化剂等因素的优化角度对重油分子受阻扩散研究进行展望。     

Sorption of binary liquid mixtures in methacrylate‐based biomaterials; Simultaneous determination of the diffusion coefficients and the uptake fraction at equilibrium of the components of ethanol‐water mixtures by a new iterative method

The present investigation is concerned with the development of a new iterative method permitting, for a Fickian sorption of a binary liquid mixture in thin polymer sheets, the simultaneous determination of the self‐diffusion coefficients of the components of the mixture, and their uptake fractions at equilibrium. The approach is based on a new equation describing a parallel Fickian sorption of the components of the mixture into thin polymer sheets. The procedure was tested with ideal and Monte Carlo simulated data. The method, applied to ideal simulated data that corresponded to various values of D₁, D₂ and f, perfectly extracted the desired parameters. The application of the method to Monte Carlo simulated data revealed that this method is fairly applicable even when the simulated data are considerably obscured by “noise”. Finally, the proposed method was successfully applied to the experimental data concerning the sorption kinetics of ethanol–water mixture (75 vol % in EtOH) at 37°C in thin polymeric sheets of triethyleneglycol dimethacrylate (TEGDMA). © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008