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.

Development of a first-order kinetics-based model for the adsorption of nickel onto peat

The use of peat for the removal of nickel from aqueous solutions has been investigated at various pH values by means of static conditions. The present research shows that the ability of Ni to bind to peat increases as the pH value increases. The solutions reach adsorption equilibrium rapidly. A reasonable kinetic model, first-order in nickel concentration, has been developed and fitted to the adsorption of nickel （Ⅱ） onto peat. The first-order model provides a good correlation to the experimental data. The characteristic parameters of the Langmuir isotherm were determined at various temperatures. The relationship between kinetics and equilibrium isotherms was established through the forward- and backward-rate-constants, k~ and k2, and the equilibrium constant, K.

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.

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

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

Description of martensitic transformation kinetics in Fe-C-X(X = Ni,Cr,Mn,Si) system by a modified model

Controlling the content of athermal martensite and retained austenite is important to improving the mechanical properties of high-strength steels,but a mechanism for the accurate description of martensitic transformation during the cooling process must be addressed.At present,frequently used semi-empirical kinetics models suffer from huge errors at the beginning of transformation,and most of them fail to exhibit the sigmoidal shape characteristic of transformation curves.To describe the martensitic transformation process accurately,based on the Magee model,we introduced the changes in the nucleation activation energy of martensite with temperature,which led to the varying nucleation rates of this model during martensitic transformation.According to the calculation results,the relative error of the modified model for the martensitic transformation kinetics curves of Fe-C-X(X = Ni,Cr,Mn,Si) alloys reached 9.5% compared with those measured via the thermal expansion method.The relative error was approximately reduced by two-thirds compared with that of the Magee model.The incorporation of nucleation activation energy into the kinetics model contributes to the improvement of its precision.

Estimation of Landfill Gas and Its Renewable Energy Potential from the Polesgo Controlled Landfill Using First-Order Decay (FOD) Models

Methane generation in landfills and its inadequate management represent the major avoidable source of anthropogenic methane today. This paper models methane production and the potential resources expected (electrical energy production and potential carbon credits from avoided CH4 emissions) from its proper management in a municipal solid waste landfill located in Ouagadougou, Burkina Faso. The modeling was carried out using two first-order decay (FOD) models (LandGEM V3.02 and SWANA) using parameters evaluated on the basis of the characteristics of the waste admitted to the landfill and weather data for the site. At the same time, production data have been collected since 2016 in order to compare them with the model results. The results obtained from these models were compared to experimental one. For the simulation of methane production, the SWANA model showed better consistency with experimental data, with a coefficient of determination (R²) of 0.59 compared with the LandGEM model, which obtained a coefficient of 0.006. Thus, despite the low correlation values linked to the poor consistency of experimental data, the SWANA model models methane production much better than the LandGEM model. Thus, despite the low correlation values linked to the poor consistency of the experimental data, the SWANA model models methane production much better than the LandGEM V3.02 model. It was noted that the poor consistency of the experimental data justifies these low coefficients, and that they can be improved in the future thanks to ongoing in situ measurements. According to the SWANA model prediction, in 27 years of operation a biogas plant with 33% electrical efficiency using biogas from the Polesgo landfill would avoid 1,340 GgCO2e. Also, the evaluation of revenues due to electricity and carbon credit gave a total revenue derived from methane production of US$27.38 million at a cost of US$10.5/tonne CO2e.

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.

White-rot Fungus Growth Conditions and Its Metabolic Kinetic Models

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

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

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

Reaction kinetics modeling for lithium and cobalt recovery from spent lithium-ion batteries using acetic acid

Lithium and cobalt recovery from spent lithium-ion batteries(LIBs) is a major focus because of their increased production and usage. The conventional method for recycling spent LIBs using inorganic acids produces harmful byproducts. In this work, the leaching agent was substituted with a less expensive and more environmentally friendly alternative—acetic acid—and a mathematical model was developed to describe the kinetics of the recovery process. The variables used were the pH value, temperature, H_2O_2 concentration, and the solid-to-liquid(S/L) ratio. The mathematical model used was the shrinking core model, which was modified to accommodate an equilibrium reaction. The experimental results show that the rate of recovery of Li and Co over time was only affected by temperature. The leaching behaviors of Li and Co were found to oppose each other. An increase in temperature resulted in increased recovery of Li but decreased recovery of Co because of the product-favoring endothermic reaction of Li and the reactant-favoring exothermic reaction of Co. The product of Li has a lower entropy value than the reactant as a free-moving ion, whereas the product of Co leaching has a higher entropy value as a stiff crystal complex. Thus, temperature conditioning is a pivotal factor in the leaching of spent LIBs.

Application of convolutional neural networks to large-scale naphtha pyrolysis kinetic modeling

System design and optimization problems require large-scale chemical kinetic models. Pure kinetic models of naphtha pyrolysis need to solve a complete set of stiff ODEs and is therefore too computational expensive. On the other hand, artificial neural networks that completely neglect the topology of the reaction networks often have poor generalization. In this paper, a framework is proposed for learning local representations from largescale chemical reaction networks. At first, the features of naphtha pyrolysis reactions are extracted by applying complex network characterization methods. The selected features are then used as inputs in convolutional architectures. Different CNN models are established and compared to optimize the neural network structure.After the pre-training and fine-tuning step, the ultimate CNN model reduces the computational cost of the previous kinetic model by over 300 times and predicts the yields of main products with the average error of less than 3%. The obtained results demonstrate the high efficiency of the proposed framework.

Comparison of kinetic models for isothermal CO_2 gasification of coal char–biomass char blended char

This study investigated the isothermal gasification reactivity of biomass char （BC） and coal char （CC） blended at mass ratios of 1：3, 1：1, and 3：1 via isothermal thermogravimelric analysis （TGA） at 900, 950, and 1000℃ under CO2. With an increase in BC blending ra- tio, there were an increase in gasification rate and a shortening of gasification time. This could be attributed to the high specific surface area of BC and the high uniformity of carbon structures in CC when compared to those in BC. Three representative gas-solid kinetic models, namely, the volumetric model （VM）, grain model （GM）, and random pore model （RPM）, were applied to describe the reaction behavior of the char. Among them, the RPM model was considered the best model to describe the reactivity of the char gasification reaction. The activa- tion energy of BC and CC isothermal gasification as determined using the RPM model was found to be 126.7 kJ/mol and 210.2 kJ/mol, re- spectively. The activation energy was minimum （123.1 kJ/mol） for the BC blending ratio of 75%. Synergistic effect manifested at all mass ratios of the blended char, which increased with the gasification temperature.

Repeated-Batch and Continuous Production of L-Lactic Acid by Rhizopus oryzae Immobilized in Calcium Alginat Beads:ReactorPerformance and Kinetic Model

Repeated-batch and continuous production of L-lactic acid by immobilized Rhizopusoryzae with calcium alginate entrapment method in a three-phase fluidized-bed bioreactor was stud-ied.The operation conditions were optimized.The productivity based on total reactor volume wasabout 3 times higher than that with free cells in a traditional stirred tank bioreactor.A mathemat-ical model was proposed and the model predictions were in good agreement with the experimentaldat.

Progress in Modeling of Phase Transformation Kinetics

Several methods representing the evolution of microstructure were introduced, which include the Johnson-Mehl-Avrami-Kolmogorov （JMAK） equation, Internal State Variable （ISV） framework, Koistinen-Marburger （K-M） equation, modified Magee＇s rule and phase field model, etc. By combining calculation of martensite transformation kinetics, considering the selection of parameters with the effect of austenite grain size （AGS）, some suitable ways of obtaining better results have been proposed.

Adsorption and Ozonation Kinetic Model for Phenolic Wastewater Treatment

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

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

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

Nucleation of Kinetic Ising Model Under Oscillating Field

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

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.

Adsorption Kinetics of β-Carotene and Chlorophyll onto Acid-activated Bentonite in Model Oil

The textural properties of acid-activated bentonite （AAB）, which were prepared using four different concentrations of sulfuric acid, were analyzed by adsorption-desorption isotherm of nitrogen using an automated specific surface area and porosity analyzer. The total pore volume, specific surface area and average pore diameter of these four kinds of AAB show a regular changing trend, increasing first and then decreasing, the optimum of which can be achieved at a sulfuric acid concentration of 25% （sample A25）. The kinetic analysis of the adsorption of β-carotene and chlorophyll in model oil solutions, namely, xylene and edible oil solution, has been investigated by using AAB. Experimental results indicated that the adsorption data fit the pseudo-second-order model well. The whole adsorption process of the two pigments on AAB was divided basically into two parts： the initial adsorption of pigments was rapid in the first l0 rain, followed by a slower adsorption process till equilibrium was attained at 60 rain. In addition, the amount and rate of adsorption on A25 increase synchronously with the initial pigment concentration and temperature. The results showed that the adsorption kinetics behavior of AAB with respect to the pigments is not influence by the xylene and edible oil solution.