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.

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).

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.

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.

Mechanism and Kinetic Model of In-situ TiB_2/7055Al Nanocomposites Synthesized under High Intensity Ultrasonic Field

In-situ TiB2/7055Al nanocomposites are fabricated by in situ melt chemical reaction from 7055Al-K2TiF6-KBF4 system under high intensity ultrasonic field,and the mechanism and kinetic model of in-situ melt chemical reaction are investigated.X-ray diffraction （XRD） and scanning electron microscope （SEM） analyses indicate that the sizes of in-situ TiB2 nanoparticles are in the range of 80-120 nm.The results of ice-water quenched samples show that the whole process contains four stages,and the overall in-situ reaction time is 10 minutes.The in situ synthesis process is controlled mainly by chemical reaction in earlier stage （former 3 minutes）,and by the particulate diffusing in later stage.The mechanism of key reaction between Al3Ti and AlB2 under high intensity ultrasonic in the 7055Al-K2TiF6-KBF4 system is the reaction-diffusion-crack-rediffusion.Furthermore,the reactive kinetic models in 7055Al-K2TiF6-KBF4 system are established.

Kinetic Model of Fixed Bed Reactor with Immobilized Microorganisms for Removing Low-Concentration SO_2

On the basis of the analysis of the process of treating low concentrations of sulfur dioxide （SO2） gas in a fixed bed reactor, a kinetic model is proposed for this process after taking into consideration the effects of internal diffusion, cell concentration, and production yield of microorganisms but ignoring the effect of external diffusion. The results obtained from the model simulation show that this model can indicate the influence of the process factors, Cin, η μmax, Cx, A, h, Kin, and Q, on the removal of SO2 and that the prediction of the results by this model is also satisfactory. This kinetic model can also provide some very important indications regarding the preparation of immobilized microorganisms, selection and domestication of proper species of microorganisms, as well as the design of bioreactors.

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.

Kinetic Parameters Estimation of MgO-C Refractory by Shrinking Core Model

Kinetics of oxidation of MgO-C refractories was investigated by shrinking core modeling of the gas-solid reactions taking place during heating the porous materials to the high temperatures. Samples containing 4.5-17 wt pct graphite were isothermally oxidized at 1000-1350℃. Weight loss data was compared with predictions of the model. A mixed 2-stage mechanism comprised of pore diffusion plus boundary layer gas transfer was shown to generally control the oxidation rate. Pore diffusion was however more effective, especially at graphite contents lower than 10 wt pct under forced convection blowing of the air. Model calculations showed that effective gas diffusion coefficients were in the range of 0.08 to 0.55 cm^2/s. These values can be utilized to determine the corresponding tortuosity factors of 6.85 to 2.22. Activation energies related to the pore diffusion mechanism appeared to be around （46.44±2） kJ/mol. The estimated intermolecular diffusion coefficients were shown to be independent of the graphite content, when the percentage of the graphite exceeded a marginal value of 10.

A new kinetic model for the common juniper essenstial oil extraction by microwave hydrodistillation

The main objective of the present study was to model the kinetics of essential oil extraction from swelled ground juniper berries by classic hydrodistillation(HD) and microwave-assisted hydrodistillation(MAHD). A new phenomenological kinetic model was developed on the basis of the juniper essential oil extraction mechanism that assumed three mass transfer processes occurring simultaneously: washing, unhindered diffusion and hindered diffusion. The new model was compared to the existing kinetic models. Among the tested models,the new model had the smallest mean relative percentage deviation and the highest corrected Akaike information criterion value. In addition, that, the new model was verified for HD and MAHD of essential oils from some other plant materials. On the basis of the above-mentioned facts, the new model can be recommended for modeling the kinetics of essential oil extraction by both HD and MAHD.

Effects of heavy metal ions Cu^(2+)/Pb^(2+)/Zn^(2+)on kinetic rate constants of struvite crystallization

Struvite(MAP)crystallization technology is widely used to treat ammonia nitrogen in waste effluents of its simple operation and good removal efficiency.However,the presence of heavy metal ions in the waste effluents causes problems such as slow crystallization rate and small crystal size,limiting the recovery rate and economic value of the MAP.The present study was conducted to investigate the effects of concentrations of three heavy metal ions(Cu^(2+),Zn^(2+),and Pb^(2+))on the crystal morphology,crystal size,average growth rate,and crystallization kinetics of MAP.A relationship was established between the kinetic rate constant Ktcalculated by the chemical gradient model and the concentrations of heavy metal ions.The results showed that low concentrations of heavy metal ions in the solution created pits on the MAP surface,and high level of heavy metal ions generated flocs on the MAP surface,which were composed of metal hydroxides,thus inhibiting crystal growth.The crystal size,average growth rate,MAP crystallization rate,and kinetic rate constant Ktdecreased with the increase in heavy metal ion concentration.Moreover,the Ktdemonstrated a linear relationship with the heavy metal concentration ln(C/C~*),which provided a reference for the optimization of the MAP crystallization process in the presence of heavy metal ions.

Kinetics and model of gas generation of source rocks in the deepwater area, Qiongdongnan Basin

In order to investigate the hydrocarbon generation process and gas potentials of source rocks in deepwater area of the Qiongdongnan Basin, kinetic parameters of gas generation （activation energy distribution and frequency factor） of the Yacheng Formation source rocks （coal and neritic mudstones） was determined by thermal simulation experiments in the closed system and the specific KINETICS Software. The results show that the activation energy （Ea） distribution of C1–C5 generation ranges from 50 to 74 kcal/mol with a frequency factor of 2.4×1015 s–1 for the neritic mudstone and the Ea distribution of C1–C5 generation ranges from 49 to 73 kcal/mol with a frequency factor of 8.92×1013 s–1 for the coal. On the basis of these kinetic parameters and combined with the data of sedimentary burial and paleothermal histories, the gas generation model of the Yacheng Formation source rocks closer to geological condition was worked out, indicating its main gas generation stage at Ro （vitrinite reflectance） of 1.25%–2.8%. Meanwhile, the gas generation process of the source rocks of different structural locations （central part, southern slope and south low uplift） in the Lingshui Sag was simulated. Among them, the gas generation of the Yacheng Formation source rocks in the central part and the southern slope of the sag entered the main gas window at 10 and 5 Ma respectively and the peak gas generation in the southern slope occurred at 3 Ma. The very late peak gas generation and the relatively large gas potential indices （GPI：20×10^8–60×10^8 m^3/km^2） would provide favorable conditions for the accumulation of large natural gas reserves in the deepwater area.