Theoretical evaluation of the performance characteristics of a combined hemodialysis/hemoperfusion system — I. Single pass flow

A mass transfer model with single pass flow is proposed for evaluating the performance characteristics of a combined system composed of a dialyzer for hemodialysis (HD) and a coated adsorbent packed cartridge for hemoperfusion (HP). In the dialyzer, the mass transfer equation is represented in terms of three dimensionless parameters, i.e., extraction ratio, number of transfer unit, and ratio of flow rates. For the hemoperfusion cartridge, the model equations are derived by formulating the following four processes: convective mass transfer in the bed, fluid phase mass transfer around a coated adsorbent particle, transport across a film of coated membrane, and diffusion within an adsorbent particle. The Freundlich isotherm model is used for the adsorption on adsorbent particles. Applications of the mathematical model to systems to be potentially used in clinical practice are discussed. Solutions for two different sequences of arrangement, i.e., HD-HP and HP-HD, are obtained and discussed in terms of their performance efficacies. Theoretical results demonstrate that the HD-HP arrangement will give better performance in most clinical encounters.     

Simulation and validation of ethanol removal from water in an adsorption packed bed: Isotherm and mass transfer parameter determination in batch studies

Preferential adsorption of ethanol from ethanol/water mixtures in batch equilibrium and kinetic experiments were carried out on a commercially available activated carbon adsorbent Filtrasorb 600 (F‐600). A model based on finite difference method was developed and employed to determine the mass transfer parameters and equilibrium behaviour for the adsorption of ethanol from simple batch systems. The estimates of the adsorption isotherm along with the mass transfer parameters were used to simulate the transient performance that could be expected in a packed bed under various operating conditions (feed flow rate, feed concentration, and particle size). The applicability of the simulation results were found to be a good match with experimental packed bed experiments over the entire range of operating conditions tested.     

Modeling of Adsorptive Drying of N-Propanol

On the basis of experimental work connected with mathematical modeling, a parameter analysis was conducted on the adsorptive drying of water-miscible organic liquids. The experimental work involved dehydration of n-propanol using two desiccants, 3A and 4A zeolite molecular sieves. The equilibrium relationship and fixed bed breakthrough curves were determined experimentally. The parameters required by the model are the equilibrium constants, liquid film mass transfer coefficient, intraparticle diffusion coefficient, and axial diffusivity. A linear driving force (LDF) relation was applied to represent the mass transfer rate in the particle liquid film and inside the adsorbent particle. The fit of the model to experimental breakthrough data was quite good.     

Modeling of protein adsorption to DEAE sepharose FF: Comparison of data with model simulation

The equilibrium and kinetic characteristics of the adsorption of human serum albumin (HSA) and ovalbumin (OVA) to the DEAE Sepharose FF weak anion exchanger were experimentally determined. The rate for protein adsorption was simulated with two different models, the first being based on a single lumped kinetic parameter, while the second includes the individual mass transfer processes occurring prior to the adsorption intervention, i.e., diffusion across the liquid film surrounding individual particles and diffusion within the ion exchanger particle itself. The actual adsorption of OVA to DEAE Sepharose FF in fully mixed stirred vessels and in packed bed columns was consistent with both models. In the case of HSA, however, the adsorption profile in an agitated vessel was consistent only with the pore diffusion model and neither model could correctly predict the latter part of the breakthrough profile observed in packed bed experiments.     

Development of design charts for fixed-bed adsorption

A mathematical model of the dynamic behaviour of non-isothermal fixed-bed adsorbers has been developed which takes into account the various mass and heat transfer resistances. Comparison of experimental and simulated results confirms that the model can predict the adsorption and desorption breakthrough curves of an adiabatically operated column, using only equilibrium data and tortuosity factors obtained from single pellet experiments. A simplified model with a reduced number of parameters was derived by investigation of the dimensionless transfer parameters under industrial conditions. It becomes evident that the main transfer mechanisms are convective heat and mass transfer in the bulk flow and diffusion within the pores of the particle. Dimensionless effluent concentration is expresses in terms of dimensionless time, a transport parameter, a non-isothermal parameter, the adsorption equilibrium and the inlet and initial concentrations and temperatures in the simplified model. For a chosen system of adsorbate and adsorbent, design charts can be developed by computer simulation, to determine graphically the breakthrough time as a function of significant process parameters, i.e. the dimensionless transfer parameter and the feed concentration.     

Water Purification from Heavy Metal Ions in a Packed Column

The process of adsorption from water solutions containing ternary system of Cu(II), Zn(II) and Ni(II) ions in time-variable conditions in a packed column with lyophilized chitosan beads is considered. The system of partial differential equations describing the adsorption column, due to the assumption of a properly defined variable is transformed into a system of ordinary nonlinear equations which enables the identification of object parameters in simple experiments. Analytical solution of that system was possible due to the assumptions made regarding the equation describing sorption kinetics. Using experimental data, the effective diffusion coefficient D_eff and the sorption kinetic constants K in the real environment were identified. The sorption capacity q* was obtained in separate sorption equilibrium experiments. Using a mathematical model the influence of initial concentration and solution flow rate on the breakthrough curve was determined. The approach which is presented provides a new method for modeling of sorption in a packed column.     

Analysis of Protein Adsorption to Ion Exchangers in a Finite Bath

The adsorption of proteins to ion exchangers was investigated by finite bath experiments and by computer simulations using existing rate models. Experimental data were obtained for the binding of bovine serum albumin at different feed concentrations to both cation and anion exchangers. The results were interpreted together with model predictions and the values of the parameters characterizing the mass transfer mechanisms as well as the interaction rates of the adsorbate–adsorbent complex were estimated. The best agreement between theory and experiment throughout the whole period of adsorption process was obtained with a complex model where several steps of the overall mechanism were simultaneously controlling the overall rate. The simplified models, which offer rapid solution requiring less computational power, can be used at low feed concentrations of the proteins where the mechanisms controlling the adsorption rate are less complex. As the interaction rate mechanism and the intraparticle mass transfer mechanism in the adsorbent particles are the same in both finite bath and column adsorption systems, the information presented in this paper can be used to predict the protein adsorption in a column chromatography system. © 1997 SCI.     

The effect of electrophoretic convection for the separation of solute in the chromatography column (I)

A theoretical model has been derived in an electrophoretic packed column where an electric potential is applied to a column in the axial direction. The effect of electrophoretic convection in gel particles packed in the column significantly contributes to the separation of large polyelectrolytes because the conformation of polyelectrolyte quickly orients in the field direction. The dependence of the transport in the gel particle upon field intensity and molecular size aids in understanding the transport of polyelectrolyte in the packed column, since the convective velocity of polyelectrolyte is accelerated inside a porous gel particle. There are few convection studies of large poly-electrolyte in a column packed with porous gel particles under an electric field for the separation. Convective-diffusive transport of a large polyelectrolyte is analyzed using Peclet number described by electrophoretic mobility and diffusion coefficient measured experimentally. The separation of two different polyelectrolytes in the packed column is performed using a value ofPe _f/Pe_g of individual polyelectrolyte by molecular size and an electric field. The purpose of this paper is to study the separation of solute from a mixture in the column using the physicochemical properties in the gel particle which are measured experimentally.     

Biosorption of the Reactive Blue 5G Dye in a Fixed Bed Column Packed with Orange Bagasse: Experimental and Mathematical Modelling

The removal of reactive dye in a fixed bed column packed with orange bagasse was modelled using a model that considers the effects of axial dispersion, external and internal mass transfer limitations, and the equilibrium in the liquid-solid interface. The equilibrium and kinetic parameters were obtained through fit the model to the experimental data. In the parameters identification procedure the PSO optimization method was used. The mathematical model showed good performance when describing the dye adsorption process. Furthermore, orange bagasse is an attractive and cost-effective alternative as an adsorbent to remove reactive blue 5G dye from wastewaters.     

大型填料塔内液相分布状态的研究

本文针对填料塔内液体运动的分散方程,提出了新的边界条件,并得到描述填料塔内液体运动规律的新模型.通过实验确定了模型中的各参数.实验结果与理论模型的比较,两者吻合较好.用激光- 光导纤维测试系统测定了液体在填料层内的平均停留时间分布,作出了塔内液体的等平均停留时间曲线,并进一步分析了液体在填料塔内的流动特性.     

Predictive model for design of a packed column: Parameter analysis

The effect of convective velocity in the packed column is presented. When an electric field is applied, the conformation of polyelectrolyte quickly orients in the field direction. The convective velocity of polyelectrolyte inside a porous gel particle is accelerated. The dependence of the transport in the gel particle upon field intensity and molecular size aids in understanding the transport of polyelectrolyte in the packed column. To date, few dynamictudies of polyelectrolyte in a porous gel particle have been attempted for the separation of polyelectrolyte in the packed column. Convective-diffusive transport of DNA is analyzed by physical properties measured experimentally, such as the diffusion coefficient, the electrophoretic mobility and the gel porosity. The purpose of this study is to show how the variation of physicochemical properties in the gel particle affects the separation of DNA from a mixture in the packed column. A theoretical model using the characteristic method is used to calculate the separation point in the packed column.     

纤维素/钛白粉复合微球的扩张床吸附性能

采用反相悬浮热再生法,将超细钛白粉颗粒包埋于纤维素骨架之中,经环氧氯丙烷活化后与二乙胺反应,制得球形阴离子交换吸附剂.研究表明: 吸附剂的扩张行为遵从Richardson-Zaki准则,扩张床内的流动接近于平推流;以牛血清白蛋白(BSA)为模型蛋白质,发现其在扩张床中的穿透行为与固定床中接近,10％穿透时的吸附容量为42.6 mg BSA•ml^-1.     

Reactive Chromatography for the Synthesis of 2-Ethylhexyl Acetate

Abstract

Reactive chromatography (RC) combines reaction and chromatography in a single unit. Due to simultaneous separation of products it can be advantageously used for reversible reactions to obtain the enhanced performance. It is a promising alternative to reactive distillation when the components are temperature sensitive and less volatile. In the present work, we study the application of RC for the synthesis of 2-ethylhexyl acetate through esterification of acetic acid with 2-ethylhexanol. Amberlyst-15 has been used as a catalyst/adsorbent. Several aspects such as reaction kinetics, multicomponent adsorption equilibria, and reaction-separation study using fixed bed chromatographic reactor are covered. The kinetics was studied in a stirred batch reactor. The effects of various parameters such as speed of agitation, particle size, temperature, mole ratio of reactants, and catalyst loading have been investigated. Kinetic modeling was performed using modified activity based Langmuir-Hinshelwood-Hougen-Watson (LHHW) model. Non-reactive binary adsorption experiments were performed to determine the parameters of Langmuir adsorption isotherm by minimizing the errors between the experimental and predicted breakthrough curves. Further, the reactive chromatography experiments were performed to obtain the reactive breakthrough curves which indicate a clear potential for the use of reactive chromatography for this reaction. The obtained data has been compared with the predictions of mathematical model of the chromatographic reactor.     

Phenomena and Modeling of Hydrophobic Interaction Chromatography

Comprehension of the mechanisms of hydrophobic interaction chromatography is not as deep as for other chromatographic steps. This article shows the combination of modeling and experimental model parameter determination. Original mammalian cell culture is applied for validation instead of often-used test systems with for example, three pure proteins. This approach can have a huge benefit for process development and optimization of production processes under project conditions. To simulate the separation by hydrophobic interaction chromatography, a distributed plug flow model with inner pore diffusion is applied. The needed model parameters are determined by small scale experiments on a 1 ml column to reduce feed amount consumption and experimental procedure. Effects caused by system setup are optimized in relation to the volume. Gradient experiments are performed for the determination of isotherm parameters. The model parameters determined are experimentally validated at different set-ups of operation parameters as well as scaled up to 10 ml columns. The practicability of the proposed stepwise procedure of physico-chemical modeling in combination with laboratory scale experiments for the prediction of separation performance of original mammalian cell culture is proved. A model parameter determination directly with fermentation mixture is as well feasible.     

Evaluation and comparison of the biosorption process of copper ions onto olive stone and pine bark

Olive stone (OS) and pine bark (PB) were used as effective biosorbents for the removal of Cu(II) from aqueous solutions. The biosorbents were characterized by elemental analysis, potentiometric titrations, surface area and pore size distribution and FTIR analyses. Batch adsorption experiments were carried out as a function of pH, particle size, biosorbent dosage, contact time and initial copper concentration. Equilibrium data agreed well with Langmuir isotherm. The kinetics data fitted well into the pseudo-second-order model with correlation coefficient greater than 0.99. Finally, dynamic biosorption studies were carried out using a packed bed column and the main column parameters were determined.     

Hydrodynamics of gas-solid two-phase mixtures flowing upward through packed beds

The work reported here represents part of an effort to address the challenges related to a newly proposed process for hydrogen production through steam-methane reforming, in which a fine adsorbent carried by the gaseous reactants moves through a packed catalyst bed. Comprehensive experimental work was carried out on the hydrodynamic aspects of gas-solid two-phase mixtures flowing upwards through packed beds. The effects of column diameter, packed particle size, and suspended particle size on the pressure drop and solids hold-ups were investigated. It was observed that the pressure drop of gas-solid two-phase flows depended approximately linearly on the solids flux under the conditions of this work, and the dependence was affected by the suspended particle size, packed particle size, packed column diameter, and gas velocity. However, when the data were reprocessed in terms of the Euler number and the solid-to-gas mass flux ratio, they collapsed into a single line for a given packing condition, and the suspended particle size was found to impose little effect. An analysis was conducted on the pressure drop using a modified version of Metha-Hawley equation by taking into account the effects of suspended particles on the viscosity and density. A reasonably good agreement with experimental data was obtained. The experimental results of the solids hold-ups showed that the particle concentration in packed particle interstices was much higher than that at the entrance to the packed column. Effort was also made to relate the solids hold-ups to the operating parameters. It was found that the dynamic hold-up related fairly well to the solid-to-gas velocity ratio as well as the suspended-to-packed particle size ratio for a given packed column, whereas no clear relationship was obtained for the static solids hold-up. Based on the results of this study, recommendations for future work are given.     

A 3-zone model for protein adsorption kinetics in expanded beds

The adsorption behavior of expanded beds is more complex than that of fixed beds, since the adsorbent particle size, local bed voidage and liquid axial dispersion will vary axially with expanded height. Models applicable to fixed beds maybe not adequately describe the hydrodynamic and adsorption behavior in expanded beds. In this paper, a 3-zone model is developed, in which the model equations are written for the bottom zone, middle zone, and top zone of the column, respectively, and the model parameters, such as the adsorbent particle diameter, bed voidage and liquid axial dispersion coefficient, are zonal values. In-bed breakthrough curves are predicted by the 3-zone model, and tested against literature data for lysozyme adsorption on Streamline SP in an expanded bed.Model parametric sensitivity is analyzed. The effects of film mass transfer resistance, liquid axial dispersion and adsorbent axial dispersion on the breakthrough curves are weaker than that of protein intraparticle diffusion resistance for stable expanded beds. Adsorbent particle size axial distribution and bed voidage axial variation significantly affect in-bed breakthrough curves, therefore, model parameters should not be assigned uniform values over the whole column; instead the model should account for the adsorbent particle size axial distribution and bed voidage axial variation.     

Thermodynamic and Kinetic Study of Adsorption of R,S‐α‐Tetralol Enantiomers on the Chiral Adsorbent CHIRALPAK AD

Abstract

Experimental results for the separation of S,R‐α‐Tetralol enantiomers obtained on preparative columns packed with particle size 20 µm of chiral adsorbent CHIRALPAK AD are presented. The total porosity was measured by using the non‐retained compound 1,3,5‐Tri‐tert‐butylbenzene and was 0.61. The permeability of the bed packed with CHIRALPAK AD was calculated as 4.4×10^?13 m². The efficiency of columns was characterized by the height equivalent to a theoretical plate (HETP) and a linear dependency has been found over tested flow rates. The HETP of S‐α‐Tetralol and R‐α‐Tetralol calculated at the flow rate 5.0 cm³/min were 320 µm and 340 µm, respectively. Thermodynamic adsorption parameters enthalpy, ΔH and entropy, ΔS, have been calculated from van't Hoff plot. Equilibrium and kinetics of adsorption of single enantiomers and racemic mixture of α‐Tetralol on CHIRALPAK AD were evaluated as well. The parameters for multicomponent isotherm linear‐Langmuir model are presented. The breakthrough curves of α‐Tetralol enantiomers are simulated with a mathematical model that accounts for axial dispersion and linear driving force for the intraparticle mass transfer.     

Separation of Submicron Particles in Packed Columns – Optimization and Scale-up of the Process

Particle enlargement by heterogeneous condensation and – based on it – separation of submicron particles in packed columns of technical scale are investigated. The activation of submicron particles and droplet growth by heterogeneous condensation is briefly described. Calculations of the droplet growth are performed and compared with experimental results. The enlargement and the separation of submicron particles by cascading packed columns trickled with water which is alternately colder or warmer than the gas is experimentally studied in a technical scale pilot plant consisting of three packed columns with a diameter of 300 mm. Droplet size distributions are measured by means of an optical particle sizer at the outlet of the columns. In order to optimize the separation process, the influence of different parameters on the separation of the submicron particles is investigated. These are the gas and the water temperature, the gas and the water flow rate, and the particle concentration. Moreover, the supersaturation of the air stream in the column is calculated by means of a rate-based nonequilibrium process model as a function of different parameters.     

Performance evaluation of carbon adsorbents for automobile canisters

To assess the performance of carbon adsorbents for automobile canisters, we have studied the adsorption and desorption of n-butane and gasoline vapor experimentally in a column charged with pelletized carbons, Car-115 and DP-1. Norit Car-115, which is a well-known carbon adsorbent for canisters, was chosen as a standard adsorbent to compare with a domestic pelletized carbon (DP-1). The use of n-butane as a reference compound for the assessment of adsorbents was proven to be very reliable when compared with the adsorption of real gasoline vapors. According to the results obtained, the carbon adsorbent for automobile canisters requires at least two basic characteristics such as the development of well-defined mesopores and high specific area, which are essential for rapid uptake rate and high working capacity.