Effective Pore Diffusivity Research Articles

Study of Sorption-Retarded U(VI) Diffusion in Hanford Silt/Clay Material

A diffusion cell method was applied to measure the effective pore diffusion coefficient (Dp) for U(VI) under strictly controlled chemical conditions in a silt/clay sediment from the U.S. Department of Energy Hanford site, WA. "Inward-flux" diffusion studies were conducted in which [U(VI)] in both aqueous and solid phases was measured as a function of distance in the diffusion cell under conditions of constant concentration at the cell boundaries. A sequential extraction method was developed to measure sorbed contaminant U(VI) in the solid phase containing extractable background U(VI). The effect of sorption kinetics on U(VI) interparticle diffusion was evaluated by comparing sorption-retarded diffusion models with sorption described either as equilibrium or intraparticle diffusion-limited processes. Both experimental and modeling results indicated that (1) a single pore diffusion coefficient can simulate the diffusion of total aqueous U(VI), and (2) the local equilibrium assumption (LEA) is appropriate for modeling sorption-retarded diffusion under the given experimental conditions. Dp of 1.6-1.7 x 10(-6) cm2/s was estimated in aqueous solution at pH 8.0 and saturated with respect to calcite, as relevant to some subsurface regions of the Hanford site.

IgG adsorption on a new protein A adsorbent based on macroporous hydrophilic polymers. I. Adsorption equilibrium and kinetics

Experimental determination and modeling of IgG binding on a new protein A adsorbent based on a macroporous resin were performed. The new adsorbent consists of polymeric beads based on hydrophilic acrylamido and vinyl monomers with a pore structure optimized to allow favorable interactions of IgG with recombinant protein A coupled to the resin. The particles have average diameter of 57 μm and a narrow particle size distribution. The IgG adsorption equilibrium capacity is 46 mg/cm 3 and the effective pore diffusivity determined from pulse response experiments for non-binding conditions is 8.0 × 10 −8 cm 2/s. The IgG adsorption kinetics can be described with the same effective diffusivity by taking into account a heterogeneous binding mechanism with fast binding sites, for which adsorption is completely diffusion controlled, and slow binding sites for which adsorption is controlled by the binding kinetics. As a result of this mechanism, the breakthrough curve exhibits a tailing behavior, which appears to be associated with the slow binding sites. A detailed rate model taking into account intraparticle diffusion and binding kinetics is developed and is found capable of predicting both batch adsorption and breakthrough behavior over an ample range of experimental conditions. The corresponding effective diffusivity is independent of protein concentration in solution over the range 0.2–2 mg/cm 3 and of protein binding as a result of the large pore size of the support matrix. Overall, the small particle size and low diffusional hindrance allow capture of IgG with short residence times while attaining substantial dynamic binding capacities.

Effect of ionic capacity on dynamic adsorption behavior of protein in ion-exchange electrochromatography

Four anion-exchangers of different ion-exchange capacities (21–129 μmol/mL) were prepared by coupling diethylaminoethyl to Sepharose 6FF. The adsorbents were used to study the dynamic protein adsorption in ion-exchange electrochromatography with an oscillatory transverse electric field perpendicular to the mobile-phase flow (IEEC). The static adsorption capacity of bovine serum albumin (BSA) increased from 67 to 186 mg/mL in the ionic capacity range, but the effective pore diffusion coefficient of the protein decreased from 10.9 × 10 −12 to 1.85 × 10 −12 m 2/s with increasing the ionic capacity due to the hindrance effect of the bound protein molecules at the pore entrance. So, the dynamic binding capacity (DBC) of protein in ion-exchange chromatography decreased with increasing the ionic capacity. By applying an electric field of 30 mA, the DBC in IEEC packed with ion-exchangers of high ionic capacities (53 and 129 μmol/mL) increased significantly (over 30% and 100%, respectively). This was because the high surface charge density led to high electroosmotic flow that enhanced intraparticle mass transfer in IEEC. In comparison, the DBC in IEEC packed with ion-exchangers of low ionic capacities (21 and 35 μmol/mL) increased only slightly (ca. 10%) under the same condition. The results indicated the minor effect of electrophoretic mobility on the intraparticle mass transfer. Hence, it is beneficial to use ion-exchangers of high ionic capacity for high-capacity purification of proteins by IEEC.

Evaluation of chelating ion-exchange resins for separating Cr(III) from industrial effluents

In this study two chelating resins containing iminodiacetic acid groups (Amberlite IRC 748 and Diaion CR 11) and a chelating resin based on sulfonic and diphosphonic acid groups (Diphonix) were investigated in order to separate Cr(III) from industrial effluents produced in hard and decorative electroplating. Samples of two industrial plants were characterized during a period of about one year and a half in terms of the metals content (Cr, Cu, Na, Ca, Fe and Ni), Total Suspended Solids (TSS), Total Dissolved Solids (TDS), Chemical Oxygen Demand (COD) and pH. Some of the physical properties of the resins, namely the moisture content, apparent density, intraparticle porosity and the particle size distribution were also evaluated. To quantify the sorption capacity of the resins, batch experiments were performed using synthetic solutions of Cr(III), as well as solutions of Fe in the case of Diphonix. The Langmuir and Langmuir–Freundlich isotherms enabled a good description of the ion-exchange equilibrium data, and the maximum sorption capacity determined for Amberlite and Diaion was 3.6 mequiv./g dry resin. For Diphonix that parameter was 3.4 mequiv./g dry resin. The Diphonix resin exhibits a high selectivity for transition metals (Fe, Ni) over the chromium trivalent. Therefore, it was screened as the most suitable for selectively removing those metal impurities from chromium electroplating effluents. For this resin, the sorption capacity is strongly dependent on the initial pH of the solution. Though, high regeneration efficiencies of Diphonix for stripping Cr(III) were found by using a mixture of NaOH/H 2O 2. The mathematical model tested for describing the dynamics of the process allowed a good fitting to the experimental data and enabled the estimation of effective pore diffusivity of Cr(III). The saturations of Diphonix with industrial effluents demonstrated that the breakthrough capacity of the resin is affected by the presence of other species in solution, such as Fe and Ni. Nevertheless, these effluents may be treated with this resin, being possible to separate Cr(III) from other transition metallic ions in solution.

Protein adsorption and transport in agarose and dextran-grafted agarose media for ion exchange chromatography: Effect of ionic strength and protein characteristics

This work investigates the effects of ionic strength and protein characteristics on adsorption and transport of lysozyme, BSA, and IgG in agarose-based cation exchangers with short ligand chemistry and with charged dextran grafts. In all cases, the adsorption equilibrium capacity decreased with increasing salt. However, the adsorption kinetics was strongly influenced by the adsorbent structure and protein characteristics. For the smaller and positively charged lysozyme, the effective pore diffusivity was only weakly dependent on salt for the dextran-free media, but declined sharply with salt for the dextran-grafted materials. For this protein, the dextran grafts enhanced the adsorption kinetics at low salt, but the enhancement vanished at higher salt concentrations. For BSA, which was near its isoelectric point for the experimental conditions studied, the effective diffusivity was low for all materials and almost independent of salt. Finally, for the larger and positively charged IgG, the effective diffusivity varied with salt, reaching an apparent maximum at intermediate concentrations for both dextran-free and dextran-grafted media with the kinetics substantially enhanced by the dextran grafts for these conditions. Microscopic observations of the particles during protein adsorption at low ionic strengths showed transient patterns characterized by sharp adsorption fronts for all materials. A theory taking into account surface or adsorbed phase diffusion with electrostatic coupling of diffusion fluxes is introduced to explain the mechanism for the enhanced adsorption kinetics observed for the positively charged proteins.

Isobutane/butenealkylation on microporous and mesoporous solid acid catalysts: probing the pore transport effects with liquid and near critical reaction media

The alkylation of isobutane with 1-butene was investigated on microporous (β-zeolite) and mesoporous (silica supported heteropolyacids) catalysts in a slurry reactor. The reaction was investigated in the range of 25–100 bar and 15–95 °C in liquid phase and in near critical reaction media with either dense CO2 or dense ethane as diluent, partially replacing the excess isobutane. At 75 °C, the selectivity towards trimethylpentanes (TMP) in the liquid phase is 70%+ initially, but decreases with time on all the catalysts investigated. While near-critical reaction mixtures were employed in order to enhance pore diffusion rates, the conversion and selectivity profiles obtained with such mixtures are comparable to those obtained with liquid phase reaction mixtures in both microporous and mesoporous catalysts. This implies that pore diffusion effects play a limited role at higher temperatures (75–95 °C). In contrast, the liquid phase results at sub-ambient temperatures indicate that the catalyst is deactivated before the TMPs diffuse out of the pores, indicating that pore diffusion effects play an important role in the deactivation process at low temperatures. Our results suggest that novel approaches that enhance the pore-diffusion rates of the TMPs at lower temperatures must be pursued.

Protein adsorption kinetics in charged agarose gels: Effect of agarose content and modeling

AbstractThe adsorption kinetics of myoglobin in charged gels of varying agarose content have been measured macroscopically, through batch uptake experiments, and microscopically, using light microscopy with gels supported in microfluidics chips. The apparent effective pore diffusivities, determined by fitting either set of rate data to the shrinking core model, were greater than the free solution diffusivity and concentration‐dependent. Moreover, the microscopically derived concentration profiles were qualitatively different from the predicted ones. Therefore, a new model taking into account an assumed favorable partitioning of the protein in the pore liquid is proposed to describe the adsorption kinetics. The new model yields effective pore diffusivities that are in approximate agreement with the values determined chromatographically under nonbinding conditions and with hindered diffusion theory. In addition, it predicts concentration profiles in the gel that are consistent with those observed microscopically. The overall increase in mass transfer is attributed to the favorable partitioning of the protein in the pores at low ionic strength, which results in a greater diffusional driving force. © 2008 American Institute of Chemical Engineers AIChE J, 2009

Application of the Film–Pore Diffusion Model to the Sorption of Phenol onto Activated Carbons Prepared from Peanut Shells

In this work, the film–pore diffusion model was applied to the adsorption of phenol onto peanut shell activated carbon in a batch stirred vessel. This two-resistance model was applied to predict the phenol concentration decay curves for different initial phenol concentrations, carbon particle sizes and dosages. The predicted concentration decay curves were compared with the experimental findings. The optimum best-fit values of the external mass-transfer coefficient and effective diffusion coefficients were found by minimizing the difference between the experimental and model-predicted phenol solution concentration. It was found that, under the experimental conditions employed in this study, the influence of the external mass-transfer resistance was low. A single value of the mass transport coefficient, kf, of (4.8 ± 1.3) × 10−3 (cm/s) described the whole range of system conditions. The difference between the corresponding values of the effective diffusivity, Deff, was not statistically significant. Consequently, a constant value of the effective pore diffusivity of (4.1 ± 0.4) × 10−6 (cm2/s) was sufficient to provide an accurate correlation of the decay concentration curve.

Modeling char oxidation behavior under Zone II burning conditions at elevated pressures

For accurate modeling of the coal combustion process at elevated pressures, account must be made for variations in char-particle structure. As pressure is increased, particle swelling increases during the devolatilization of certain bituminous coals, yielding a variety of char-particle structures, from uniform high-density particles to thin-walled non-uniform low-density particles having large internal void volumes. Since under Zone II burning conditions the char conversion rate depends upon the accessibility of the internal surfaces, the char structure plays a key role in determining particle burnout times. In our approach to characterize the impact of char structure on particle burning rates, effectiveness factors appropriate for thin-walled cenospherical particles and thick-walled particles having a few large cavities are defined and related to the effectiveness factor for uniform high-density particles that have no large voids, only a random distribution of pores having a mean pore size in the sub-micron range. For the uniform case, the Thiele modulus approach is used to account for Zone II type burning in which internal burning is limited by the combined effects of pore diffusion and the intrinsic chemical reactivity of the carbonaceous material. In the paper, the impact of having a variety of char structures in a mix of particles burning under Zone II burning conditions is demonstrated.

5-Aminoindole, a new ligand for hydrophobic charge induction chromatography

Hydrophobic charge induction chromatography (HCIC) is a mixed-mode chromatography that achieves high adsorption capacity by hydrophobic interaction and facile elution by pH-induced charge repulsion between the solute and ligand. This article reports a new medium, 5-aminoindole-modified Sepharose (AI-Sepharose) for HCIC. The adsorption equilibrium and kinetics of lysozyme and bovine serum albumin (BSA) to AI-Sepharose were determined by batch adsorption experiments at different conditions to provide insight into the adsorption properties of the medium. The influence of salt type on protein adsorption to AI-Sepharose corresponded with the trend for other hydrophobicity-related properties in literature. Both ligand density and salt concentration had positive influences on the adsorption of the two proteins investigated. The adsorption capacity of lysozyme, a basic protein, decreased rapidly when pH decreased from 7 to 3 due to the increase of electrostatic repulsion, while BSA, an acidic protein, achieved maximum adsorption capacity around its isoelectric point. Dynamic adsorption experiments showed that the effective pore diffusion coefficient of lysozyme remained constant at different salt concentrations, while that of BSA decreased with increased salt concentration due to its greater steric hindrance in pore diffusion. High protein recovery by adsorption at pH 7.10 elution at pH 3.0 was obtained at a number of NaCl concentrations, indicating that the adsorbent has typical characteristics of HCIC and potentials for applications in protein purification.

Rapid monoclonal antibody adsorption on dextran-grafted agarose media for ion-exchange chromatography

The binding capacity and adsorption kinetics of a monoclonal antibody (mAb) are measured for experimental cation exchangers obtained by grafting dextran polymers to agarose beads and compared with measurements for two commercial agarose-based cation exchangers with and without dextran grafts. Introduction of charged dextran polymers results in enhanced adsorption kinetics despite a dramatic reduction of the accessible pore size as determined by inverse size-exclusion chromatography. Incorporation of neutral dextran polymers in a charged agarose bead results instead in substantially lower binding capacities. The effective pore diffusivities obtained from batch uptake curves increase substantially as the protein concentration is reduced for the resins containing charged dextran grafts, but are much less dependent on protein concentration for the resins with no dextran or uncharged dextran grafts. The batch uptake results are corroborated by microscopic observations of transient adsorption in individual particles. In all cases studied, the adsorption kinetics is characterized by a sharp adsorption front consistent with a shell-progressive, diffusion limited mechanism. Greatly enhanced transport rates are obtained with an experimental resin containing charged dextran grafts with effective pore diffusivities that are 1–9 times larger than the free solution diffusivity and adsorption capacity approaching 300 mg/cm 3 of particle volume.

Mathematical modelling of Collie coal pyrolysis considering the effect of steam produced in situ from coal inherent moisture and pyrolytic water

Low-rank coals have high inherent moisture content, and high yield of pyrolytic water formed from the functional groups in the coal during pyrolysis. Steam produced from coal moisture can lead to significant in-situ char gasification during pyrolysis under conditions where there are strong and prolonged interactions between the char and the in-situ steam. This phenomenon can be encountered in many practical processes yet is often overlooked in pyrolysis modelling. Using Collie coal as an example, this study presents a mathematical model on low-rank coal pyrolysis, considering primary and secondary coal pyrolysis reactions, heat transfer, mass transports, as well as char gasification and volatiles cracking/reforming by steam produced in situ during pyrolysis due to both coal inherent moisture and pyrolytic water. Under conditions where there are strong and prolonged interactions between the pyrolysis products (particularly char) and steam produced in situ from the coal inherent moisture and pyrolytic water, lower char yields from both raw and demineralised coal are predicted, in agreement with the experimental data, under the current experimental conditions. This effect increases with increasing coal inherent moisture content, but decreases with increasing particle size due to the slower heating rate incurred during pyrolysis and the pore diffusion effect during char gasification for the large particles. Volatile steam reforming competes with char gasification for available steam, especially at high temperatures and for large particles. Experiments as well as model prediction also clearly demonstrate that char steam gasification reactivity data should be obtained from experiments carried out on the in-situ basis as the in-situ reactivity is significantly higher than that on the ex-situ basis.

Kinetic Modeling of Large‐Scale Reaction Systems

This review gives a brief account of basic ideas underlying approaches to analysis and modeling of large‐scale reaction systems. The emphasis is on model simplification and mechanism/dimension reduction via heuristic concepts and formal mathematical techniques. Among the key topics discussed are: top‐down and bottom‐up modeling approaches, graph/matrix representation of chemical reactions, mechanistic vs. pathways models, quantitative structure‐reactivity relationships, mathematical reduction of dimensionality, high‐fidelity surrogate models, continuum approximation, lumping of nonlinear kinetics, overall behavior/kinetics of many reactions, effect of pore diffusion, steady state multiplicity and stability. Some common features of dimension reduction methodologies are noted. Areas where further work will be valuable are identified.

Hydrophobic interaction chromatography of proteins: III. Transport and kinetic parameters in isocratic elution

The effective pore diffusivities, D e, of five model proteins (ribonuclease A, lysozyme, α-lactalbumin, ovalbumin, and BSA) in eight commercial phenyl hydrophobic interaction chromatography (HIC) media were determined by analyzing the plate height data from isocratic elution using the first two moments of the general linear rate model. The adsorbents represent a diverse set of HIC media that are widely used for protein purification. The estimated pore diffusivities were used to calculate the elution profiles of proteins in these adsorbents and were compared with the elution profiles obtained experimentally. High protein loading and sample protein concentration led to the underestimation of the pore diffusivity by the linear rate model. Comparisons between the calculated and the experimental profiles suggest that the pore diffusivities obtained from the linear rate model are generally accurate for proteins with low structural flexibility but not for more flexible ones, presumably because conformational change effects contribute significantly to the overall HETP. The general linear rate model was modified to account for the protein folding/unfolding kinetics, and parameter values could be estimated by fitting the experimental elution profiles to the modified model. In addition to conformational change, adsorbent type also had a significant effect on the accuracies of the pore diffusivities estimated by the linear rate model. The results also show that pore diffusion was the rate-limiting step in all absorbents for rigid proteins such as ribonuclease A and lysozyme. For structurally flexible proteins, conformational change contributed significantly to the overall reduced plate heights of the isocratic elution peaks. The physical properties of adsorbents, such as protein accessible porosity, pore size distribution, pore radius and pore connectivity, play important roles in determining the effective protein pore diffusivities.

Film and Pore Diffusion Effects in Catalytic Vapor Phase Alkylation of Aniline

Catalytic vapor phase alkylation of aniline with ethanol was effected in the presence of a zeolite catalyst in a fixed bed reactor at atmospheric pressure and moderate temperatures. Experimental runs were carried out at five different temperatures (350, 370, 390, 410 and 430 °C) with a constant aniline to ethanol ratio (1:5) and different catalyst loadings to find the limits of external and internal resistance zones. The resistance due to external mass transfer was overcome by operating at high velocities and the pore diffusion resistance was nullified by conducting experiments with different particle sizes of the catalyst. The effectiveness factor was determined experimentally and the optimum zone of operation where the diffusional resistances are absent was obtained for kinetic experiments to be conducted. The results indicated that below 0.6 cm/sec velocity external mass transfer was likely to influence the rate of reaction. The effect of pore diffusion was accounted for by the effectiveness factor which was nearly unity for an operative range of particle size < 2 mm. Pore diffusion will therefore play a role for a particle size > 2 mm.

Preparative weak cation-exchange chromatography of monoclonal antibody variants: I. Single-component adsorption

The retention behavior of a monoclonal antibody has been characterized on a weak cation exchanger, Fractogel EMD COO −(s). This new generation of resin materials comprise of a higher mechanical strength compared to softer gel-type matrices while maintaining elevated capacities, resulting in higher productivity and longer lifetimes. These parameters are extremely important when working with large bio-molecules such as proteins, and in particular monoclonal antibodies. In the first part of this work a parameter estimation strategy is presented to fully characterize the retention behavior of a single monoclonal antibody and determine suitable model parameters. Literature correlations were used for the estimation of mass transfer rates. The transport limiting parameter, pore diffusion, was regressed experimentally. Various methods for the adsorption isotherm determination have been applied, their combinations resulting in little experimental effort and accurate predictions of elution profiles. The process has been modelled with a complete pore diffusion model and the agreement between experimental and predicted profiles is good in general. However, a very marked sensitivity to changes in the effective pore diffusion coefficient has been observed. A correlation describing the effect of the separation conditions on the diffusion rate is therefore needed in order to have a fully predictive mathematical model.

Attainable regions of reactive distillation—Part I. Single reactant non-azeotropic systems

Reactive distillation (RD), a promising multifunctional reactor, can be used to improve the selectivity of the desired product by manipulating the concentration profiles in the reactive zone of the column. In this work, a new approach has been proposed to obtain the feasible regions of RD for the reactive systems involving single reactants, e.g. dimerization, aldol condensation, etc. Two new models namely the reactive condenser and the reactive re-boiler have been proposed. These models indicate the best location of the reactive zone in a column. Multistage versions of these models namely, reactive rectification and reactive stripping further expand the feasible region and are capable of representing the performance offered by a conventional RD unit. Several hypothetical non-azeotropic ideal systems have been extensively studied using these models and it has been shown that selectivity close to 100% is attainable over the entire range of conversion for a series as well as a combination of series and parallel reactions with positive reaction orders. Two industrially important cases of aldol condensation of acetone and dimerization of isobutylene have also been addressed using this approach. For porous catalysts, the presence of intra-particle diffusion resistance may limit the feasible region and even in the case of ideal non-azeotropic systems it may not be possible to obtain 100% selectivity. A methodology to incorporate pore diffusion effects is also illustrated.

Deactivation of WNiPd/TiO 2Al 2O 3 catalyst during the upgrading of LCO

The deactivation of a novel catalyst during the production of a high-quality low-emission diesel component has been studied experimentally in a hydrotreating microplant. This process is compared with a commercial operation that used a conventional HDT catalyst. Catalysts were tested by incrementing temperature as a function of cycle length to keep the sulfur constant in the product, maintaining all other operating conditions constant. Spent catalysts were characterized using solid 13CNMR and XPS spectroscopy, pyridine adsorption, GC–MS of the coke extracted, and chemical analysis. Effective pore diffusivity was measured with pentane, and the catalyst activity and selectivity were measured with LCO and probe molecules to verify naphthenic ring opening capability. An important decline in hydrogenation and ring opening activity was detected along the cycle length due to acid site deactivation. The deactivation is attributed to LCO poly-aromatics adsorption on a particular type of acid site. A commercially deactivated HDT catalyst that operated with LCO presents a similar type of coke to that of the pilot plant.

Dynamic analysis of sorption of Methylene Blue dye on granular and powdered activated carbon

Removal of dyes and pigments from wastewaters of dying and printing industries is a major environmental issue. Sorption rate and equilibrium parameters of Methylene Blue on granular and powdered activated carbons were investigated in a batch adsorber. Due to the significance of pore diffusion resistance and partial closure of pore mouths by dissociatively chemisorbed dyes, both sorption rate and sorption capacity values evaluated for granular carbon were lower than the corresponding values for powdered activated carbon. Concentration independent effective pore diffusivity values in the order of magnitude of 10 −9 cm 2 /s were obtained by the moment analysis of a proposed diffusion model (Model 1).

Optics-intrinsic double-circle phenomenon in protein adsorption visualized by confocal laser scanning microscopy

Confocal laser scanning microscopy (CLSM) has been introduced in the research of chromatographic adsorption and the technique provides a direct and noninvasive way to measure and characterize intraparticle concentration distributions of proteins on a single particle level. In this work, an optics-intrinsic double-circle phenomenon that occurs in protein adsorption visualized by CLSM is exhibited and its optical mechanism is reasonably explained by an evolutive version of the attenuation equation. The time course of intraparticle fluorescence intensity profiles obtained from CLSM (even the double-circle phenomenon) in this research is vividly reproduced by model simulation, which takes into account the light attenuation by combining the attenuation equation with an effective pore diffusion model.