Two-parameter model for evaluating effectiveness factor for immobilized enzymes with reversible Michaelis-Menten kinetics

A two-parameter mathematical model was developed to calculate the effectiveness factor for immobilized enzymes in porous spherical particles. The model was resolved for reversible Michaelis-Menten kinetics, including simple Michaelis-Menten and product competitive inhibition kinetics. Since only two dimensionless moduli are involved in the model, the effectiveness factor for the three kinetic equations considered can be estimated by using only one generalized graph.     

Catalyst effectiveness in sulfur dioxide oxidation

The sensitivity of the relationship between catalyst effectiveness in SO₂ oxidation and the Thiele parameter to: (1) the kinetic expression with respect to the presence or absence of strong SO₃ inhibition, (2) the activation energy in the range of 16–32 kcal/g mol, (3) the conversion of SO₂ up to 90%, (4) the temperature at the exterior surface of the pellet in the range of 450–600°C, and (5) the feed composition ranging from 6–10% SO₂ in air, was investigated. A nonisothermal model was used and the calculations were carried close to equilibrium. Far from equilibrium, the relationship is essentially unaffected except by conversion at the pellet surface for the case of strong product inhibition. Close to equilibrium, the relationship is significantly influenced by conversion, temperature, and the inlet composition but the form of the kinetics is not important. The activation energy is not a significant variable. Catalyst size, surface area, and density were not specified while it was necessary to fix the ratios of the transport properties for the calculations. The properties of the American Cyanamid V₂O ₅ catalyst were used for this purpose.     

Catalyst particle effectiveness with unsymmetrical boundary conditions

In trickle-bed reactors part of the surface of the catalyst particles may be covered by liquid and part by gas. Under such conditions conventional expressions for effectiveness factors are not applicable because the surface concentration is not uniform. In this paper more general equations for both particle and overall effectiveness factors are derived. The first development is for slab geometry where the two plane surfaces of equal areas have different reactant concentrations. This is followed by treatment of a cubic particle where one or more faces are covered by liquid. Approximate methods are then presented for evaluating the effectiveness factor for any fractional liquid coverage, f. Comparison of the results at permissible values of f indicates that a simple weighting-factor method gives good results. The method is illustrated by comparing predicted and experimental reaction rates for a case where experimental results are available—the hydrogenation of α-methyl styrene.     

Limiting kinetic equation for describing a first-order chemical reaction with spatially nonuniform diffusion and kinetic coefficients

A spatially nonuniform system in which a first-order chemical reaction occurs is considered. Both the diffusion coefficient and the kinetic coefficient of the reaction are assumed to be dependent on spatial coordinates. An asymptotically valid method is proposed for reducing a diffusion equation (under the described conditions) in the presence of a source (a reaction) to a simple kinetic equation containing a constant kinetic coefficient. A functional is derived that makes it possible to use variational methods for determining the kinetic coefficient.     

A simple model for the vanadium redox battery

A two-dimensional stationary model, based on the universal conservation laws and coupled with electrochemical reactions, is applied to describe a single all-vanadium redox flow cell. Emphasis is placed on studying the effects of applied current density, electrode porosity and local mass transfer coefficient on the cell performance. The model results indicate that bulk reaction rate depends on the applied current density. The transfer current density and over-potential increase almost twice as the applied current density doubled. A decrease in electrode porosity leads to a more rapid depletion of the reactant concentration, a higher integral average value of the transfer current density and a more uniform distribution of the over-potential. The local mass transfer coefficient only affects the value of the over-potential.     

热浸镀镀层厚度的动态控制方程

利用简化的动态模型过程 ,推导了热浸镀条件下的膜层厚度控制方程 ,并通过实验手段对此方程作了验证。结果表明 ,该方程作为工程快速估算是可行的     

A kinetic model for pyrolysis of cellulose

It has been shown that the pyrolysis of cellulose at low pressure (1.5 Torr) can be described by a three reaction model. In this model, it is assumed that an “initiation reaction” leads to formation of an “active cellulose” which subsequently decomposes by two competitive first-order reactions, one yielding volatiles and the other char and a gaseous fraction. Over the temperature range of 259–341°C, the rate constants of these reactions, k_i (for cellulose → “active cellulose”), k_v (for “active cellulose” → “volatiles”), and k_c (for “active cellulose” → char + the gaseous fraction) are given by k_i = 1.7 × 10²¹e^{? (58,000/RT)} min ^?1, k_v = 1.9 × 10¹⁶e^{? (47,300/RT)} min^?1, and k_c = 7.9 × 10¹¹e^{? (36,600/RT)} min^?1, respectively.     

A general kinetic model for epoxy polymerization

A general kinetic framework to study epoxy polymerization is developed. Best-fit values of five rate constants are obtained using some experimental chromatographic data available in the open literature on a system involving a single liquid phase. Detailed sensitivity studies are then carried out to identify the most important rate constants. Average molecular weights and the polydispersity index are predicted using these parameters. The present model is more general than earlier kinetic models, and does not have the drawbacks of probabilistic models. The present model is used to predict the effect of intermediate addition of NaOH, to illustrate how general it really is. The model can easily be extended to apply to industrial reactors, which have additional physico-chemical phenomena associated with them, as for example, non-isothermal polymerization, presence of two liquid phases, etc. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 70: 1859–1876, 1998     

A kinetic model for bleaching vegetable oils

Very little data and very few kinetic models are available describing and evaluating the performance of bleaching processes, earths, and equipment. This work presents a general kinetic model for the adsorption of pigments by adsorbent earths in several edible oils. It reports the kinetic parameters found for two bleaching earths (one developed in the laboratory and one commercial) for the clarification of soybean oil, as well as their activation energies. The proposed kinetic model is second order in the dimensionless pigment concentration and is in good agreement with our experimental data. A very simple mechanistic explanation based on adsorption/deactivation is offered to justify its application. We also present mathematical modeling based on balance equations to show how the kinetic parameters can be used for bleaching earths and for industrial equipment evaluation and design, such as for the transient fed-batch stirred bleaching vessel. The model seems appropriate to represent data under different operating conditions such as temperature and adsorbent load. The simulation shows that startup procedures are very important in the bleaching process—at least as important as the batch step, in which the oil color reaches its desired standard.     

A new kinetic model for wool dyeing

Previous kinetic models of the dyeing process are reviewed in an attempt to describe the exhaustion profile of acid dyes on wool fibres. A new kinetic model is proposed that describes the dye uptake throughout the whole kinetic period, and that takes into account the amount of dye and acid supplied at the beginning of dyeing. The equation is used to achieve isoreactive dyeing by calculating the amount of dye to add during the dyeing process.     

Determining gas hydrate kinetic inhibitor effectiveness using emulsions

In this study we measure the effect of hydrate kinetic inhibition in emulsions. Because hydrate nucleation is stochastic, many experiments normally are needed to obtain accurate analysis of the effectiveness of kinetic inhibitors. Using differential scanning calorimetry (DSC), we show how emulsions can reduce the number of kinetic samples needed to obtain a statistical analysis of the effectiveness of polyvinylcaprolactam, PVCap, a common kinetic inhibitor. PVCap is shown to delay the average hydrate nucleation time and also causes hydrate nucleation to become more stochastic. This novel method uses less material and experimental time compared to traditional methods used to test kinetic inhibitors.     

啤酒过滤用废硅藻土的热解特性及动力学

通过热重分析研究了废硅藻土在室温~1 173 K下的热解特性,实验在高纯氮气气氛下进行,升温速率分别为5,10,15 K/m in。结果表明,热解过程分为3个阶段,主要热解阶段为酵母细胞和蛋白质分解过程,随着升温速率的增加,DTG曲线峰值向高温区移动。采用积分法Coats-Redfem方程得出废硅藻土热解过程符合3级反应机理模型,并得到了5,10,15 K/m in升温速率下的表观活化能51.13,58.14,69.21 kJ/mol和指前因子2.5E+04,1.1E+04,6.8E+05 m in-1。     

A kinetic model for methanol conversion to hydrocarbons

We developed a detailed kinetic model for methanol conversion to hydrocarbons over zeolites. The dimethylether at equilibrium with methanol, generates carbene; it attacks the oxygenates giving light olefins, and the latter forming higher olefins. The olefins, through carbenium ions, form aromatics and paraffins. The kinetic parameters, identified by nonlinear optimization techniques, and the model predictions, agree quite well with the experiment and literature available data.     

A kinetic model for continuous-flow stirred biological reactors

A kinetic model is proposed to describe the mechanisms of substrate removal in continuous-flow, stirred bioteactors for bacterial autocatalytic reactions. A lumped parameter, defined as the average number of contacts between microorganisms and limiting substrate per unit time per unit of biomass, is used to study the overall effect of mixing on reactor performance. Under all the conditions studied, the overall effect is such that the larger the value of the parameter the better the reactor performance. The influence of formation and decomposition of cell-substrate intermediate on substrate removal is also presented.     

自絮凝颗粒酵母表观生长动力学

首先利用激光聚焦反射颗粒测量系统在线监测了自絮凝颗粒酵母粒径分布,通过提高发酵罐搅拌速率减小了颗粒粒径,消除了内扩散影响,获得了本征动力学模型。进而基于颗粒内部薄壳物料衡算理论,建立了表观动力学模型,并通过不同底物浓度和自絮凝酵母颗粒粒径分布条件下发酵实验数据拟合,获得了模型的参数。在此基础上,分析了内扩散效应导致颗粒内部可能出现死区的影响,绘制了发酵培养基初始糖和自絮凝颗粒酵母粒径影响的操作图,分析了这一发酵体系的性能。结果表明对于工业生产中普遍采用的多级串联连续乙醇发酵系统,主发酵罐和后发酵罐由于残糖水平差别较大,使颗粒内部因底物枯竭而导致内扩散效应的可能性显著不同：主发酵罐适宜于较大粒径自絮凝颗粒酵母体系,以利于固定化,提高发酵罐中细胞密度和生产强度;而后发酵罐适宜于较小粒径自絮凝颗粒酵母,以减轻底物内扩散影响,保持所需的发酵活性。因此需要综合考虑工程操作和动力学行为,对自絮凝颗粒酵母粒径分布进行优化控制。