Experiments and kinetic modeling of the sorbitol dehydration to isosorbide catalyzed by sulfuric acid under conditions of non-constant volume

Isosorbide is a novel bio-based material derived as a secondary dehydration product of sorbitol.This work focuses on the kinetics of sulfuric acid-catalyzed dehydration of sorbitol under conditions of nonconstant volume.Herein,the effects of stirring rate,catalyst dosage,reaction temperature,and reaction time on the dehydration reaction of sorbitol were investigated.The yield of isosorbide up to 77.13%was obtained after 1.5 h of reaction time under conditions of 2 kPa,1.0%(mass)catalyst dosage,and 413.15 K.Based on the sorbitol dehydration reaction mechanism and a simplified reaction network,a kinetic model was developed in this work.A good agreement was accomplished between kinetic modeling and experiments between 393.15 and 423.15 K.The fitting results indicate that side reactions with higher activation energies are more affected by reaction temperatures,and the main side reaction that influences the selectivity of isosorbide is the oligomerization reaction among the primary dehydration products of sorbitol.The model fitting of the catalyst amounts effect shows that the effective concentration of sulfuric acid would be reduced with the increase of dosage due to the molecular agglomeration effect.Hopefully,the kinetic experiments and modeling results obtained in this work will be helpful to the design and optimization of the industrial sorbitol dehydration process.

Evaluation and application of kinetic models for Cu-catalyzed acetylene hydrochlorination

The development of environmentally friendly catalysts has become a top priority for acetylene hydrochlorination.However,difficulties remain in systematic studies on the applicability of kinetic models for the industrialization of Cu-based catalysts.Therefore,a strategy involving reactor modeling,parameter estimation,and model testing is developed to evaluate the predictive ability of kinetic models.In order to search for reliable and widely applicable reaction kinetic models for Cu-based catalysts,a case study is conducted.Multiple possible kinetic models derived from the power law,adsorption mechanism,and reaction path are sifted through collecting and testing activity data from tens of Cu-based catalysts.Different optimum applicable ranges of these kinetic models are presented.According to the comparative analysis on their applications in various industrial scenarios,this research suggests that kinetic models derived from reaction path exhibits the best extrapolation ability and has the greatest potential for application in the scale-up design of reactors.

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.

Modeling the Drying Kinetics of Pigeon Pea [Cajanus cajan (L.) Millspaugh]

We set out to model the oven-drying kinetics of a legume known as pigeon pea, harvested in the Bouenza department in the south-west of the Republic of Congo. The drying kinetics of pigeon peas was carried out in an oven under experimental conditions using temperatures of: 50°C, 60°C and 70°C. Seven mathematical models were used to describe pigeon pea drying. During drying, water loss was faster and shorter at 70°C [10.446 g/25 g wet weight (wwb) for 320 min (5.3 h)] compared to 50°C [10.996 g/25 g wet weight (wwb) for 520 min (8.6 h)] and 60°C [10.616 g/25 g wet weight (wwb) for 420 min (7.0 h)] where it was slower and longer. With regard to modeling, and based on the principle of choosing the right model focusing on the high value of R2 and low values of χ2 and RMSE, two models were selected, the Midili model for temperatures of 50°C and 60°C and the Henderson and Pabis model modified for temperature of 70°C showed better results. The R2, χ2 and RMSE values calculated for pigeon pea are 0.99985, 3.93404E-5 and 0.00627;0.9997, 9.245E-5 and 0.00962;0.99996, 1.56332E-5 and 0.00395 respectively at 50°C, 60°C and 70°C.

Multi-lump Kinetic Parameter Estimation and Simulation of Trickle-bed Reactor for Ultra-deep Hydrodesulfurization of Diesel

A three-lumping Langmuir-Hinshelwood kinetic model was established based on the structures and reactivities of sulfur compounds.This model described the ultra-deep hydrodesulfurization(UDHDS)performance of diesel,reducing sulfur content from 10000μg/g to less than 10μg/g,with experimental and predicted data showing a discrepancy of less than 10%.The diesel UDHDS reaction was simulated by combining the mass transfer,reaction kinetics model,and physical properties of diesel.The results showed how the concentrations of H2S,hydrogen,and sulfur in the gas,liquid,and solid phases varied along the reactor length.Moreover,the study discussed the effects of each process parameter and impurity concentrations(H2S,basic nitrogen and,non-basic nitrogen)on diesel UDHDS.

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.

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.

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).

White-rot Fungus Growth Conditions and Its Metabolic Kinetic Models

To investigate the growth conditions of white-rot fungus and simulate its metabolism kinetic models, the rules how the factors such as biomass, culture fluid, pH value, glucose consumption and exopolysaccharides generation, etc., changed during the batch culture process of white-rot fungi by using an air-lift fermenter, as well as metabolic kinetics of white-rot fungi were studied. Based on Logistic equation, Luedeking-Piret equation and experimental data, the correlation model parameters of mycelia biomass, glucose consumption and exopolysaccharide generation were obtained and found to be change with time in metabolism process. Detailedly, μm=0.071 8 h-1,α= 0.831 8 g/(g·h), β= 0.002 g/(g·h), b1=0.016 3 g/(g·h) and b2=3.023 3 g/(g·h). Hence the mycelial growth kinetic model, exopolysaccharide generation kinetic model and substrate consumption kinetic model which describe fermentation process of white-rot fungi were established. Meanwhile, the experimental data were verified by this model, and a good fitting result with an average relative error less than 10% between the data obtained from experiments and the model was yielded. The results show that these models can predict the growth and metabolic rules of white-rot fungus, the fermentation process of exopolysaccharides and the kinetic mechanism of white-rot fungus accurately.

Photoionization Mass Spectrometric and Kinetic Modeling of Low-pressure Pyrolysis of Benzene

Pyrolysis of benzene at 30 Torr was studied from 1360 K to 1820 K in this work. Synchrotron vacuum ultraviolet photoionization mass spectrometry was employed to detect the pyroly- sis products such as radicals, isomers and polycyclic aromatic hydrocarbons, and measure their mole fraction profiles versus temperature. A low-pressure pyrolysis model of benzene was developed and validated by the experimental results. Rate of production analysis was performed to reveal the major reaction networks in both fuel decomposition and aromatic growth processes. It is concluded that benzene is mainly decomposed via H-abstraction reaction to produce phenyl and partly decomposed via unimolecular decomposition reac- tions to produce propargyl or phenyl. The decomposition process stops at the formation of acetylene and polyyne species like diacetylene and 1,3,5-hexatriyne due to their high thermal stabilities. Besides, the aromatic growth process in the low-pressure pyrolysis of benzene is concluded to initiate from benzene and phenyl, and is controlled by the even carbon growth mechanism due to the inhibited formation of C5 and C7 species which play important roles in the odd carbon growth mechanism.

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.

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.

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.

Adsorption and Ozonation Kinetic Model for Phenolic Wastewater Treatment

A three phase fluidized bed reactor was used to investigate the combined effect of adsorption and oxidation for phenolic wastewater treatment.Aqueous solutions containing 10 mg·L 1of phenol and ozone were continuously fed co-currently as upward flow into the reactor at constant flow rate of 2 and 1 L·min 1,respectively.The phenolic treatment results in seven cases were compared：（a）O3 only,（b）fresh granular activated carbon（GAC）,（c） 1st reused GAC,（d）2nd reused GAC,（e）fresh GAC enhanced with O3,（f）1st reused GAC enhanced with O3,and （g）2nd reused GAC enhanced with O3.The phenolic wastewater was re-circulated through the reactor and its concentration was measured with respect to time.The experimental results revealed that the phenolic degradation using GAC enhanced with O3 provided the best result.The effect of adsorption by activated carbon was stronger than the effect of oxidation by ozone.Fresh GAC could adsorb phenol better than reused GAC.All cases of adsorption on GAC followed the Langmuir isotherm and displayed pseudo second order adsorption kinetics.Finally,a differential equation for the fluidized bed reactor model was used to describe the phenol concentration with respect to time for GAC enhanced with O3.The calculated results agree reasonably well with the experimental results.

APPLICATION OF THE SHRINKING CORE MODEL TO THE KINETICS OF ZINC OXIDE DESULFURIZATION

The kinetics of H2S removal by zinc oxide desulfurizer was studied through thermogravimetricanalysis.The experimental results show that desulfurization rate was controlled,at high temperatureand low conversion,by the chemical reaction rate,and at low temperature and high conversion by thegrain diffusion rate.The reaction is first order with respect to H2S concentration in the differentcontrolled stages.The kinetic behavior can be modeled through the employment of the shrinking coremodel.The values of the model parameters were determined.The variation tendencies with temperatureand concentration of H2S at the controlled stages were discussed.

Nucleation of Kinetic Ising Model Under Oscillating Field

We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that the nucleation time shows a clear-cut minimum with the variation of oscillation frequency, wherein the average size of the critical nuclei is the smallest, indicating that an oscillating external field with an optimal frequency can be much more favorable to the nucleation process than a constant field. We have also investigated the effect of the initial phase of the external field, which helps to illustrate the occurrence of such an interesting finding.