Description of martensitic transformation kinetics in Fe-C-X(X = Ni,Cr,Mn,Si) system by a modified model

Controlling the content of athermal martensite and retained austenite is important to improving the mechanical properties of high-strength steels,but a mechanism for the accurate description of martensitic transformation during the cooling process must be addressed.At present,frequently used semi-empirical kinetics models suffer from huge errors at the beginning of transformation,and most of them fail to exhibit the sigmoidal shape characteristic of transformation curves.To describe the martensitic transformation process accurately,based on the Magee model,we introduced the changes in the nucleation activation energy of martensite with temperature,which led to the varying nucleation rates of this model during martensitic transformation.According to the calculation results,the relative error of the modified model for the martensitic transformation kinetics curves of Fe-C-X(X = Ni,Cr,Mn,Si) alloys reached 9.5% compared with those measured via the thermal expansion method.The relative error was approximately reduced by two-thirds compared with that of the Magee model.The incorporation of nucleation activation energy into the kinetics model contributes to the improvement of its precision.

Investigating the first-order flotation kinetics models for Sarcheshmeh copper sulfide ore

This study was performed in two phases of work.In the first stage,four conventional first-order flotation kinetics models were fitted to the measured recoveries data and the best model were selected.In the second stage,influence of pH,solid concentration,water chemistry and the amount of collector dosage were investigated on kinetics parameters including flotation rate constant and ultimate recovery.The results indicated that that perfectly mixed reactor model and Kelsall model gave the best and the weakest fit to the experimental data,respectively.It was observed that flotation rate constant and ultimate recovery were strongly affected by chemical factors investigated especially water quality.The flotation rate constant decreased with increasing the solids content,while ultimate recovery increased to certain value and thereafter reduced.It was also found that the most values of flotation rate constant and ultimate recovery obtained in dosage of collector are 30 and 40 g/t,respectively.

A comparative single-pulse shock tube experiment and kinetic modeling study on pyrolysis of cyclohexane,methylcyclohexane and ethylcyclohexane

The pyrolysis of cyclohexane,methylcyclohexane,and ethylcyclohexane have been studied behind reflected shock waves at pressures of 5 and10 bar and at temperatures of 930-1550 K for 0.05%fuel diluted by Argon.A single-pulse shock tube(SPST)is used to perform the pyrolysis experiments at reaction times varying from 1.65 to 1.74 ms.Major products are obtained and quantified using gas chromatography analysis.A flame ionization detector and a thermal conductivity detector are used for species identification and quantification.Kinetic modeling has been performed using several detailed and lumped chemical kinetic mechanisms.Differences in modeling results among the kinetic models are described.Reaction path analysis and sensitivity analysis are performed to determine the important reactions controlling fuel pyrolysis and their influence on the predicted concentrations of reactant and product species profiles.The present work provides new fundamental knowledge in understating pyrolysis characteristics of cyclohexane compounds and additional data set for detailed kinetic mechanism development.

Extend ethylene aromatization single-event kinetic modeling with physical and chemical descriptor based on ZSM-5 catalyst

The ethylene aromatization is critical for the methanol to aromatics and light alkane dehydroaromatization process.The single-event microkinetic(SEMK)model combining the linear free energy theory and solid acid distribution concept were established and extend for the ethylene aromatization process,which can reduce the kinetic parameters and simplify the reaction network by comparison with the SEMK model including subtype elementary steps based on the type of carbenium ions.Further introducing deactivation parametersφinto the model and applying the linear free energy model to the deactivation experimental data,the obtained deactivation parametersφindicate that the carbon deposition precursors have the greatest impact on reducing the reaction rate of single-molecular reactions and the smallest impact on the hydrogen transfer reaction.Meanwhile,according to the change of reaction enthalpy,effect of carbenium ion structure on methylation,ethylation,cyclization and endo-βscission was investigated by introducing linear free energy concept into the SEMK model.The effect of different acid strengths on elementary steps was investigated based on the acid strength distribution model,it was found that the methylation and oligomerization reactions,the ali-βscission reaction,endo-βscission reaction and the cyclization reaction were more sensitive to strong acidity sites.The physisorption and chemisorption heat are separated from the protonation heat in the linear free energy kinetic model and the acid strength distribution kinetic model,and the absolute values of the obtained physisorption and chemisorption heat increase with the carbon number of carbenium ions.Furthermore,the parameters of the acid strength distribution kinetic model were applied to propane dehydroaromatization on H-ZSM-5 and the ethane dehydroaromatization on Zn/ZSM-5 to confirm the independence of parameters in the SEMK model with the similar reaction network.

A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem

The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep characteristics of the viscoplastic stage from the perspective of internal energy to analyze the mechanism of rock creep failure and determine the threshold of accelerated creep initiation.Based on the kinetic energy theorem,Perzyna viscoplastic theory,and the Nishihara model,a unified creep constitutive model that can describe the whole process of decaying creep,stable creep,and accelerated creep is established.Results reveal that the energy consumption and creep damage in the process of creep loading mainly come from the internal energy changes of geotechnical materials.The established creep model can not only describe the viscoelasticeplastic creep characteristics of rock,but also reflect the relationship between rock energy and creep deformation change.In addition,the research results provide a new method for determining the critical point of creep deformation and a new idea for studying the creep model and creep mechanical properties.

Kinetic Modeling of an Opinion Model on Social Networks

It is commonly accepted that, on social networks, the opinion of the agents with a higher connectivity, i.e., a larger number of followers, results in more convincing than that of the agents with a lower number of followers. By kinetic modeling approach, a kinetic model of opinion formation on social networks is derived, in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion exchange process is governed by a Sznajd type model with three opinions, ±1, 0, and the social network is represented statistically with connectivity denoting the number of contacts of a given individual. The asymptotic mean opinion of a social network is determined in terms of the initial opinion and the connectivity of the agents.

Kinetic Modeling of Light Naphtha Hydroisomerization in an Industrial Universal Oil Products Penex^(TM)Unit

Recently,the isomerization of light naphtha has been increasingly significant in assisting refiners in meeting sternness specifications for gasoline.Isomerization process provides refiners with the advantage of reducing sulfur,olefin,and benzene in the gasoline basin without significantly victimizing the octane.The mathematical modeling of a chemical reaction is a critical tool due to it can used to optimize the experimental data to estimate the optimum operating conditions for industrial reactors.This paper describes light naphtha isomerization reactions over a Pt/Al_(2)O_(3)-Cl catalyst at the Al-Dura Oil Refinery(Baghdad,Iraq)using a newly developed universal mathematical model.The proposed kinetic model involves 117 isomerization reactions and 90 cracking reactions to describe 52 real components graded from methane to n-octane.A Genetic Algorithm stochastic optimization technique applied in MATLAB R2020a software was employed to estimate the optimal set of kinetic parameters.The calculated activation energies for hydrocracking reactions was found to be higher than the other reactions because of hydrocracking reactions occur at higher range of temperatures.By benchmarking between the experimental and theoretical results for all 117 data sets,the mean absolute error was obtained to be 0.00360 for all 52 components.Also,a positive effect of increasing reaction temperatures was recognized on enhancing the research octane number(RON).

Comparison of kinetic models for isothermal CO_2 gasification of coal char–biomass char blended char

This study investigated the isothermal gasification reactivity of biomass char （BC） and coal char （CC） blended at mass ratios of 1：3, 1：1, and 3：1 via isothermal thermogravimelric analysis （TGA） at 900, 950, and 1000℃ under CO2. With an increase in BC blending ra- tio, there were an increase in gasification rate and a shortening of gasification time. This could be attributed to the high specific surface area of BC and the high uniformity of carbon structures in CC when compared to those in BC. Three representative gas-solid kinetic models, namely, the volumetric model （VM）, grain model （GM）, and random pore model （RPM）, were applied to describe the reaction behavior of the char. Among them, the RPM model was considered the best model to describe the reactivity of the char gasification reaction. The activa- tion energy of BC and CC isothermal gasification as determined using the RPM model was found to be 126.7 kJ/mol and 210.2 kJ/mol, re- spectively. The activation energy was minimum （123.1 kJ/mol） for the BC blending ratio of 75%. Synergistic effect manifested at all mass ratios of the blended char, which increased with the gasification temperature.

Kinetic models of natural gas combustion in an internal combustion engine

In this study, combustion of methane was simulated using four kinetic models of methane in CHEMKIN 4.1.1 for 0-D closed internal combustion （IC） engine reactor. Two detailed （GRIMECH3.0 ＆ UBC MECH2.0） and two reduced （One step ＆ Four steps） models were examined for various IC engine designs. The detailed models （GRIMECH3.0, ＆ UBC MECH2.0） and 4-step models successfully predicted the combustion while global model was unable to predict any combustion reaction. This study illustrated that the detailed model showed good concordances in the prediction of chamber pressure, temperature and major combustion species profiles. The detailed models also exhibited the capabilities to predict the pollutants formation in an IC engine while the reduced schemes showed failure in the prediction of pollutants emissions. Although, there are discrepancies among the profiles of four considered model, the detailed models （GRIMECH3.0 ＆ UBC MECH2.0） produced the acceptable agreement in the species prediction and formation of pollutants.

Application of Different Models for the Prediction of the Kinetics of Direct Reduction of Natural Iron Ores

Simulation of the direct reduction conditions was performed in a laboratory furnace. Lump samples from natural hematite iron ore were reduced by a gas mixture of H2 and CO (H2/CO =1.5) at temperatures of 700°C, 800°C and 900°C. The effect of reduction temperature on the reduction degree, reduction rate of samples and carbon deposition were investigated and discussed in this study. The thermo-gravimetric data obtained from the reduction experiments was run in a programme that calculates the solid conversion rate. Also, three models: 1) Grain Model (GM), 2) Volumetric Model (VM), and 3) the Random Pore Model (RPM), were used to estimate the reduction kinetics of natural iron ores. It was found that the RPM model result agreed best with the obtained experimental results. Furthermore, it gave better predictions of the natural iron oxide conversion and thereby the reduction kinetics.

Mass Transfer, Gas Holdup, and Kinetic Models of Batch and Continuous Fermentation in a Novel Rectangular Dynamic Membrane Airlift Bioreactor

Compared with conventional cylinder airlift bioreactors(CCABs)that produce coarse bubbles,a novel rectangular dynamic membrane airlift bioreactor(RDMAB)developed in our lab produces fine bubbles to enhance the volumetric oxygen mass transfer coefficient(k_(L)a)and gas holdup,as well as improve the bioprocess in a bioreactor.In this study,we compared mass transfer,gas holdup,and batch and con-tinuous fermentation for RNA production in CCAB and RDMAB.In addition,unstructured kinetic models for microbial growth,substrate utilization,and RNA formation were established.In batch fermentation,biomass,RNA yield,and substrate utilization in the RDMAB were higher than those in the CCAB,which indicates that dynamic membrane aeration produced a high k_(L)a by fine bubbles;a higher k_(L)a is more bene-ficial to aerobic fermentation.The starting time of continuous fermentation in the RDMAB was 20 h ear-lier than that in the CCAB,which greatly improved the biological process.During continuous fermentation,maintaining the same dissolved oxygen level and a constant dilution rate,the biomass accumulation and RNA concentration in the RDMAB were 9.71% and 11.15% higher than those in the CCAB,respectively.Finally,the dilution rate of RDMAB was 16.7% higher than that of CCAB during con-tinuous fermentation while maintaining the same air aeration.In summary,RDMAB is more suitable for continuous fermentation processes.Developing new aeration and structural geometry in airlift bioreac-tors to enhance k_(L)a and gas holdup is becoming increasingly important to improve bioprocesses in a bioreactor.

MACROSCOPIC KINETIC MODELS OF GLYCEROL BATCH FERMENTATION WITH OSMOTOLERANT YEAST

Kinetics of glycerol production by fermentation with osmotolerant yeast Candida krusei was studied. Suppositions of cell negative effect on and glucose inhibition in specific growth rate and glycerol assumption for energy maintenance were made. Based on the suppositions, a set of unstructured kinetic models including cell groWth, glucose consumption and glycerol accumulation rate was proposed. To avoid the significant decrease of produced glyccerol in the latter fermentation stage, the fermentation was suggested to be ended when the concentration ratio of glycerol to glucose is close to 7.

Modern information technologies in construction of kinetic models for reactions of metal complex catalysis

For detailed study of complex chemical reactions mechanisms experiment is conducted for selected private reactions. This causes a problem of kinetic parameters getting--the same set of rate constants must describe both public and private reaction stages, and also a general mechanism. In this paper, solution of this problem for a reaction of olefins hydroalumination is proposed. To optimize the computational process a methodology of parallelization is elaborated. On the base of parallel computations, a kinetic model for the reaction assigned is constructed, and on its base, the physical and chemical conclusions about reaction mechanism are done.

Kinetic Models for Drying Techniques—Food Materials

Drying operations can help in reducing the moisture content of food materials for avoidance of microbial growth and deterioration, for shelf life elongation, to minimize packaging and improving storage for easy transportation. Thin-layer drying of materials is necessary to understand the fundamental transport mechanism and a prerequisite to successfully simulate or scale up the whole process for optimization or control of the operating conditions. Researchers have shown that to rely solely on experimental drying practices without mathematical considerations for the drying kinetics, can significantly affect the efficiency of dryers, increase the cost of production, and reduce the quality of the dried product. An effective model is necessary for the process design, optimization, energy integration and control;hence, the use of mathematical models in finding the drying kinetics of agricultural products is very important. The statistical criteria in use for the evaluation of the best model(s) has it that coefficient of determination (R2) has to be close to unity while the rest statistical measures will have values tending to zero. In this work, the essence of drying using thin-layer, general approaches to modeling for food drying mechanisms thin layer drying models and optimization of the drying processes have been discussed.

In vitro evaluation of transdermal permeation effects of Fu’s cupping therapy via six diffusion kinetics models

本研究建立吲哚美辛亲水凝胶贴剂的体外经皮渗透的6种动力学模型:零级、一级、Higuchi级、Ritger-Peppas级、Weibull级与Hixcon-Crowell级动力方程Q1/3=kt+b,评价付罐疗法(FCT)体外经皮促渗作用与特点。3%氮酮和5%氮酮化学促渗剂与离子导入为参比,用HPLC-工作曲线对吲哚美辛(IM)定量,进行体外透皮扩散,结果进行回归建模。结果表明:FCT促渗处理组能明显提高吲哚美辛的透皮效果,改善体外透皮的Higuchi级与Weibull级动力学参数,提高透皮速率与渗透系数,减低时滞。FCT作为新的物理经皮给药促渗新技术,效果明显,具有中医特色和重要的临床应用价值。

Bioregeneration of spent activated carbon:Review of key factors and recent mathematical models of kinetics

The disposal of spent activated carbon(AC) will inevitably create secondary pollution. In overcoming this problem, the spent AC can be regenerated by means of biological approach. Bioregeneration is the phenomenon in which through the action of microorganisms, the adsorbed pollutants on the surface of the AC will be biodegraded and this enables further adsorption of pollutants to occur with time elapse. This review provides the challenges and perspectives for effective bioregeneration to occur in biological activated carbon(BAC)column. Owing to very few reported works on the bioregeneration rate in BAC column, emphasis is put forward on the recently developed models of bioregeneration kinetic in batch system. All in all, providing potential solutions in increasing the lifespan of AC and the enhancement of bioregeneration rate will definitely overcome the bottlenecks in spent AC bioregeneration.

Reaction kinetics modeling for lithium and cobalt recovery from spent lithium-ion batteries using acetic acid

Lithium and cobalt recovery from spent lithium-ion batteries(LIBs) is a major focus because of their increased production and usage. The conventional method for recycling spent LIBs using inorganic acids produces harmful byproducts. In this work, the leaching agent was substituted with a less expensive and more environmentally friendly alternative—acetic acid—and a mathematical model was developed to describe the kinetics of the recovery process. The variables used were the pH value, temperature, H_2O_2 concentration, and the solid-to-liquid(S/L) ratio. The mathematical model used was the shrinking core model, which was modified to accommodate an equilibrium reaction. The experimental results show that the rate of recovery of Li and Co over time was only affected by temperature. The leaching behaviors of Li and Co were found to oppose each other. An increase in temperature resulted in increased recovery of Li but decreased recovery of Co because of the product-favoring endothermic reaction of Li and the reactant-favoring exothermic reaction of Co. The product of Li has a lower entropy value than the reactant as a free-moving ion, whereas the product of Co leaching has a higher entropy value as a stiff crystal complex. Thus, temperature conditioning is a pivotal factor in the leaching of spent LIBs.

Application of convolutional neural networks to large-scale naphtha pyrolysis kinetic modeling

System design and optimization problems require large-scale chemical kinetic models. Pure kinetic models of naphtha pyrolysis need to solve a complete set of stiff ODEs and is therefore too computational expensive. On the other hand, artificial neural networks that completely neglect the topology of the reaction networks often have poor generalization. In this paper, a framework is proposed for learning local representations from largescale chemical reaction networks. At first, the features of naphtha pyrolysis reactions are extracted by applying complex network characterization methods. The selected features are then used as inputs in convolutional architectures. Different CNN models are established and compared to optimize the neural network structure.After the pre-training and fine-tuning step, the ultimate CNN model reduces the computational cost of the previous kinetic model by over 300 times and predicts the yields of main products with the average error of less than 3%. The obtained results demonstrate the high efficiency of the proposed framework.

Repeated-Batch and Continuous Production of L-Lactic Acid by Rhizopus oryzae Immobilized in Calcium Alginat Beads:ReactorPerformance and Kinetic Model

Repeated-batch and continuous production of L-lactic acid by immobilized Rhizopusoryzae with calcium alginate entrapment method in a three-phase fluidized-bed bioreactor was stud-ied.The operation conditions were optimized.The productivity based on total reactor volume wasabout 3 times higher than that with free cells in a traditional stirred tank bioreactor.A mathemat-ical model was proposed and the model predictions were in good agreement with the experimentaldat.

Progress in Modeling of Phase Transformation Kinetics

Several methods representing the evolution of microstructure were introduced, which include the Johnson-Mehl-Avrami-Kolmogorov （JMAK） equation, Internal State Variable （ISV） framework, Koistinen-Marburger （K-M） equation, modified Magee＇s rule and phase field model, etc. By combining calculation of martensite transformation kinetics, considering the selection of parameters with the effect of austenite grain size （AGS）, some suitable ways of obtaining better results have been proposed.