特征线法在求解非线性液相吸附色谱模型中的应用

本文应用特征线法求解非线性液相吸附色谱分离过程模型，论述了特征线法的原理和步骤，讨论了时间步长和空间步长对模型数值解的影响，并用色谱分离甘露醇和山梨醇以及分离蔗糖和还原糖的实验进行验证，用特征线法计算的理论流出曲线与实验流出线吻合较好。本文还分折了模型中各个参数的灵敏度，结果表明：吸附等温方程Q＝Ci*／（ai＋biCi*）中参数ai比参数bi以及总传质系数ki有更高的灵敏度。     

DETERMINATION OF THERMODYNAMIC AND KINETIC PARAMETERS OF LARGE SCALE CHROMATOGRAPHIC SEPARATION OF SUGAR AND REDUCING SUGAR

The parameter identification model of large scale chromatography separation process is proposed.The phase equilibrium constants and lumped mass transfer coefficients of sugar and reducing sugar adsorption on D1,D2 and D3 resins as well as the axial dispersion coefficients of the fluid through packed columns are determined by means of the pulse-response experiment technique with an inert substance as a tracer and the chromatography measuring technique.The elution curve calculated from these parameters is good agreement with the experimental elution curve.The sensitivity analysis of these parameters is carried out ,and the result shows that the elution curves of chromatography separation are more sensitive to the variations of the phase equilibrium relationship than to the variation of the axial dispersion as well as the lumped mass transfer coefficients.     

DETERMINATION OF THERMODYNAMIC AND KINETIC PARAMETERS OF LARGE SCALE CHROMATOGRAPHIC SEPARATION OF SUGAR AND REDUCING SUGAR

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Concentration dependence of lumped mass transfer coefficients linear versus non-linear chromatography and isocratic versus gradient operation

The general rate model provides a reliable platform to predict elution bands in both linear and non-linear chromatography provided the required equilibrium functions and the coefficients quantifying the mass transfer in and around the particles are available. If further the variation of the equilibrium functions with changes in the mobile phase composition is known, this model is also able to predict gradient elution chromatography. Significant disadvantages of the model are the need to specify three kinetic coefficients and the amount of computing time required for the numerical solution of the underlying equations. Thus, several simplified models have been suggested lumping mass transfer resistances together. In this work the accuracy of predicting chromatographic bands based on the numerical solution of two lumped models has been analyzed. Elution profiles calculated by (a) the transport-dispersive and (b) the equilibrium-dispersive models were compared between each other and with the solution of the more detailed general rate model. In the analysis performed both linear and non-linear chromatography was considered under isocratic and gradient conditions.     

大型液相色谱分离甘露醇和山梨醇的热力学及动力学参数辨识

本文研究了液相色谱分离过程的吸附平衡常数、传质系数参数的估值模型，用色谱技术和以惰性物示踪的扰动应答实验技术测定甘露醇和山梨醇在钙型吸附剂上的吸附相平衡常数和总传质系数以及床层中的轴向扩展系数，结果表明：吸附平衡常数和吸附剂的选择性随温度的升高而下降；液固相间的总传质系数随温度的升高而增大；轴向扩散系数随流速的增大而增大，参数灵敏度分析的结果表明，相平衡关系，尤其是吸附选择性，对色谱分离的影响有较     

吸附剂性能和操作参数对液相色谱流出峰不对称性的影响

色谱流出峰的拖尾现象普遍存在于制备和大型色谱分离过程中,它直接影响分离的产率和回收率．本文提出采用色谱流出峰形的不对称偏差度来表征色谱流出峰的拖尾程度;并基于液相制备色谱分离过程FAD－SMT模型及吸附速率理论,通过计算机模拟,定量分析了吸附剂性能和操作参数对色谱流出峰形不对称性的影响。结果表明：不仅是吸附剂的热力学和动力学性能（包括吸附相平衡关系、液固两相间的传质阻力）;而且柱的设计和吸附剂的装填状况（包括轴向扩散系数）,以及色谱分离的操作条件（进料时间、浓度和流速等）都直接影响色谱流出峰形的不对称性。随着吸附相平衡等温线的非线性程度增大,或者总传质系数的减小,色谱流出峰形的不对称偏差度明显增大;吸附剂吸附容量的减小也将引起色谱流出峰形的不对称偏差度的增加;色谱流出峰形的不对称偏差度与进科体积、浓度和流体线速,以及轴向扩散系数的增大成正比。     

Simultaneous determination of two‐component isotherm parameters and lumped mass transfer coefficients in RPLC with the 0‐1 model‐inverse method

The 0‐1 model‐inverse method of nonequilibrium nonlinear chromatography was developed to simultaneously determine the isotherm parameters and the lumped mass transfer coefficients of the two‐component systems in RPLC. By comparing the simulated elution curves with experimental curves with regard to profiles and areas, the suitable isotherm parameters and the lumped mass transfer coefficients were obtained with the 0‐1 model‐inverse method. With a solute cell unit width of cm, the average errors of the peak areas were 0.178% for one component and ?0.40% for two components, and the numerical diffusions of the 0‐1 model for the contribution to band broadening may be negligible. In addition, the results showed that the lumped mass transfer coefficients decrease as the solute concentration increases. The 0‐1 model‐inverse method has not only the advantages of high calculation speed (less than 10 min for one‐component systems or approximately 3 h for two‐component systems using an ordinary computer) and high accuracy in simultaneously obtaining thermodynamic parameters and kinetic parameters of two‐component systems, but this method also possesses the potential to optimally design and control the time‐variant preparative chromatographic system due to the thermodynamic state recursion and the Lagrangian‐Eulerian presentation of the 0‐1 model.     

双柱交替循环色谱分离甘露醇山梨醇过程

本文在非线性非平衡双柱循环色谱分离过程数学模型的基础上,进行了双柱交替循环色谱分离甘露醇山梨醇的实验,对模型进行了实验验证。结果表明：采用非线性非平衡双柱循环色谱模型计算的流出曲线与实验结果相吻合。计算机模拟的结果从理论上证明了对本实验体系采用双柱交替循环色谱分离模式比采用传统的色谱分离模式能获得更高的分离产率,产率随循环次数的增加而增加,使用双柱交替循环色谱分离操作模式获得的分离效率超过使用传统长色谱柱操作模式获得的分离效率。当轴向扩散比较严重、液固两相间的传质阻力较大,或者吸附的表观选择性系数较小时,采用双柱循环色谱模式比使用传统单柱色谱模式能获得更高的产率。     

THE DETERMINATION OF ADSORPTION ISOTHERMS AND SOLID DIFFUSION COEFFICIENTS OF MANNITOL AND SORBITOL BY LIQUID CHROMATOGRAPHY TECHNIQUE

The parameter identification model is proposed for determining the linear adsorption isotherms and the solid diffusion coefficients by using adsorption chromatorgaphy.Axial dispersion coefficients is firstly determined by pulse-respond experiment technique with an inert substance as tracer,then the elution curves of chromatography separating the isomer mannitol and sorbitol are determined by the chromatographic measuring technique,and pinally the adsorption isotherms and the solid diffusion coefficients of mannitol and sorbitol on Ca^2+ resins are estimated by using this model.The results show that the axial dispersion coefficients increase with fluid velocity increasing,The adsorption equilibrium constants decrease with temperature rising;and the solid diffusion coefficients increase with temperature rising.The theoretical elution curves are good agreement with the experimental elution curves of the liquid adsorption chromatography separating the mannitol and the sorbitol.The model provides a simple and reliable procedure to estimate the kinetic and thermodynamic parmeters of the adsorption.     

THE DETERMINATION OF ADSORPTION ISOTHERMS AND SOLID DEFFUSION COEFFICIENTS OF MANNITOL AND SORBITOL BY LIQUIDCHROMATOGRAPHY TECHNIQUE

1INTRODUCTIONTheseparationprocessoflarge-scaleliquidchromatographyisaunstabletransferprocess.Theseparationefficiencyisaffecteddirectlybytheadsorptionisotherms,themasstransferresistancewithinsolidadsorbentparticleandtheoperationparametersinthesystem.Therefore,thedeterminationoftheisothermsandisnecessaryfordesigningandoptimizingthechromatographicprocess.Thereareseveralmethodstodeterminekineticparameters.Carl(1992)carriedoutthekineticexperimentoftheadsorptioninacontinuousstirredtankadsorberl…     

A FAD-SMT Model of Large Scale Liquid Adsorption Chromatography

The paper proposes a FAD-SMT model of large-scale liquid chromatography by which a continuous equation of chromatographic separation is decomposed into a convection dispersion partial differential equation and a set of ordinary differential equations. The numerical method for the FAD-SMT model is established. The stability and the convergence condition of numerical solution, and the choice of time and space interval are discussed. The FAD-SMT model is used to simulate liquid adsorption chromatography and cycling adsorption chromatography. Results show that the elution curves calculated by FAD-SMT model are good agreement with the experimental elution curves of the separation of glucose and fructose, the separation of sucrose and reducing sugar and the separation of mannitol and sorbitol. The result of parameter sensitivity analysis shows that the chromatographic elution curves are more sensitive to the changes of the parameter ai in Langmuir isotherms than to the changes of other parameters in the studied system.     

液相制备吸附色谱流出峰对称性的若干影响因素

在色谱分离连续性方程和质量传递速率方程基础上,对色谱分离过程进行计算机模拟,定量分析了分离体系的热力学、动力学参数和操作条件对色谱流出峰形对称性的影响。结果表明,吸附相平衡关系、液固两相间的传质阻力及进料体积、进料浓度和流体线速等都将直接影响色谱流出峰形的对称性。流出峰形的不对称程度随着吸附等温线的非线性程度、液固两相间的传质阻力、流体线速、进料体积、进料浓度的增大而增大;在线性条件下,随着吸附剂吸附容量的减小而增大。     

Investigation of the steric mass action formalism in the simulation of breakthrough curves on a monolithic and a packed bed column

The simulation of the behaviour of two proteins (cytochrom c and alpha-chymotrypsinogen) on two types of stationary phases (monolithic and porous particle-based) was attempted for non-linear (simulation of breakthrough curves) and linear (simulation of elution peaks) cation exchange chromatography. It was found that the combination of a stoichiometric model (steric mass action, SMA) with the lumped pore diffusion (POR) model allows a simulation of high predictive value. Using one set of SMA and transport parameters for a given column morphology and/or protein, breakthrough curves and peaks could be simulated that agreed well with the experimental data while no dependency on either the protein load or the mobile phase composition (salt content) was observed. One of the SMA parameters, namely the characteristic charge needed some slight adjustment (within the error of the experimental determination of this parameter) in order to optimise the fit.     

Comparative modeling of breakthrough curves of bovine serum albumin in anion-exchange chromatography

The experimental results of a previous study of the mass transfer kinetics of bovine serum albumin (BSA) in ion-exchange chromatography, under nonlinear conditions, were reevaluated using the general rate model of chromatography. Solutions of this model were obtained numerically. The influences of axial dispersion, the resistance to mass transfer from the bulk mobile phase to the surface of the packing particles, and the intraparticle mass transfer resistances on the profiles of the breakthrough curves of BSA were investigated. The results obtained are compared to those of a previous investigation of the same data, using the simple transport-dispersive model and the lumped pore diffusion model. The results obtained show that the use of an oversimplified model for the analysis of chromatographic data can lead to erroneous interpretations of the experimental data and to misunderstandings of the fundamentals of the processes involved. Finally, a theoretical comparison between the properties and the range of application of the three models is provided.     

Non-equilibrium model of liquid column chromatography : I. Exact expressions for elution profile moments and relation to plate height theory

A model for column chromatography that includes non-equilibrated mass transfer, diffusion, and generalized boundary conditions at the top of the column is solved by the method of moments. The theory predicts that as the macroscopic velocity u becomes very small, the plate height approaches a constant (rathe than diverging as u⁻¹. As u increases, the plate height drops to a minimum and then increases. We show that the past assumptions that mass transfer and various types of diffusion contribute additively to the plate height, hold only at or beyond the minimum. We show further that our expression fits observed data with only a single adjustable lumped parameter. The parameter contains the mass transfer rate k⁻¹ for moving out of a bead. The data fit, as well as an analytical approximation that we derive for the position of the minimum, provides a relation between k₋₁ and bead particle size (d_p) and consequently between d_p and profile dispersion. Conditions under which the peak of the elution profile is a good approximation to the mean are described. For a suitably chosen flow-rate, the mass transfer rates can be estimated from the observed dispersion in the elution profile.     

A theoretical plate model accounting for slow kinetics in chromatographic elution

The chromatographic elution has been studied from different perspectives. However, in spite of the simplicity and evident deficiencies of the plate model proposed by Martin and Synge, it has served as a basis for the characterization of columns up-to-date. This approach envisions the chromatographic column as an arbitrary number of theoretical plates, each of them consisting of identical repeating portions of mobile phase and stationary phase. Solutes partition between both phases, reaching the equilibrium. Mobile phase transference between the theoretical plates is assumed to be infinitesimally stepwise (or continuous), giving rise to the mixing of the solutions in adjacent plates. This yields an additional peak broadening, which is added to the dispersion associated to the equilibrium conditions. It is commonly assumed that when the solute concentration is sufficiently small, chromatographic elution is carried out under linear conditions, which is the case in almost all analytical applications. When the solute concentration increases above a value where the stationary phase approximates saturation (i.e. becomes overloaded), non-linear elution is obtained. In addition to overloading, another source of non-linearity can be a slow mass transfer. An extended Martin and Synge model is here proposed to include slow mass-transfer kinetics (with respect to flow rate) between the mobile phase and stationary phase. We show that there is a linear relationship between the variance and the ratio of the kinetic constants for the mass transfer in the flow direction (τ) and the mass transfer between the mobile phase and stationary phase (ν), which has been called the kinetic ratio (κ=τ/ν). The proposed model was validated with data obtained according to an approach that simulates the solute migration through the theoretical plates. An experimental approach to measure the deviation from the equilibrium conditions using the experimental peak variances and retention times at several flow rates is also proposed.     

Determination of the lumped mass transfer rate coefficient by frontal analysis

The validity of measurements of the lumped mass transfer rate coefficient (k_m,L) is studied on the basis of experimental data acquired under Langmuir isotherm conditions, in reversed-phase liquid chromatography. Two different methods were used, the perturbation method and frontal analysis. Accurate values of k_m,L can be properly obtained by the perturbation method because, with this method, the chromatographic processes take place under locally linear isotherm conditions. Values of k_m,L can also be derived from the breakthrough curves obtained in frontal analysis. Because the contribution of axial dispersion to band broadening was larger than that of the mass transfer resistances, the apparent axial dispersion coefficient (D_a) was first derived from the breakthrough curve by applying the equilibrium–dispersive model. Then, the value of k_m,L was calculated from D_a. The values of k_m,L determined by the two methods were in close agreement in the range of nondimensional Langmuir equilibrium constants (r=1/[1+K_LC₀]) between 0.32 and 0.85, irrespective of the mobile phase flow velocity. Thus, frontal analysis can be used for kinetic studies of the mass transfer in chromatographic columns.     

Non-equilibrium model of liquid column chromatography : II. Explicit solutions and non-ideal conditions

the analysis begun in the previous paper of a general model for liquid chromatography in a column is continued here. Explicit solutions are obtained for small-zone and large-zone non-equilibrium chromatography models both without and with diffusion. The effects on the moments of the elution profile of a distribution function which characterizes molecular heterogeneity (such as molecular size) or bead non-uniformities are analyzed. A first-order correction to the mean value of the elution profile when sorption—desorption kinetics are concentration dependent is derived.Numerical simulations of the elution profile indicate the following. (1) The peak and mean may differ by as much as a factor of two for slow mass transfer (k₁ 0.01). Since the mean is uniquely detemined by the equilibrium constant but the peak is not, the use of the peak to characterize the equilibrium constant for broad asymmetric profiles may lead to serious errors. (2) When the rate of mass transfer from the void to penetrable volumes becomes comparable to u/h, a second peak will develop in the elution profile. This happens even for a completely homogeneous population under conditions, and is caused by molecules that traverse the column without penetrating beads. The dispersion of this peak is therefore determined entirely by effects other than mass transfer. (3) In the non-linear regime (i.e., when mass transfer rates are concentration dependent), the equilibrium constant is, in general, no longer uniquely determined by the mean. Uniqueness is, however, obtained in the limit as both mass transfer coefficients become very small, with their ratio remaining moderate.     

质粒DNA在灌注色谱基质上的吸附行为

Anion exchange chromatography is the most popular chromatographic method for plasmid separation.POROS R1 50 is a perfusio n chro mato graphic suppo rt w hich is a reversed phase matrix and is an alternative to co nventio nal o nes due to its mass transfer pro perties.The adso rptio n and elutio n o f the pIDKE2 plasmid o nto reversed phase POROS R1 50 w as studied.Langmuir iso therm mo del w as adjusted in o rder to get the max imum adso rptio n capacity and the disso ciatio n co nstant fo r POROS R1 50-plasmid DNA(pDNA) system.Breakthro ugh curves w ere o btained fo r vo lumetric flo w s betw een 0.69-3.33 mL/min,given dynamic capacity up to 2.3 times higher than tho se repo rted fo r io nic ex change matrix used during the purificatio n pro cess o f plasmids w ith similar size to that o f pIDKE2.The efficiency w as less than 45% fo r the flo w co nditio ns and initial co ncentratio n studied,w hich means that the suppo rt w ill no t be o perated under saturatio n circumstances.