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 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.

Modeling analysis of cobalt-based Fischer-Tropsch catalyst particles

The influences of particle size,shape,and catalyst distribution on the reactivity and hydrocarbon product selectivity of a cobalt-based catalyst for Fischer-Tropsch synthesis were investigated in the present work.A self-consistent kinetic model for Fischer-Tropsch reaction proposed here was found to correlate experimental data well and hence was used to describe the consumption rates of reactants and formation rates of hydrocarbon products.The perturbed-chain statistical associating fluid theory equation of state was used to describe vapor-liquid equilibrium behavior associated with Fischer-Tropsch reaction.Local interaction between intraparticle diffusion and Fischer-Tropsch reaction was investigated in detail.Results showed that in order to avoid the adverse influence of intraparticle diffusional limitations on catalyst reactivity and product selectivity,the use of small particles is necessary.Large eggshell spherical particles are shown to keep the original catalyst reactivity and enhance the selectivity of heavy hydrocarbon products.The suitable layer thickness for a spherical particle with a diameter of 2 mm is nearly 0.15 mm.With the same outer diameter of 2 mm,the catalyst reactivity and heavy product selectivity of hollow cylindrical particles with a layer thickness of 0.25 mm are found to be larger than eggshell spherical particles.From the viewpoint of catalytic performance,hollow cylindrical particles are a better choice for industrial applications.

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.

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 Modeling the Formation of Low-mature Gases and Analysis of the Possibility to Be Accumulated

At present, shallow gases have received much attention due to low cost in exploration and production. Low-mature gases, as one significant origin to shallow gas, turns to be an important research topic. The present understanding of low-mature gases is confined within some geological cases, and few laboratory studies have been reported. Therefore, the potential and characters of low- mature gases are not clear up to now. Here, two premature samples （one coal and the other shale） were pyrolyzed in a gold confined system. The gaseous components including hydrocarbon gases and non-hydrocarbon gases were analyzed. Based on kinetic modeling, the formation of low-mature gases was modeled. The results showed that during low mature stage, about 178 mL/gTOC gas was generated from the shale and 100 mL/gTOC from the coal. Two third to three fourth of the generated gases are non-hydrocarbon gases such as H2S and CO2. The total yields of C1-5 for the two samples are almost the same, 30-40 mL/gTOC, but individual gaseous hydrocarbon is different. The shale has much lower C1 but higher C2-5, whereas the coal has higher C1 but lower C2-5. Hydrocarbon gases formed during low-mature stage are very wet. The stable carbon isotope ratios of methane range from -40‰ to -50‰ （PDB）, in good consistence with empiric criterion for low-mature gases summed up by the previous researchers. The generation characters suggest that the low-mature gases could be accumulated to form an economic gas reservoir, but most of them occur only as associated gases.

Kinetic Model of LCO Selective Hydrogenation on NiMoW/Al_(2)O_(3) Catalyst

In order to investigate the hydrofining process of LCO for producing aromatics and gasoline,the selective hydrogenation of polycyclic aromatic hydrocarbons(PAHs),a major component of light cycle oil(LCO),was studied using a NiMoW/Al_(2)O_(3)catalyst.Based on the study of the reversible hydrogenation reaction,PAHs in the selective hydrogenation process could be effectively simulated by the modeled CH and CH_(2) groups,and the hydrodesulfurization and hydrodenitrogenation kinetic models could be further established in this process.The results showed that the kinetic models developed could fit the experimental data effectively and predict the content of S,N,and aromatics in the selective hydrogenation products of LCO.

Kinetic modeling of gamma-aminobutyric acid production by Lactobacillus brevis based on pH-dependent model and rolling correction

Gamma-aminobutyric acid(GABA)is a natural non-protein functio nal amino acid,which has potential for fermentation industrial production by Lactobacillus brevis.This work investigated the batch fermentation process and developed a kinetic model based on substrate restrictive model established by experimental data from L25(5~6)orthogonal experiments.In this study,the OD600 value of fermentation broth was fixed to constant after reaching its maximum because the microorganism death showed no effect on the enzyme activity of glutamate decarboxylase(GAD).As pH is one of the key parameters in fermentation process,a pH-dependent kinetic model based on radial basis function was developed to enhance the practicality of the model.Furthermore,as to decrease the deviations between the simulated curves and the experimental data,the rolling correction strategy with OD600 values that was measured in real-time was introduced into this work to modify the model.Finally,the accu racy of the rolling corrected and pH-dependent model was validated by good fitness between the simulated curves and data of the initial batch fermentation(pH 5.2).As a result,this pH-dependent kinetic model revealed that the optimal pH for biomass growth is 5.6-5.7 and for GABA production is about 5,respectively.Therefore,the developed model is practical and convenient for the instruction of GABA fermentation production,and it has instructive significance for the industrial scale.

Modeling and Estimation of the Kinetics of Seeded Solvent-mediated Phase Transformation in a Batch Crystallizer

Modeling the kinetics of the preparing process is necessary to produce a product with the appropriate particle properties and minimum production cost.Owing to the lackness of crystal size distributor （CSD） information,however,solvent-mediated phase transformation encounters difficulty in modeling the kinetics as compared to solution crystallization.Consequently,a model was established by making the product CSD to move along by horizontal translation to obtain the CSDs of the stable phase in the process of transformation.Then the moment method was used to solve the popular balance equation,and the least square nonlinear regression method was applied to estimate the kinetics parameters.The model has been successfully used to simulate the transformation of CaSO4？2H2O to α-CaSO4？1/2H2O in an isothermal seeded batch crystallizer with different stirring speeds,and it is beneficial to producing high performance α-CaSO4？1/2H2O crystals which have the right particle characteristics.

KINETIC MODEL FOR DIFFUSION-CONTROLLED INTERMOLECULAR REACTION OF HOMOGENOUS POLYMER UNDER STEADY SHEAR

The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N^-1.5 （N is the length of chains）, which is in consistent with de Gennes＇s result.

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.

Vacuum residue coking process simulation using molecular-level kinetic model coupled with vapor-liquid phase separation

In this work,a molecular-level kinetic model was built to simulate the vacuum residue(VR)coking process in a semi-batch laboratory-scale reaction kettle.A series of reaction rules for heavy oil coking were summarized and formulated based on the free radical reaction mechanism.Then,a large-scale molecularlevel reaction network was automatically generated by applying the reaction rules on the vacuum residue molecules.In order to accurately describe the physical change of each molecule in the reactor,we coupled the molecular-level kinetic model with a vapor–liquid phase separation model.The vapor–liquid phase separation model adopted the Peng-Robinson equation of state to calculate vapor–liquid equilibrium.A separation efficiency coefficient was introduced to represent the mass transfer during the phase separation.We used six sets of experimental data under various reaction conditions to regress the model parameters.The tuned model showed that there was an excellent agreement between the calculated values and experimental data.Moreover,we investigated the effect of reaction temperature and reaction time on the product yields.After a comprehensive evaluation of the reaction temperature and reaction time,the optimal reaction condition for the vacuum residue coking was also obtained.

Kinetic Ising model in a time-dependent oscillating external magnetic field:effective-field theory

Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory （EFT） and a mean-field theory （MFT）. The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency （w） and static external field amplitude （h0） for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.

Kinetics modeling for the mixed reforming of methane over Ni-CeO_2/MgAl_2O_4 catalyst

Kinetics model was developed for the mixed （steam and dry） reforming of methane, which is useful for the control of H2/CO ratio. The equilibrium constants of reaction rate were determined using the experimental equilibrium data at different reaction temperatures, while the forward reaction rate constants were estimated using the experimental data under non-equilibrium （high inert fraction and high space velocity） conditions. The comparison between calculated and experimental data clearly showed that the developed model described satisfactorily, and further analysis using the parametric sensitivity determined the wall temperature and CO2 fraction in the feed gas as effective parameters for the manipulation of CH4 conversion and H2/CO ratio of synthesis gas under the equilibrium condition. Meanwhile, the inert fraction, rather than the residence time, was selected as additional parameter under non-equilibrium condition.

Numerical simulation of metal evaporation based on the kinetic model equation and the direct simulation Monte Carlo method

Metal evaporation on the basis of the kinetic model equations(BGK and S-model) and the direct simulation Monte Carlo(DSMC) method was investigated computationally under the circumstances of collimators existing or not. Numerical data of distributions of number density, bulk velocity and temperature were reported over a wide range of evaporation rate.It was shown that these results reached a good agreement for the case of small evaporation rate, while the deviations became increasingly obvious with the increase of evaporation rate, especially when the collimators existed. Moreover, the deposition thickness over substrate obtained from the kinetic model equations were inaccurate even though the evaporation rate was small. All of the comparisons showed the reliability of the kinetic model equations, which require less computational cost at small evaporation rate and simple structure.

Kinetic Model of Hypophosphite Oxidation on a Nickel Electrode in D_2O Solution

Kinetic model of hypophosphite oxidation on a nickel electrode was studied in D2O solution in order to reach a better understanding of the oxidation mechanism. In the model;he electrooxidation of hypophosphite undergo a H abstraction of hypophosphite from the P-H bond to form the phosphorus-centered radical (PWO2-)-P-., which subsequently is electrochemically reacted with water to form the final product, phosphite. The kinetic equations were derived, and the kinetic parameters were obtained from a comparison of experimental results and the kinetic equations. The process of hypophosphite electrooxidation could be well simulated by this model.