Shrinking Particle Model Research Articles

Modeling of conversion of a single fuel particle in a CFD model for CFB combustion

In CFD simulation of CFB combustion, computation of the local instantaneous conversion rate of a single fuel particle should be fast. Since fuel conversion is limited by mass and heat transfer and the rates of chemical reactions inside the particle, the optimal model would produce the internal conditions as a function of location. As rigorous 1D, 2D and 3D fuel conversion models presented in the literature are often too time-consuming for CFD environment, simplified 0D approaches have been suggested. To reduce the amount of simplification, the present study introduces an alternative approach that converts a rigorous fuel conversion model into correlations that can be implemented in a CFD code. As a demonstration example, a 1D shrinking particle model for coal combustion is converted into a correlation based description. The single particle model is used to produce a data set of net reaction rates averaged over particle volume in a wide range of fluidization, temperature and composition conditions. The data is then used to train neural network models that are fast to compute and easy to implement in a CFD code.

Modeling the influence of potassium content and heating rate on biomass pyrolysis

This study presents a combined kinetic and particle model that describes the effect of potassium and heating rate during the fast pyrolysis of woody and herbaceous biomass. The model calculates the mass loss rate, over a wide range of operating conditions relevant to suspension firing. The shrinking particle model considers internal and external heat transfer limitations and incorporates catalytic effects of potassium on the product yields. Modeling parameters were tuned with experimentally determined char yields at high heating rates (>200Ks−1) using a wire mesh reactor, a single particle burner, and a drop tube reactor. The experimental data demonstrated that heating rate and potassium content have significant effects on the char yield. The importance of shrinkage on the devolatilization time becomes greater with increasing particle size, but showed little influence on the char yields.

Study of chalcopyrite leaching from a copper concentrate with hydrogen peroxide in aqueous ethylene glycol media

The use of polar aqueous solvents, such as acetone, methanol and ethylene glycol, together with hydrogen peroxide and sulfuric acid solutions, have been shown to increase chalcopyrite dissolution. However, the reason for this improvement is not clear, especially in the case of ethylene glycol. The objective of the present study is to investigate the nature of chalcopyrite leaching, with and without the presence of ethylene glycol (EG), and to understand the role of this polar solvent in the modification of the characteristic behavior involved. For this purpose, a relatively pure chalcopyrite concentrate was leached at 20°C and atmospheric pressure (79kPa, México City) with hydrogen peroxide in aqueous sulfuric acid solutions, with and without EG. The results showed that, in the absence of EG, the decomposition of 99% of the initial hydrogen peroxide in 24h, was catalyzed by the Fe2+, Fe3+ and Cu2+ ions (Fenton reagents) present as a consequence of the leach itself. Furthermore, after the first six hours, the copper and iron dissolution effectively ceased (44 and 37%, respectively). In contrast, in the presence of EG, the H2O2 consumption was minimal (~16%) in the same time period and mostly due to the oxidation reactions. The final extractions for copper and iron were 90 and 71%, with an ascendant tendency. It was suggested that hydroxyradicals, product of the Fenton-type reactions, are the driving force for peroxide decomposition and, these were shown to be absent in solutions containing ethylene glycol.Chalcopyrite dissolution kinetics in the presence of ethylene glycol, are well described by the reaction-controlled shrinking particle model. The kinetic expression is a first order function of the hydrogen peroxide concentration and is not dependent on the H+ concentration, although peroxide decomposition slightly increased at higher pH values. The reaction controlling the dissolution process was determined to be the conversion of the chalcopyritic sulfide to elemental sulfur; this was followed by its oxidation to sulfate, although apparently did not affect the leaching kinetics.

Kinetic study of the dissolution of metallic nickel in sulphuric acid solutions in the presence of different oxidants

AbstractThe dissolution of metallic nickel particles in sulphuric acid solutions has been studied in this work. The effect of temperature, sulphuric acid concentration, and oxidant type has been assessed. In the presence of hydrogen peroxide or dissolved oxygen the dissolution of nickel was fast.A shrinking particle model was used to fit the experimental data and estimate kinetic parameters. The apparent reaction rate constants calculated at 55 °C when dissolved oxygen, ferric sulphate, and hydrogen peroxide were used as oxidants were, respectively, 0.17, 0.02, and 7.13 ms−1. The dissolution of Ni in the presence of ferric sulphate occurred under surface chemical control, with an activation energy of 82.3 kJ/mol, while in the presence of hydrogen peroxide and dissolved oxygen the reaction seemed to have been mass transfer controlled. The dissolution of Ni in ferric sulphate solutions was also pH sensitive, possibly due to the formation of NiFe2O4 or NiO that was prevented when sulphuric acid concentration was 1 mol/L. The dissolution rate in ferric sulphate‐free solutions was affected negatively by temperature due to a decrease in O2 solubility.

Effect of oxygen concentration and reaction order on char inventory in fluidized bed combustion

Population balance modeling is applied to develop calculation methods for mass inventory of char in fluidized bed combustion (FBC). The focus is on the effect of gas oxygen concentration and the reaction order of char with respect to oxygen, which is important in understanding and simulating combustion in high oxygen concentration. The well-known shrinking particle model describing the single particle combustion is simplified by applying a dimensionless particle size and dimensionless time with a specifically chosen characteristic reference diameter and time constant. Methods and analytical solutions to calculate particle size distribution (PSD), particle combustion time and char mass in FBC are presented.

Model for attrition-enhanced char combustion in fluidized beds

Attrition in fluidized beds can be important due to particle collisions removing fines from the surface of a large char particle. A model for the attrition enhanced combustion of a char particle is presented. When oxygen penetrates the surface of a particle and reacts with the solid, the surface layer becomes more fragile. Fine particles are generated due to percolation and attrition contributing to the mass loss from the mother particle in addition to burning. A shrinking particle model including the effects of attrition and gasification has been developed. The oxidation is assumed to take place at the particle external surface in the classical shrinking particle model i.e. in a layer with zero thickness. The basis for the shrinking particle model is explained by studying the diffusion and reaction processes taking place in a narrow layer on the particle surface in more detail. The Arrhenius-type chemical reaction kinetics parameters (pre-exponential coefficient, activation energy, reaction order) are not purely of chemical nature but they are apparent in the classical shrinking particle model. A more realistic model, where oxidation takes place in a thin layer instead of taking place at the surface and gasification takes place in the core region, is discussed. The model predicts the thickness of this layer and oxygen concentration and char conversion (or density) profiles in this layer. The classical shrinking particle model is, however, applicable with modifications. Pore diffusivity, intrinsic reaction rate and attrition all contribute to the apparent parameters for kinetics calculated with respect to outer surface.

In situ experimental study on the combustion characteristics of captured chars on the molten slag surface

Captured char particles on the molten slag continue to burn or transform into residual carbon in a slagging combustor or furnace, which affect the complete carbon conversion. This study applied a high temperature stage microscope to investigate the combustion behavior of captured chars on the molten slag surface. The combustion process of captured chars with air on the slag surface was observed and recorded, compared to the original char combustion. Particle size evolution calculated from the measured cross section area versus time indicated that the burnout time of chars was prolonged on the molten slag surface. Besides the heat transfer analysis also showed that the temperatures of char particles on the molten slag were decreased due to the thermal conduction between char and slag. Molten slag layer reduced the char reactivity from the analysis of combustibility index, indicating the captured char combustion on the molten slag surface was hindered. Coupled with heat transfer analysis, shrinking particle model (SPM) was applied and modified to predict the combustion time at carbon conversion of 0.9, and results showed an agreement with the experimental data.

Dynamic Model of a Slagging Entrained-Flow Gasifier Including Models of Slag Transport, Deposition, and Slag Layer

Molten slag flows along the wall of slagging entrained-flow gasifiers. A lower operating temperature of these gasifiers can result in slag buildup that may eventually lead to shut down. Thus, the thickness of the slag layer is an important operating variable. However, it is difficult to monitor the thickness of the slag layer due to the extremely harsh environment inside these gasifiers. To investigate the impact of various operating conditions on the slag layer thickness, a dynamic model has been developed by including models of slag deposition, transport, and a flowing slag layer in a previously developed hybrid shrinking-core, shrinking-particle model of a gasifier. The enhanced model is used to study the effect of particle size distribution, switch in coal type, change in ash composition, and various operating conditions on the slag layer thickness. The model is used to identify important variables that significantly affect the slag layer thickness. The study shows that optimal operating conditions sh...

A char combustion sub-model for CFD-predictions of fluidized bed combustion - experiments and mathematical modeling

The Grain-Thermo-Balance (GTB) rig was built for generation of the char, at high heating rates, and for experimental determination of its oxidation rates. A zero-dimensional mathematical model for calculating oxidation rates of millimeter-size char particles was developed to serve as a char particle sub-model in a CFD-based software for predicting performance of fluidized bed boilers. When morphology of the char was determined using mercury porosimetry and the char oxidation rates in the kinetic regime were measured using TGA, the zero-dimensional Shrinking Particle Model was able to reproduce the GTB measurements well - with exception of the last 2% burnout where due to a model singularity the calculated temperatures exceeded the measured values. When the char was generated in TGA, at low heating rates, its intrinsic reactivity was four times lower and the reactivity decrease was attributed to alterations to the char morphology (40% slow-down) and annealing (60%).

Kinetic Modeling of High-Pressure Pyrite Oxidation with Parameter Estimation and Reliability Analysis Using the Markov Chain Monte Carlo Method

The aim of this work was to develop a comprehensive kinetic model for aqueous-phase oxidation of pyrite that can explain all the relevant phenomena that govern pyrite oxidation, including the effects of temperature, oxygen partial pressure, particle size, and multiple surface and bulk phase reactions at different slurry concentrations. The developed model is based on experimental data presented in the literature. For the current case the reaction process formulation of the shrinking particle model in the usual integrated form is challenging, and the model is therefore given as differential equations that are solved numerically. A surface passivation model was implemented to explain experimentally observed surface passivation. The kinetic model includes multiple experimental parameters, which were estimated by comparison with experimental data. The reliability of the estimated parameters and model predictions was studied using novel Markov chain Monte Carlo (MCMC) methods. The MCMC analysis indicated that ...

Kinetics of the pressure leaching of enargite in FeSO4–H2SO4–O2 media

The pressure leaching of enargite in FeSO4–H2SO4–O2 media was studied with the aim to determine the role of the ferrous ions on the rate of arsenic dissolution in the temperature range of 140–200°C. Thus, the effect of ferrous sulfate addition into the leaching of enargite was determined under partial pressure of oxygen in the range of 207–1379kPa. The results showed that the addition of ferrous ions greatly enhanced the leaching rate of enargite, which confirmed that the ferric ion generated in the solution is the major oxidant of enargite while the role of the oxygen in this system was essentially to regenerate the ferric ion. It was also determined that the cupric ions from the enargite dissolution catalyzed the oxidation of ferrous ions to ferric. The kinetics data of the enargite dissolution in this system was analyzed by using the shrinking particle model for monosized particles considering a surface chemical reaction control. The apparent activation energy determined with this model was 111.8kJ/mol for the temperature range 140 to 200°C.

Development of a hybrid shrinking‐core shrinking‐particle model for entrained‐flow gasifiers

Slagging entrained‐flow gasifiers operate above the melting temperature of the ash. As slag is highly nonwetting on the surface of char (carbon) particles, it is likely that it will agglomerate into one or several slag droplets and some of these droplets can detach from the char particles. If the slag exists in the form of droplets on the char surface rather than as a solid shell around the unreacted char particle, a shrinking particle model would be more physically realistic representation in comparison to the widely used shrinking core model (SCM). In the early section of the gasifier, the temperature remains below the ash melting temperature and, therefore, the SCM is more appropriate in this region. With this motivation, a novel hybrid shrinking‐core shrinking‐particle model has been developed. The model provides spatial profile of a number of important variables that are not available from the traditional SCM. © 2015 American Institute of Chemical Engineers AIChE J, 62: 659–669, 2016

Sulfuric acid leaching kinetics of South African chromite

The sulfuric acid leaching kinetics of South African chromite was investigated. The negative influence of a solid product layer constituted of a silicon-rich phase and chromium-rich sulfate was eliminated by crushing the chromite and by selecting proper leaching conditions. The dimensionless change in specific surface area and the conversion rate of the chromite were observed to exhibit a proportional relationship. A modified shrinking particle model was developed to account for the change in reactive surface area, and the model was fitted to experimental data. The resulting model was observed to describe experimental findings very well. Kinetics analysis revealed that the leaching process is controlled by a chemical reaction under the employed experimental conditions and the activation energy of the reaction is 48 kJ·mol−1.

Diversity of chemical composition and combustion reactivity of various biomass fuels

A simple and fast method for measuring simultaneously the chemical compositions and combustion reactivities of biomasses and evaluating their heterogeneity was developed using a commercial thermogravimetric analyzer. Wood, straw, and bark pellets were selected as the biomass fuels. Compared to the variations observed for volatiles and char contents, the variations of moisture and ash contents for the three types of biomass were large in an individual pellet. The straw char was more reactive than the bark char and wood char, probably due to the high ash content of the straw, which is especially rich in potassium. Furthermore, the variations of the characteristic temperatures and kinetics in an individual pellet increased from the wood char to bark char to straw char. The experimental results for char combustion can be described by the two simple reaction models: the volumetric model and the shrinking particle model. For each type of biomass, the differences in predictions between the two reaction models were much smaller than the differences in the accuracy of the measured kinetics for the different particles. For the kinetic parameters, the activation energy E and the natural logarithm of apparent pre-exponential factor A∗ (lnA∗) showed a linear correlation in the two applied models (A∗=e(0.2140E-8.713)), while the measured activation energies of the two applied reaction models were also linear (Eshrinkingparticle=0.8136Evolumetric). The performed analyses revealed that 10 biomass samples could ably characterize the conversion of a batch of biomass char particles and the average kinetics of the reactions. In addition, the distribution of conversion rates of the different chars in a batch at a specific time or temperature could be estimated from the standard deviation of the average value for the kinetics.

Ferric sulphate leaching of metals from waste printed circuit boards

Leaching of copper and other metals (i.e., Ni, Ag and Pd) from waste printed circuit boards (WPCBs) in acidic ferric sulphate solutions was studied. The effects of concentration of H2SO4 (0.05–1M), Fe(III) (0.05–0.5M) and temperature (20–80°C) on the extent and kinetics of extraction of metals were investigated using response surface methodology. Under the suitable conditions, high extractions of copper (i.e., ≥98%) were readily achieved over a leaching period of 120min. The kinetic data derived from the shrinking particle model for copper were used as the response for the analysis of data. All the leaching parameters were statistically significant within an order of temperature>[Fe(III)]>[H2SO4] and increasing their levels had positive influence on the leaching kinetics. The activation energy for extraction of copper was found to be 18.3kJ/mol. In addition to copper, nickel extractions were also high (i.e., up to 92.5% over 120min) whilst silver and palladium extractions were limited to ≤21.4% and ≤69.4%, respectively. Further tests indicated that increasing the solids ratio from 1% to 15% w/v had a deleterious influence on the leaching of metals apparently due to limited availability and rapid depletion of Fe(III) at high solids ratios. The supply of air/oxygen (2L/min) or H2O2 (585mg/L) for in-situ regeneration of Fe(III) improved the leaching of copper by ≈35% over 180min, with oxygen being the most effective. This indicates the requirement for the continual regeneration of Fe(III) in the leaching medium. The addition of chloride (25.6–116.5g/L Cl−) was found to promote the leaching of metals, particularly silver and palladium with their almost complete extraction (≥99% Ag/Pd) over 120min. These findings suggest that acidic ferric sulphate solutions can be suitably used as a potent lixiviant system for the extraction of metals from WEEE.

Treatment of manufacturing scrap TV boards by nitric acid leaching

The leachability tests for manufacturing scrap TV boards (STVB) have indicated the release of metals beyond the limit levels with potential problems for environmental pollution. Treatment of STVB is therefore requisite for its safe disposal in landfills. The nitric acid leaching of STVB for the removal/recovery of valuable metals (Cu and Ag) was studied by adopting the Box–Behnken design. Statistical analysis of data has revealed that the concentration of nitric acid is the most influential parameter affecting the leaching process. Effects of solids ratio and temperature on the rate and extent of the extraction of copper were also proved to be statistically significant. However, the interaction effects of these parameters were found to be insignificant. The leaching kinetics were consistent with the shrinking particle model under chemical control with an activation energy of 38.6kJ/mol. High concentrations of nitric acid (2–5M HNO3) were required to achieve high copper extractions (88.5–99.9%) at a pulp density of 6% w/v. The extraction of silver was enhanced from 14% to 68% with increasing the concentration of nitric acid from 1 to 5M. These findings also demonstrate that copper may well be selectively extracted from STVB by adjusting the concentration of nitric acid.

Anglesite (PbSO4) leaching in citrate solutions

The thermodynamics and kinetics of anglesite leaching in citrate solutions was studied at room temperature. Solution pH and pulp density were found to have a pronounced effect on lead extraction. Thermodynamic analysis suggested that the lead solubility in citrate is maximized at pH values near 7, which was corroborated through leaching tests. The limited solubility was found to severely hamper the leaching rate at high pulp densities. A shrinking particle model with solubility control was used to describe the results.

Kinetics of the dissolution of ilmenite in oxalic and sulfuric acid solutions

ABSTRACTIn this study, the effects of particle size, type and concentration of acid solution on dissolution kinetics of ilmenite are investigated. The results showed that both oxalic and sulfuric acid and their concentrations had relatively high effects on the dissolution rate of titanium, which increased with an increase in acid concentration. About 86.4% of titanium could be leached in 10 h when using 4 M oxalic acid, 1 : 20 solid/liquid ratio, 90 °C temperature and particle size less than 45 µm. Under similar experimental conditions with the exception of sulfuric acid concentrations of 4, 8 and 12 M, the titanium solubilization was 16.1%, 48.2% and 52.0%, respectively. The experimental data followed reaction kinetics and indicated that the shrinking particle model controlled the chemical reaction. The observed titanium dissolution rates could be expressed as 1 − (1 − x)1/3 = 0.0092C1.2022t for oxalic acid for concentration varying between 1 and 4 M and 1 − (1 − x)1/3 = 0.0006C1.5977t for sulfuric acid for concentration varying between 2 and 12 M, respectively. The fitted models for estimating the titanium dissolution rate from the experimental data indicated good accuracy with coefficient of determination (R2) higher than 0.96. © 2013 Curtin University of Technology and John Wiley & Sons, Ltd.

Material size distribution in concurrent bio-leaching and precipitation: Experimental procedure and modelling

This study presents the approach used to develop a model for a continuous bioleaching system in stirred tank reactors. In bioleaching of metallic sulfides, precipitation concurrently occurs with dissolution of sulfides. Therefore, the model incorporates both the leaching and the precipitation kinetics. It is based on a shrinking particle model for the leaching part and a Mixed Suspension Mixed Product Removal (MSMPR) crystallizer model with germination and growing kinetics for the precipitation part.To establish the model, it was necessary to have access to the size distribution of both sulfide and precipitated particles. A procedure for the bioleached residue characterization was developed in the BRGM laboratory to be able to dissociate sulfide and precipitated particles in the solid phase.The current paper presents the analytical procedure, the mathematical model in detail and its application to a continuous pilot plant test.

Comprehensive analysis of direct aqueous mineral carbonation using dissolution enhancing organic additives

Direct aqueous mineral carbonation using organic anions has been presented by many as a promising strategy for mineral carbonation, on the basis that additives such as oxalate increase the rate and extent of dissolution of magnesium silicates several folds. Through geochemical modelling and detailed solid characterisation, this paper discusses and extends our current understanding of this process. The role of disodium oxalate as a dissolution enhancing agent for olivine is thoroughly examined through experiments in which all phases are carefully analysed. We show that under 20bar of CO2 pressure formation of strong oxalate–magnesium complexes in solution and precipitation of MgC2O4·2H2O (glushinskite) impede any chance of obtaining significant amounts of magnesium carbonate. Other promising ligands from a dissolution perspective, namely citrate and EDTA salts, are also investigated. Contrary to oxalate, these ligands do not form any solid by-products with magnesium, and yet they do not produce better carbonation results, thereby casting strong doubts on the possibility of developing a direct aqueous mineral carbonation process using organic salts. Geochemical modelling permits successful simulation of the dissolution kinetics of magnesium silicate using a shrinking particle model that accounts for the precipitation of glushinskite, amorphous silica and a magnesium phyllosilicate at advanced stages of the dissolution process.