Modeling of the adsorption breakthrough behaviors of Pb2+ in a fixed bed of ETS-10 adsorbent

On the basis of experimental breakthrough curves of lead ion adsorption on ETS-10 particles in a fixed-bed column, we simulated the breakthrough curves using the two-phase homogeneous diffusion model (TPHDM). Three important model parameters, namely the external mass-transfer coefficient (k(f)), effective intercrystal diffusivity (D(e)), and axial dispersion coefficient (D(L)), were optimally found to be 8.33x10(-5) m/s, 2.57x10(-10) m(2)/s, and 1.93x10(-10) m(2)/s, respectively. A good agreement was observed between the numerical simulation and the experimental results. Sensitivity analysis revealed that the value of D(e) dictates the model performance while the magnitude of k(f) primarily affects the initial breakthrough point of the breakthrough curves.     

Hydrophobic interaction chromatography of proteins IV. Kinetics of protein spreading

Adsorption of proteins on surfaces of hydrophobic interaction chromatography media is at least a two-stage process. Application of pure protein pulses (bovine serum albumin and beta-lactoglobulin) to hydrophobic interaction chromatography media yielded two chromatographic peaks at low salt concentrations. At these salt concentrations, the adsorption process is affected by a second reaction, which can be interpreted as protein spreading or partial unfolding of the protein. The kinetic constants of the spreading reaction were derived from pulse response experiments at different residence times and varying concentrations by applying a modified adsorption model considering conformational changes. The obtained parameters were used to calculate uptake and breakthrough curves for spreading proteins. Although these parameters were determined at low saturation of the column, predictions of overloaded situations could match the experimental runs satisfactorily. Our findings suggest that proteins which are sensitive to conformational changes should be loaded at high salt concentrations in order to accelerate the adsorption reaction and to obtain steeper breakthrough curves.     

Protein adsorption and transport in dextran-modified ion-exchange media. II. Intraparticle uptake and column breakthrough

Protein transport behavior was compared for the traditional SP Sepharose Fast Flow and the dextran-modified SP Sepharose XL and Capto S resins. Examination of the dynamic binding capacities (DBCs) revealed a fundamental difference in the balance between transport and equilibrium capacity limitations when comparing the two resin classes, as reflected by differences in the locations of the maximum DBCs as a function of salt. In order to quantitatively compare transport behavior, confocal microscopy and batch uptake experiments were used to obtain estimates of intraparticle protein diffusivities. For the traditional particle, such diffusivity estimates could be used to predict column breakthrough behavior accurately. However, for the dextran-modified media, neither the pore- nor the homogeneous-diffusion model was adequate, as experimental dynamic binding capacities were consistently lower than predicted. In examining the shapes of breakthrough curves, it was apparent that the model predictions failed to capture two features observed for the dextran-modified media, but never seen for the traditional resin. Comparison of estimated effective pore diffusivities from confocal microscopy and batch uptake experiments revealed a discrepancy that led to the hypothesis that protein uptake in the dextran-modified resins could occur with a shrinking-core-like sharp uptake front, but with incomplete saturation. The reason for the incomplete saturation is speculated to be that protein initially fills the dextran layer with inefficient packing, but can rearrange over time to accommodate more protein. A conceptual model was developed to account for the partial shrinking-core uptake to test whether the physical intuition led to predictions consistent with experimental behavior. The model could correctly reproduce the two unique features of the breakthrough curves and, in sample applications, parameters found from the fit of one breakthrough curve could be used to adequately match breakthrough at a different flow rate or batch uptake behavior.     

Chromatographic quantitation using fractions of the peak areas

Quantitative chromatographic analysis is liable to errors due to peak asymmetry because the uncertainty in the detected position of the end of the peak tail decreases the reliability of the computed peak area. This dependence may be a severe drawback whenever peaks of different areas must be compared, as in the case of calibration curves. A new approach to overcome the uncertainties of area calculation due to peak asymmetry is reported in this paper. The approach consists of calculating only the area included between the start and the maximum of the chromatographic peak. Simulated and experimental chromatographic data were used in this study. Both the peak start-to-peak maximum area (SMA) and the start-to-end or total area (TA) were calculated and the quantitative results were compared. Within the scope of this work it is concluded that the SMA yields calibration curves that are more linear and have intercepts closer to zero than the calibration curves obtained using the TA.     

Influence of the particle porosity on chromatographic band profiles

The mass transfer kinetics of butyl benzoate, eluted on a monolithic RPLC column with methanol-water (65:35, v/v) as the mobile phase was investigated, using the perturbation method to acquire isotherm data and the mobile phase velocity dependence of the height equivalent to a theoretical plate of perturbation peaks to acquire kinetics data. The equilibrium isotherm of butyl benzoate is accounted for by the liquid-solid extended multilayer BET isotherm model. The total porosity of the column varies much with the butyl benzoate concentration, influencing strongly the parameters of its mass transfer kinetics and the profiles of the breakthrough curves. Using all these parameters, the general rate model of chromatography predicts band profiles and Van Deemter curves that are in excellent agreement with experimental results provided the influence of concentration on the porosity is properly taken into account. This agreement confirms the validity of the models selected for the isotherm and for the mass transfer kinetics.     

Co-diffusion with a slow species in zeolites: cyclic experimentation and advanced modeling

In this study, a new experimental method based on cyclic breakthrough curves is presented, in order to estimate the co-diffusion coefficients for mixtures at high adsorption loadings. For this purpose, cyclic liquid phase breakthrough curves of mixtures of 2-methylpentane 3-methylpentane (fast-diffusing species) and 2,2-dimethylbutane (slow-diffusing species) have been measured experimentally for different feed compositions at 185°C. Estimation of Langmuir coefficients and self-diffusivities was attempted from simple binary breakthrough curves with the above components using a modified Maxwell-Stefan-type model. However, for the slow-diffusing species, the parameters cannot be estimated accurately from such experiments, because the quantity of 22DMB entering the zeolite network in the experiment duration is not sufficient. On the other hand, a clear influence of the slow diffusing species (22DMB) on the fast diffusing species (3MP) breakthrough curves during cycles has been demonstrated. This phenomenon confirms that 22DMB slowly accumulates in the adsorbent during the cycles, and that is becomes therefore possible to estimate the 22DMB parameters from the cyclic data.     

Using computer simulation to assist in the robustness analysis of an ion-exchange chromatography step

This paper presents a methodology to gain process knowledge and assist in the robustness analysis of an ion-exchange step in a protein purification process using a model-based approach. Factorial experimental design is common practice in industry today to obtain robustness characterization of unit operations with respect to variations in process parameters. This work aims at providing a better insight into what process variations affect quality and to further reduce the experimental work to the regions of process variation that are of most interest. This methodology also greatly increases the ability to predict process performance and promotes process understanding. The model calibration part of the methodology involves three consecutive steps to calibrate a steric mass action (SMA) ion-exchange chromatography model. Firstly, a number of gradient elution experiments are performed. Secondly, experimental breakthrough curves have to be generated for the proteins if the adsorption capacity of the medium for each component is not known. Thirdly, a multi-component loading experiment is performed to calibrate the multi-component effects that cannot be determined from the single-component experiments. The separation process studied in this work is the separation of polyclonal IgG from a mixture containing IgG, myoglobin and BSA. The calibrated model is used to simulate six process variations in a full factorial experiment. The results of the simulations provide information about the importance of the different process variations and the simulations are also used to determine the crucial points for the process parameter variations. The methodology can be used to assist in the robustness analysis normally performed in the pharmaceutical industry today as it is able to predict the impact on process performance resulting from variations in salt concentration, column load, protein concentration and flow rate.     

Adsorption of Sulfur Dioxide from Pseudo Binary Mixtures on Hydrophobic Zeolites: Modeling of the Breakthrough Curves

The adsorption of SO₂ from pseudo binary mixtures with water and CO₂ on hydrophobic zeolites (MFI and MOR type) was investigated using the breakthrough curve method. The SO₂ and water breakthrough curves were compared with theoretical ones based on an axially dispersed plug flow through the column and the linear driving force rate equation. In addition, different semi-predictive multi-component equilibrium equations were used for the breakthrough modeling: Langmuir 1, Langmuir 2 and Langmuir-Freundlich extended models. The overall mass transfer coefficients were derived by matching theoretical with experimental breakthrough curves for single component systems, i.e., water vapor or SO₂ in a carrier gas. They were also predicted from a simplified bi-porous adsorbent model and compared with experimentally derived values. The presence of CO₂ species in ternary mixtures with water vapor and SO₂, even at relatively high concentrations of 9 vol%, had no significant effect on the breakthrough behavior of the other two species. For that reason the CO₂ species was ignored in the analysis of the resulting pseudo binary mixtures. The breakthrough model was solved by finite element orthogonal collocation method using the commercial software gPROMS. Both extended Langmuir 1 and Langmuir 2 based models gave reasonable predictions of the water and SO₂ breakthrough curves for pseudo binary mixtures involving a mordenite sample for all water concentration levels used in this study (up to 3.5 vol%). However, the same models were successfully used to predict SO₂ breakthrough curves for a MFI sample only at low water concentrations, i.e., 1.5 vol%. At the higher water levels both models failed to describe equilibrium behavior in the MFI sample due to the introduction of multi-layer adsorption in the interstices between small MFI-26 crystals.     

An improved capillary model for describing the microstructure characteristics, fluid hydrodynamics and breakthrough performance of proteins in cryogel beds

A capillary-based model modified for characterization of monolithic cryogels is presented with key parameters like the pore size distribution, the tortuosity and the skeleton thickness employed for describing the porous structure characteristics of a cryogel matrix. Laminar flow, liquid dispersion and mass transfer in each capillary are considered and the model is solved numerically by the finite difference method. As examples, two poly(hydroxyethyl methacrylate) (pHEMA) based cryogel beds have been prepared by radical cryo-copolymerization of monomers and used to test the model. The axial dispersion behaviors, the pressure drop vs. flow rate performance as well as the non-adsorption breakthrough curves of different proteins, i.e., lysozyme, bovine serum albumin (BSA) and concanavalin A (Con A), at various flow velocities in the cryogel beds are measured experimentally. The lumped parameters in the model are determined by matching the model prediction with the experimental data. The results showed that for a given cryogel column, by using the model based on the physical properties of the cryogel (i.e., diameter, length, porosity, and permeability) together with the protein breakthrough curves one can obtain a reasonable estimate and detailed characterization of the porous structure properties of cryogel matrix, particularly regarding the number of capillaries, the capillary tortuousness, the pore size distribution and the skeleton thickness. The model is also effective with regards to predicting the flow performance and the non-adsorption breakthrough profiles of proteins at different flow velocities. It is thus expected to be applicable for characterizing the properties of cryogels and predicting the chromatographic performance under a given set of operating conditions.     

Sorptive elimination of fluoride from contaminated groundwater in a fixed bed column: A kinetic model validation based study

The current investigation involves a continuous adsorption experiment in a packed bed column for the sorptive elucidation of fluoride from contaminated groundwater using an activated soil-clay mixture. Through the combination of naturally accessible laterite soil with silica enriched clay (3:1 ratio), a low-cost Al–Si heterogeneous material has been developed. Following detailed characterization, the developed materials were employed in a long-time column process to achieve a high degree of fluoride separation from real-world groundwater. In a packed bed column investigation, the effect of bed height, initial fluoride concentration, and flow rate on the breakthrough properties of the adsorption system were investigated. By using a non-linear regression equation, three model kinetics, such as the Thomas Model, Adams-Bohart Model, and Yoon-Nelson Model, were fitted to validate the column-based experimental data, by analysing the breakthrough curves profiles, and distinct kinetic parameters. The Bed Depth Service Time Analysis (BDST) model was tested to express the effect of bed height on breakthrough curves, as well as to predict the time for breakthrough, and material depletion under optimal conditions. The Thomas and Yoon-Nelson models were identified to be the most appropriate ones for describing the entire breakthrough curve, whereas the Adams-Bohart model was only utilised to predict the first half of the dynamic process. With correlation coefficients (R²) 0.96, the experimental results were well suited to Thomas, Yoon-Nelson, and Adams-Bohart models. Finally, regeneration assessment was carried out where even after four cycles of operation, regenerated adsorbent showed a rejection efficacy of 78% to fluoride that proves the viability of the material and methodology.     

Breakthrough Model of Recombinant Human-Like Collagen in Immobilized Metal Affinity Chromatography

The adsorption of recombinant human-like collagen by metal chelate media was investigated in a batch reactor and in a fixed-bed column. The adsorption equilibrium and kinetics had been studied by batch adsorption experiments. Equilibrium parameters and protein diffusivities were estimated by matching the models with the experimental data. Using the parameters of equilibrium and kinetics, various models, such as axial diffusion model, linear driving force model, and constant pattern model, were used to simulate the breakthrough curves on the columns. As a result, the most suitable isotherm was the Langmuir–Freundlich model, and the ionic strength had no effect on the adsorption capacity of chelate media. In addition, the pore diffusion model fitted very well to the kinetic data. The pore diffusivities decreased with increasing the initial protein concentration, however had little change with the ionic strength. The results also indicated that the models predict breakthrough curves reasonably well to the experimental data, especially at low initial protein concentration (0.3 mg ml⁻¹) and low flow rate (34 cm h⁻¹). By the results, we optimized the experimental conditions of a chromatographic process using immobilized metal affinity chromatography to purify recombinant human-like collagen.     

Influence of particle diameter distribution on protein recovery in the expanded bed adsorption process

The General Rate model has been developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial and local variation of particle size distribution (PSD), external and intra-particle mass transfer resistances, and dispersion in liquid phase. The influence of PSD on breakthrough profiles has been analysed. The simulation results show that for a significantly high expanded bed the lower part of the breakthrough curve profiles, calculated for local particle size distribution (LPSD) and for axial average particle size distribution (APSD) are very similar. However, the upper part of breakthrough profiles calculated for LPSD approaches inlet concentration much more slowly than those calculated for APSD. The retention times of the lower part of uptake curves calculated with average particle diameter are constantly shorter than those obtained from LPSD. For the calculation of the dynamic capacity (DC), the LPSD can be replaced by APSD for large expanded bed heights. Using breakthrough profiles calculated for average particle size, DC values are constantly underestimated.     

Behavior of human serum albumin on strong cation exchange resins: I. Experimental analysis

Experiments with human serum albumin on the strong cation exchange resin Fractogel EMD SE Hicap (M) were carried out. Even though human serum albumin was used at high purity, two peaks in gradient elution experiments occurred. The obtained data can be explained by considering that human serum albumin binds to Fractogel EMD SE Hicap (M) in two different binding conformations: the protein adsorbs instantaneously in the first conformation and then changes into the second one with a kinetic limitation. The two-peak behavior of human serum albumin was analyzed in detail, especially at various gradient lengths, concentrations and temperatures. Breakthrough curves were performed at four modifier concentrations and three velocities. The characteristic adsorption behavior, found for gradient experiments, was confirmed by the breakthrough curves. The two-peak elution pattern of human serum albumin was also found for other strong cation exchange resins, but not for weak cation exchange resins. It is concluded that the described behavior is peculiar for the interaction of human serum albumin with the strong cation exchange ligand of the resin.     

Kinetics of carbon dioxide absorption from air in a flow reactor with a fixed bed of K<Subscript>2</Subscript>CO<Subscript>3</Subscript>-based sorbent

Sorption of carbon dioxide from air in a flow reactor with a bulky fixed bed of the K₂CO₃/Al₂O₃ composite sorbent was studied. The dynamic sorption capacity of the material was shown to depend on the relative humidity of the inlet air. A numerical model was constructed for evaluating the profile of СО₂ concentration in the layer and kinetic curves of CO₂ breakthrough at the outlet of the reactor. The results of simulation allowed us to adequately describe the experimental kinetic curves at 20–40% humidity.     

Effect of temperature on the adsorption behavior of tryptophan in reversed-phase liquid chromatography

Single-component adsorption isotherm data of l-tryptophan on a C(18)-bonded silica column were acquired by frontal analysis (FA), with aqueous mobile phases containing 5% of acetonitrile at five different temperatures between 23 and 62 degrees C. The non-linear fitting of these data provided the bi-Moreau model for all temperatures as the best isotherm model. The inverse method (IM) was used to derive the parameters at these temperatures from the parameters of the 25 degrees C isotherm. The adsorption constants and the saturation capacities of the low and high-energy sites decreases by increasing the temperature, while the adsorbate-adsorbate parameters of both sites increase. An excellent agreement was found between the experimental and calculated overloaded band profiles at all the temperatures used. The breakthrough curves obtained and the overloaded band profiles obtained were found to have different shapes according to the range of concentration studied and the temperatures. At low concentration 0.05-0.5 g/L the breakthrough curves and the overloaded band profiles have a front shock and diffuse rear, which indicates langmuirian behavior, but at intermediate 1-2 g/L and high concentration 8 g/L they start to have diffuse fronts and shocks at the rear or more than one shock at the rear which indicates non-langmuirian behavior. At 23 degrees C the isotherm has another langmuirian part, which appears at high concentration. The behavior of the breakthrough curves is explained by the shape of the isotherm in which all of the isotherms have a langmuirian part (the isotherm is concave upward) and an antilangmuirian part (the isotherm is concave downward). The temperature affected the breakthrough curves by decreasing the time of the appearance of the fronts for all concentration ranges studied, and by decreasing the time difference between the highest concentration and lowest concentration of the fronts, especially the low concentration range at 0.5 g/L. The fronts of the breakthrough curves at high concentration seems to be the most affected by temperature.     

活性炭的高温脱氧改性及其床层对全氟异丁烯的吸附动力学研究

在N2气保护下对颗粒状活性炭进行了不同温度(400—800 ℃)下的高温改性, 考察了不同的空气流湿度(30%—80% R.H.)下全氟异丁烯(PFIB)在活性炭床层中的吸附穿透行为. 利用Wheeler方程对穿透数据进行了处理, 并采用线性平衡吸附体系的动力学模型对床层的穿透实验数据进行了关联. 结果表明, 基炭经高温改性后, 活性炭的孔隙结构没有明显变化, 表面含氧量随处理温度的提高而减少, 在高湿条件下对全氟异丁烯的选择性吸附能力显著提高, 活性炭床层可使PFIB的防护时间延长. 各种实验条件下的理论穿透曲线与实验值数据吻合, 可以利用线性平衡吸附体系的动力学模型来预示PFIB在活性炭层中的穿透行为, 进行防毒面具的滤毒罐参数的选取和设计.     

Mathematical model using non-uniform flow distribution for dynamic protein breakthrough with membrane adsorption media

A mathematical model has been investigated to predict protein breakthrough during membrane adsorption/chromatography operations. The new model incorporates a non-uniform boundary condition at the column inlet to help describe the deviation from plug flow within real membrane adsorption devices. The model provides estimated breakthrough profiles of a binding protein while explicitly accounting for non-uniform flow at the inlet of the separation operation by modeling the flow distribution by a polynomial. We have explored experimental breakthrough curves produced using commercial membrane adsorption devices, as well as novel adsorption media of nanolayered nanofiber membranes, and compare them to model predictions. Further, the impact of using various simplifying assumptions is considered, which can have a dramatic effect on the accuracy and predictive ability of the proposed models. The new model, using only simple batch equilibrium and kinetic uptake rate data, along with membrane properties, is able to accurately predict the non-uniform and unsymmetrical shape for protein breakthrough during operation of membrane adsorption/chromatography devices.     

Evaluation of protein-A chromatography media

In process-scale antibody purification, protein-A affinity chromatography is commonly used as the initial purification step. In this paper, two different protein-A media were evaluated. These adsorbents have a porous glass backbone with different pore sizes: 700 A and 1000 A. Adsorption equilibrium data of human immunoglobulins on these media were measured via a batch technique and correlated using the Langmuir isotherm model. A larger static capacity was found for the smaller pore size material, which is probably a result of the larger specific surface area and associated higher ligand concentration. The protein uptake kinetics were also obtained via a stirred tank experiment using different initial protein concentrations. A surface layer model was used to represent the protein uptake by the media and to estimate values of a concentration-independent effective diffusivity within the particle. Experimental breakthrough curves were also obtained from packed beds operated under different conditions. Calculated breakthrough profiles were found to be in good agreement with the experimental results. Experimental breakthrough data were used to determine the dependence of the dynamic capacity of the media as a function of the fluid residence time. A larger dynamic capacity was also found for the smaller pore size media. The permeability of large scale packed beds was also reported and used in conjunction with the dynamic capacity to calculate the process production rate.