Kinetic Modelling of Liquid-Phase Adsorption of Sulfate onto Raw Date Palm Seeds

Adsorption kinetics in multi-component systems has been a subject of intensive research because it is of both theoretical and practical importance. In this paper, raw date palm seeds （RDPS） were investigated to assess the possible use of this raw material as an effective adsorbent for the removal of sulfate from aqueous solution. The influence of various parameters such as sulfate initial concentration, pH, adsorbent dose and stirring time has been studied for the adsorption of sulfate in batch mode. Effects of foreign anions on the adsorption of sulfate onto RDPS have been also investigated. The pseudo-second-order, Elovich and intraparticle diffusion kinetic models have been developed to predict the rate constants of adsorption and equilibrium capacities. The maximum adsorption capacity of sulfate （qe ≈3.2 mg/g） onto RDPS was reached for the initial sulfate concentration = 100 mg/L, pH - 3.5, adsorbent dose = 10 g/L and for a stirring intensity = 200 rpm at 25 ± 2 ℃. The results showed that the adsorption of sulfate onto this raw materials followed pseudo-second-order rate kinetic predicting a chemisorption process.

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%.

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.

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.

Hexagon-Islands Density and Size Distribution on Growing Single-Walled Carbon Nanotubes in the Kinetic 5-Vertex Model

A kinetic 5-vertex model is used to investigate hexagon-islands formation on growing single-walled carbon nanotubes (SWCNT). In the model, carbon atoms adsorption and migration processes on the SWCNT edge are considered. These two dynamic processes are assumed to be mutually independent as well as mutually dependent as far as the whole growth of the nanotube is concerned. Key physical parameters of the model are the growth time t, the diffusion length Γ defined as the ratio of the diffusion rate D to the carbon atomic flux F and the SWCNT chiral angle. The kinetic equation that describes the nanotube edge dynamics is solved using kinetic Monte Carlo simulations with the Bortz, Kalos and Lebowitz update algorithm. The behaviors of islands density and size distribution are investigated within the growth parameters’ space. Our study revealed key mechanisms that enable the formation of a new ring of hexagons at the SWCNT edge. The growth occurs either by pre-existing steps propagation or by hexagon-islands growth and coalescence on terraces located between dislocation steps, depending on values of model parameters. This should offer a road map for edge design in nanotubes production. We also found that in appropriate growth conditions, the islands density follows Gaussian and generalized Wigner distributions whereas their size distribution at a given growth time shows a decreasing exponential trend.

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.

Dynamic recrystallization kinetics of as-cast AZ91D alloy

The flow behavior and dynamic recrystallization（DRX） behavior of an as-cast AZ91 D alloy were investigated systematically by applying the isothermal compression tests in temperature range of 220-380 ℃ and strain rate range of 0.001-1 s^-1.The effect of temperature and strain rate on the DRX behavior was discussed.The results indicate that the nucleation and growth of dynamic recrystallized grains easily occur at higher temperatures and lower strain rates.To evaluate the evolution of dynamic recrystallization,the DRX kinetics model was proposed based on the experimental data of true stress-true strain curves.It was revealed that the volume fraction of dynamic recrystallized grains increased with increasing strain in terms of S-curves.A good agreement between the proposed DRX kinetics model and microstructure observation results validates the accuracy of DRX kinetics model for AZ91 D alloy.

Kinetics of cerium(Ⅳ) and fluoride extraction from sulfuric solutions using bifunctional ionic liquid extractant(Bif-ILE)[A336][P204]

The extraction kinetics of Ce（Ⅳ） and Ce（Ⅳ）-F^- mixture systems from sulfuric solutions to n-heptane solution containing Bif-ILE[A336][P204]（[trialkylmethylammonium][di-2-ethylhewanxylphosphinate]） with a constant interfacial area cell with laminar flow were studied,just to elucidate the extraction mechanism and the mass transfer models.The data were analyzed in terms of pseudo-first-order constants.The effects of stirring speed,specific interfacial area and temperature on the extraction rate in both systems were discussed,suggesting that the extractions were mixed bulk phases-interfacial control process.Supported by the experimental data,the corresponding rate equations for Ce（Ⅳ） extraction system and Ce（Ⅳ）-F^- mixture extraction system were obtained.The experimental results indicated the rate-controlling step.The kinetics model was deduced from the rate-controlling step and consistent with the rate equation.

Microstructure evolution in cooling process of Al-Zn-Mg-Cu alloy and kinetics description

The microstructure evolution of Al-Zn-Mg-Cu alloy was studied by differential scanning calorimetry （DSC） and transmission electron microscopy （TEM） during different rate cooling processes. Based on the DSC results, the kinetics analysis was carried out. The results indicate that the precipitation of η phase is the predominant transformation for the alloy during the cooling process after the solution treatment. And the η phase nucleates on dispersoids and at grain boundaries. The amount of η phase decreases with increasing cooling rate, and reduces by 75% as the cooling rate increases from 5 to 50 ℃/min. The kinetics of the precipitation of η phase can be described by the Kamamoto transformation model when the cooling rate is a constant.

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.

Kinetic degradation of amoxicillin by using the electro-Fenton process in the presence of a graphite rods from used batteries

This study reports the removal of amoxicillin(AMX)in aqueous media using the electroFenton process in the presence of a graphite cathode recovered from used batteries.The impact of the relevant parameters on the electroFenton process,namely the applied current intensity,the temperature,the initial concentration of AMX and the initial concentration of ferrous ions were investigated.The results showed that the optimal values were:I=600 mA,T=25℃,[AMX]_(0)=0.082 mmol·L^( 1) and[Fe^(2+)]=1 mmol·L^(1),leading to 95%degradation and 74%mineralization.The model parameters of AMX mineralization were determined using nonlinear methods,showing that it follows a pseudosecondorder kinetic.The Energy consumption(EC)calculated under the optimal values was found to be 0.79 kWhg 1,which was of the same order of magnitude of those reported in other findings;while it is noteworthy that the electrodes used in our study are of a lower cost.

Kinetic study of oxidative coupling of methane over Mn and/or W promoted Na_2SO_4/SiO_2 catalysts

A comprehensive kinetic model for oxidative coupling of methane（OCM）over Mn and/or W promoted Na2SO4/SiO2 catalysts was developed based on a micro-catalytic reactor data.The methane conversion and ethylene,ethane,carbon monoxide and carbon dioxide selectivities were obtained in a wide operating condition range of 750 - 825-C,CH4/O2=2.5 - 10 and contact time=267 - 472 kg s m-3.Reaction networks of six models with different rate equation types were compared together.The kinetic rate parameters of each reaction network were estimated using linear regression or genetic algorithm optimization method（GA）.A reaction network suggested by Stansch et al.for OCM was found to be the best one and was further used in this work.The suggested model could predict the experimental results of OCM reaction within a deviation range of ± 20%.

A Kinetic Approach to Photomineralization of Methane in Air by Membranes Based on TiO2/WO3

Photomineralization of methane in air(10.0-1,000 ppm(mass/volume)of C)at 100%relative humidity(dioxygen as oxygen donor),was systematically studied at 318±3 K,in an annular laboratory-scale reactor,by photocatalytic membranes immobilising titanium dioxide and tungsten trioxide as co-photocatalysts.Kinetics of both substrate disappearance,to yield intermediates,and total organic carbon(TOC)disappearance,to yield carbon dioxide,were followed.A kinetic model was employed,from which,by a set of differential equations,four final optimised parameters,k1 and K1,k2 and K2,were calculated,able to fit the whole kinetic profile adequately.Modelling of quantum yields,as a function of substrate concentration and irradiance,as well as of concentration of photocatalysts,was carried out very satisfactorily.Kinetics of hydroxyl radicals reacting between themselves,leading to hydrogen peroxide,other than with substrate or intermediates leading to mineralization,were considered,paralleled by second competition kinetics involving superoxide radical anion.When using appropriate blends of the two photocatalysts,limiting quantum yieldsF∞values increase considerably and approach the maximum allowable value for the investigated molecule,in a much wider range of irradiances than that shown by the single catalysts mainly at low irradiances.This may be interpreted by strong competition kinetics of superoxide radicals generated by the catalyst defects,in the corresponding range of high irradiances.By this way,operation at high irradiance values is possible,without losing any efficiency for the mineralization process.

Kinetics of the hydrogen absorption and desorption processes of hydrogen storage alloys: A review

High hydrogen absorption and desorption rates are two significant index parameters for the applications of hydrogen storage tanks.The analysis of the hydrogen absorption and desorption behavior using the isothermal kinetic models is an efficient way to investigate the kinetic mechanism.Multitudinous kinetic models have been developed to describe the kinetic process.However,these kinetic models were de-duced based on some assumptions and only appropriate for specific kinetic measurement methods and rate-controlling steps(RCSs),which sometimes lead to confusion during application.The kinetic analysis procedures using these kinetic models,as well as the key kinetic parameters,are unclear for many researchers who are unfamiliar with this field.These problems will prevent the kinetic models and their analysis methods from revealing the kinetic mechanism of hydrogen storage alloys.Thus,this review mainly focuses on the summarization of kinetic models based on different kinetic measurement methods and RCSs for the chemisorption,surface penetration,diffusion of hydrogen,nucleation and growth,and chemical reaction processes.The analysis procedures of kinetic experimental data are expounded,as well as the effects of temperature,hydrogen pressure,and particle radius.The applications of the kinetic models for different hydrogen storage alloys are also introduced.

Kinetic adsorption of application of carbon nanotubes for Pb(Ⅱ) removal from aqueous solution

The capability of carbon nanotubes （CNTs） to adsorb lead （Pb） in aqueous solution was investigated. Batch mode adsorption experiment was conducted to determine the effects of pH, agitation speed, CNTs dosage and contact time. The removal of Pb（II） reached maximum value 85% or 83% at pH 5 or 40 mg/L of CNTs, respectively. Higher correlation coefficients from Langmuir isotherm model indicates the strong adsorptions of Pb（II） on the surface of CNTs （adsorption capacity Xm = 102.04 mg/g）. The results indicates that the highest percentage removal of Pb （96.03%） can be achieved at pH 5, 40 mg/L of CNTs, contact time 80 min, and agitation speed 50 r/min.

Thermodynamics and kinetics of hydriding and dehydriding reactions in Mg-based hydrogen storage materials

Mg-based materials are one of the most promising hydrogen storage candidates due to their high hydrogen storage capacity,environmental benignity,and high Clarke number characteristics.However,the limited thermodynamics and kinetic properties pose major challenges for their engineering applications.Herein,we review the recent progress in improving their thermodynamics and kinetics,with an emphasis on the models and the influence of various parameters in the calculated models.Subsequently,the impact of alloying,composite,and nanocrystallization on both thermodynamics and dynamics are discussed in detail.In particular,the correlation between various modification strategies and the hydrogen capacity,dehydrogenation enthalpy and temperature,hydriding/dehydriding rates are summarized.In addition,the mechanism of hydrogen storage processes of Mg-based materials is discussed from the aspect of classical kinetic theories and microscope hydrogen transferring behavior.This review concludes with an outlook on the remaining challenge issues and prospects.

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.

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

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

Reduction kinetics of iron oxide pellets with H_2 and CO mixtures

Reduction of hematite pellets using H2-CO mixtures with a wide range of H2/CO by molar （1：0, 3：1, 1：1, 1：3, and 0：1） at different reducing temperatures （1073, 1173, and 1273 K） was conducted in a program reducing furnace. Based on an unreacted core model, the effective diffusion coefficient and reaction rate constant in several cases were determined, and then the rate-control step and transition were analyzed. In the results, the effective diffusion coefficient and reaction rate constant increase with the rise in temperature or hydrogen content. Reduction of iron oxide pellets using an H2-CO mixture is a compound control system; the reaction rate is dominated by chemical reaction at the very beginning, competition during the reduction process subsequently, and internal gas diffusion at the end. At low hydrogen content, increasing temperature takes the transition point of the rate-control step to a high reduction degree, but at high hydrogen content, the effect of temperature on the transition point weakens.

Kinetics of Asymmetric Reduction of Phenylglyoxylic Acid to R-(-)-Mandelic Acid by Saccharomyces Cerevisiae FD11b

The kinetics of asymmetric production of R-（-）-mandelic acid （R-MA） from phenylglyoxylic acid （PGA） catalyzed by Saccharomyces cerevisiae sp. strain FD11b was studied by fed-batch cultures. The concentrations of glucose and PGA were controlled respectively with a dual feeding system. When the electron donor glucose was supplied at the rate of 0.0833mmol·gdw^-1·h^-1, the specific production rate （qp） and the enantiomeric excess of R-MA reached the maximum 0.353mmol·gdw^-1·h^-1 and 97.1%, respectively. The apparent reduction activity of yeast FD 11 b was obviously affected by both substrate PGA and product MA. The qp value reached the maximum 0.36-0.38mmol·gdw^-1·h^-1 when the PGA concentration was controlled between 25 and 35mmol·L^-1. The obvious substrate inhibition of bioconversion was observed at the PGA concentrations higher than 40mmol·L^-1. The accumulation of product MA also caused a severe feed-back inhibition for its production when the product concentration was above 60mmol·L^-1. The kinetic model with the inhibition effect of both substrate and product was simulated by a computer-based least-square arithrnatic. The established kinetic model was in good agreement with the experimental data.