A strategy for tailored design of efficient and low‐pressure drop packed column chromatography

Packed chromatographic column, with higher efficiency and lower pressure drop is designed by using inert core adsorbents as stationary phase. The analytical solutions for moments and height equivalent to a theoretical plate (HETP) are given under the conditions of linear adsorption kinetics by taking into account of the axial dispersion, film mass‐transfer resistance, intraparticle diffusion resistance, and the sorption rate for chromatographic column packed with inert core adsorbents. By minimizing HETP, a nonlinear algebraic equation was derived to predict the optimized value of the inert core radius. For a given adsorbent with the optimized inert core radius, a strategy was presented to tailor the design of new packed chromatographic column with higher efficiency and lower pressure drop. As an example for supercritical carbon dioxide chromatography, reduced equations in terms of dimensionless inert core radius were derived by “order of magnitude” analysis. The quantitative analysis shows that the major benefit of the inert core adsorbent is a shorter diffusion path compared to conventional fully porous particles. The shorter diffusion path reduces dispersion of solutes and minimizes peak broadening leading to lower pressure drop while maintaining high‐separation efficiency. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Modeling separation of proteins by inert core adsorbent in a batch adsorber

Adsorption/desorption kinetics of protein on the binding ligand of inert core adsorbent in a batch adsorber is analyzed theoretically for Langmuir isotherm coupled with the intraparticle diffusion and film mass transfer resistances. For the two limiting cases of Langmuir isotherm, there are analytical solutions. New analytical solutions are derived for Henry isotherm, and the analytical solution of shrinking core model is recommended for rectangular isotherm. The effects of the inert core radius, equilibrium constant, intraparticle diffusion and film mass transfer resistances on the time evolution of bulk concentration and particle radial profiles were investigated. The applicable range of the analytical solution with rectangular isotherm is given. A new method to estimate both film mass transfer coefficient, k_f, and effective pore diffusivity, D_pe, from a single bulk concentration-time curve in batch adsorber is given and tested with literature data for the adsorption of BSA on CB-6AS inert core adsorbent.     

Perturbation chromatography with inert core adsorbent: Moment solution for two-component nonlinear isotherm adsorption

The moment analysis is applied to study two-component perturbation chromatography with linearized nonequilibrium adsorption. General expressions for the first and second chromatographic moments of components and waves are given by taking into account axial dispersion, film mass transfer resistance, and intraparticle diffusion resistance for chromatographic column packed with inert core adsorbents. The well-known results for moment solution of the single-component case and special two-component case are extended to the general two-component case.     

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.     

Analysis of the constant molar flow semi-batch adsorber loaded with inert core adsorbents

An analytical solution for a constant molar flow semi-batch adsorber loaded with inert core adsorbents is obtained for the linear isotherm coupled with intraparticle diffusion and external film diffusion. The solution obtained in this study consists of two parts. One is the asymptote, to which the bulk concentration approaches as time is sufficiently large. The other is the relaxation term, which dictates how the mass in the bulk phase flows into the adsorbent within the adsorption vessel. For a given value of the inert core radius, the slope of the asymptote is a function of the equilibrium parameter only and the intercept is a function of the kinetic parameter as well as the equilibrium parameter. The intercept of the asymptote consists of two parts. One is the contribution due to the external film resistance; the other is the contribution due to the intraparticle diffusion resistance. Hence, we can obtain the information of the equilibrium constant, the film mass transfer coefficient, and the effective diffusivity from the asymptote of the solution presented in this study.     

Sorption dynamics in fixed‐beds of inert core spherical adsorbents including axial dispersion and Langmuir isotherm

The effects of axial dispersion and Langmuir isotherm on transient behavior of sorption and intraparticle diffusion in fixed‐beds packed with monodisperse shell‐type/inert core spherical sorbents are studied. The system of partial differential equations of the mathematical model is solved numerically using finite difference methods. Results are presented in the form of breakthrough curves for adsorption and desorption processes. Results reveal that the shape of the breakthrough curves is influenced by both hydrodynamic and kinetic factors. Hydrodynamic factor is governed by axial dispersion and is controlled by changes of Peclet number. Simulation results reveal that when linear adsorption isotherm is used, the effect of axial dispersion on breakthrough curves of the system is important for Peclet numbers smaller than 50, whereas, for Langmuir isotherm axial dispersion is considerable for Peclet numbers less than 80. In addition, effects of type of adsorption isotherms and size of adsorbents on breakthrough curves are investigated, and results are compared with existing reports in the pertinent literature. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A general rate model approach for the optimization of the core radius fraction for multicomponent isocratic elution in preparative nonlinear liquid chromatography using cored beads

Cored beads (also known as pellicular, superficially porous, and fused-cored beads or particles) offer advantages over fully porous beads in reduced diffusional mass transfer resistances in particle macropores and separation times in liquid chromatography (LC). They are also used to regulate bead densities. The core of a bead has a relatively small volume and yet presents a large linear distance for diffusional mass transfer inside particle macropores. Using a non-porous inert core, intraparticle diffusional mass transfer resistance can be reduced with a relatively small loss in binding capacities. In multicompnent isocratic elution chromatography, cored beads are a compromise between fully porous beads and non-porous beads. Non-porous beads completely eliminate intraparticle diffusion, providing sharp elution peaks with the shortest retention times. However, they do not provide a sufficient retention time range for peaks to separate in preparative LC because of their limited binding capacities. At the other end, fully porous beads offer the largest retention time differences, but suffering from excessive band broadening. For a particular multicomponent elution system, core radius fraction can be optimized to take the advantages of both fully porous beads and non-porous beads. This work presented a general rate model for cored beads and its numerical solution strategy. The model considered axial dispersion, interfacial mass transfer, intraparticle diffusion, and multicomponent Langmuir isotherm. Computer simulation was used to study the effects of core radius fraction on breakthrough curves and elution peaks. The model was used to optimize the core radius fraction for a preparative ternary elution system as an example case.     

Frequency response of the adsorption vessel loaded with inert core adsorbents

An analytical solution for the frequency response of a semi-batch adsorption vessel with sinusoidal modulation of molar flow rate, loaded with inert core adsorbents is obtained for a linear isotherm coupled with intraparticle diffusion and external film diffusion. The low-frequency limiting values of the in-phase and the out-of-phase characteristic functions of the frequency response are found to be explicit functions of the size of the inert core and the external mass transfer parameter. Simulation results of the in-phase and the out-of-phase characteristic functions show that there exist a crossover frequency and overshoot of the in-phase characteristic function when external mass transfer resistance is present.     

Modelling of porous core–shell adsorbent particles with various morphologies suspended in batch adsorber from analytical solutions of diffusion equations

Considering both intra-particle diffusion and film resistance for mass transfer, analytical solutions of transient concentration of adsorbate inside adsorbents with spherical, cylindrical, or slab-type particles were derived for batch adsorbers by solving governing equations using the Laplace transform. Assuming Henry's or rectangular isotherm, the average concentration inside adsorbents as well as transient bulk concentration were also obtained for the particles with or without the inert core. Computations were performed to compare the results according to the shape of adsorbents by adjusting adsorbent loading, Biot number (Bi), and inert core thickness. Regardless of particle morphologies, steady-state bulk concentration was only affected by adsorbent loading and inert core thickness, whereas the effect of Bi was confirmed from the decreasing reduction rate of adsorbate concentration with decreasing Bi. When diffusivity was dependent on time, time-decaying diffusivity caused the increase in steady-state concentration that was predicted by eigenfunction expansion. Experimental results using porous fibres by electrospinning were compared with the mathematical solution of a cylindrical adsorbent for the estimation of intra-particle diffusivity. Using the solutions of the diffusion equation model, novel core–shell cylindrical adsorbents can be designed and synthesized as core–shell fibres by electrospinning with a coaxial nozzle to save the cost of the active shell layer. Such core–shell structured fibres can be adopted as adsorbents for novel batch adsorption processes and the present modelling results can be extended to other processes like fixed bed adsorbers.     

活性炭纤维吸附填充床突破曲线预测(Ⅰ)精确解与近似解

针对活性炭纤维吸附填充床,当吸附等温方程为线性时,考虑轴向弥散、纤维内扩散以及纤维外对流传质阻力,获得了阶跃进样时突破曲线的精确解以及拟对数概率密度函数近似解和二次方近似解。并在讨论模型参数对突破曲线影响的同时,对精确解和两种近似解进行了比较。结果表明,在较宽的模型参数范围内,两种近似解与精确解均吻合较好,但二次方近似解复杂,计算困难;而拟对数概率密度函数近似解简单,计算方便。     

Modeling and Experimental Studies of Adsorptive Dewatering of Selected Aliphatic Alcohols in Temperature Swing Adsorption System

Based on experimental work, closely coupled with mathematical modeling, an analysis was performed of the adsorptive drying of selected water-aliphatic alcohol solutions. The experimental work involved ethanol, n-propanol, and n-butanol dehydration using two adsorbents, 3A and 4A zeolite molecular sieves. The isothermal model developed in this paper incorporates an overall linear mass driving force, including liquid film mass transfer and intraparticle diffusion coefficients, a variable axial diffusivity, and experimentally determined Langmuir-Freundlich isotherms. Breakthrough curves generated by the model were compared with those obtained experimentally, giving a fairly good fit. The model simulations enabled determination of the water content profiles in adsorbent beds.     

活性炭纤维填充床内多组分竞争吸附

建立了活性炭纤维填充床内多组分竞争吸附传质动力学模型 ,采用正交配置方法求解数学模型以预测突破曲线 ,从理论上探讨了竞争吸附平衡及吸附质在填充床内的轴向弥散、纤维内扩散和纤维外对流传质等因素对强、弱吸附组分突破曲线的影响。在间歇和填充床吸附器内进行了脱除水溶液中酚类化合物的实验 ,测定了活性炭纤维吸附水溶液中苯酚和氯代苯酚的吸附等温线 (间歇吸附 )以及苯酚和氯代苯酚在活性炭纤维填充床内竞争吸附时的突破曲线 ,并与模型计算值进行了比较。结果表明 ,吸附质在活性炭纤维内扩散和纤维外对流传质阻力不是填充床内吸附过程的控制步骤 ,而轴向弥散影响显著 ,不可忽略     

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.     

Dynamical adsorption in fixed bed

The behavior of an adsorbent fixed-bed had been investigated for irreversible equilibrium when the adsorption rate is limited by internal diffusion. Breakthrough curves equations has been established for spherical or cubic sorbent particles considering axial dispersion. It has been found out a linear law between the extrapolated breakthrough time and the inverse of adsorbate flowrate. That allows the evaluation of internal diffusion and axial dispersion coefficients.The breakthrough curves of propylene on 13X molecular sieves are interpreted accurately when it is admitted that the adsorption rate is limited by the action of combined internal and external difrusions and when the axial diffusion is taken into account.When the axial diffusion is neglected, the breakthrough curves can be also computed but the coefficients of mass transfer chosen for a good fitting do not agree with those predicted by classical formula.     

The Adsorption of Gold Cyanide onto Porous Adsorbents: Relation between Liquid-Phase Concentration,Suspended Solids,and Mass-Transfer Mechanisms

Abstract

Much progress has been made during the last decade on carbon-in-pulp and resin-in-pulp technology for the extraction of gold and silver from leached pulps. In this study a systematic investigation was conducted on the mass transfer of gold cyanide to activated carbon and ion-exchange resins in suspended solids under conditions of different gold solution-phase concentrations. The different mass transfer phenomena were studied by measuring the concentration profile of gold in solution. Two distinct mass transfer mechanisms have been identified: 1) at low gold solution-phase concentrations, where the rate of adsorption is controlled by film diffusion, the presence of fine inert particles had no effect on either the rate of adsorption or the equilibrium loading of gold cyanide; 2) at high gold solution-phase concentrations, where intraparticle diffusion becomes rate controlling, the inert particles affected the rate of adsorption of gold cyanide for both the adsorbents. Furthermore, the inert particles did not affect the equilibrium loading of gold at the high solution-phase concentration. It was also found that under certain conditions the silica particles in suspension enhanced the mass transfer of gold cyanide to the adsorbents. This was attributed mainly to the fact that the silica particles act as an adsorbent, thereby increasing the actual loading of gold cyanide onto the adsorbents.     

Dynamics of pressurization and blowdown of an adiabatic adsorption bed: 4. Intraparticle diffusion/convection models

The importance of intraparticle mass transfer during pressurization and blowdown steps of PSA processes in an adiabatic adsorption bed was assessed by comparing intraparticle diffusion/ convection and intraparticle diffusion models. Film mass/heat transfer resistances are also considered in the model. The film heat transfer resistance is more important than the heat transfer resistance inside the particle; it can be assumed to be negligible in PSA processes when the temperature variation is not very large, otherwise it leads to serious errors when the adsorption capacity of adsorbents is high and the heat capacity of the system is not high. Intraparticle convection improves the mass transfer inside the particle and leads to faster heat releases into and out of the adsorbents.     

Study on mass transfer of ethyl acetate in polymer adsorbent by experimental and theoretical breakthrough curves

A new polymeric adsorbent with highly hypercrosslinked structure was developed for the removal of VOCs from polluted air. The purpose of this work is to obtain the intraparticle mass transfer coefficient of the adsorbent particles. Adsorption experiments for obtaining breakthrough curves were carried out with a fixed bed system. A dynamic mathematical model for the fixed bed adsorption system was developed. By model fitting, the overall mass transfer coefficient was determined when the deviation error was minimum. Then, the intraparticle mass transfer coefficient of the adsorbent was determined when the external mass transfer resistance was eliminated at higher velocities. Furthermore, a linear relationship of the intraparticle mass transfer coefficient and equilibrium coefficient at lower inlet gas concentrations range was correlated. Moreover, an equation for predicting external mass transfer coefficient at low Reynolds number range at room temperature was obtained.     

Recovery of 1,4‐Dimethyl Piperazine from Aqueous Solutions Using Polymeric Adsorbent and Ion‐Exchange Resins

Abstract

Strong and weakly acidic ion exchange resins and polymeric adsorbents are used for recovery of 1,4‐dimethyl piperazine (DMP) from aqueous solutions. Sorption of the amine in undissociated form is the primary mechanism of uptake of DMP on the ion‐exchange resins. Equilibrium adsorption data for DMP on the resins, at various temperatures, are fitted in Langmuir adsorption isotherm. Kinetic studies show that intraparticle diffusional resistance controls the sorption of DMP into the resin matrix. A mathematical model based on intraparticle diffusion and external mass transfer is used for simulating breakthrough profiles and compared with the experimental results for a fixed bed of weakly acidic Indion‐652 resin. The DMP loaded bed of the resin was effectively regenerated with methanol.     

Intraparticle Diffusion/Convection Models for Pressurization and Blowdown of Adsorption Beds with Langmuir Isotherm

Abstract

Intraparticle diffusion/convection and equilibrium models are used to simulate the bed dynamics of pressurization and blowdown steps of PSA processes with binary mixtures of inert and adsorbable species. The effect of the nature of the equilibrium isotherm, i.e., linear and Langmuir isotherms, is discussed. The improvement of mass transfer inside the adsorbent by increasing particle permeability or decreasing particle size is addressed. Simulation results show that using “large-pore” adsorbents, i.e., increasing permeability to cause a high intraparticle convective flow instead of decreasing particle size to reduce intraparticle mass transfer resistances, is a good choice in PSA processes.     

Kinetic Analysis off Ion-Exclusion Chromatography by the Moment Method

Abstract

The separation of sodium chloride and alcohols by ion exclusion was studied by an pulse response technique. Kinetic parameters were evaluated by the moment method. The HETP was calculated and the contributions of each mass transfer process to the HETP were elucidated. Both axial dispersion and intraparticle diffusion were dominant for alcohols. Agreement between experimental and calculated elution curves is excellent.