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.

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.

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.

Progress in Modeling of Phase Transformation Kinetics

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

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

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

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.

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

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

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.

Modeling of Soot Formation in Gas Burner Using Reduced Chemical Kinetics Coupled with CFD Code

A computational study of soot formation in ethylene/air coflow jet diffusion flame at atmospheric pres-sure was conducted using a reduced mechanism and soot formation model. A 20-step mechanism was derived from the full mechanism using sensitivity analysis,reaction path analysis and quasi steady state(QSS) approximation. The model in premixed flame was validated and with computing savings in diffusion flame was applied by incor-porating into a CFD code. Simulations were performed to explore the effect of coflow air on flame structure and soot formation. Thermal radiation was calculated by a discrete-ordinates method,and soot formation was predicted by a simple two-equation soot model. Model results are in good agreement with those from experiment data and detailed mechanism at atmospheric conditions. The soot nucleation,growth,and oxidation by OH are all enhanced by decrease in coflow air velocity. The peak soot volume fraction region appears in the lower annular region be-tween the peak flame temperature and peak acetylene concentration locations,and the high soot oxidation rate due to the OH attack occurs in the middle annular region because of high temperature.

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.

Kinetics of zinc sulfide concentrate direct leaching in pilot plant scale and development of semi-empirical model

The direct leaching kinetics of an iron-poor zinc sulfide concentrate in the tubular reactor was examined.All tests werecarried out in the pilot plant.To allow the execution of hydrostatic pressure condition,the slurry with ferrous sulfate and sulfuric acidsolution was filled into a vertical tube(9m in height)and air was blown from the bottom of the reactor.The effects of initial acidconcentration,temperature,particle size,initial zinc sulfate concentration,pulp density and the concentration of Fe on the leachingkinetics were investigated.Results of the kinetic analysis indicate that direct leaching of zinc sulfide concentrate follows shrinkingcore model(SCM).This process was controlled by a chemical reaction with the apparent activation energy of49.7kJ/mol.Furthermore,a semi-empirical equation is obtained,showing that the order of the iron,sulfuric acid and zinc sulfate concentrationsand particle radius are0.982,0.189,-0.097and-0.992,respectively.Analysis of the unreacted and reacted sulfide particles bySEM-EDS shows that insensitive agitation in the reactor causes detachment of the sulfur layer from the particles surface in lowerthan60%Zn conversion and lixiviant in the face with sphalerite particles.

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.

Experimental and Modeling Study of Kinetics for Methane Hydrate Formation with Tetrahydrofuran as Promoter

The kinetics behavior of methane hydrate formation in the presence of tetrahydrofuran （THF） as promoter was studied. A set of experimental equipment was designed and constructed. A series of kinetics data for the formation of methane hydrate in the presence of THF were measured with the isochoric method. The influences of temperature, pressure and liquid flow rate on the methane consumption rate were studied respectively. Based on the Chen-Guo hydrate formation mechanism, a kinetics model for the formation of methane hydrate in the presence of THF by using the dimensionless Gibbs free energy difference of quasi-chemical reaction of basic hydrate formation, -△G/RT, as the driving force was proposed. The model was used to calculate the rate of methane consumption and it was shown that the calculated results were in good agreement with the experimental results.

Modeling of metadynamic recrystallization kinetics after hot deformation of low-alloy steel Q345B

Based on the steady-state strain measured by single-pass hot compression tests,the method by a double-pass hot compression testing was developed to measure the metadynamic-recrystallization kinetics.The metadynamic recrystallization behavior of low-alloy steel Q345B during hot compression deformation was investigated in the temperature range of 1 000-1 100℃,the strain rate range of 0.01-0.10 s -1 and the interpass time range of 0.5-50 s on a Gleeble-3500 thermo-simulation machine.The results show that metadynamic recrystallization during the interpass time can be observed.As the deformation temperature and strain rate increase,softening caused by metadynamic recrystallization is obvious.According to the data of thermo-simulation,the metadynamic recrystallization activation energy is obtained to be Qmd=100.674 kJ/mol and metadynamic recrystallization kinetics model is set up.Finally,the error analysis of metadynamic recrystallization kinetics model proves that the model has high accuracy(correlation coefficient R=0.988 6).

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.

Interface kinetics modeling of binary alloy solidification by considering correlation between thermodynamics and kinetics

By considering collision-limited growth mode and short-range diffusion-limited growth mode simultaneously,an extended kinetic model for solid−liquid interface with varied kinetic prefactor was developed for binary alloys.Four potential correlations arising from effective kinetics coupling the two growth modes were proposed and studied by application to planar interface migration and dendritic solidification,where the linear correlation between the effective thermodynamic driving force and the effective kinetic energy barrier seems physically realistic.A better agreement between the results of free dendritic growth model and the available experiment data for Ni−0.7at.%B alloy was obtained based on correlation between the thermodynamics and kinetics.As compared to previous models assuming constant kinetic prefactor,a common phenomenon occurring at relatively low undercoolings,i.e.the interface migration slowdown,can be ascribed to both the thermodynamic and the kinetic factors.By considering universality of the correlation between the thermodynamics and kinetics,it is concluded that the correlation should be considered to model the interface kinetics in alloy solidification.

Empirical correction of kinetic model for polymer thermal reaction process based on first order reaction kinetics

Based on the theory of first-order reaction kinetics,a thermal reaction kinetic model in integral form has been derive.To make the model more applicable,the effects of time and the conversion degree on the reaction rate parameters were considered.Two types of undetermined functions were used to compensate for the intrinsic variation of the reaction rate,and two types of correction methods are provided.The model was explained and verified using published experimental data of different polymer thermal reaction systems,and its effectiveness and wide adaptability were confirmed.For the given kinetic model,only one parameter needs to be determined.The proposed empirical model is expected to be used in the numerical simulation of polymer thermal reaction process.