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.

In vitro evaluation of transdermal permeation effects of Fu’s cupping therapy via six diffusion kinetics models

In this study,six kinetics models of indomethacin hydrophilic gel patch transdermal in vitro release was established,including zero-level,first-order,Higuchi-level,Ritger-Peppas,Weibull and Hixcon-Crowell dynamic equations.The chemical permeation enhancers,including 3%and 5%Azone,and iontophoresis were used as the control.Transdermal diffusion tests were performed in vitro and indomethacin was quantified by high performance liquid chromatography system.The transdermal parameter of the Higuchi and Weibull dynamic equations,indicated that Fu’s cupping therapy(FCT)could significantly improve Higuchi and Weibull kinetic parameters in vitro transdermal,increased transdermal rate and permeability coefficient,reduced lagging time.Additionally,statistical analysis speculated the skin barrier function could be restored after 46 h treatment.Hence,as a new physical transdermal drug delivery technology,transdermal permeation effects produced by FCT are obvious,which has the characteristics of traditional Chinese medicine and has important clinical application value.

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

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

Kinetics model of aerobic phase in hybrid anoxic-oxic process

Kinetics models of COD degradation,biomass growth of the anoxic-oxic ( A/O) system as well as NH3-N degradation in aerobic phase were presented according to the mass balance theory,reaction-diffusion theory and Fick law. Then these models were testified by comparson with experimental results. It is demonstrated that the variation trends of theoretical and experimental values for COD degradation and biomass growth are similar. The deviation rate between theoretical and experimental values is always under 20% even it increases along with the fluctuation of influent organic loading. In terms of NH3-N degradation,nitrification can also be well simulated by the model as the substrates of influent are sufficient. It indicates that the model can accurately reflect the reaction in hybrid A/O process. Models presented herein provide a theoretical basis for the design, operation and control of hybrid A/O process.

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.

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.

Static Recrystallization Kinetics Model After Hot Deformation of Low-Alloy Steel Q345B

The static recrystallization behavior of low-alloy steel Q345B during double-pass hot compression deformation tests was investigated in the temperature range of 900-1000 ℃,the true strain range of 0.15-0.25 and the interpass time range of 0.5-50 s on Gleeble-3500 thermo-simulation machine.The results show that static recrystallization during the interpass time is observed.As the deformation temperature and strain increase,softening caused by static recrystallization is obvious.According to the analysis and calculation of thermo-simulation data,the static recrystallization activation energy was obtained and static recrystallization kinetics model was built.Finally,the error analysis of static recrystallization kinetics model proved that the model had good accuracy.Therefore,this model provides a theoretical basis for static recrystallization（SRX）and will contribute to the development of multipass hot rolling process,in order to control the rolling process more accurately.

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 the kinetics of methane conversion in steam reforming process of coke-oven gas based on experimental data

Steam-reforming is an effective approach for upgrading methane and hydrocarbon of coke-oven gas into CO and HE, but the kinetic behavior needs more study. We investigated the conversion of methane in coke-oven gas by steam reforming process in an electric tubular flow at 14 kPa with temperature varying from .500 ℃ to 9.50 ℃, and developed a kenetic model for, ignoring the effects of adsorption and diffusion. The optimal dynamic conditions for methane conversion 14 kPa are as follows： the ratio of the amount of water to the amount of methane is from 1.1 to 1.3; the reaction temperature is from 1 223 K to 1 273 K. The methane conversion rate is larger than 95% when the ratio of the amount of water to the amount of methane is 1.2 at a temperature above 1 223 K with the residence time up to 0.75 s.

Fixed-Bed Column Adsorption Modeling of MnO4- Ions from Acidic Aqueous Solutions on Activated Carbons Prepared with the Biomass

Activated carbons calcined at 400˚C and 600˚C (AC-400 and AC-600), prepared using palm nuts, collected in the town of Franceville in Gabon, were used to study the dynamic adsorption of MnO4- ions in acidic media on fixed bed column and on the kinetic modeling of experimental data of breakthrough curves of MnO4- ions obtained. Results on the adsorption of MnO4- ions in fixed-bed dynamics obtained on AC-400 and AC-600 adsorbents beds indicated that the AC-400 bed appears to be the most efficient in removing MnO4- ions in acidic media. Indeed, the adsorbed amounts, the adsorbed capacities at saturation and the elimination percentage of MnO4- ions obtained with AC-400 (31.24 mg;52.06 mg·g-1 and 41.65% respectively) were higher compared to those obtained with AC-600 (9.87 mg;16.45 mg·g-1 and 17.79% respectively). The breakthrough curves kinetic modeling revealed that the Thomas model and the pseudo-first-order kinetic model were the most suitable models to describe the adsorption of MnO4- ions on adsorbents studied in our experimental conditions. The results of the intraparticle diffusion model showed that intraparticle diffusion was involved in the adsorption mechanism of MnO4- ions on investigated adsorbents and was not the limiting step and the only process controlling MnO4- ions adsorption. In contrast to AC-400, the intraparticle diffusion on AC-600 bed plays an important role in the adsorption mechanism of MnO4- ions.

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 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.

A Model-based Phenomenological Investigation of Char Combustion Kinetics through Thermogravimetry

Five coal char samples were burnt in thermobalance with ramp heating rate of 30 K/min. The pore structure of these char samples was studied through mercury intrusion method. Combined with the kinetic theory of gases, the data of surface area was used in fitting the results. As a result, the kinetic triplet was given. The analysis showed that five char samples share almost the same intrinsic activation energy of the overall reaction. The phenomenological implication of the derived combustion rate equation was given.

Bioregeneration of spent activated carbon:Review of key factors and recent mathematical models of kinetics

The disposal of spent activated carbon(AC) will inevitably create secondary pollution. In overcoming this problem, the spent AC can be regenerated by means of biological approach. Bioregeneration is the phenomenon in which through the action of microorganisms, the adsorbed pollutants on the surface of the AC will be biodegraded and this enables further adsorption of pollutants to occur with time elapse. This review provides the challenges and perspectives for effective bioregeneration to occur in biological activated carbon(BAC)column. Owing to very few reported works on the bioregeneration rate in BAC column, emphasis is put forward on the recently developed models of bioregeneration kinetic in batch system. All in all, providing potential solutions in increasing the lifespan of AC and the enhancement of bioregeneration rate will definitely overcome the bottlenecks in spent AC bioregeneration.

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.

Hot-deformation kinetics analysis and extrusion parameter optimization of a dilute rare-earth free magnesium alloy

The fundamental research on thermo-mechanical conditions provides an experimental basis for high-performance Mg-Al-Ca-Mn alloys.However, there is a lack of systematical investigation for this series alloys on the hot-deformation kinetics and extrusion parameter optimization. Here, the flow behavior, constitutive model, dynamic recrystallization(DRX) kinetic model and processing map of a dilute rare-earth free Mg-1.3Al-0.4Ca-0.4Mn(AXM100, wt.%) alloy were studied under different hot-compressive conditions. In addition, the extrusion parameter optimization of this alloy was performed based on the hot-processing map. The results showed that the conventional Arrhenius-type strain-related constitutive model only worked well for the flow curves at high temperatures and low strain rates. In comparison, using the machine learning assisted model(support vector regression, SVR) could effectively improve the accuracy between the predicted and experimental values. The DRX kinetic model was established, and a typical necklace-shaped structure preferentially occurred at the original grain boundaries and the second phases. The DRX nucleation weakened the texture intensity, and the further growth caused the more scattered basal texture. The hot-processing maps at different strains were also measured and the optimal hot-processing range could be confirmed at the deformation temperatures of 600~723 K and the strain rates of 0.018~0.563 s^(-1). Based on the optimum hot-processing range, a suitable extrusion parameter was considered as 603 K and 0.1 mm/s and the as-extruded alloy in this parameter exhibited a good strength-ductility synergy(yield strength of ~ 232.1 MPa, ultimate strength of ~ 278.2 MPa and elongation-to-failure of ~ 20.1%). Finally, the strengthening-plasticizing mechanisms and the relationships between the DRXed grain size, yield strength and extrusion parameters were analyzed.

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.

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.