Modified Shrinking Core Model Research Articles

Kinetic analysis of the interactions between calcium ferrite and coal char for chemical looping gasification applications: Identifying reduction routes and modes of oxygen transfer

Chemical Looping Gasification (CLG) is an emerging technology that shows promise for efficient coal gasification by eliminating the need for energy intensive gas separations to achieve a non-nitrogen diluted syngas stream. Oxygen from oxygen carriers, such as CaFe2O4, are used for coal gasification in place of conventionally produced gaseous oxygen from cryogenic separation of air. These oxygen carriers are unique for their ability to selectively oxidize coal to form syngas and show limited reactivity with syngas components (H2, CO). This study was carried out to determine the kinetic model representation and parameters associated with the selective oxidation of coal derived char (Wyodak and Illinois #6) with a metal ferrite (CaFe2O4) of which are needed for advancement of the process concept. Using thermogravimetric analysis (TGA) coupled with mass spectrometry, the selective oxygen release from metal ferrite in the presence of char by proximal contact was examined. The application of model fitting approaches was used to describe controlling resistances during oxygen release. A combination of the modified shrinking core model (SCM) with planar oxygen ion diffusion control and reaction order based models were applied for kinetic parameter determination. CaFe2O4 particle size plays a major role in the prevailing mode of oxygen release. Particle sizes on the range of 40–50µm tend to favor first order kinetically controlled regimes independent of geometric and diffusion controls. The probability for oxygen ion diffusion controlling regimes increased when the particle size range of the oxygen carrier was increased up to 350µm. Char type also impacted the prevalence of the controlling regime. Higher ranked chars react in a slower manner, limiting the gradient for oxygen ion release from the oxygen carrier. Activation energies determined for this process range from 120 to 200kJ/mol and oxygen ion diffusion coefficients are on the order of 10−8cm2/s. It is suggested that oxygen ion movement is regulated by lattice diffusion out of partially reduced phases (Ca2Fe2O5) and through reduced outer layers composed of CaO and Fe. The controlled movement of oxygen ions influences the rate of carbon oxidation in the char and therefore the selectivity towards partial oxidation products, which are desirable in CLG applications.

A Modified Shrinking Core Model for Leaching of Aluminum from Sludge Solid Waste of Drinking Water Treatment

A Modified Shrinking Core Model for Leaching of Aluminum from Sludge Solid Waste of Drinking Water Treatment

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.

Preparation and kinetics of a heterogeneous sorbent for CO2 capture from the atmosphere

Capturing CO2 directly from the atmosphere using chemicals (air capture) is a strategic approach to mitigate global warming. Before the widespread deployment of air capture, technical challenges, such as the poor kinetics under ultra-low CO2 concentrations, must be addressed. This work aims to characterize and optimize the mass transfer process of a novel moisture swing adsorption method for air capture. The phase inversion technique is employed to fabricate a heterogeneous structured sorbent. The modified shrinking core model and a revolving bed reactor are developed to evaluate the adsorption kinetics. The sorbents exhibit significant diffusion-controlled kinetics under most of the measurement conditions. The effects of ambient conditions on kinetics, such as temperature and relative humidity, were investigated. The diffusion and chemical reaction rate drop sharply as the temperature decreases from 20 to 0°C. The relative humidity shows a more obvious effect on the chemical reaction than on the physical diffusion process due to the mechanisms of hydration water involved in the chemical reaction. On the other hand, reducing the size of the sorbent particles to several micrometers could effectively avoid the substantial reduction in the adsorption rate under lower temperatures. Using the determined kinetic parameters, suggestions for kinetics optimization are proposed for air capture under different weather conditions.

Bidisperse Shrinking Core Model for Supercritical Fluid Extraction

AbstractThe broken‐and‐intact‐cell model is conventionally used for interpretation of overall extraction curves (OECs) observed in supercritical fluid extraction (SFE) of ground oilseeds. Another possibility, considered here, assumes that the packed beds of the ground material always contain a significant amount of very small particles, i.e., dust, which control the initial extraction rates. The bidisperse representation of particle ensembles allows accurate description of OECs on the basis of the modified shrinking core model. A simple asymptotic solution has been derived for bidisperse granulometric distributions under typical SFE conditions. Special microscopic observations have been performed to reveal and examine the dust fraction in ground seed substrates.

A shrinking core model for seeds oil extraction with particularization to Camelina oil separation

The oil extraction from a spherical particle in an adequate solvent is analyzed by a dynamic model. The oil extraction occurs by moving the unsolubilized solid/solute-free phase interface toward the center of the particle. We assume that the transport of solute molecules has three resistances: (1) the resistance due to oil core dissolving; (2) the resistance due to the solute-free portion of the particle; (3) the resistance due to a surface layer near solid–liquid interface. Generally, the equation governing the dynamic behavior of oil extraction is numerically solved. However, sometimes analytical expressions for the time dynamics of the size of the unsolubilized oil portion can be obtained in some special cases. The present analysis on oil process extraction takes into account the effect of variable bulk solute concentration and of seed internal characteristics such as particle porosity, particle tortuosity and core oil dissolving kinetics. Result consists in a general mathematical model whose particularization is given for the case of Camelina seeds oil extraction. For Camelina seeds the oil hexane extraction has been characterized by particularization of the general modified shrinking core model. It has obtained that the particle dimensionless porosity is set to 0.08, while the constant of kinetic process from the shrinking core surface is strongly dependent on core position and on the temperature after relation kd=kd0(t)(rc/R)n with n=4 and kd0(t) in the range 4.3–8.3 10−8m/s.

A modified shrinking core model for the reaction between acid and hetero-granular rough mineral particles

The liquid–solid heterogeneous non-catalytic reaction between acid and minerals is the foremost principle of matrix acidizing. Previous mathematical models failed to describe the acid etching issue of rock particle clusters with the property of fractal surface in a three-dimensional space. We apply fractal geometry principles to characterize the area and volume of the rough rock particles on the basis of a mathematical model of a single particle. Based on chemical reaction kinetics and mass transfer theory, we present a modified shrinking core model for the acid–rock reaction of a mineral particle cluster that is undergoing a surface reaction. Using logarithmic normal distribution functions to describe the grain distribution of rocks, we describe the variations of the extent of leaching under surface reaction control. Our analysis indicates that clusters with larger fractal dimensions, smaller mean sizes and less disperse particles will be less dissolved when most of the other factors are kept constant.

Dissolution characteristics of calcium‐based alkaline industrial derived wastes

Accurately evaluating the rate at which calcium‐based alkaline industrial derived wastes (CAIDW) dissolve is very important in the design and development of CAIDW‐type wet flue gas desulfurization plants. The dissolution characteristics of alkaline slag (AS) and salt mud (SM) have been studied using pH stat method, and the effects of various parameters such as reaction temperature, sorbent particle size and solution acidity are studied to determine the dissolution kinetics of AS and SM. The production process of CAIDW presents high influence on its dissolution performance in acidic conditions. The kinetics analysis based on the modified shrinking core model (MSCM) indicates that AS dissolution kinetics, which is accompanied by surface reaction control, follows the film diffusion, and the activation energies of the two steps are 4.62 ± 0.8 and 36.34 ± 3.1 kJ/mol, respectively. Meanwhile, the SM dissolution obeys the surface reaction model with the activation energy of 9.69 ± 1.9 kJ/mol.

Targeted kinetic strategy for improving the thermal conductivity of epoxy composite containing percolating multi-layer graphene oxide chains

By adding 2 wt% multi-layer graphene oxide (MGO) to an epoxy resin, the thermal conductivity of the compos- ite reached a maximum, 2.03 times that of the epoxy. The presence of 2 wt%MGO percolating chains leads to an unprece- dentedly sharp rise in energy barrier at final curing stage, but an increased epoxy curing degree (!IR) is observed; however, this !IR difference nearly disappears after aging or thermal annealing. These results suggest that the steep concentration gra- dient of -OH, originated from the 2 wt%MGO percolating chains, exerts the vital driving force on the residual isolated/ trapped epoxy to conquer barrier for epoxy-MGO reaction. A modified Shrinking Core Model customized for the special layered-structure of MGO sheet was proposed to understand the resistance variation during the intercalative epoxy-MGO reaction. It shows that the promoted intercalative crosslinking is highly desirable for further improving the thermal conduc- tivity of the composite, but it meets with increased resistance. Guided by the kinetic studies, targeted optimization on the cure processing strategy was accordingly proposed to promote the intercalative crosslinking, a thermal conductivity, 2.96 times that of the epoxy, was got with only a small amount (30°C) increase of the post-heating temperature.

Platinum and rhenium extraction from a spent refinery catalyst using Bacillus megaterium as a cyanogenic bacterium: Statistical modeling and process optimization

The present study evaluated the potential of Bacillus megaterium as a cyanogenic bacterium to produce cyanide for solubilization of platinum and rhenium from a spent refinery catalyst. Response surface methodology was applied to study the effects and interaction between two main effective parameters including initial glycine concentration and pulp density. Maximum Pt and Re recovery was obtained 15.7% and 98%, respectively, under optimum conditions of 12.8g/l initial glycine concentration and 4% (w/v) pulp density after 7days. Increasing the free cyanide concentration to 3.6mg/l, varying the pH from 6.7 to 9, and increasing the dissolved oxygen from 2 to 5mg/l demonstrated the growth characteristics of B. megaterium during bioleaching process. 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 is the rate controlling step.

Cr and Ni recovery during bioleaching of dewatered metal-plating sludge using Acidithiobacillus ferrooxidans

This study determined the optimal conditions required to attain maximum metal recovery in the bioleaching process of dewatered metal-plating sludge using Acidithiobacillus ferrooxidans (A. ferrooxidans). Adaptation of this strain was carried up to 1% (w/v) of the sample. Three factors including initial pH, initial Fe3+ concentration and pulp density were selected as the effective factors and were optimized using a central composite design of response surface methodology. An initial pH of 1, pulp density of 9g/l and initial Fe3+ concentration of 1g/l were determined to be optimum values by the statistical models. The highest extractions for Cr and Ni under optimal conditions were 55.6% and 58.2%, respectively. Bioleaching kinetics was investigated using a modified shrinking core model to better understand the mechanism of the leaching reaction. The model predictions indicate that the diffusion step controlled the overall dissolution kinetics and is the rate controlling step.

Modified Shrinking Core Model for Atomic Layer Deposition of TiO2on Porous Alumina with Ultrahigh Aspect Ratio

When atomic layer deposition (ALD) is performed on a porous material by using an organometallic precursor, minimum exposure time of the precursor for complete coverage becomes much longer since the ALD is limited by Knudsen diffusion in the pores. In the previous report by Min et al. (Ref. 23), shrinking core model (SCM) was proposed to predict the minimum exposure time of diethylzinc for ZnO ALD on a porous cylindrical alumina monolith. According to the SCM, the minimum exposure time of the precursor is influenced by volumetric density of adsorption sites, effective diffusion coefficient, precursor concentration in gas phase and size of the porous monolith. Here we modify the SCM in order to consider undesirable adsorption of byproduct molecules. <TEX>$TiO_2$</TEX> ALD was performed on the cylindrical alumina monolith by using titanium tetrachloride (<TEX>$TiCl_4$</TEX>) and water. We observed that the byproduct (i.e., HCl) of <TEX>$TiO_2$</TEX> ALD can chemically adsorb on adsorption sites, unlike the behavior of the byproduct (i.e., ethane) of ZnO ALD. Consequently, the minimum exposure time of <TEX>$TiCl_4$</TEX> (~16 min) was significantly much shorter than that (~71 min) of DEZ. The predicted minimum exposure time by the modified SCM well agrees with the observed time. In addition, the modified SCM gives an effective diffusion coefficient of <TEX>$TiCl_4$</TEX> of <TEX>${\sim}1.78{\times}10^{-2}\;cm^2/s$</TEX> in the porous alumina monolith.

Kinetic Analysis of Paper White Mud Dissolution at Constant pH

One of the most important steps in the wet limestone–gypsum flue gas desulfurization (WFGD) process is limestone dissolution, which provides the dissolved alkalinity necessary for SO2 absorption. Accurately evaluating the rate controlling step in sorbent dissolution process is important in the design and efficient operation of WFGD plants. In the present work, the kinetics of paper white mud(PWM) in dissolution process has been studied by using a pH-stat method. The results obtained indicated that PWM dissolution in WFGD conditions obeys the modified shrinking core model. PWM dissolution kinetics follows the film diffusion and surface reaction control and the rate controlling step of PWM is film diffusion control. The activation energies of PWM in film diffusion and surface reaction steps are 11.9±0.7 kJ/mol and 13.7±1.3 kJ/mol, respectively.

Flue Gas Desulphurization at Low Temperatures Using Coal Fly Ash/Ca-Based Sorbent: Determination of Rate Limiting Step

A kinetic model for flue gas desulphurization (FGD) using siliceous sorbent was carried out using various different potential/exponential expressions for the rate equation and structural/volumetric expressions for the solid phase equation. The kinetic parameters of the mathematical model were obtained from a series of desulphurization experimental reactions conducted under isothermal conditions at various operating parameters. MATLAB software was utilized to solve the partial differential equations using the finite difference method. It was found that the rate limiting step is a combination of reaction and ash diffusion, in which the former dominates initially and the latter dominates at the later reaction stage. Pre-exponential factor of rate constant, ko, and activation energy, Ea, have been determined as 0.15 s?1 and 15,052 J/mol?1, respectively. As a result, a modified shrinking core model with reaction control coupled with exponential expression of the rate equation was found to best describe the experimental data with an error of 4.8%.

Effect of Al Antioxidant on the Rate of Oxidation of Carbon in MgO–C Refractory

Kinetics of air oxidation of MgO–C–Al refractory at 600°–1300°C were investigated using the software based on the modified shrinking core model (KDA). Commercial bricks containing 88.5% MgO, 10% residual carbon, and 1.5% aluminum anti‐oxidant were oxidized isothermally with air. Combination of experimental data with model calculations indicated gas diffusion through solid material and pores as a major controlling step. Previously observed chemisorption process was eliminated from the rate‐controlling mechanism with addition of aluminum antioxidant. Comprehensive rate equations were devised for MgO–C–Al and MgO–C oxidation reactions. Overall activation energies of Qid (internal diffusion)=139.15 kJ/mol at T≤800°C and Qpd (pore diffusion)=25.48 kJ/mol at T&gt;800°C were obtained for MgO–C–Al oxidation reactions. Corresponding values were determined to be Qid=134.85 kJ/mol and Qca (chemical adsorption)=66.69 kJ/mol at T≤800°C and Qpd=18.95 kJ/mol and Qca=66.69 kJ/mol at T&gt;800°C for MgO–C oxidation reactions. Addition of aluminum anti‐oxidant indicated a reducing effect on oxidation of MgO–C bricks at 800°C≤T≤1250°C. Reverse behavior was observed at T≤700°C.

Recovery of benzaldehyde from aqueous streams using extractant impregnated resins

The performance of Extractant Impregnated Resin (EIR) technology for extraction of aldehydes from aqueous solutions has been investigated. The extraction capabilities of several different aliphatic and aromatic primary amines towards aldehydes were tested and compared. Aliphatic amines showed high affinity. The most promising extractant, Primene ® JM-T, was immobilized in a porous particle. As a solid support three different macroporous adsorbents were tested, XAD-16, MPP and Stamypor. Their capacities for the removal of aldehydes were compared with the non-impregnated resin and the resin impregnated with the non-reactive solvent. It was shown that the addition of a reactive extractant can increase the adsorption capacity of an otherwise poor adsorbent for several orders of magnitude. The capacity for the removal of aldehydes was increased with the increase of amine loading on the particle. Temperature influence on the sorption of benzaldehyde on fully impregnated MPP was studied. It was shown that with temperature increase, sorption capacity is increased. The stability of EIRs regarding the loss of the extractant due to the leakage in water was also studied. It was shown that immobilization reduces the extractant’s solubility in water. Sorption kinetics was investigated for fully impregnated XAD-16 and MPP. The modified shrinking core model was used to determine the rate controlling step and it was shown that this sorption is most likely controlled by both chemical reaction and diffusion in the particle.

Alkaline Hydrolysis of Waste Poly(Ethylene Terephthalate): A Modified Shrinking Core Model

Hydrolytic decomposition of waste poly(ethylene terephthalate) (PET) is studied in the presence of an aqueous potassium hydroxide solution. A modified shrinking core model with a depleting product layer of waste PET is developed under finite solution volume conditions. An analytical solution is obtained for the model based on average molar distribution coefficient of aqueous potassium hydroxide solution. This model assumes the first order depolymerization kinetics with respect to the concentration of potassium hydroxide solution. The convrsion of the waste PET is determined after filtration of the unreacted PET left after depolymerization. The conversion of PET is also compared with the amount of terephthalic acid obtained after acidification of the filtrate. Infra red (IR) spectroscopy studies of unreacted PET samples at different hydrolysis time intervals are carried out. It is observed that the transmittance at ∼1700 cm−1 decreases gradually with reaction time, which confirms the increased concentration of carbonyl group generated from aryl carboxylic acid group and the major reaction is occurring on the polymer chain end on the solid PET surface. Average molar distribution coefficient of aqueous potassium hydroxide solution, intrinsic PET depolymerization rate constant, frequency factor and activation energy of PET depolymerization are estimated based on the modified shrinking core model.

Chemical recycling of poly(ethylene terephthalate) (PET) by hydrolysis and glycolysis.

In this paper we review an interesting method of PET recycling, i.e. chemical recycling; it is based on the concept of depolymerizing the condensation polymer through solvolytic chain cleavage into low molecular products which can be purified and reused as raw materials for the production of high-quality chemical products. In this work our attention is confined to the hydrolysis (neutral, acid and alkaline) and glycolysis processes of PET chemical recycling; operating conditions and mechanism of each method are reported and described. The neutral hydrolysis has an auto accelerating character; two kinetic models have been proposed: an half-order and a second order kinetic model. The acid hydrolysis could be explained by a modified shrinking core model under chemical reaction control and the alkaline hydrolysis by a first-order model with respect to hydroxide ion concentration. To describe glycolysis, two different kinetic models have been proposed where EG can act or not as internal catalyst. Further experimental and theoretical investigations are required to shed light on the promising processes of PET chemical recycling reviewed in this work.

Kinetics of the dissolution of sand into alkaline solutions: application of a modified shrinking core model

The batch dissolution kinetics of sand particles in concentrated alkaline sodium hydroxide solutions was investigated at high temperature and high pressure. The influence of the particle size, the operating temperature (150–220 °C) and the hydroxide ion molality on the kinetic rate were studied. Experimental data fit well into a developed model based on the shrinking core model approach in which a variable activation energy term was introduced. Kinetic analysis of the experimental results reveals that the associated energy and the rate-controlling mechanism are dependent upon both sample temperature as well as the extent of the reaction.

α-Phenylglycine Extraction with a Trialkylmethylammonium Chloride-Impregnated Macroporous Resin: 2. Kinetics

The sorption rates of α-phenylglycine in sodium hydroxide solutions by Amberlite XAD-4 resin impregnated with trialkylmethylammonium chloride (Tomac), at pH 11 and 12 at 30°C, have been investigated in a batch stirred tank. By using a modified shrinkingcore model that considers reversibility of the sorption process, it was shown that the amino acid sorption was controlled by particle diffusion. A more rigorous diffusion model was also used; both models led to similar diffusion coefficient values. The amino acid uptake was comparatively faster under the initial conditions of higher Tomac concentration in the resin, higher amino acid concentration in the aqueous phase and at pH = 11.