Hybrid neural network model of an industrial ethanol fermentation process considering the effect of temperature

In this work a procedure for the development of a robust mathematical model for an industrial alcoholic fermentation process was evaluated. The proposed model is a hybrid neural model, which combines mass and energy balance equations with functional link networks to describe the kinetics. These networks have been shown to have a good nonlinear approximation capability, although the estimation of its weights is linear. The proposed model considers the effect of temperature on the kinetics and has the neural network weights reestimated always so that a change in operational conditions occurs. This allow to follow the system behavior when changes in operating conditions occur.     

煤颗粒脱挥发分的数学模拟研究

煤颗粒脱挥发分的数学模拟研究王国金，李术元，王剑秋，钱家麟，朱亚杰（石油大学化工系，北京１０００８３）关键词煤脱挥发分，煤热解，模拟煤脱挥发分过程是煤的焦化、气化和燃烧等工艺中的基础步骤，开发煤颗粒脱挥发分的数学模型对于煤加工工艺操作参数的制定、生产...     

Kinetics of propylene epoxidation with hydrogen peroxide

The kinetics of propylene oxidation to propylene oxide in the presence of a titanium-containing zeolite in an isopropyl alcohol medium is reported. The influence of the concentrations of the starting substances and reaction products and temperature on the rate of the process is considered. A mathematical model has been derived from the experimental data obtained. The rate constants, adsorption equilibrium constants, and activation energies of the reactions have been calculated.     

粉末多孔镍电极电化学阻抗谱及其数学模型

镍电极反应动力学在大多情况下是受固态质子扩散过程控制的，以此为出发点建立了具有明确物理意义的镍电极电化学阻抗谱（EIS）的数学模型．并以该模型为基础，讨论了一些模型参数如双电层电容C（d1）、质子扩散系数D及活性物质位于半径γ0等的改变，电极的不同行电状态以及多孔镍电极中的传质过程对镍电极阻抗谱的影响．理论模型较好地解释了一些实验结果．     

粉末多孔镍电极电化学阻抗谱及其数学模型

镍电极反应动力学在大多情况下是受固态质子扩散过程控制的，以此为出发点建立了具有明确物理意义的镍电极电阻抗谱（ＥＩＳ）的数学模型，并以该模型为基础，讨论了一些模型参数如双电层电容Ｃｄ１，质子扩散系数Ｄ及活性物质粒子半径ｒ０等改变，电极的不同荷电状态及多孔镍电极中的传质过程对镍电阻阻抗谱的影响，理论模型较好地解释了一些实验结果。     

Mathematical simulation of the formation of liquid products from catalytic cracking gases over a zeolite-containing catalyst modified with Group VI and VIII metals

The kinetics of the formation of liquid products from catalytic cracking gases over a zeolite-containing catalyst in a flow reactor in the temperature range from 260 to 420°C at GHSV = 30–264 h^–1 and an on-stream time of 5–25 s has been investigated. A kinetic model for the process proceeding according to a likely scheme is proposed. The rate constants and activation energies of certain reactions involved in the process have been determined. A mathematical model of the process taking into account the mass and heat balances, as well as hydrodynamic conditions, has been developed. The concentration and temperature fields and the pressure over the catalyst bed height have been calculated. The target product yield on has been plotted as a function of the on-stream time.     

On the kinetics of styrene emulsion polymerization above CMC. I. A mathematical model

A detailed mathematical model of the kinetics of styrene emulsion polymerization has been proposed. Its main features/assumptions are compartmentalization, micellar and homogeneous nucleation, particle formation by both initiator‐derived and desorbed radicals, dependence on the particle size of the rate coefficients, thermodynamic considerations, and aqueous phase kinetics. The model predicts that micellar nucleation dominates over homogeneous nucleation and that the evolution of the nucleation rate reaches a maximum, where desorbed radicals have an important contribution. Initiator‐derived radicals with only one monomeric unit have also a significant contribution on the rate of capture in particles. The results suggest that the correctness of the instantaneous termination approach depends not only on the size of the particle, but also on the type of entering radical (initiator‐derived or monomeric). © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2201–2218, 2000     

Mathematical model of suspension flocculation kinetics

A mathematical model of suspension flocculation kinetics which describes its evolution in a wide time interval, and later stages is presented. The rate constant of floc formation has been found. The calculated dependence of particle number in volume unit on time correlates well with experimental data.     

Kinetics of electron tunneling stimulated by mobility of lithium cations in lithium gadolinium borate crystals

The kinetics of electron tunneling between electron and hole sites, stimulated by mobility of lithium cations in lithium gadolinium orthoborate (Li₆Gd(BO₃)₃) crystals has been studied. A mathematical model has been proposed to describe the kinetics in the wide time interval of 10⁻⁸–100 s after pulsed irradiation. The calculation results have been compared with experimental data on the decay kinetics of transient optical absorption (TOA) in Li₆Gd(BO₃)₃ crystals in the visible and UV spectral regions. The nature of radiation defects responsible for TOA is discussed, as well as the dependence of the TOA kinetics on temperature, excitation power, and other experimental conditions.     

Analytical expression of non-steady-state concentrations and current pertaining to compounds present in the enzyme membrane of biosensor

A mathematical model of trienzyme biosensor at an internal diffusion limitation for a non-steady-state condition has been developed. The model is based on diffusion equations containing a linear term related to Michaelis-Menten kinetics of the enzymatic reaction. Analytical expressions of concentrations and current of compounds in trienzyme membrane are derived. An excellent agreement with simulation data is noted. When time tends to infinity, the analytical expression of non-steady-state concentration and current approaches the steady-state value, thereby confirming the validity of the mathematical analysis. Furthermore, in this work we employ the complex inversion formula to solve the boundary value problem.     

Crystallization in poly(n-octadecyl methacrylate) monolayers

The crystallization kinetics of poly(n-octadecyl methacrylate) has been studied at the air–water interface. The rate of the crystallization has been measured by the decrease in the area of monolayers with time at various temperatures and surface pressures. The crystallization isotherms have been analyzed by the general mathematical treatment of the kinetics of phase changes, and the results show linear growth to be dominant. The variation of the rate constant with temperature and pressure has been illustrated by the difference in the supersaturation defined by introducing the equilibrium pressure-area isotherms.     

A study on performance characteristics of granular-media trickling filters

Mass transfer within microbial films is described using Monod type biological kinetics in terms of the properties of packing material and the feed solution. For this purpose computer techniques have been first developed for the numerical evaluation of the normalized biofilm mathematical model. A second-order partial differential equation describing the mechanism of dispersion phenomena inside the liquid layer is then solved to determine the mass transfer coefficient. The application of the theory to experimental data reported in literature has also been demonstrated using the values of mass transfer coefficients and the computer programs developed.     

Mathematical modeling of cellulose conversion to ethanol by the simultaneous saccharification and fermentation process

Ethanol, a promising alternative fuel, can be produced by the simultaneous saccharification and fermentation (SSF) of lignocellulosic biomass, which combines the enzymatic hydrolysis of cellulose to glucose and the fermentation of glucose to ethanol by yeast in a single step.

A mathematical model that depicts the kinetics of SSF has been developed based on considerations of the quality of the substrate and enzyme, and the substrate-enzyme-microorganism interactions. Critical experimentation has been performed in conjunction with multiresponse nonlinear regression analysis to determine key model parameters regarding cell growth and ethanol production. The model will be used for rational SSF optimization and scale-up.

     

Study of Michaelis-Menten kinetics with linear-type product inhibition in ultrafiltration membrane reactors: Mathematical model,experimental and data

A method is proposed for the study of enzymatic reactions affected by product inhibition. The use of continuous and stirred ultrafiltration membrane reA mathematical model has been defined which depicts Michaelis-Menten kinetics with a linear-type product inhibition for all competitive, non-competitivThe experimental procedure needed to identify the inhibition pattern and to evaluate the set of kinetic constants is detailed. Two model systems, the h     

Fundamentals of lead-acid cells: Part XII. The reduction of lead sulphate

The reduction of lead sulphate grown anodically on planar and porous electrodes has been studied by a potentiostatic step technique. Both “planar” and “porous” electrodes behave in a similar manner and indicate that the electrode reduction reaction has a finite depth of penetration into the electrode. The kinetics of the formation of metallic lead on both electrodes appear to be instantaneous nucleation and two-dimensional growth processes with subsequent current limitations due to overlap and lead sulphate depletion. The current limitation processes are very complex and it has not been found possible to fit a satisfactory mathematical model.     

KINETICS OF REVERSIBLE PHOTOCHROMIC REACTIONS IN THE SERIES OF 1,5-DISUBSTITUTED 3,3-DIMETHYL-6'-NITRO-8'-BROMOSPIRO-[(2'H, 1 -BENZOPYRAN)–2,2'-INDOLINES]

Abstract— A method has been worked out for finding parameters that characterize the photochromism of spiropyrans. It involves statistical processing of the experimental results. The method is programmable. The fact that discoloration does exist has been verified through mathematical modelling. The result agrees with data reported in the literature. Coloration and discoloration quantum yields have been found for a number of novel spiropyrans. An attempt was made to rationalize the photochromism kinetics as a function of effects displayed by the substituents attached to positions 1 and 5 of the indoline site.     

Analytical investigation of two-step adsorption kinetics on surfaces

Analytical equations of two-step adsorption kinetics on surface have been derived. Moreover, computer simulations have been carried out to interpret various experimental adsorption kinetics previously reported. In the first case, molecules are further adsorbed from a solution onto a layer consisting of previously adsorbed molecules. This model was applied to the adsorption kinetics of hexadecyltrimethylammonium chloride (C16TAC) on a self-assembled monolayer (SAM) of 3-mercaptopropionic acid (T. Imae, H. Torii, J. Phys. Chem. B 104 (2000) 9218). The second case is that some of the initially adsorbed molecules are released from the adlayer with further time course. The adsorption of C16TAC on 1-dodecanethiol SAM (T. Imae, T. Takeshita, K. Yahagi, Stud. Surf. Sci. Catal. 132 (2001) 477) agrees with this mechanism. The strict mathematical developments presented in this work are demanded to specify the physical meaning of observed non-Langmuir adsorption kinetics, consisting of the two exponential terms.     

An example of a two-stage chemical reaction whose kinetics may be found in an analytical form

In the present work, on an example of the chemical reaction of the disodium ethylene glycol salt and acetyl chloride, a mathematical model has been formulated and the corresponding analytical solutions of four nonlinear evolutionary equations have been found. The phase portrait of the model has been constructed, and the half-life periods of the reagents have been determined. It has been emphasized that, for the analytical solvability, of significance are a rather high symmetry and the dimensionless form of the corresponding evolutionary equations of the presented mathematical model.     

Kinetics and Mechanism of Cumene Oxidation Initiated by N‐Hydroxyphthalimide

This paper discusses the results of investigations on the kinetics of cumene oxidation to cumene hydroperoxide by molecular oxygen in the presence of N‐hydroxyphthalimide as a catalyst. A mathematical model has been developed on the basis of the regularities of hydroperoxide and by‐products formation. The model adequately describes changes in all reaction components in the course of the reaction. It has also been established that the role of N‐hydroxyphthalimide in the process consists in the creation of a steady‐state concentration of N‐phthalimide radicals initiating oxidation by interacting with the hydrocarbon.