General rate equations and their applications for cyclic reaction networks: multi-cycle systems

The network reduction technique and the Bodenstein approximation of quasi-stationary behavior of reaction intermediates were systematically applied to derive general yield ratio and rate equations for multi-cycle reaction networks in homogeneous catalysis. Dual-cycle reaction networks connected by a linear pathway, multi-cycle networks stemming from the same intermediate, and single-cycle with arbitrary number of pathways between two intermediates were considered. The general yield ratio and rate equations derived in this study are applicable for most enzymatic reactions and for homogeneous catalytic reactions. Examples of homogeneous catalysis were used to illustrate the application of the general yield ratio and rate equations for network elucidation.     

General rate equations and their applications for cyclic reaction networks: multi-pathway systems

Many chemical reactions of industrial importance involve complex reaction pathways and networks; and the determinations of the reaction rate laws are very difficult. The accurate or proper rate expression is the most desired information in design phase however. In this study, the network reduction technique and the Bodenstein approximation of quasi-stationary behavior of reaction intermediates were systematically applied to derive general rate and instantaneous rate ratio equations for multi-pathway reaction networks in homogeneous catalysis or enzyme system. Multiple small reaction cycles in a main cycle, and multiple-pathways stemming from an intermediate and ending at different nodes in a cycle were considered. The general rate and rate ratio equations derived in this study are applicable for most homogeneous catalytic reactions and enzymatic reactions. Two examples of multi-pathway cyclic enzyme reaction were used to illustrate the applications of the general rate and rate ratio equations for network elucidation.     

连续多级串联完全混合槽中固体颗粒反应产率计算方法

本文针对级内颗粒完全混合一级间无颗粒返混的多级反应器,探讨了按停留时间分布计算固体颗粒反应率的方法。首先分析了用δ（0）函数示踪法与多元独立随机变量和的分布密度函数法求颗粒停留时间分布的特点;应用后一种方法推得了计算颗粒反应产率的一般公式。从固体颗粒固相反应物浓度分布密度函数也可以推得此公式。在此基础上对一类特殊的反应速度方程,解析求出了直接计算任何一级反应产率的通式;对求解计算通式困难的反应速度方程,论证了两种逐级计算方法:以反应时间作计算参量及以颗粒固相反应物浓度作计算参量。     

基于蛋白质结构知识解析活性多肽的酶解制备反应行为(Ⅰ)酶解反应动态特性的3-D图形表征

提出了一种基于生物信息学知识与凝胶排阻色谱技术及图形拟合处理相结合的生物大分子复杂酶解反应行为定量分析、直观表征及模拟解析的新方法.研究中以全酪蛋白-胰蛋白酶为模式水解体系,根据完整的HPSEC实验谱图,经分子模拟多肽结构,获得了大量产物多肽信息;绘制了表征酶解反应动态特性的3-D曲面图与2^1/2维伪彩色图,并对拟合曲面方程进行了数学分析,为调控酶解反应、定向和定量地高效获取目标活性多肽提供了理论依据.     

乙基叔戊基醚合成反应动力学的协同学法分析

用协同学方法分析了乙基叔戊基醚合成反应体系的反应速率问题,通过引入一种非奇异变换将相应的反应速率方程组直接转换成Haken形式,从而发现对系统演化影响较大的序参量,进而通过绝热消去法处理而得到反应体系的各组分浓度与反应时间的演化解析表达式.用该方法求解动力学参数避免了传统方法所遇到的求解微分方程组的困难,计算所得结果与实验值吻合很好.     

Batch Kinetics of Metal Biosorption: Application of the Bohart-Adams Rate Law

The most common rate model formulations for metal biosorption in batch systems assume that the uptake process is limited by surface reaction, with the so-called pseudo first order and second order rate equations being the most popular. However, from a modeling perspective the rate coefficients of these equations are of limited use as it is not clear how they can be utilized in the modeling of other process configurations such as fixed bed columns. As an alternative, we advocate a modeling approach predicated on the Bohart-Adams surface reaction rate law because it is of a form that can be readily integrated with the governing equations for batch and fixed bed systems, allowing explicit analytical solutions to be obtained. In this work we fit the batch solution of the Bohart-Adams rate law to kinetic data taken from the literature using a genetic algorithm. The resultant parameter estimates can be used in the fixed bed solution of the Bohart-Adams rate law to generate breakthrough predictions. Moreover, the batch Bohart-Adams rate law is compared with a general nth order surface reaction rate law using the Akaike information criterion approach.     

A numerical analysis of rate data for packed bed reactors in gas-solid reaction systems

A numerical solution of the pseudo-steady state governing equations on the basis of the Langmuir-Hinshelwood type rate equation was obtained by the approximate finite difference method in packed bed reactors for gas-solid reaction system. It was proved that the numerical method has good accuracy compared with the strict solution in the special case that the reaction rate can be represented by the first-order kinetics in terms of gaseous reactant and the effectiveness factor is unity druing the reaction. The numerical method is proposed to predict the transient of exit-gas compositions of a packed bed reactor used for gas-solid reaction systems. The exit-gas composition can be predicted from the conversion data of a single particle with varying reaction time. The present method can be easily applied to the systems involving adsorptive gaseous reactants and complex reaction behavior with structural changes of particles.     

The reaction order and general equations for electrode kinetics

The method of the reaction order for investigating reaction mechanism, systematically treated by Vetter with reference to electrode processes, is extended applicable not only to charge-transfer-controlled processes but also to those for which a chemical step controls the over-all rate. In order to generalize the method, first, the stoichiometric number of the rate-determining step is explicitly taken into consideration and secondly, all the equations are derived starting with a general rate equation rather than the equation used by Vetter, which is applicable only to charge-transfer-controlled processes.     

Product distribution of casein tryptic hydrolysis based on HPSEC analysis and molecular mechanism

Tryptic hydrolysis of whole casein was analyzed by high performance size exclusion chromatography (HPSEC) in combination with the degree of hydrolysis (DH). In terms of chromatograms obtained at different DH values and mass percentage calculated equations established by the normalization method, the complex process of enzymatic reaction and the molecular mass distribution of multiple hydrolysates were quantitatively characterized via 2-D plot. Based on the information of casein micelle structure, the possible reaction mechanism was deduced from a series of chromatographic results and experimental analysis. Taking into account the primary structure of whole casein and the target amino acid of trypsin, the distribution of theoretical peptides was accurately calculated by determining the split sites of complete enzymatic hydrolysis. According to the relationship between retention time and molecular mass, the corresponding chromatogram absorption peaks of active peptides in hydrolysates were identified, and caseinophosphopeptides (CPPs) sequence was also characterized.     

GAS-LIQUID REACTORS WITH VOLATILE LIQUID REACTANTS: APPROXIMATE SOLUTION FOR CONSECUTIVE BIMOLECULAR REACTIONS OF GENERAL ORDER

An approximate solution of the film model in presence of volatile liquid reactants is presented for the case of a general van de Vusse-like reaction scheme and general power-law reaction rates. The solution is obtained in a closed-form and simply requires the numerical solution of a system of nonlinear equations. The developed approximate solution is valid for any reaction regime and any number of reactions taking place within the liquid him. The application to a CSTR is discussed; this also serves as a test of the accuracy of the approximate solution carried out by comparison with the complete film model solved via the orthogonal collocation method. The numerical studies show that the approximate solution can be used with confidence for the usual encountered rate laws and that the volatility of the liquid reactants affects the performance of the CSTR mostly at the intermediate value of the Halt a number.     

Kinetics of the photocatalytic total oxidation of different alkanes and alkenes on TiO2 powder

Although photocatalyzed total oxidation reaction of hydrocarbon species has been discussed in the literature, most of these studies were performed to obtain an appropriate reaction mechanism. Studies on the kinetics of this type of reaction are rare. Using titanium dioxide as the photo catalyst, the kinetics of the total oxidation of methane, ethane, ethene, as well as propene, have been investigated using a continuous‐stirred tank reactor. In the experiments, the hydrocarbon concentrations, the oxygen concentration, and the irradiation intensity were varied. The results obtained are evaluated on the basis of a kinetic model to derive rate equations which can be used for reactor design.     

甲醇制烯烃反应动力学

在固定床等温积分反应器内进行了甲醇制烯烃反应动力学研究,借助集总动力学的概念,充分考虑到水和积炭对反应过程的影响,得到甲醇制烯烃反应动力学模型方程.采用Runge-Kutta法求解动力学微分方程,并优化动力学参数,最终得到了可计算各集总组分反应速率的总动力学方程.然后根据乙烯、丙烯、丁烯相互之间的比值随温度的变化规律,分别计算出乙烯、丙烯、丁烯在任一条件下的反应速率方程.通过统计检验及计算值与实验值的比较,结果较为满意.     

ESTIMATION OF UPPER BOUNDS FOR THE RATES OF ENZYMATIC REACTIONS

A general methodology that allows the estimation of maximum rates of enzymatic reactions is described. For a typical mechanism of an enzymatic reaction, the rate is a function of kinetic parameters which are unknown but required to obey certain constraints. Specifically, the ratio of forward to backward rate constants must be consistent with the equilibrium constant, and the rate of each bimolecular reaction-step must be less than the rate of collision of the two reactant species. If additional information is available on the reaction rate, more constraints can be introduced. By maximizing the rate expression with respect to the kinetic parameters, subject to all applicable constraints, a first-principles upper bound is obtained for the reaction rate. If the reaction rate is actually known, the methodology can alternatively estimate an extremum for the concentration of the enzyme, a substrate, or a product. Simple thermodynamic arguments could also provide bounds for concentrations or the direction (but not the magnitude) of the rate, by examining only the overall transformation of reactants to products and completely ignoring the mechanism. The collision-limit treatment proposed here exploits basic internal characteristics of enzymatic reaction mechanisms to predict better bounds for the concentrations and the thermodynamically allowable maximum magnitude of the rate.     

A kinetic model for pretreated wheat straw saccharification by cellulase

A kinetic model for enzymatic hydrolysis of pretreated wheat straw able to describe the reaction process considering only macroscopic properties of enzyme and substrate would be useful in reactor design and scale-up. In this study Michaelis-Menten equations were used for different reaction schemes to fit experimental results obtained, working with enzyme loads between 5 and 44 i.u. g^?1 pretreated straw. Kinetic parameters were obtained by means of an optimization computer program.     

Modeling and simulation of dynamics of chemical reactors

The rate of the homogenous exothermic hydrolysis reaction of acetic anhydride catalyzed by sulfric acid in solvent acetic acid was estimated from nonisothermal experimental batch reactor transient temperature data. Rate equations based on three different reaction mechanisms of hydrolysis published in the literature were fitted to the experimental rate data. The experimental results on runaway and limit cycle behavior obtained with this reaction were explained by using the mechanism-based rate equations for hydrolysis in the reactor dynamic models, and good agreement was obtained between the predicted and the experimental dynamic data.     

Viscometric study of high-cis polybutadiene in cyclohexane solution at 30 °C

Summary High-cis polybutadiene solutions were prepared in cyclohexane at 30 °C. Six different equations were used to calculate intrinsic viscosities and viscosimetric constant values from Huggins, Kraemer, Martin and Schulz-Blaschke equations by graphic extrapolation, and Solomon-Ciuta, Deb-Chantterjee and again Schulz-Blaschke equations, through a single point determination, which presents the advantage of being a faster method. The molecular mass of the polymers was determined applying Mark-Houwink-Sakurada equation. The values of intrinsic viscosity and viscosity-average molecular mass, obtained by both types of determination, were compared and the percentual differences between them were calculated in order to verify the validity of the single point determination for the system analyzed. The results suggest that the single point determination can be applied and Deb-Chantterjee equation showed to be the most suitable for those calculations.     

MASS TRANSFER OVER AN EXPONENTIALLY STRETCHING POROUS SHEET EMBEDDED IN A STRATIFIED MEDIUM

The boundary layer flow and mass transfer towards an exponentially stretching porous sheet embedded in a stratified medium is presented in this analysis. A first-order constructive/destructive chemical reaction is also considered. Similarity transformations were used to convert the partial differential equations corresponding to the momentum and concentration into highly nonlinear ordinary differential equations. Numerical solutions of these equations were obtained by the shooting method. Mass absorption at the surface was found in the case of a stratified medium, and it increased with an increase of stratification parameter. Due to increasing reaction rate parameter the concentration decreased. It is important to note that concentration overshoot was observed in the case of a stratified medium.     

The Instrument Spreading Correction in GPC. I. The General Shape Function Using a Linear Calibration Curve

Abstract

A general shape function is proposed for describing the instrumental spreading behavior in gel permeation chromatography (GPC) columns due to axial dispersion and skewing effects. The general shape function contains statistical coefficients which describe the axial dispersion, skewing, and flattening of ideal monodisperse standards. A method denoted as the “method of molecular weight averages” is used to derive equations to correct GPC number- and weight-average molecular weights and intrinsic viscosities calculated from linear molecular weight calibration curves. The validity of these equations is experimentally verified with data for polystyrene, polybutadiene, and polyvinyl chloride polymers in tetrahydrofuran. The physical significance of the correction equations and their statistical coefficients is discussed in relation to the observed GPC chromatograms. Application of this shape function to the numerical Fourier analysis method for correcting differential molecular weight distribution (DMWD) curves is outlined. Also, a method is presented for obtaining corrected DMWD curves from a fitted molecular weight calibration curve corrected for instrument spreading by use of the hydrodynamic volume concept.     

THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS I. Integral Equations for Diverse Reaction Rate Regimes

Design equations for non-isothermal Laminar Flow Tubular Reactors (LFTRs) with homogeneous and heterogeneous - at the reactor wall - reactions with arbitrary kinetic equations have been satisfactorily treated transforming the original P.D.E. problem into a system of integral equations. The kernels of the integral operators are related to an eigenvalue problem which does not depend on the kinetic equations; this avoids repetitive computational effort in the treating of different reaction kinetics.

To render a more efficient numerical treatment and according to the governing reaction rate regime, modified expressions of the general solution were obtained was follows: (i) a solution with kernels depending only on the diffusion and convective times was obtained for a low reaction regime; (ii) another solution with kernels including the reaction lime, besides the diffusion and convective ones, was necessary for a fast reaction regime and (iii) the local quasi-steady-state approximation was obtained as limiting case of solution (ii) for a instantaneous reaction regime.