CALCULATION METHODS FOR DISTILLATION SYSTEMS WITH REACTION

A calculation procedure is presented for the solution of the equations describing a distillation process in which reaction is taking place. A mathematical model based on matrix notation is used to formulate the system equations. It is assumed that the distillation process can be represented by a system of interconnected stages, each of which is well mixed with the vapor and liquid phases in equilibrium. Reaction may take place in the vapor phase, liquid phase, or both. The equations describing this system are first presented. Then a calculation sequence and a correction algorithm are derived for the case in which the liquid and vapor solutions are ideal—that is, the equilibrium ratios are functions only of temperature and pressure and not of composition. The calculation sequence uses as variables of iteration the vectors of vapor flow rate, temperature, and reaction extents. A derivative correction method is used, and equations for the calculation of the Jacobian matrix are derived. The application of the method is illustrated by solution of two sample problems. The special case in which the heat of reaction is small, and constant molal overflow can be assumed, and the case in which the reaction rate is very fast and chemical equilibrium exists in each stage are considered.     

CALCULATION METHODS FOR DISTILLATION SYSTEMS WITH REACTION

A calculation procedure is presented for the solution of the equations describing a distillation process in which reaction is taking place. A mathematical model based on matrix notation is used to formulate the system equations. It is assumed that the distillation process can be represented by a system of interconnected stages, each of which is well mixed with the vapor and liquid phases in equilibrium. Reaction may take place in the vapor phase, liquid phase, or both. The equations describing this system are first presented. Then a calculation sequence and a correction algorithm are derived for the case in which the liquid and vapor solutions are ideal—that is, the equilibrium ratios are functions only of temperature and pressure and not of composition. The calculation sequence uses as variables of iteration the vectors of vapor flow rate, temperature, and reaction extents. A derivative correction method is used, and equations for the calculation of the Jacobian matrix are derived. The application of the method is illustrated by solution of two sample problems. The special case in which the heat of reaction is small, and constant molal overflow can be assumed, and the case in which the reaction rate is very fast and chemical equilibrium exists in each stage are considered.     

八碳芳烃临氢异构反应系统动力学模型——(Ⅱ)射线向量的数学表达式及其应用

线性反应系统和一些非线性反应系统的一个重要结构特点就是存在直线反应路线.本文指出了M~α(?)型线性反应系统中唯一可观测的直线反应路线的二维表达式的特点,并由此出发推导了该直线反应路线的初组成—射线向量的数学表达式和它与热力学平衡组成向量的关系;同时也指出了建立可逆线性反应系统和某些非线性反应系统的直线反应路线的初组成和速度常数之间的数学关系的可能性.本文利用射线向量的数学表达式作为反应系统中速度常数的线性等式约束,用可变误差多面体法求出了八碳芳烃临氢异构反应系统的相对速度常数,并在工业条件下的选择性动力学研究中得到验证.实践证明这种作法减少了曲线拟合时所估参数的不定性,从而为复杂反应系统速度常数的估值提供了一种有效的手段.     

Kinetic parameters of the thermoplastic/thermoset epoxy reaction by fourier transform infrared spectroscopy

The melt state reaction, or fusion process of bisphenol-A and the diglycidyl ether of bisphenol-A can produce both linear phenoxy backbone chains and crosslinked network structures. The linear chains can be thought of as thermoplastic polymer, while the crosslinked molecular matrix is a thermoset; therefore, this resin system can be termed a thermoplastic/thermoset epoxy. Fourier transform infrared spectroscopy has been employed to study the chemical kinetics of the urea catalyzed system. The reaction of bisphenol-A and the diepoxide follows first order kinetics with respect to epoxide concentration, through 95 percent consumption of the epoxide for reaction temperatures of 130°C and above while lower temperatures show deviation from first order behavior at 75 percent conversion. When the differential form of the kinetic equation is used for analysis, the system follows first order behavior through 60 percent conversion of the epoxide at which point the order increases to a value of 1.5. Rapid spectral collection techniques have been employed to study this behavior for the temperatures 110 to 160°C. Upon incorporation of 3,4′ bisphenol-A into the system first order behavior still adequately describes the kinetic behavior; however the rate of epoxide consumption and the activation energy are affected. Since the stoichiometric ratio of bisphenol-A to diepoxide was found to affect the rate constant, the reaction mechanisms of linear chain growth and crosslinking cannot be clearly distinguished by the sole use of this technique.     

热校平对钛基材在草酸中的腐蚀速度影响

研究了热校平工艺对钛基材在草酸溶液中的腐蚀速度的影响.结果表明,未热校平的钛基材在草酸中以0.474 g/(m2·min)的恒定腐蚀速度溶解,而经热校平处理的钛基材的腐蚀过程分则为三个阶段:第一阶段为氧化膜破损过程,速度最慢;第二阶段为微电池反应过程,腐蚀速度最大;第三阶段为基体钛的匀速腐蚀过程,腐蚀速度与未热校平基材腐蚀速度一致.建立了钛基材质量损失-酸蚀时间的函数方程式,可作为制定钛基材酸蚀工艺参数的计算工具.     

基于结构导向集总的废弃油脂催化裂化分子尺度动力学模型

利用结构导向集总与Monte Carlo模拟方法相结合构建了废弃油脂催化裂化反应的分子尺度动力学模型。模型选取17个结构向量表示废弃油脂分子,生成1000个原料分子表示废弃油脂原料,利用模拟退火算法对原料矩阵进行优化,同时针对废弃油脂体系的脱氧反应新增12条反应规则,利用Materials Studio 8.0软件求取其速率常数,完成动力学模型的构建。结果表明模型可以很好地对原料性质和产物分布进行预测,模拟值与实验值的绝对误差都在比较合理的范围内,说明求取的速率常数和编制的反应规则是合理的。     

Cure kinetics of methacrylate-type resin that include cyclohexane moiety

Two methacrylate-type resin including cyclohexane moiety were synthesized and characterized. The curing characteristics of these resins were investigated according to the change of thermal initiator. An autocatalytic kinetic reaction occurs in these systems, and the kinetic parameters of all systems were reported in terms of generalized kinetic equation that considered the diffusion term. It can be shown that the reaction conversion rate of one methacrylate-type resin (NC-9110-MA) is faster than another resin (EHPE-3150-MA), regardless of the kinds of thermal initiator, which is attributed to the reaction rate constant increases of NC-9110-MA with lower activation energy compared with EHPE-3150-MA. It can be seen that the conversion reaction rate of these resin systems with BPO as thermal initiator at low temperature is higher than those with AIBN. A main factor of reaction conversion rate increase for the NC-9110-MA resin system is a reaction rate constant; however, that for the EHPE-3150-MA resin system is a total reaction order. These resin with BPO as thermal initiator represent a lower cure reaction activation energy and collision frequency factor than those with AIBN.     

Theoretical Analysis of Reaction and Diffusion Processes in a Biofuel Cell Electrode

A mathematical model for reaction diffusion processes in a biofuel cell electrode is discussed. This model is based on reaction diffusion equations containing a non‐linear term related to the rate of the enzyme reaction. Theoretical treatment of a reaction and diffusion processes in a biofuel cell electrode, for the steady and non‐steady state condition is discussed. Approximate analytical expressions for the steady and non‐steady state current density at the electrode surface are calculated by using the new approach to homotopy perturbation method and complex inversion formula. An analytical expression for the steady state current density is compared with numerical results and found to be excellent in agreement. A novel graphical procedure for estimating the Michaelis‐Menten constants and turnover rate solely from the current‐potential curve is suggested. Influence of the controllable parameters such as diffusion of the mediator, Michaelis‐Menten constant for substrate, second‐order rate constant, thickness of the film, turnover rate and initial substrate concentration on the current density are discussed.     

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas–solid and fluid–solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection–diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection–diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov–Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor–corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus.     

A kinetic study of hydrothermal reaction in γ-C2S-quartz system II. Influence of the granulometry of quartz and of the treatment of samples

The kinetics and mechanism of hydrothermal reaction in the γ-C₂S-SiO₂ system at 200°C for initial CaO/SiO₂ molar ratio 1 was studied. The analysis of the reaction kinetics was carried out by a method assuming that at given reaction intervals the reaction rate can be simultaneously contorlled by nucleation and growth of the reaction product, phase-boundary interaction and diffusion through the layer of reaction product. According to the obtained results, at initial reaction stages the reaction rate is determined by all the three processes simultaneously; at later stages it is determined by nucleation and growth as well as fast diffusion if the reactants are powdered mixtures, and by very slow diffusion in case of compacted mixture. While the period of value increase of the diffusion rate constant coincides with the period of xonotlite crystallisation in the reactions of powdered mixtures, in the reaction of compacted mixture a slight lowering in the value of the diffusion rate constant was observed in the period of 3.01 Å phase crystalisation.     

Interpretation of equilibrium exchange rates for nonelementary reactions

In a system that is close to chemical equilibrium, the relaxation of each elementary step toward equilibrium obeys the linear laws of nonequilibrium thermodynamics. For a series reaction in which the concentration of the intermediate species are low or do not change with time, the relaxation can be characterized by one time constant, which can be associated with an overall equilibrium exchange rate for the overall reaction. The relationship between the overall equilibrium exchange rate and the equilibrium exchange rates of the individual steps is analogous to that between the overall conductance and the individual conductances of a network of electrical resistors in series. A numerical example is presented to show the range of validity of this relationship. Finally, a condition for the determinability of exchange rates is presented. Exchange rates are independently determinable if and only if the determinant of the matrix, whose elements are made up of squares of the inner products of the vectors that are made up of the stoichiometric coefficients of the species in the reactions, is non-zero.     

Cure behavior of epoxy/MWCNT nanocomposites: The effect of nanotube surface modification

The effect of carboxyl and fluorine modified multi-wall carbon nanotubes (MWCNTs) on the curing behavior of diglycidyl ether of bisphenol A (DGEBA) epoxy resin was studied using differential scanning calorimetry (DSC), rheology and infrared spectroscopy (IR). Activation energy (E_a) and rate constants (k) obtained from isothermal DSC were the same for the neat resin and fluorinated MWCNT system (47.7 and 47.5 kJ/mol, respectively) whereas samples containing carboxylated MWCNTs exhibited a higher activation energy (61.7 kJ/mol) and lower rate constant. Comparison of the activation energies, rate constants, gelation behavior and vitrification times for all of the samples suggests that the cure mechanisms of the neat resin and fluorinated sample are similar but different from the carboxylated sample. This can be explained by the difference in how the fluorinated nanotubes react with the epoxy resin compared to the carboxylated nanotubes. Although the two systems have different reaction mechanisms, both systems have similar degrees of conversion as calculated from the infrared spectroscopic data, glass transition temperature (T_g), and predictions based on DSC data. This difference in reaction mechanism may be attributed to differences in nanotube dispersion; the fluorinated MWCNT system is more uniformly dispersed in the matrix whereas the more heterogeneously dispersed carboxylated MWCNTs can hinder mobility of the reactive species and disrupt the reaction stoichiometry on the local scale.     

硅灰石与盐酸反应动力学规律探讨

在ｐＨ和温度恒定的条件下,对硅灰石与盐酸反应动力学进行了实验研究。发现其反应动力学规律分为两阶段,初始阶段反应速度只与硅灰石总表面有关;当反应率（Ｇ）达到一定值时,反应动力学符合固相多元体系的杨德尔速度方程。同时,对产物ＳｉＯ２物理状态和临界反应率（Ｇ）的意义进行讨论。     

EXTRACTION RATE OF W-AMYL ACETATE WITH ALKALINE HYDROLYSIS IN AQUEOUS PHASE

It is confirmed experimentally that a “Diffusion controlled slow reaction model'“ explains very well the alkaline hydrolysis of n-amyl acetate at constant inlerfacial area. Mass transfer coefficient obtained from the model agrees well with that obtained from pure mass transfer experiment. Mass transfer coefficient can be correlated against Reynolds number, Schmidt number and vessel dimensions. Effect of diluents and solutes can also be explained using the above model. From the extraction rate of H-amyl acetate dispersed in aqueous phase in an agitated vessel, the second order reaction rate constant for hydrolysis of the ester with alkali in aqueous phase is estimated based on the above model. The estimated value of second order reaction rate constant for H-amyl acetate is almost identical to that for iso-amyl acetate or n-butyl acetate.     

Chemical shrinkage and diffusion-controlled reaction in a cresol novolac epoxy

The reaction kinetics with a diffusion control mechanism, as well as the volumetric change upon curing, of a cresol novolac epoxy/o-cresol-formaldehyde novolac hardener system were studied. Simple equations to model the change in linear coefficients of thermal expansion with reacting thermosetting system conversion were also derived. Based on the heat of the reaction of monomeric monofunctional model compounds, the true degree of conversion of this crosslinking epoxy system can be obtained. The reaction is then modeled as a reaction of shifting order: it first reacts autocatalytically and later switches into diffusion control. The reaction in the diffusion-controlled region can be modeled by an n-th order kinetic equation with its rate constant described by a WLF-type equation. Both experimental linear coefficients of thermal expansion above and below the glass transition temperature decrease linearly with the degree of conversion, which agrees with the derived equations. The importance of chemical shrinkage upon curing is also discussed.     

A Quasi-steady-state analysis of the dynamics of two-species heterogeneous catalytic reactions

This study demonstrates how low-order algebraic non-linearities that exist in a simple two-component Langmuir-Hinshelwood type reaction kinetics (CO oxidation) are sufficient to produce rate multiplicities and oscillatory steady states (periodic solutions). A singular perturbation analysis is employed wherein certain quasi-steady-state considerations are made which lead to the definition of system manifolds and invariants along which the large-time dynamics of the system can be discerned without recourse to numerical integration. New results, confirmed by simulation, include an explanation for such experimentally observed pathological phenomena as the coexistence of oscillatory and stationary steady states and multi-peak oscillations. It is shown how the existence of oscillatory states and a plausible “buffering” physisorption surface reaction mechanism causing a periodic switching between these states and coexisting stationary ones can give rise to these multi-peak oscillations.     

The principle of critical simplification in chemical kinetics

The paper introduces the concept of critical simplification for chemical kinetics. The principle is valid in the presence of a dominant competitive reaction and critical phenomena. A justification based on singular perturbation and bifurcation analysis is provided. A simple methodology is identified by which kinetic mechanisms and reaction rate parameters may be readily identified from a mono-parametric experiment (reaction rate vs. reaction parameter).     

A variable reaction order model for prediction of curing kinetics of thermosetting polymers

Based on the study of the curing reaction of an fluorinated aliphatic cyanate ester resin using an isothermal Differential Scanning Calorimetric (DSC) method, a new kinetics model with variable reaction order was proposed to describe the curing of thermosetting resins in both the chemical controlled and diffusion controlled regions. α-T_g relationship was used to calculate the diffusion controlled reaction rate constant during cure. Then the chemical and diffusion rate constants were combined in the Simon-Gillham equation to model the overall rate constant for the entire reaction. By using the overall rate constant combined with the variable reaction order, a simple model can be built up for prediction of curing kinetics of thermosetting polymer in both the chemical and the diffusion controlled regions. The new model is simple, easy to use and has very good agreement with the experimental results.     

On the effect of the uncompensated solution resistance on the applicability of the galvanostatic relaxation techniques and comparison to steady-state techniques for electrode kinetic measurements

The effect of the uncompensated resistance between the reference and working electrodes was investigated on the applicability fields of the single and double pulse galvanostatic relaxation techniques for the determination of exchange current density. The applicability field is defined in terms of three characteristic times of the electrode system: τ_c, the time constant of the double layer capacitance—reaction resistance system; τ_d, the time constant of the diffusion impedence—reaction resistance system; and τ_r, the time constant of the double layer capacitance—uncompensated solution resistance system. Within the boundaries of this field, the exchange current density can be determined with a maximum error of ±20%. It was found that the techniques are limited by the uncompensated solution resistance to τ_r ? 0.2τ_c. An applicability diagram was also constructed for steady-state measurement techniques. In this case, the applicability field is defined in terms of k₀ (the apparent standard rate constant of the reaction), k_m (rate constant of diffusion), and τ_r and τ_c. A comparison reveals that, at small τ_c values, the relaxation techniques can be used for systems with larger k_o values than can the steady-state techniques, but at large τ_c the situation is reversed. The crossover point depends on the specific techniques compared; for example, for the double pulse galvanostatic technique with computer curve-fitting data evaluation compared to the rotating disc electrode steady-state technique, the crossover is τ_c τ~ 10^?2 s.     

MASS TRANSFER WITH A FIRST ORDER CATALYTIC REACTION IN A THREE-PHASE SYSTEM. TRICKLE FLOW ANALYSIS IN A PERIODICALLY CURVED CATALYTIC SOLID

The present work analyzes the process of mass transfer with chemical reaction in a system formed by a periodically curved catalytic wall, which is wetted by a descending film. Through the film a limiting gaseous reactant is transferred from the stagnant gas phase to the catalyst where the chemical reaction takes place.

The film hydrodynamics is first solved with the unknown free surface through a regular perturbation technique, by expanding the resulting equations in terms of a small parameter: the ratio between the film average thickness and the wave length of the curved solid wall. Assuming that the system is isothermal and at steady state, the mass transfer of the gas is afterwards incorporated. A first order kinetics whose limiting reactant is in the gas phase occurs in the solid phase.

Once the model is established and solved, the influence of the dimensionless parameters upon the effectiveness factor and the solid-liquid Biot number is then studied; important effects are found by changing the solid surface curvature at constant flow rate and catalyst volume. Besides, changes in the flow rate, the Peclet number and the ratio between the solid average width and the film average thickness, show significant effects on the net mass transfer process.