STAGE SEPARATION WITH CHEMICAL REACTION STEADY STATE COUNTERCURRENT EQUILIBRIUM STAGE SEPARATION WITH CHEMICAL REACTION BY RELAXATION METHOD

The relaxation method is used to calculate mole fractions and temperature profiles in a rectification column where a chemical reaction takes place. The method is general and the non-ideal vapor-liquid equilibria can be easily incorporated. The computer time is very low and the danger of divergence can be alleviated by an appropriate guess of relaxation factor. Calculated problems involving esterification reactions are presented.     

DESORPTION WITH CHEMICAL REACTION IN CONTACTING DEVICES

Chemical processes where a gas is absorbed into a liquid and reacts to give a product that desorbs back into the gas are quite common in the industry. In this study, the reaction between the absorbed gaseous reactant and a nonvolatile reactant is considered to be slow, fast or instantaneous, while the volatile product may react further in a slow reaction. Effects of various operating parameters such as the liquid and gas flow rates, the gas-liquid interfacial area and the coefficients for mass transfer are examined. Situations can arise where the absorbing gas reacts but the product diffuses completely to the bulk of the liquid, and the rate of desorption is null. The expressions presented here define conditions to avoid this situation and allow the calculation of the optimal design and operation of the gas-liquid contacting device     

含反应节点过程数据校正的扩展独立物流法

Among the techniques developed for bilinear data reconciliation problems, the method based on independent flows is well known in terms of both accuracy and efficiency. However, the independent flow method is not effective when reactor units are present in the process. In this paper, an extended independent flow method is proposed for the data reconciliation of the process with chemical reaction. By the new method, the independent flows finding algorithm is adjusted to avoid the difficulties caused by the reactors in the process, and the reaction constraints are introduced into the objective function of data reconciliation. As a result, the new method can be applied to the process with chemical reaction while retaining high solution accuracy. To test the performance, the new method and the most typical Crowe‘s projection method are used in the data reconciliation of a typical industrial process. The results show that the new method can effectively accomplish the data reconciliation of the muhicomponent process with chemical reaction and gives more accurate estimates than the Crowe‘s method.     

ORTHOGONAL COLLOCATION IN CHEMICAL REACTION ENGINEERING

The orthogonal collocation method is used to obtain approximate solutions to the differential equations modeling chemical reactors. There are two ways to view applications of the orthogonal collocation method. In one view it is a numerical method for which the convergence to the exact answer can be seen as the approximation is refined in successive calculations by using more collocation points, which are similar to grid points in a finite difference method. Another viewpoint considers only the first approximation, which can often be found analytically, and which gives valuable insight to the qualitative behavior of the solution. The answers, however, are of uncertain accuracy, so that the calculation must be refined to obtain useful numbers. However, with experience and appropriate caution, the first approximation is often sufficient and is easy to obtain. Thus it is very often useful in engineering work, where valid approximations are accepted. We present both viewpoints here: we use the first approximation to gain insight into a problem and we refine the calculations to obtain numerical convergence to the exact result. In this later view the method is similar to and in direct competition with finite difference methods, and some of the references listed in the next section discuss the relative advantages of the orthogonal collocation method.     

ORTHOGONAL COLLOCATION IN CHEMICAL REACTION ENGINEERING

The orthogonal collocation method is used to obtain approximate solutions to the differential equations modeling chemical reactors. There are two ways to view applications of the orthogonal collocation method. In one view it is a numerical method for which the convergence to the exact answer can be seen as the approximation is refined in successive calculations by using more collocation points, which are similar to grid points in a finite difference method. Another viewpoint considers only the first approximation, which can often be found analytically, and which gives valuable insight to the qualitative behavior of the solution. The answers, however, are of uncertain accuracy, so that the calculation must be refined to obtain useful numbers. However, with experience and appropriate caution, the first approximation is often sufficient and is easy to obtain. Thus it is very often useful in engineering work, where valid approximations are accepted. We present both viewpoints here: we use the first approximation to gain insight into a problem and we refine the calculations to obtain numerical convergence to the exact result. In this later view the method is similar to and in direct competition with finite difference methods, and some of the references listed in the next section discuss the relative advantages of the orthogonal collocation method.     

NUMERICAL SOLUTION OF UNSTEADY CONVECTIVE DIFFUSION WITH CHEMICAL REACTION IN TIME DEPENDENT FLOWS

An earlier computer model for tubular high pressure polyethylene reactors is extended to take into account two radical generating sources, in addition to an injected initiator: a long-lived intermediate, possibly generated from the interaction of ethylene with trace amounts of oxygen, and the ethylene itself undergoing thermal polymerization. The first of these reactions can account for the smoothing of the temperature profile near the peak temperature, attributed by Lee to initiator and radical carryover; the second, whose inclusion is justified by experiments recently performed by Buback, can account for the explosive decomposition of ethylene known to occur in LDPE reactors if the temperature is allowed to exceed about 350°C, and it also can contribute significantly to polymer production at very high temperatures. The contribution of both reactions must be evaluated quantitatively, if reliable heat transfer coefficients are to be obtained from experiment.     

ADIABATIC GAS ABSORPTION AND STRIPPING WITH CHEMICAL REACTION IN PACKED TOWERS

In the design of adiabatic gas absorption, the temperature distribution within the column is an important consideration. Temperature influences the degrees of heat and mass transfer through the thermodynamic phase equilibrium relationships and reaction rates. The capacity of an absorber is limited through the formation of a temperature plateau. Gas absorption in a chemically reactive solvent in an adiabatic packed column is modelled rationally for the first time taking into account the major heat effects. An iterative computational method for computing packed bed height is presented. The design procedure is illustrated by sample calculations for carbon dioxide (CO₂) absorption in monoethanolamine (MEA).     

PERTURBATION ANALYSIS OF GAS ABSORPTION WITH CHEMICAL REACTION: A NONVOLATILE LIQUID REACTANT

Enhancement factors for gas absorption in a liquid containing a nonvolatile reactant are calculated using a regular perturbation technique. The perturbation solutions are found to be quite accurate in the slow reaction regime but lead to erroneous results for moderate and large reaction rates. To extend these solutions to the intermediate and fast reaction regimes, we have used the method of Padé approximants and Shanks transformations. The results obtained by these acceleration techniques are shown to be in excellent agreement with the direct numerical solutions for the enhancement factors in the intermediate and fast reaction regimes.     

SEPARATION OF 13C NMR RELAXATION MECHANISMS IN VISCOUS SOLUTIONS

The ¹³C NMR analysis of relaxation data from viscous solutions requires the application of complex mathematical functions. These equations can be combined and solved exactly using a series of iterative algorithms. Correct analysis of typical relaxation data obtained for several viscous ionic liquids provides rotational correlation times that describe the molecular dynamics of these and other viscous solutions. The ¹³C NMR relaxation data for 1-methyl-3-nonyl-imidazolium PF₆ ionic liquid is used to illustrate the details of this method using iterative techniques in a stepwise manner. This approach is outlined such that other investigators can easily duplicate the algorithms.     

ANALYSIS OF CHEMICAL REACTION SYSTEMS

This paper examines strategies for integration of the stiff ordinary differential equations that comprise the mass balances in a complex reaction scheme. A reduced set of mass balances is obtained by taking certain reactions at equilibrium and applying the method of Sorensen and Stewart (1980). The GEAR integrator is coupled with the Rand algorithm for minimization of Gibbs free energy. Advantages and disadvantages of this approach are considered, with emphasis on combustion of hexane in a tube.     

MASS TRANSFER TO A DROPLET WITH A FIRST-ORDER CHEMICAL REACTION

The steady-state mass transfer to a droplet with a first-order chemical reaction is i nvestigated as a function of the Damkohler number (Da₁₁) for the special case of very high Peclet number flow. The flow field in the droplet employed in this work is Hill's spherical vortex. The resistance to mass transfer is assumed to occur inside the droplet with negligible resistance to mass transfer in the continuous phase.     

SEPARATION OF 13C NMR RELAXATION MECHANISMS IN VISCOUS SOLUTIONS

The ¹³C NMR analysis of relaxation data from viscous solutions requires the application of complex mathematical functions. These equations can be combined and solved exactly using a series of iterative algorithms. Correct analysis of typical relaxation data obtained for several viscous ionic liquids provides rotational correlation times that describe the molecular dynamics of these and other viscous solutions. The ¹³C NMR relaxation data for 1-methyl-3-nonyl-imidazolium PF₆ ionic liquid is used to illustrate the details of this method using iterative techniques in a stepwise manner. This approach is outlined such that other investigators can easily duplicate the algorithms.     

MASS TRANSFER WITH CHEMICAL REACTION IN A FROTH BED REACTOR

A model to predict conversions in a froth bed reactor has been developed. The model is then compared against the available experimental data on the oxidation of sodium sulfide in a foam bed contactor. The predictions using the present model are also compared against those based on the model of a foam bed reactor developed earlier. The predictions using the present model agree fairly well with the experimental data and, in some cases, are even in better quantitative agreement than the previous single stage model of a foam bed reactor. The case of significant surface resistance due to surfactant has also been analyzed theoretically, obtaining analytical solutions for the concentration profile and fractional gas absorption in a liquid froth shell.     

三辛胺萃取分离乳酸-醋酸

选择三辛胺为络合剂、正辛醇为稀释剂、乳酸和醋酸为被萃溶质 ,系统地研究了水相pH值及络合剂含量对单组分乳酸、醋酸及其混合物萃取特性的影响。在适当假设条件的基础上 ,建立了考虑络合萃取及物理萃取的单组分及双组分体系的相平衡分配系数表达式。在本文的实验条件下 ,随络合剂含量的升高 ,乳酸、醋酸的单组分及其混合物中各组分相平衡分配系数皆升高 ,分离因子 β增大 ;随水相平衡pH值的升高 ,相平衡分配系数均降低 ,分离因子也呈下降的趋势 .采用本文的模型进行模型参数拟合 ,其精度较好。利用单组分的络合反应平衡常数可成功地预测双组分体系中各组分的相平衡分配系数值     

ANALYSIS OF CHEMICAL REACTION SYSTEMS

This paper examines strategies for integration of the stiff ordinary differential equations that comprise the mass balances in a complex reaction scheme. A reduced set of mass balances is obtained by taking certain reactions at equilibrium and applying the method of Sorensen and Stewart (1980). The GEAR integrator is coupled with the Rand algorithm for minimization of Gibbs free energy. Advantages and disadvantages of this approach are considered, with emphasis on combustion of hexane in a tube.     

SIMULATION OF STEADY DISTILLATION PROCESS ACCOMPANIED WITH MULTIPLE CHEMICAL EQUILIBRIUM REACTIONS BASING ON TRANSFORMED VARIABLES

The equations describing the steady state operation of distillation column with simultaneous equilibrium chemical reactions have been transformed into a new set or MESH equations by introducing transrormed composition, flow rate and enthalpy variables. The new set of equations are similar to equations describing traditional non-reactive distillation, and it is general when one or several reactions occur and inert components are present.

An algorithm combining relaxation method and modified Newton-Raphson method is proposed to solve the new equations, the relaxation method is used to estimate initial values, while the modified Newton-Raphson method is used to set solution. The reactive distillation processes of MTBE synthesis with n-butane and the separation of meta- and para-xylene are simulated as numerical examples     

A GENERALIZED PERTURBATION APPROACH TO THE ANALYSIS OF MASS TRANSFER WITH CHEMICAL REACTION

A generalized perturbation approach is presented for the analysis of the simultaneous absorption of two gases in a liquid accompanied by a chemical reaction. The main objective is to derive approximate analytical solutions for the enhancement factors of the solute gases, for all reaction rates. The method consists of constructing a regular perturbation solution for slow reaction, whose convergence is accelerated by means of an Euler transformation, thereby extending its range of utility for larger reaction rates. Convergence is further improved by suppressing the leading singularity of the Euler-transformed series. The accelerated solution is found to predict the enhancement factors very accurately in the slow, intermediate and fast reaction regimes, and in particular, approach the boundary layer limit associated with fast reaction.     

CATALYST PRODUCT SEPARATION TECHNIQUES IN HECK REACTION

The Heck reaction finds several applications in industry because it is one of the effective tools for the formation of a new C─C bond. In addition to the catalytic activity and selectivity, catalyst-product separation strategies are very important for the industrial application. There are various methods of interest ranging from conventional heterogeneous catalysts to heterogenization of homogeneous catalysts. The heterogeneous catalysts are classified into supported metal catalysts, zeolite-encapsulated catalysts, colloids-nanoparticles, and intercalated metal compounds. The homogeneous metal complexes catalysts are heterogenized using modified silica catalysts, polymer-supported catalysts, biphasic catalysts, supported liquid-phase catalysts, nonionic liquids solvents, perfluorinated solvents, and reusable homogeneous complexes. In general, heterogeneous catalysts are effective and stable at higher temperatures, which may be important for the activation of less reactive but less expensive chloroaryls substrates. However, the heterogeneous catalysts have a major drawback of poor selectivity toward Heck coupling products. The heterogenized metal complexes catalysts operate under relatively mild conditions as compared with heterogeneous catalysts, and so they can be applied to the production of pharmaceuticals and fine chemicals. Catalysis using supercritical solvents with catalyst separation techniques is promising for the development of green chemistry processes. Although the concepts described in this article have been reviewed mainly for Heck reactions, they should be applicable to a wide range of other chemical transformations (hydrogenation, carbonylation, hydroformylation, and so on) that, currently, are homogeneously catalyzed reactions.     

TIME-SCALE ANALYSIS OF CHEMICAL REACTION SYSTEMS DYNAMICS†

In dynamic simulation and control of chemical reaction systems physical state variables (compositions) are not often defined so as to facilitate the practical use of the system model. This ill-posedness frequently arises due to the presence of hidden time scales in the reaction dynamics. Transformation of variables is then often an efficient manner to facilitate the simulation and control of chemical reactors. In this paper, we emphasize the physical situation by examples and also present a manifold-based analysis which permits to construct a nonsingular transformation for expressing the original model in a explicit form. Using the coordinated-free approach, time scales in kinetic models are interpreted in terms of relaxation and conservation properties. As a whole, the paper provides conceptual fundamentals for a novel and powerful characterization of time-scale reaction variants and invariants