Modified Shrinking Core Model Research Articles

The green reductive leaching of manganiferous iron ore and Mn3O4 nanoparticles production: Kinetic modeling and comparison of various reductants

BackgroundSecuring critical metals is crucial for the transition from fossil fuels to renewable energies. In this regard, extracting metals from various sources and low-grade ores can lead to the sustainable production of metals. Manganese, as a strategic metal, can play a significant role in achieving this goal. MethodsIn this study, various reductants such as oxalic acid, citric acid, ascorbic acid, acetic acid, tannic acid, hydrogen peroxide, iron (II) sulfate, sodium thiosulfate, and DL-malic acid were used to evaluate the feasibility and comparison on the manganiferous iron ore leaching. Significant findingsDL-malic acid was chosen as the main reductant to investigate other factors because it is novel (as a reductant), eco-friendly, cost-effective, accessible, and easily storable. Therefore, more detailed studies on the dissolution of manganiferous iron ore in the presence of DL-malic acid as the reductant were carried out considering different levels of temperature, particle size, acid concentrations, and leaching time. Increasing the temperature from 298 K to 348 K notably boosted the leaching recovery from 27.00 % to 70.11 %. It was observed that decreasing the ore particle size from -212 μm to -38 μm resulted in an enhancement of leaching recovery from 57.74 % to 70.11 %. Also, adding only 250 % stoichiometry of DL-malic acid notably increased the leaching recovery to 70.11 %, compared to just 5.32 % in a reductant-free medium. It should be noted that the concentration of sulfuric acid had a direct impact on leaching recovery, increasing by 28.28 % with a concentration of 0.5 M and by 93.08 % with a concentration of 4 M. In this research work, the kinetic of the leaching process was modeled using the modified shrinking core model (MSCM). The calculated activation energy was about 33 kJ/mole, which confirmed that the mixed mechanism controlled the reaction. Mn3O4 nanoparticles were synthesized using a pregnant leach solution (PLS) and through a multi-stage co-precipitation method. In this method, hydrogen peroxide was used to modify the manganese hydroxide phase as a more eco-friendly method than other heat treatment methods. The SEM and EDX analyses revealed an average particle size of 80 nm with spherical shapes and no impurities. The XRD pattern of the synthesized nanoparticles confirmed the Mn3O4 phase composition.

Leaching Kinetics of Spent 6F22 Dry Cells Roast Residue in Nitric and Hydrochloric Acids Using a Modified Shrinking Core Model

Leaching Kinetics of Spent 6F22 Dry Cells Roast Residue in Nitric and Hydrochloric Acids Using a Modified Shrinking Core Model

Kinetic analysis on CO2 sequestration from flue gas through direct aqueous mineral carbonation of circulating fluidized bed combustion fly ash

In this work, the suitability of fly ash from 600 MW circulating fluidized bed boiler for CO2 sequestration through direct aqueous route was evaluated. The circulating fluidized bed combustion fly ash exhibited favorable carbon capture characteristics with a maximum CO2 sequestration capacity of 0.128 g CO2/g CFA and a corresponding carbonation efficiency of 78.17 %. A modified shrinking core model incorporated gaseous CO2 dissolution and time-dependent effective coefficient of internal diffusion was proposed to determine the gas–liquid-solid carbonation kinetics. The key kinetic parameters were assessed as a function of various carbonation conditions including reaction temperature, solid–liquid (S/L) ratio, energy input and superficial gas velocity. The mass diffusion through the liquid film near the gas–liquid interface was the rate-controlling step during the initial period of time, while diffusion through the expanded passivation layer constituted the controlling mechanism at the final stage. The model provides a more accurate representation of the gas–liquid-solid carbonation process and can be generalized to describe the carbonation of other solid wastes of interest.

A modified shrinking core model for microwave-assisted leaching of aluminum from peat clay

Aluminum oxide in peat clay has the potential to be used as a catalyst, coagulant, and adsorbent for the water treatment process. The usefulness of aluminum oxide in peat clay is enhanced by the leaching process. Aluminum was leached from peat clay in a variety of microwave power, HCl concentrations, and particle size. The effect of the microwave leaching parameters on the aluminum leaching rate was observed. The shrinking core (SC) model used in microwave-assisted leaching was assumed a pseudo steady state with chemical reactions. Effective diffusivity (De), mass transfer coefficient (kc), and reaction rate constants (k) are used as fitting parameters. The best fitting parameters De, kc , and k obtained 0.0049 cm2/s, 2.49 cm/s, and 10.5 cm/s, respectively. The comparison of experimental data and model calculations shown that the SC model can describe experimental data well for all microwave-assisted leaching conditions. Precious information on the results of this research can be given for the goal of the scaling-up and design of the microwave assisted leaching process.

Influence of Zinc on Nonisothermal Gasification Kinetics of Coke in a Blast Furnace.

The effect of zinc on the kinetics of coke gasification was studied by a nonisothermal method. The results indicated that with the increase of zinc content, coke gasification tended to move to the low-temperature zone, it occurred earlier, and the reaction rate increased. The main curve fitting method was used to analyze the mechanism function of coke gasification before and after adding zinc. The modified shrinking core model was found to be the optimal mechanism function for coke gasification, with which the kinetic parameters obtained showed that the pre-exponential factor and apparent activation energy of coke gasification decreased significantly with the increase of zinc adsorption amount. Moreover, a kinetic compensation effect was found to exist in the effect of zinc on coke gasification. Combined with X-ray diffraction (XRD) and the peak fitting technique, it was found that the difference in the catalytic effect of zinc on coke gasification was attributed to the carbon structure.

Ultrasound‐Assisted Leaching of Vanadium and Yttrium from Coal Ash: Optimization, Kinetic and Thermodynamic Study

AbstractVanadium (V) and yttrium (Y) were extracted from coal fly ash by a leaching process utilizing sulfuric acid with assistance of ultrasonic and hydrogen peroxide. Response surface methodology was applied to optimize main factors including solid‐to‐liquid (S/L) ratio, H2SO4 percentage, and H2O2 percentage. Under optimal conditions recovery rates for V and Y were 100 % and 97 %, respectively. A modified shrinking core model to study the kinetic leaching showed that the mass diffusion step controlled the reaction rate. The enthalpies for V and Y recovery indicated that the process was endothermic. Gibbs energy for both metals was negative, i.e., the process was spontaneous. Field emission scanning electron microscopy was applied to determine the effects of acid concentration and ultrasound on the surface of coal fly ash. Results demonstrated that the leaching agent could degrade and diffuse to coal ash particles.

The influence of particle size on the potential of enhanced basalt weathering for carbon dioxide removal - Insights from a regional assessment

Enhanced weathering through basalt application on agricultural land represents a proposed strategy for the removal of carbon dioxide from the atmosphere. It has been shown that enhanced weathering is principally feasible on a global scale, but there is still uncertainty with respect to the predicted drawdown in a given timeframe. This information is however vital to evaluate, if enhanced weathering should be further considered as a factor to alleviate the impact of the climate crisis. With this in mind, this article reviews of the current state of research and estimates the CO2 drawdown for scenarios using basalt powders of different particle size distribution (<100 μm, <10 μm and <1 μm). Calculated with a modified shrinking core model, the amount of powder dissolved within a timeframe of 10 years is approximately 16% (<100 μm), 55% (<10 μm) and 99.9% (<1 μm). This corresponds to a gross CO2 removal of 0.045 t CO2 t−1 of rock (<100 μm) and 0.153 t CO2 t−1 of rock, (<10 μm). We evaluate our results on regional scale through a case study for Austria, including emissions from mining, comminution, application and transport. Assuming an average distance of 300 km from mine to field, the net CO2 drawdown decreases to approximately 0.027 t CO2 t−1 of rock (<100 μm) or 0.096 t CO2 t−1 (<10 μm), when rail transport is used. For truck transport, the numbers are reduced to −0.030 t CO2 t−1 of rock (<100 μm) or 0.039 t CO2 t−1 (<10 μm), respectively. Accordingly, at the current CO2 intensity, transport related emissions may cancel out any drawdown if grain sizes (<100 μm) are used. Our estimates suggest that enhanced weathering will only significantly contribute to net CO2 drawdown if grain sizes (<10 μm) are used. Under these conditions the large-scale application of particles with a diameter <10 μm may remove about 2% of Austria's annual Greenhouse gas emissions. We discuss challenges towards this goal, including the enormous amounts of rock needed and the energy requirement related to grinding, as well as uncertainties related to actual field weathering rates. Those uncertainties hinder the precise quantification of CO2 drawdown as of now. While enhanced weathering remains a promising path for climate change mitigation, further research at laboratory and field scale is required to put this technology to optimal use.

Study on gas desorption and diffusion kinetic behavior in coal matrix using a modified shrinking core model

An accurate model of gas desorption and diffusion is the necessary prerequisite to accurately predict gas transfer and evaluation of gas content in the coal. A new modified shrinking core model was proposed and modified based on the shrinking core model and taking into account the time-depend diffusivity. It was to predict the kinetic process of gas desorption and diffusion including three processes: (1) desorption on the undesorbed core surface, (2) diffusion through the desorbed layer, and (3) diffusion through the gas film. The kinetic data of gas desorption and diffusion was obtained from a series of experimental tests conducted under isothermal conditions. The model showed the best agreement with the experimental data, comparison with the shrinking core model, the simplified unipore diffusion model, and the simplified bidisperse diffusion model. Comparison and validation of simulated curves and experimental data indicated the diffusion through the desorbed layer had a dominant role in the whole process of gas transfer in coal particle. The effect of adsorption equilibrium pressure, temperature, and particle size on the initial diffusivity was discussed by using the modified shrinking core model to model the experimental data. The initial diffusivity was affected slightly by the adsorption pressure and increased with the increase in temperature and the particle size. This research provides a new modified shrinking core model to describe the gas transfer process in coal particles better.

Investigating the Kinetics, Mechanism, and Activation Energy of Limestone Calcination Using Isothermal Analysis Methods

In the current research, isothermal experiments of kinetic analysis were performed at different temperatures (800–1050 °C) and particle sizes (885 to 10,763 μm) to investigate the calcination kinetics of high-purity limestone. Thermal analyses were carried out in a zirconia crucible, 1 cm in height, for different temperatures and particle sizes. The reaction rate coefficients were varied in the 2.2 × 10−5-1.62 × 10−3-m0.6.s−1 range. Moreover, various isothermal kinetic analysis methods were applied to assess the decomposition mechanism and the calcination function governing the process. The modified shrinking core model was found as the best representation of the high-purity limestone kinetic data. The activation energy was evaluated using the Arrhenius curve, and an average value of 86 kJ.mol−1 was obtained.

Research on properties evolution of ultrafine fly ash and cement composite

Compared with fly ash, addition of ultrafine fly ash manufactured by mechanical grinding will significantly improve the performances of the cement-based materials. In this paper, firstly the cement hydration is simulated based on the modified shrinking core model with the concept of multi components. Then it is combined with the fly ash pozzolanic reaction via the contents of capillary water and calcium hydroxide (CH) in the blended cement paste. The effects of the heterogeneous nucleation, fineness of fly ash and local w/c augmentation are quantitatively analyzed and incorporated into the hydration models. The integrated models are validated by the contents of CH and non-evaporable water (NEW) in the (ultrafine) fly ash and cement composite The coupled evolution of cement hydration, pozzolanic reaction and porosity is presented using the integrated hydration models. Compared with the fly ash and cement composite (FAC), it is found that the extent of the pozzolanic reaction significantly increases in the ultrafine fly ash and cement composite (UFAC) while the increment of cement hydration extent due to nucleation effect is relatively small. Furthermore, the contributions of gel content by different effects are quantitatively calculated and compared between UFAC and FAC. Finally, an empirical formula is established to predict the compressive strength of the hardening UFAC. The filling effect of the ultrafine fly ash, gel content and cumulative pore volume are adopted to evaluate the development of the compressive strength. The results indicate that the physical filling effect of ultrafine grains reflected on the compressive strength of UFAC will gradually increase during the first seven days of curing and then keeps constant. With the increase of cement replacement ratio (0 ~ 0.5), the physical filling effect brought by UFA will be greatly enhanced. The analyses presented in this paper will give a better understanding on the hydration process and strength development for the FAC and UFAC.

Diffusion Model of Methane Hydrate Formation in “Dry Water”

The kinetics of methane hydrate formation in “dry water” is studied using a diffusion model (the well-known modified shrinking core model). An analytical solution is found and substantiated for equations describing the formation of methane hydrate for “dry water” in the quasi–steady state approximation. The particle size distribution of aqueous phase in “dry water,” stabilized by different silicas, is determined. The predominantly bimodal character of this distribution is established. The kinetic curves of the formation of methane hydrates in “dry water” stabilized by different silicas is obtained. The kinetic curves of the formation of methane hydrates in “dry water” are calculated using the proposed diffusion model to show the theoretical and experimental kinetic parameters of hydrate formation are in good agreement, confirming the adequacy of the developed model and the obtained solution.

Bioleaching of dewatered electroplating sludge for the extraction of base metals using an adapted microbial consortium: Process optimization and kinetics

The main objective of this study was to optimize bioleaching process parameters for high co-extraction of base metals (Cu, Ni, Zn, and Cr) from hazardous electroplating sludge using an adapted microbial consortium and to explore the relevant bioleaching mechanisms. Microbial cultivation and sludge bioleaching were separated. The effect of the relevant process parameters (i.e., bulk pH, pulp density, and Fe2+ concentration) on the extraction of four selected metals through bioleaching by an adapted microbial consortium was investigated in a 1 L stirred tank reactor. Results indicated that maximum metal solubilization (>95.6% for each of Cu, Zn, and Ni, and 90.3% of Cr) was achieved at a bulk pH of 2.0, Fe2+ of 9.0 g/L, and pulp density of 15% (w/v). Bioleaching kinetics of the selected metals was described by a modified shrinking core model. This indicated that the interfacial transfer and diffusion across the solid film layer was the rate controlling step and controlled the dissolution kinetics. Data from bioleaching and chemical leaching systems showed that bioleaching had some advantages over simple chemical leaching. The mechanisms of improved Cu, Ni, Zn, and Cr extraction by bioleaching were demonstrated. Bioleaching improved metal release, especially from the residual fraction, as indicated by Community Bureau of Reference (BCR) three-stage sequential extraction analysis. Most of the Cu, Ni, and Zn extraction was attributed to H+ attack, as these metals were primarily distributed in the water/acid soluble and exchangeable fractions, along with Fe and Mn oxyhydroxides (>72.3%). For the extraction of Cr, besides H+, microorganisms and Fe3+ were also responsible. They improved Cr extraction, especially from the residual fraction. These findings indicate that bioleaching with an adapted microbial consortium appears promising for recycling and reutilizing valuable heavy metals from hazardous electroplating waste.

CO2 sorption kinetic study and modeling on doped-Li4SiO4 under different temperatures and CO2 partial pressures

The present study investigated the CO2 sorption mechanism on lithium orthosilicate (Li4SiO4) doped with potassium carbonate (K2CO3) in form of powders and macroporous pellets. The CO2 sorption performance was studied under different temperatures (540–580 °C) and CO2 partial pressures (0.04–0.50 atm). The results showed that the addition of K2CO3 improved the CO2 uptake rate and capacity, mainly at low-moderate CO2 partial pressures, owing to an increase of diffusion rate through the product layer. Moreover, a modified shrinking core model was developed to explain the mechanisms that occur during the sorption introducing a CO2 diffusion coefficient through the product layer depending on the Li4SiO4 conversion. The results showed an excellent fitting of the modified shrinking core model to the experimental data obtained in the tested sorption temperature and CO2 partial pressure range, both for the sorbent in powder and pellet form. Thus, the proposed model could be employed to well simulate the CO2 sorption kinetic behavior on K2CO3 doped Li4SiO4-based sorbents.

Experimental Determination of Co2 Mineralization Depth of Slag Minerals at Co2 Concentrations Available in Iron and Steelmaking Flue Gases

We report the diffusion coefficient relevant to CO2 mineralization using minerals commonly encountered in ironmaking and steelmaking slag. Diffusion coefficients were gained from CO2 mineralization achieved under passive conditions consistent with processes that are likely to maintain net CO2 emission reduction. In other words, no chemical, thermal, or mechanical enhancement was applied. Tests were performed at 30 ˚C with molar CO2 concentrations of 5%, and 20%. We applied the diffusion coefficients using the shrinking core model with a modification to account for the full particle size distribution of a sample and the fractal surface roughness. Results indicate that CO2 mineralization efficacy is highly variable among minerals common to slag; thus, the slow kinetics and low conversion common to slag-based CO2 mineralization is likely due in part to blockage of reactive species by unreactive species. Further, the modified shrinking core model matches early phase CO2 mineralization rates where the traditional models fail. Analysis of slag-based CO2 mineralization methods should thus account for the specific mineralogy, particle size distribution, and micromorphology of tested slag.

Selective Removal of Sodium from Low-Rank Xinjiang Coal upon Multistage Countercurrent Water Washing: Experimental Investigation and Kinetics Modeling

Prior washing of coal is an essential step for the minimization of ash-related slagging and fouling inside a coal-fired boiler. With regard to the coal washing process, the recyclability of the washing reagent, usually water, is critical from both cost-effective and efficiency perspectives. This paper addresses the washing kinetics of water-soluble Na+ from two different low-rank Xinjiang coals using both fresh and used/recycled water to alleviate the ash-related fouling in low-rank coal-fired boilers. Apart from once-through fresh water washing, washing using recycled water via both multicycle single-stage and three-stage countercurrent processes was studied in detail to investigate the recyclability of water. Additionally, a modified shrinking core model (SCM) was developed to reveal the Na+ removal mechanism under all washing conditions. Our experimental results showed that the Na+ removal extent decreased with the recycling of used water due to an increase in the Na+ concentration in the recycled water and/or a decrease in the Na+ content in the washed coal. The saturation point of Na+ in the used water, beyond which the water can no longer remove Na+, is far below the solubility of NaCl in water. The modeling approach further confirmed that the overall rate for the removal of water-soluble Na+ is dominated by the intraparticle diffusion within the coal matrix. The effective diffusion coefficient of Na+ was within the range of 0.28 × 10–6 to 3.75 × 10–6 cm2/s, which agrees with reported values in the literature. Additionally, a novel iterative calculation method integrating the modified SCM into the three-stage countercurrent washing process has been proposed to predict the Na+ removal at each stage for each cycle. The results show that the water can be recycled a maximum of 15 times in the three-stage countercurrent process.

Digesting high-aluminum coal fly ash with concentrated sulfuric acid at high temperatures

The decomposition of coal fly ash (CFA) digested with concentrated H2SO4 at a high temperature has been proven to be an efficient way to leach aluminum in view of extracting useful metals from solid wastes. In this research the reaction between the CFA collected from Jungar in Inner Mongolia, China, and concentrated H2SO4 was studied to get a high level of leaching efficiency, which is industrially applicable to extract aluminum. The microstructures, mineralogical transformation and mass transfer were investigated by means of X-ray diffraction, chemical composition analyses, polarization microscopy, electron probe micro-analysis, scanning electron microscopy, and transmission electron microscope observation. The surface of CFA spheres consisting mainly of crystalline phases, e.g., mullite, corundum, was found to be digested by concentrated H2SO4 much easier than the vitreous phases. Most of the CFA spheres can be disrupted at high temperatures (T > 230 °C). The mineralogical transformation in this art follows a route as mullite, corundum + H2SO4 → millosevichite (Al2(SO4)3) → leached metal ions + residues rich in SiO2. Base on the EPMA analyses the element of chromium that was distributed as substitutions in mullite or corundum was found to be enriched in form of chromium oxide. The maximum leaching efficiency of aluminum reaches 86.0% under the optimized conditions as T = 300 °C, t = 110 min, and molar ratio of H2SO4:CFA = 1.2. A modified shrinking core model was used to describe the diffusion controlled kinetics, and the apparent rate constant (kd) were found to be 1.18–1.89 × 10−3 min−1 at the temperature of 230–300 K. The activation energy of the internal diffusion-controlled reaction in the digesting reaction was evaluated to be 19.23 kJ mol−1.

Effect of the CaO sintering on the calcination rate of CaCO3 under atmospheres containing CO2

For the calcination of CaCO3 under CO2‐containing atmospheres, a mathematical model taking into account the CO2‐catalyzed sintering of the CaO product layer is developed. In this model, a modified shrinking core model is coupled with a population balance‐based sintering model. By comparing model predictions with experimental data, it is found that CO2 strongly affects the overall calcination rate both at high temperature and CO2 partial pressure, since under these conditions CaO densification considerably reduces the effective diffusivity of CO2 within product layer. It is observed that for large particles, the CO2‐catalyzed sintering of CaO can produce the “die off” phenomenon, which takes place when the reaction stops due to the blockage of pores within product layer. Finally, it was determined that limestone impurities do not significantly affect the calcination reaction under atmospheres containing CO2, because CO2 causes a much greater increase of the CaO sintering rate than limestone impurities do. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3638–3648, 2018

Protein a resin lifetime study: Evaluation of protein a resin performance with a model-based approach in continuous capture

ABSTRACTA modified shrinking core model (MSCM) has been used to describe the mechanism for the degradation of Protein A resin particles taking place under continuous chromatographic operation. The model is based on the hypothetical shrinkage of the boundary layer of the resin particles, which house the active Protein A ligands within their pores. The caustic during the sanitization phase of chromatography has been determined to cause the Protein A ligand degradation. Protein A resins provided by manufacturers possess unique caustic stability, which has been used in MSCM to appraise the ligand degradation. The kinetic model utilized semiempirical parameters including diffusion constant, rate constant, stoichiometric factor, and reaction order. The parameters were estimated from column breakthrough experiments to simulate continuous Protein A chromatography for three distinct resins. The reaction order has been identified as the key parameter for predicting the degradation kinetics. The recorded reaction orders vary for three different resins with the resin B showing the highest reaction order of 4 and lowest being 1.65 for the resin C. The model can predict the effects of caustic on resin performance and displayed that minimal degradation of the resins A and B occurred, when exposed to 0.1 N and 0.2N NaOH, retaining up to 96% binding capacity after 240 cycles. The adsorption study conducted for the resin B demonstrated the dynamic physical and chemical changes transpiring through the life cycle of the resin, further supported the degradation model. The performance data demonstrate that the resin B exhibits the desirable performance, with higher reaction order indicating slower resin degradation, higher binding capacities, and increased sustenance of this binding capacity for extended duration. The degradation model can be extended to build effective cleaning strategies for continuous downstream processing.

The optimization of Cu and Fe bioleaching from converter slag using Acidithiobacilus ferrooxidans

The main objective of this work was to assess the optimization of Fe and Cu bioleaching from converter slag using Acidithiobacillus ferrooxidans. Important parameters that contribute to the bioleaching process include initial pH, initial Fe2+ concentration and pulp density. In order to optimize these parameters, the response surface methodology (RSM) was applied. The maximum simultaneous Fe and Cu recovery yields were 95% and 100%, respectively. The optimum conditions were initial pH 1.8, initial density 1.4 g/100 mL and initial Fe2+ 7.3 g/L. The comparison between chemical leaching and bioleaching results showed that bioleaching improved the recovery yields of Fe and Cu by 26% and 33%, respectively. The modified shrinking core model was used to determine the rate-limiting step of the process. It was found that diffusion through the product layer and chemical reaction are the rate controlling steps.

Adaptation of Modified Shrinking Core Model for the Description of Salicylic Acid Adsorption on Olive Stones Activated Carbons

This work aimed to apply a modified shrinking core model (SCM) for describing the kinetic adsorption process of a solute in a microporous activated carbon in an agitated finite batch aqueous system. To apply the SCM, the diffusion-adsorption process in the pore of the adsorbent is transposed to a diagram of diffusion-reaction according to a mobile front. Indeed, solid adsorbent particle is assumed formed by two layers. The first layer is an inner core, not yet reached by the adsorbate, and the second layer is an outer shell, where diffusion and binding to particle sites are occurring. In this study, two mass transfer resistances are considered; the external liquid film resistance and intraparticle resistance. The developed modified SCM, applied to experimental data for the adsorption of salicylic acid onto olive stone activated carbons and a commercial one, give a more realistic prediction and shows a good accuracy in describing batch adsorption in mixed suspension. The kinetic parameters: the effective diffusivity and the mass transfer coefficient were determined. Using the estimated parameters, a parametric study was carried out to observe the effects of the particle size of adsorbent, the initial adsorbate concentration and the stirring velocity on the system kinetics.