用正交配置法求算双重孔催化剂的有效因子

本文讨论了基于正交配置法的双重孔催化剂有效因子计算法;成功地求解了具有耦合边界条件的二阶微分方程组:考察了用Legendre多项式与Jacobi多项式作为配置法的试验函数,以及在催化剂颗粒和微粒内配置点组合格式对计算的收敛速度和精确度的影响.文中给出了不可逆反应、可逆反应条件下双重孔催化剂的有效因子值.一级不可逆反应的计算值与精确解吻合;二级不可逆反应的计算值与Jayaraman的试差解相当接近.文中还给出了Langmuir-Hinshelwood动力学模型有效因子曲线组.     

Analysis of wiped film reactors using the orthogonal collocation technique

Transport equation for ARB polymerization in wiped film reactors have been written. These have been reduced to the moment generation equations and using a suitable moment closure approximation, the zeroth and the second moments of the polymer have been numerically solved using the finite difference as well as the orthogonal collocation techniques. In the numerical solution by the finite difference technique, it is necessary to divide the dimensionless film thickness into at least 250 grid points to obtain stable results. The use of nine collocation points by the orthogonal collocation technique gives results close to those by the finite difference method and leads to considerable computational saving. The transport equations for the bulk and the film are found to involve four dimensionless parameters, and their effect upon the polymer formed at the end of the reactor has been studied.     

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.     

Solving partial differential equations of gas–solid reactions by orthogonal collocation

In this work the solution of the coupled partial differential equations for noncatalytic gas–solid reactions has been considered by orthogonal collocation. First of all, by an integral transformation and then by applying the orthogonal collocation method, these partial differential equations are converted to the ordinary differential equations. Then the equations are solved and the conversion–time profiles are obtained. The solution of the equations for volume reaction model, grain model and grain model with product layer resistance, modified grain model, random pore model, nucleation model and reaction of two gas with one solid has been presented in this work. The orthogonal collocation is a rapid method for solving of these equations and shows a good accuracy with respect to other solution techniques in the literature.     

Ester exchange reactions in polyarylate/poly(ethylene terephthalate) blends

Blends coagulated by a solution/precipitation procedure of a polyarylate (PAr) based on bisphenol A and tere/isophthalates with poly(ethylene terephthalate) (PET) have been studied by a variety of experimental methods. Differential scanning calorimetry experiments have shown that in blends containing more than 30% PET, conditioning of the blends at high temperatures required for calorimetric measurements resulted in progressive ester exchange reactions. The 10% and 20% PET mixtures, in which this extreme conditioning was not required, showed a single glass transition, contrary to the behaviour of the other PET compositions. These differences may be attributed to the shape of the spinodal curve, which has been simulated according to the McMaster model for polymer mixtures. The progression of the interchange reactions has been followed by solvent extraction of the resulting products and subsequent Fourier transform infra-red spectroscopy analysis. A parallel decrease in the PET heat and temperature of fusion in the insoluble fractions was observed. In our opinion this was due to the incorporation of PAr units in the PET chains, which caused a decrease in their crystallizable segment length.     

Evaluation of weighted residual methods for the solution of the pellet equations: The orthogonal collocation,Galerkin, tau and least-squares methods

In recent years a number of publications have adopted the least-squares method for chemical reactor engineering problems such as the population balance equation, fixed bed reactors and pellet equations. Evaluation of the performance of the least-squares method compared to other weighted residual methods is therefore of interest. Thus, in the present study, numerical techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau, and least-squares methods, have been adopted to solve a non-linear comprehensive and highly coupled pellet problem. The methanol synthesis and the steam methane reforming process have been adopted for this study.Based on the residual of the governing equations, the orthogonal collocation method obtains the same accuracy as the Galerkin and tau methods. Moreover, the orthogonal collocation method is associated with the simplest algebra theory and thus holds the simplest implementation. Another benefit of the orthogonal collocation method is that the technique is more computational efficient than the other methods evaluated. The least-squares method does not obtain the same accuracy as the other weighted residual methods. In particular, the least-squares method is not suitable for strongly diffusion limited systems that give rise to steep gradients in the pellet. On the other side, considering the spectral–element framework, the least-squares method is less sensitive to the placement of the element boundaries than observed for the orthogonal collocation, Galerkin and tau methods.The present paper outlines the algebra of the weighted residual methods and illustrate the numerical solution techniques through a simplified pellet problem.     

A comparison of transient reactor models for non-catalytic gas-solid processing

Transient behaviour of packed bed reactors for non-catalytic gas-solid reactions has been simulated using the sharp interface, finite reaction zone and the particle-pellet model for the reaction process occurring within the individual pellets. The solution procedures to the system of equations is based on the orthogonal collocation method. The effect of perturbations in the reactor inlet conditions on the temperature profiles encountered in the bed has also been examined.     

Chemistry of the ternary blends of poly(ethylene terephthalate), bisphenol-a-polycarbonate,and polypropylene

Poly(ethylene terephthalate) (PET) and bisphenol-a-polycarbonate (PC) are known to form a miscible blend whereas ternary blends of PET, PC, and polypropylene (PP) form two phases. This is based on the considerations of various chemical events which may occur in these systems. The role of ester-carbonate interchange reactions during melt mixing and fabricating is found to be unimportant. Differential scanning calorimetric analysis of the ternary blends shows that there appears to occur an exothermic transition in the heating mode of the instrument. This exothermic event was found to be suppressed considerably by incorporating suitable additives into the system. Degradation reactions studied by thermogravimetric analysis and a dilute solution viscometric technique reveal that there exists some kind of interaction among the components even with the immiscible PP component.     

用正交配置法求解血液透析超滤的传质动力学模型

提出了血液透析、血液超滤和血液透析超滤过程传质的通用模型,并利用正交配置技术分析了影响传质速率的各种因素.结果表明,采用正交配置法进行上述传质过程的模拟时,简单的三点配置即与解析解的结果接近.采用正交配置法比有限差分法简单、快速和准确.     

聚酯终缩聚过程模型化进展

总结了聚酯终缩聚过程的化学反应及其动力学，对于聚酯终缩聚的间歇和连续两种不同生产方式的模型化分别进行了评述，指出了没有恰当地考虑传质与反应的耦合作用是目前模型化过程中存在的主要问题，提出了副产物含量控制、模型动态化和参数优化是未来模型化发展方向。     

Solution by triple collocation for periodic operation of heat regenerators

The problem of periodic, countercurrent operation of packed-bed heat regenerators is considered and solved using triple collocation. This novel method uses collocation in two space variables: along the bed length and along the radius of the solid particles, and collocation in time. The method reduces the problem to a solution of a set of linear algebraic equations and bypasses either lengthy integration of open methods or iterative schemes of closed methods of solution both of which have been used previously for problems of this type. It is shown that the accuracy achieved is good. The effect of various system parameters such as Stanton, Biot and Peclet number on exit temperature and regenerator efficiency are examined and discussed.     

Extraction with reaction in both phases

Some aspects of liquid extraction accompanied by chemical reaction in both the phases have been considered on the basis of the two film theory. The problem of depletion of the reactant at the interface involves a complex boundary value situation and was solved by using a collocation technique. In some cases analytical solution for the specific rate of reaction of the solute could be obtained.     

Combustion and pyrolysis of poly(ethylene terephthalate). I. The role of flame retardants on products of pyrolysis

The products of pyrolysis of untreated and flame-retarded poly(ethylene terephthalate) (PET) have been studied at two temperatures using a flash pyrolysis/gas chromatography technique. The pyrolysis products were identified by gas chromatography/mass spectrometry and reaction mechanism for their formation are proposed. A quantitative and qualitative analysis of these products reveals that the phosphorus-only flame retardants have no effect on the solid-phase pyrolysis of PET. The two bromine-containing flame retardants, however, while capable of influencing the pyrolysis, were not capable of producing large changes in the major products. Their main role in the pyrolysis appears to alter slightly the balance of several competing secondary pyrolysis reactions.     

MATHEMATICAL MODELING OF NON-CATALYTIC LIQUID-SOLID REACTION AND ITS SOLUTION BY ORTHOGONAL COLLOCATION

The mathematical model of non-catalytic liquid-solid diffusion reactions discussed in this paper can be applied to quite different cases. The models in the literature such as unreacted shrinking core model, two stage model and homogeneous model can be considered as special cases of the above model which has been derived for leaching vanadium from steel slag with sodium carbonate and]or sodium bicarbonate solution reacting with two components in the slag simultaneously. The vanadium leaching reaction is inhibited by the solid product formed during the reaction. The power law equation can be used to represent the kinetic experimental data of leaching reaction. The model equations have been solved by orthogonal collocation and semi-implicit Runge-Kutta method. The parameters of the model have been estimated by the complex method. The calculated results based on this model is in good agreement with experimental data.     

Solution of diffusion–dispersion models using a computationally efficient technique of orthogonal collocation on finite elements with cubic Hermite as basis

In this paper, linear and non linear diffusion–dispersion models involving fluid flow through porous cylindrical particles are solved using orthogonal collocation on finite elements with cubic Hermite as basis. The technique involves partitioning of axial domain into equal elements and then orthogonal collocation method with cubic Hermite as basis function is applied within each element. Exit concentration profiles are drawn for Peclet numbers ranging from 0 (perfect mixing) to ∞ (perfect displacement). Proposed technique is computationally efficient, stable and yields accurate solution, even for nonlinear stiff problem. Correlation with industrial parameters is also presented.     

Computational models for cylindrical catalyst particles

A study is made of computational methods for predicting the performance of cylindrical catalyst particles in reactions with nonlinear kinetics. Accurate two-dimensional collocation solutions are obtained and used to test simplified solution methods. A novel parametric integration method is used to traverse the region of multiple solutions. The local stability of several states is determined.     

Anhydride chain ends functionalization of poly(ethylene terephthalate)

This paper aims at the end-capping of poly(ethylene terephthalate) (PET) chainends in order to introduce anhydride moieties on this polymer. An acid chloride reactive carrier of anhydride was chosen because it selectively reacts by alkoxy-dehalogenation with the hydroxyl chain ends of PET. This type of functionalization has already been described and claimed (1–3) on various polymers. However, in the present paper, a solid-liquid synthesis is reported for the first time: The reaction was performed on solid PET powder swollen in a solvent of the trimellitic anhydride chloride. This new reaction method prevents the polymer from degrading. This point is supported by parallel studies of similar reactions performed in the melt and in solution.     

Miscibility and interchange reactions in blends of bisphenol-A-type epoxy resin and poly(ethylene terephthalate)

Blends of diglycidyl ether of bisphenol A (DGEBA) and poly(ethylene terephthalate) (PET) were prepared by solution casting from 1,1,2,2-tetrachloroethane. The miscibility and interchange reactions in DGEBA–PET blends were studied by differential scanning calorimetry (DSC) and optical microscopy. PET was found to be miscible with DGEBA, as revealed by the existence of a single composition-dependence glass transition temperature (T_g). Interchange reactions between DGEBA and PET components in the blends at elevated temperatures were proven by appearance of the enhanced glass transition temperatures and the marked decrease in the crystallinity of PET. These results are attributed to the formation of copolymers based on the blend components due to interchange reactions. The morphological observations confirmed that there existed interchange reactions between DGEBA and PET. There also existed a self-crosslinking reaction among the DGEBA molecules. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 639–647, 1999     

Simulation of an adiabatic packed bed reactor

A model has been developed for adiabatic packed bed reactors which includes all the intra-particle and interphase effects plus the additional effect of axial diffusion. The computer time required for the solution was considerably less than in earlier models. The technique is based on the application of the orthogonal collocation method to both the single particle and the external field, thereby reducing the whole problem into one of solving a number of simultaneous first order ordinary differential equations.     

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.