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.

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.

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.

Effect of solvent on the initiation mechanism of living anionic polymerization of styrene:A computational study

For living anionic polymerization(LAP),solvent has a great influence on both reaction mechanism and kinetics.In this work,by using the classical butyl lithium-styrene polymerization as a model system,the effect of solvent on the mechanism and kinetics of LAP was revealed through a strategy combining density functional theory(DFT)calculations and kinetic modeling.In terms of mechanism,it is found that the stronger the solvent polarity,the more electrons transfer from initiator to solvent through detailed energy decomposition analysis of electrostatic interactions between initiator and solvent molecules.Furthermore,we also found that the stronger the solvent polarity,the higher the monomer initiation energy barrier and the smaller the initiation rate coefficient.Counterintuitively,initiation is more favorable at lower temperatures based on the calculated results ofΔG_(TS).Finally,the kinetic characteristics in different solvents were further examined by kinetic modeling.It is found that in benzene and n-pentane,the polymerization rate exhibits first-order kinetics.While,slow initiation and fast propagation were observed in tetrahydrofuran(THF)due to the slow free ion formation rate,leading to a deviation from first-order kinetics.

Role of iron ore in enhancing gasification of iron coke:Structural evolution,influence mechanism and kinetic analysis

The utilization of iron coke provides a green pathway for low-carbon ironmaking.To uncover the influence mechanism of iron ore on the behavior and kinetics of iron coke gasification,the effect of iron ore on the microstructure of iron coke was investigated.Furthermore,a comparative study of the gasification reactions between iron coke and coke was conducted through non-isothermal thermogravimetric method.The findings indicate that compared to coke,iron coke exhibits an augmentation in micropores and specific surface area,and the micropores further extend and interconnect.This provides more adsorption sites for CO_(2) molecules during the gasification process,resulting in a reduction in the initial gasification temperature of iron coke.Accelerating the heating rate in non-isothermal gasification can enhance the reactivity of iron coke.The metallic iron reduced from iron ore is embedded in the carbon matrix,reducing the orderliness of the carbon structure,which is primarily responsible for the heightened reactivity of the carbon atoms.The kinetic study indicates that the random pore model can effectively represent the gasification process of iron coke due to its rich pore structure.Moreover,as the proportion of iron ore increases,the activation energy for the carbon gasification gradually decreases,from 246.2 kJ/mol for coke to 192.5 kJ/mol for iron coke 15wt%.

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.

Modeling, Simulation and Optimization of a Whole Industrial Catalytic Naphtha Reforming Process on Aspen Plus Platform

A new 18-lump kinetic model for naphtha catalytic reforming reactions is discussed. By developing this model as a user module, a whole industrial continuous catalytic reforming process is simulated on Aspen plus plat-form. The technique utilizes the strong databases, complete sets of modules, and flexible simulation tools of the Aspen plus system and retains the characteristics of the proposed kinetic model. The calculated results are in fair agreement with the actual operating data. Based on the model of the whole reforming process, the process is opti-mized and the optimization results are tested in the actual industrial unit for about two months. The test shows that the process profit increases about 1000yuan·h-1 averagely, which is close to the calculated result.

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.

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.

Experimental and Modeling Study of the Effects of Gas Additives on the Thermal DeNO_x Process

An experimental study of thermal DeNOx process with different additives was performed in an electricityheated tubular flow reactor,showing that CO is less effective to lower the optimum temperature than H2 and CH4. The maximum NO reduction is lowered with H2 added,while it is hardly affected by CO or CH4.The temperature window is widened appreciably with CH4 added,while it is narrowed slightly by H2 or CO.The disadvantage of CH4 is that it causes CO emission due to its incomplete oxidation,and the maximum conversion of CH4 to CO is more than 50%.In general,the calculation using a detailed chemical kinetic model predicts most of the process features reasonably well.The analysis on reaction mechanism shows that the effects of these additives on NO reduction are achieved principally by promoting the production of·OH radical.

Kinetics and Modeling of Chemical Leaching of Sphalerite Concentrate Using Ferric Iron in a Redox-controlled Reactor

This work presents a study for chemical leaching of sphalerite concentrate under various constant Fe3+ concentrations and redox potential conditions. The effects of Fe3+ concentration and redox potential on chemical leaching of sphalerite were investigated. The shrinking core model was applied to analyze the experimental results. It was found that both the Fe3+ concentration and the redox potential controlled the chemical leaching rate of sphalerite. A new kinetic model was developed, in which the chemical leaching rate of sphalerite was proportional to Fe3+ concentration and Fe3+ /Fe2+ ratio. All the model parameters were evaluated from the experimental data. The model predictions fit well with the experimental observed values.

An Adsorption Kinetic Model for Sulfur Dioxide Adsorption by ZL50 Activated Carbon

A semi-empirical adsorption kinetic model was proposed with the time compensation method to describe the chemisorption of SO2 in flue gas by carbon adsorbents for flue gas purification.The change in adsorption capacity and adsorption rate with time at different water vapor concentrations and different SO2 concentrations was studied.The model was in good agreement with experimental data.The surface reaction was probably the rate controlling step in the early stage for SO2 adsorption by ZL50 activated carbon.The parameters m and n in the nth order adsorption kinetic model were related to the magnitude of the time compensation and adsorption driving force,respectively.The change of parameter n with water vapor concentrations and sulfur dioxide concentrations was studied and some physical implications were given.The sum of square errors was less than 1.0 and the average absolute percentage deviations ranged from 0.5 to 3.2.The kinetic model was compared with other models in the literature.

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.

Enhancing recovery of uranium column bioleaching by process optimization and kinetic modeling

This research aimed to enhance the column bioleaching recovery of uranium ore by Acidithiobacillus ferrooxidans.Seven factors were examined for their significance on bioleaching using a Plackett-Burman factorial design.Four significant variables([Fe2+]initial,pH,aeration rate and inoculation percent)were selected for the optimization studies.The effect of these variables on uranium bioleaching was studied using a central composite design(CCD).The optimal values of the variables for the maximum uranium bioleaching recovery(90.27±0.98)%were as follows:[Fe2+]initial=2.89g/L,aeration rate420mL/min,pH1.45and inoculation6%(v/v).[Fe2+]initial was found to be the most effective parameter.The maximum uranium recovery from the predicted models was92.01%.This value was in agreement with the actual experimental value.The analysis of bioleaching residue of uranium ore under optimum conditions confirmed the formation of K-jarosite on the surface of minerals.By using optimal conditions,uranium bioleaching recovery is increased at column and jarosite precipitation is minimized.The kinetic model showed that uranium recovery has a direct relation with ferric ion concentration.

Application of Discrete Lumped Kinetic Modeling on Vacuum Gas Oil Hydrocracking

The kinetic model of vacuum gas oil （VGO） hydrocracking based on discrete lumped approach was investigated, and some improvement was put forward at the same time in this article. A parallel reaction scheme to describe the conver- sion of VGO into products （gases, gasoline, and diesel） proposed by Orochko was used. The different experimental data were analyzed statistically and then the product distribution and kinetic parameters were simulated by available data. Fur- thermore, the kinetic parameters were correlated based on the feed property, reaction temperature, and catalyst activity. An optimization code in Matlab 2011b was written to fine-me these parameters. The model had a favorable ability to predict the product distribution and there was a good agreement between the model predictions and experiment data. Hence, the ki- netic parameters indeed had something to do with feed properties, reaction temperature and catalyst activity.

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 and Simulation Analysis for Toluene Disproportionation and C9-Aromatics Transalkylation

A new kinetic model for commercial unit of toluene disproportionation and C9-armatiocs transalkylation is developed based on the reported reaction scheme.A time based catalyst deactivation function taking weight hourly space velocity(WHSV)into account is incorporated into the model,which reasonably accounts for the loss in activity because of coke deposition on the surface of catalyst during long-term operation.The kinetic parameters are benchmarked with several sets of balanced plant data and estimated by the differential variable metric optimiza- tion method.Sets of plant data at different operating conditions are applied to make sure validation of the model and the results show a good agreement between the model predictions and plant observations.The simulation analysis of key variables such as temperature and WHSV affecting process performance is discussed in detail,giv- ing the guidance to select suitable operating conditions.