Effective Intraparticle Diffusivity Research Articles

Strontium adsorption characteristics of natural Zeolites for permeable reactive barrier in Fukushima Daiichi nuclear power station

ABSTRACT Laboratory experiments and model estimates were carried out to evaluate the effectiveness of sorbent for construction of the Permeable Reactive Barrier (PRB) at downstream of H4 tank area in Fukushima-Daiichi Nuclear Power Station in September 2014. Measurement of cation exchange capacity and X-ray diffraction analyses of crystal structures were carried out for natural zeolites. The Sr adsorption isotherms were measured for these zeolites contacted with water containing Sr or the simulated groundwater containing Na, K, Ma, Ca, and Sr. According to these equilibrium characteristics, Akita-Futastui zeolite was selected as candidate. The zeolite was served for the column tests to obtain Sr breakthrough curves with different conditions such as particle size of zeolite, Darcy Flux, Sr concentration in the simulated groundwater, and mixed bed with gravel. From the breakthrough curves, kinetic properties such as the film mass transfer coefficient and the effective intraparticle diffusivity were derived by fitting with adsorption model. Based on these kinetic properties, Sr breakthrough curves were estimated for the simulated groundwater containing 0.3 ppm Sr passed at 10 cm∙day-1 through 1.5 m thick PRB with zeolite and gravel. The breakthrough points for the PRB with 33 wt.% zeolite was evaluated as more than 70 years.

Dynamics analysis of anion exchange in layered double hydroxides

The anion exchange kinetics between NO3− and benzoate (BA) in layered double hydroxides (LDHs) have been studied. The experimental conditions were selected to favour a particle diffusion rate-controlling mechanism, subsequently confirmed by the variation of the exchange rate with temperature, resin bead size and stirring speed. Furthermore, the parallel diffusion model is successfully validated in this anion exchange process. Intraparticle effective diffusivities (Deff) of BA in these NO3-LDHs macroparticles were determined from the homogeneous Fickian diffusion model at various temperatures. Crystallites diffusion is the rate-controlling step, in which the anion exchange in the interlayer is much slower than the anion diffusion in the pores between the crystallites.

Influence of selected amides and adsorbent particle size on the adsorption of p-nitrophenol on granulated activated carbon

ABSTRACT In this paper, the influence of selected amides on the adsorption of p-nitrophenol was investigated. Commercial granulated activated carbon DARCO was used as an adsorbent. Granulations of 20–40 and 12–20 mps were used in the experiments. The presence of N-benzylbenzamide and N-methylbenzamide in the system lowered the adsorption capacity of p-nitrophenol, while N-methylpropionamide did not show influence on the adsorption capacity. The equilibrium adsorption capacities for p-nitrophenol were 46.8 mg g−1 for the smaller granulation (20–40 mps), and 45.4 mg g−1 for the larger granulation (12–20 mps). The presence of the amide in the system reduced the adsorption capacity of p-nitrophenol to as much as 6.7 mg g−1. Weber-Morris model showed two distinct phases in the adsorption process, and they were attributed to the external (film) and intraparticle diffusion. For the estimation of the adsorption mechanism external mass transfer coefficient and effective intraparticle diffusivity coefficient were obtained. Obtained Biot number values are in the range of 0.17–0.50 for the smaller granulation, and 0.03–0.29 for the larger granulation. The external diffusion is the rate-limiting step, however, both steps in the diffusion process should be considered for describing the mechanism of adsorption. Freundlich and Dubinin-Radushkevich adsorption isotherms were used for the equilibrium investigation. Freundlich adsorption isotherm showed to be better suited for describing experimental results.

Ultrafast sequestration of cadmium and lead from water by manganese oxide supported on a macro-mesoporous biochar

Porous carrier supported metal oxide composites possess significant potential for sequestration of heavy metals from various waters. However, slow diffusion of targeted metal ions within the micropores of the porous carriers is a key technical barrier limiting practical application of these hybrid adsorbents, particularly in high flow systems. In this study, we first synthesized a biochar with enlarged pore channel (namely K-BC) by adding KHCO3 during the biochar pyrolysis process and then employed the K-BC as a supporter to fabricate a new manganese oxide-based composite (namely HMO-K-BC). It is striking that the effective intra-particle diffusion coefficient D of Pb(II) inside the K-BC is comparable to that in aqueous solution (1.5 × 10−6 v.s. 2.1 × 10−6 cm2 s−1). Although the D value of Pb(II) inside the HMO-K-BC was reduced to 1.8 × 10−7 cm2 s−1, it is still 1–2 orders of magnitude higher than that of conventional adsorbents such as activated carbon, ion exchanger and biochar. As a result, the HMO-K-BC can rapidly sequestrate Pb(II) and Cd(II) within 7.5 min. The HMO-K-BC can also selectively remove Pb(II) and Cd(II) in the presence of high level Ca(II) and humic acid. Column tests further showed that HMO-K-BC was able to effectively treat simulated and real Pb(II)- and Cd(II)-polluted wastewater in a high-flow system with superficial liquid velocity of 0.53 m h−1 (20 BV h−1). All the results manifest that expanding pores of biochar is a promising measure for promoting the practical application of biochar supported composites in wastewater treatment.

Multi-scale simulation of reaction, transport and deactivation in a SBA-16 supported catalyst for the conversion of ethanol to butadiene

Abstract Effective design of heterogeneous catalytic systems requires careful coordination of physiochemical phenomena that span orders or magnitude in length and time scales. Multiscale modelling and simulation tools can provide useful insight for understanding and improving the performance of such systems. Mesoporous silica catalyst support materials present a versatile platform wherein support attributes may be tuned to control transport phenomena throughout the system. In this study we develop an integrated multiscale modelling approach for the conversion of ethanol to butadiene over a SBA-16 mesoporous silica supported catalyst. We use molecular dynamics simulations to calculate domain specific diffusivities of reactants and products in the various domains of SBA-16′s nanostructure. This is used to calculate a resultant effective diffusivity ( D e f f intra ) through its microstructure using finite element method (FEM) models of the tessellated unit cell. The resultant intraparticle effective diffusivity enables the development of a reduced-order reactor level FEM model that is able to implicitly account for the SBA-16′s transport effects without the explicit consideration of its detailed geometry. Experimental bench-scale conversion data for the ethanol to butadiene process over SBA-16 is used to extract intrinsic kinetic rate constants for a simplified reaction mechanism using this reduced order bench-scale reactor FEM model. The model is able to reproduce experimental trends in conversion and activity lifetimes. The impact of varying key support attributes such as pore-size and particle size on catalytic activity lifetimes is then explored. We demonstrate the utility of this multi-scale modelling strategy in guiding catalyst design for the development of rational strategies to improve the performance of heterogeneous supported catalytic systems.

DYNAMIC ADSORPTION OF H2S IN A FIXED BED OF SEWAGE SLUDGE PYROLYSIS CHAR

In this work, sewage sludge char was tested as a H2S adsorbent in a fixed-bed column, at 25 °C. The char was activated physically and chemically (with HCl or KOH) to enhance textural properties. Commercial activated carbon impregnated with iron was also tested for comparison. The column was filled with 18.24 g of char and, then, fed H2S (600 ppm) under 50 mL/min. The effluent gas composition was measured via photocolorimetry and the data was used to plot breakthrough curves. A mathematical modeling was used to estimate parameters such as axial diffusivity, effective intraparticle diffusivity, and external mass transfer coefficient. The main results show that the adsorption capacities varied from 7.2 to 657.60 mgH2S/gads. The percentages of H2S adsorbed varied from 43.36 to 59.04%. HCl proved to be more efficient than KOH. Due to improved textural properties, the commercial activated carbon outperformed (69.15%, 12,527.80 mgH2S/gads) all char samples.

Transport properties and size exclusion effects in wide-pore superficially porous particles

The effects of hydrodynamic radius on the transport of solute molecules in packed beds of wide-pore superficially porous particles (SPP) are studied using pore-scale simulation. The free molecular diffusion rate varies with radius through the Stokes-Einstein relation. Lattice Boltzmann and Langevin methods are used to model fluid motion and the transport of an ensemble of solute molecules in the fluid, providing statistics on solute concentration, flux, molecule age and residence time, as a function of depth in the SPP. Intraparticle effective diffusion and bed dispersion coefficients are calculated and correlated with the hydrodynamic radius and accessible porosity.The relative importance of convection and diffusion are found to depend on the molecule (tracer) size through the diffusion rate, and convection effects are more significant for larger, slower-diffusing molecules. When larger molecules are utilized, the intraparticle concentration is reduced in proportion to the local particle porosity, leading to a natural definition of the accessible porosity used in size exclusion chromatography (SEC). Although the pore shape is complex, the SEC constant K can be calculated directly from simulation. Simulation demonstrates that the effective diffusion coefficient is elevated near the particle hull, which is largely open to interstitial flow, and decreases with depth into the particle. All molecules studied here have transport access to the entire particle depth, although the accessible volume at a given depth depends on their size. The first passage time into the particle is well predicted by the diffusion rate, but residence time is influenced by convection, shortening the average visit duration. These results are of interest in “perfusion” chromatography where convection is thought to increase separation efficiency for large biomolecules.

Direct Red 28 Adsorption on Amosil and Avena sativa L.: Mass Transfer and Kinetics Modelling on the Solid/Solution Interface

Adsorption kinetics is a key issue for successful sorbent selection and the proper design of batch and fixed-bed adsorption systems. The aim of the present study was to determine the kinetics, mass transfer and diffusion coefficients and to establish the rate-controlling mechanism/s during Direct Red 28 adsorption on Amosil and Avena sativa L. biomass. Five kinetic models (pseudo-second order, Blanchard, Avrami, Ritchie and power function) and and four mass transfer (external diffusion, film diffusion, particle diffusion, intraparticle diffusion) mathematical models were applied to the experimental data. To confirm the best-fitting model(s), error analyses were conducted. The integrative comparative analyses of the values of the predicted model parameters, coefficients and error functions established that the intraparticle diffusion model best represented the experimental results of the dye sorption on dried A. sativa L. biomass, while for the Direct Red 28/Amosil system, the kinetic behavior is the best described by either the pseudo-second or Blanchard’s model. Boyd’s effective intraparticle diffusion coefficient (D i ), characterizing the dye sorption on Amosil, is significantly lower than that for the system Direct Red 28/A. sativa L. biomass. The low values of the Bi number (Bi < 0.5) suggests that the mass transfer resistance, for both systems, is concentrated at the fluid/solid phase surface.

Comprehension of Effects of Intraparticle Effective Diffusivity on Simulated Moving Bed

The influence of intraparticle effective diffusivity on simulated moving bed (SMB) is investigated in this work. The intraparticle effective diffusivity has significant influence on the separation process of SMB and it affects the upper and left sides of separation region of SMB in different styles. The result is explained according to the separation of binary mixture in single column in C1-C2 space. This indicates the necessity of considering the effects of intraparticle mass transfer processes for chemical engineers during their designing the operating conditions of SMB.

Adsorptive Removal of As(III) from Aqueous Solution by Raw Coconut Husk and Iron Impregnated Coconut Husk: Kinetics and Equilibrium Analyses

AbstractAs(III) removal from aqueous solution was conducted using low-cost adsorbents like unmodified raw coconut husk (RCH) and modified iron impregnated coconut husk (IICH). Prepared both adsorbents was characterisation by using elemental analyses, FTIR, TGA, SEM and EDX. The analysis behaviour indicates, both adsorbents are highly suitability for As(III) removal. The effects of operational parameters, such as pH, adsorbent dose and initial concentration on these adsorbents were investigated and compared with other agriculture based adsorbent. The result reveals that the As(III) removal capacity is effective in the pH range of 6.2–7.8 and the optimum pH and adsorbents dose was found as 7.0 and 40 g l−1, for RCH and IICH, respectively. Kinetic and equilibrium studies over a wide range of operating conditions are tested to evaluate the effectiveness of RCH and IICH to remove As(III) from water. The values of bothkf1andks2values are found to be nearly same and same trend was observed at higher 50 mg l−1and lower arsenic concentration 25 mg l−1for RCH and IICH. But the kinetic data is fitted better in the pseudo-second-order kinetic model than the pseudo-first order model. The effective intraparticle diffusion coefficient of As(III) ions in RCH and IICH is observed to be 2.145×10−9 cm2s−1and 1.838×10−10 cm2s−1, which indicates that the overall As(III) adsorption on both adsorbents are intraparticle diffusion control. Equilibrium isotherms for the adsorption of As(III) on RCH and IICH were analyzed at different dose and different initial concentration. At different concentration system, Freundlich isotherm and Redlich-Peterson are best fitted followed by Langmuir and Temkin isotherm models and for varying doses, all equilibrium models give almost similar fitness.

Parametric optimization and modeling of batch extraction process for extraction of betulinic acid from leaves of Vitex Negundo Linn

ABSTRACTExtraction of betulinic acid from leaves of Vitex Negundo Linn was carried out in a series of solvents (methanol, ethanol, isopropyl alcohol, and water). Methanol gave maximum yield of extraction and therefore was used to investigate influence of particle size, speed of agitation, solid loading, and temperature, etc., on the rate and recovery in a stirred batch reactor. Effective intra-particle diffusivity of the acid in each solvent at different temperatures was estimated using an unsteady state mass diffusion model. The diffusivity of betulinic acid through the cellulose matrix of leaves is in the range 1.7 x 10−13 to 9.23 x 10−11 m2/sec and is strongly influenced by the temperature of the extraction. The Response Surface Methodology was used to estimate optimal conditions for betulinic acid extraction.

Effects of Intraparticle Mass Transfer Parameters on Separation Region of Simulated Moving Bed

The effects of intraparticle mass transfer parameters on the separation region of simulated moving bed (SMB) are investigated in this work. To simplify the numerical calculations, a modified equilibrium dispersive model equivalent to the General Rate model is used in this work. The obtained results show the significant influence of the intraparticle effective diffusivity on the SMB process, which indicates the necessity of considering the effects of intraparticle mass transfer processes for the chemical engineers who design the operating conditions of SMB. The intrparticle effective diffusivity affects the two sides of separation region of SMB in different styles and the results are explained according to the results in C1–C2space of binary mixture separated in single column.

How do the HSDM and Boyd’s model compare for estimating intraparticle diffusion coefficients in adsorption processes

Adsorption kinetics is a key-issue for a successful activated carbon selection and design of the treatment system. Crucial predictive aspects are the determination of the diffusion coefficients and the establishment of the controlling adsorption step. Several kinetic models have been developed and two of the most frequently used, the homogeneous surface diffusion model (HSDM) and the Boyd’s model, were applied to microcystins, and particularly MC-LR adsorption. Different initial MC-LR concentrations and carbons (particle diameter, porosity), yielding diverse Biot numbers (Bi), were tested. The model outcomes were compared, namely the Boyd’s effective intraparticle diffusion coefficient (Di) with the HSDM surface diffusion coefficient (Ds), as well as the Bi and Boyd’s criteria to establish the controlling adsorption step, which constitute a novel approach. Very good HSDM fittings were achieved with a constant diffusion model (Ds independent of MC-LR surface concentration). Di was similar to Ds whenever Boyd plots intercepted the origin. The Biot limit above which it may be considered that intraparticle diffusion is the rate limiting step depended on the carbon. A lower limit was observed for smaller carbons.

Impact of the solute exclusion on the bed longitudinal diffusion coefficient and particle intra-tortuosity determined by ISEC

The effective diffusion coefficient of non retained toluene and polystyrenes compounds was measured by the peak parking method for two columns packed with mesoporous silica. Different models used to predict the effective diffusion are compared. These models include the conventional Knox time-averaged model and some effective medium theory models such as Maxwell, Landauer, Garnett or Torquato models. In all these models the effective intraparticle diffusion coefficient is needed. It is derived here, in non-adsorbing conditions, from internal porosity, hindrance factor, which can be estimated with the Renkin correlation, and internal tortuosity, which can be considered as either constant or calculated by the Weissberg equation τ=1−plnɛ, where ɛ is the accessible particle porosity and p a parameter characteristic of the topology. The experimental effective diffusion coefficients of toluene and polystyrenes were found to be in good agreement with the values predicted by the Maxwell, or Torquato models, provided the internal tortuosity is calculated by using the Weissberg equation.

Diffusion of heavy oil in well-defined and uniform pore-structure catalyst under hydrodemetallization reaction conditions

Intraparticle diffusion was investigated over well-defined and uniform pore-structure (WDUPS) model catalysts under reaction conditions for hydrodemetallization of heavy oil. Based on the intrinsic reaction rate constant and the apparent reaction rate constant, the intraparticle effective diffusivity was calculated. The intrinsic diffusivity and the bulk diffusivity under reaction conditions were obtained from the measured intraparticle effective diffusivity, and the porosity and tortuosity of the catalyst. The intrinsic diffusivity obtained using the WDUPS model catalyst was greatly different from that obtained using the conventional catalysts. Owing to its well-defined and uniform pore-structure and therefore definite porosity and tortuosity, the WDUPS model catalyst is more advantageous in intraparticle diffusion study than conventional catalysts, furthermore, the intrinsic diffusivity and the bulk diffusivity obtained in this research work are more reliable than those obtained before by using conventional catalysts with vague tortuosity and wide range of pore-size distribution.

Effect of MW and pH on poly(ethylene glycol) adsorption onto carbon

Poly(ethylene glycol) (PEG) is a water-soluble polymer commonly found in industrial and domestic wastewaters. In this study the adsorption onto granular activated carbon (GAC) of PEG, of different molecular weights, from aqueous solutions was examined to evaluate its applicability to wastewater treatment. Batch kinetic models have been tested to predict the rate constant of adsorption. The amount of PEG adsorbed on activated carbon depends mainly on the pH, the MW and on the solution characteristics. The adsorption at fixed temperature decrease by MW (PEG-8000 350 mg/g) at low and high pH values show a great potential for GAC. The adsorption process can be described well with the Langmuir and the pseudo first order equation. The effective intraparticle diffusion coefficients of PEG molecules in the GAC adsorbent varying according to the MW values in the range 8.45 × 10−3–9.71 × 10−7.

Chiral adsorption of phenylalanine by α-, β-cyclodextrin modified layered double hydroxides

The chiral adsorption of racemic phenylalanine (Phe) by carboxymethyl-α/β-cyclodextrin-intercalated Zn-Al layered double hydroxides (CM-α/β-CD-LDHs) has been studied. The adsorption isotherms of chiral excess adsorption and the total adsorption of Phe by these CM-α/β-CD-LDHs have been investigated. CM—CD-LDHs were found to be more suitable for chiral recognition of Phe than CM—CD-LDHs. Furthermore, the intraparticle diffusion model is successfully validated in this work. Intraparticle effective diffusivities (D eff ) of Phe in these CM-α/β-CD-LDHs macroparticles were determined from the homogeneous Fickian diffusion model at various temperatures.

Ultrasonic-Assisted Extraction of Aloin from Aloe Vera Gel

Abstract Ultrasound assisted extraction (UAE) intensifies the kinetic of the extraction process by acting upon the interfacial area, through the disintegration of particles. Compared with batch extraction, it improves the extraction process decreasing both extraction time and temperature while increasing the rate of extraction. UAE technique was used to obtain active principle aloin from a herbal plant Aloe Vera. Methanol was selected as organic solvent as found maximum extraction of aloin with it. The active principle aloin was quantified using WATER's HPLC system. The optimum extrac ion conditions were estimated as extraction temperature, extraction time and dry gel loading. Effective intraparticle diffusivity of aloin in methanol solvent was estimated using unsteady state mass diffusion model, and activation energy of diffusion using Arhenius equation respectively.

Adsorption behavior of pesticide methomyl on activated carbon in a high gravity rotating packed bed reactor

High gravity rotating packed bed (HGRPB) reactor possesses the property of high mass transfer rate, which is expected to promote the adsorption rate for the process. In this study, HGRPB has been applied on adsorption removal of methomyl from solution, adopting the adsorbent of activated carbon F400. The influence of operating parameters of HGRPB on mass transfer such as the rotating speed (NR), the flow rate of solution (FL) and initial concentration of methomyl (Cb0) were examined. The traditionally internal mass transfer models combined with Freundlich isotherm were used to predict the surface and effective diffusion coefficients. In addition, the results have also been compared with those obtained from the traditional basket stirred batch reactor (BBR). The results showed that the larger values of NR and FL enhanced the effective intraparticle diffusion and provided more accessible adsorption sites so as to result in lower equilibrium concentration in HGRPB system when compared to SBR system. The results of adsorption kinetics demonstrated that surface and effective diffusions were both significantly greater in HGRPB system instead of BBR system. Furthermore, the values of BiS also manifested less internal mass transfer resistance in HGRPB system. The contribution ratio (RF) of the surface to pore diffusion mass transport showed that the larger contribution resulted from the surface diffusion in HGRPB system. Therefore, the results reasonably led to the conclusion that when the HGRPB system applied on the adsorption of methomyl on F400, the lower equilibrium concentration and faster internal mass transfer can be obtained so as to highly possess great potential to match the gradually stricter environmental standard.

Equilibrium and intra-particle diffusion of stabilized landfill leachate onto micro- and meso-porous activated carbon

Stabilized landfill leachate has previously been treated with activated carbon (AC); however, information on the selectivity of AC depending upon the pore size is minimal. Isotherm and kinetic experiments were conducted using three commercially available AC products, one micro-porous and two meso-porous. Equilibrium adsorption and intra-particle diffusion of organic matter from stabilized leachate was studied. Isotherm experimental data were fitted to Langmuir, Freundlich, and Redlich–Peterson isotherm models in non-linear forms. Of the three isotherm models, the Redlich–Peterson model provided the best fit to the experimental data and showed a similar organic matter adsorption capacity (approximately 0.2 g total organic carbon (TOC) g −1 AC) for both micro-porous and meso-porous AC. The organic matter effective intra-particle diffusion coefficients ( D e ) in both AC types were on the order of 10 −10 m 2 s −1 for AC particle sizes greater than 0.5 mm. Meso-porous ACs showed slightly higher D e compared to micro-porous AC. Rapid small-scale tests showed a maximum of 80% TOC removal from leachate by each AC investigated. Fluorescence spectroscopy showed a preferential adsorption of fulvic-type organic matter with an increase in empty bed contact time by each AC.