Propagation of Signals of Finite Concentration in Gas Chromatography. I. The Quasi-Ideal Model

Abstract

A general system of partial differential equations describing the propagation of signals of finite concentrations in a chromatographic column is derived. These equations are related to the mass-balance equations for the solutes and the carrier gas. The model used assumes that there is no temperature or pressure variation at any point in the column when the signal is eluted, and that the equilibrium between stationary and mobile phases is instantaneous. It is shown that this model, which leads to a tractable set of equations, is generally valid. The solution of this system of equations gives new insight into the phenomena which are responsible for the peak deformations and broadening in preparative scale chromatography.     

Separation of Close-Boiling Components Using a New Chromatographic Method

Abstract

A combined continuous and preparative system of gas-liquid chromatography was developed and used for the separation of the close-boiling components diethyl ether and dichloromethane. In this system the less-absorbed component in the mixture can be obtained continuously in an almost pure state in one section and the remaining components can be separated in the other section of the column. Several experimental conditions (e.g., column length, particle size, feed concentration, and flow rates of carrier gas and desorbent) were varied in order to evaluate their effects on the performance of the chromatographic system. From the results of the experiments, additional column length and desorbent velocity were found to be the most important factors in separating the feed mixture continuously. The optimum switching time for good separation was experimentally measured, and it was mainly affected by column temperature and column length if the feed mixture and stationary phase were fixed. Throughputs of between 5 to 10 cm³/h resulted in good purity under certain experimental conditions.     

A Continuous Stirred Tank Reactor Study on Chromic Acid Removal by Ion Exchange

ABSTRACT

Dilute chromic acid removal by anion exchange was studied using a continuous stirred tank reactor (CSTR) system. A rate model based on film diffusion control was formulated for quantitative study on the chromate removal. For simplicity, the rate and mass balance equations were formulated for total Cr(VI) concentration. Equations were derived for the effluent concentration history as well as the time dependent Cr(VI) concentration in the resin. The derived equations for solid and liquid phase Cr(VI) concentration variations were tested and verified by the experimental results obtained. Effects of various operating conditions, such as resin size, feed concentration, and flow rate, were also discussed.     

Foam Fractionation Rates

Abstract

An empirical model enables the relation of the batch foam fractionation rate as a power function of the air rate and of the instantaneous residual surfactant concentration, eliminating the bubble size which is difficult to control and to measure. For the cationic surfactant, ethylhexadecyl-dimethylarnmonium bromide, the batch foam fractionation rate is directly proportional to the residual surfactant concentration to the first power, except for dilute (>45 mg/liter) solutions, and including suspensions containing colloidal ferric oxide and polynucleated, complexed cyanider Constants obtained from batch data can be used in the analogue equation for continuous operation to predict accurately the continuous foam fractionation rate, for a single air rate but over a substantial range of feed rates and feed surfactant concentrations. Continuous data from an entirely different column can be fit by a power function equation of the same form, with the power on the effluent or bottoms surfactant concentration again being unity. The accuracy of the predictive equations is in the range 10–18%.     

Continuous Separation of Carbohydrates by Ion-Exchange Chromatography

Abstract

A synthetic mixture of fructose, mannitol and sorbitol was continuously separated by a chromatographic method using a cation-exchange resin (Dowex 50W-X8) in its Ca²⁺-form as the stationary phase. An annular chromatograph (AC) was used to achieve a continuous mode of operation. Distribution and mass transfer coefficients of the three substances as well as bed properties were obtained by batch chromatography. The separation was simulated mathematically in terms of an approximate linear chromatographic theory was applied to the modeling of the behavior of the continuous separations. The influence of rotation rate, column loading, eluent flow rate and feed concentration on the resolution of the individual peaks were investigated.     

Fixed bed and reduced lumped diffusion model parameter estimation of copper biosorption using Aspergillus niger biomass

In this study, fixed bed model and reduced lumped diffusion model were used to explain biosorption behaviour of Cu (II) in a continuous column of Aspergillus niger biomass. The breakthrough time was evaluated for both models as a function of influent flow rate and bed height for a feed solution at 10 mg/L metal ion concentration and compared with experimental results. MATLAB was used to solve the partial differential equations and breakthrough curve was plotted. The breakthrough time obtained experimentally was comparable with data evaluated by these models. It was observed that fixed bed model and reduced lumped diffusion model can predict column dynamics more accurately at high flow rate, that is, at 9.8 mL/min for all (2.1, 3.1, and 4.1 cm) bed heights. © 2011 Canadian Society for Chemical Engineering     

The Improvement of Separation Theory in a Continuous Thermal Diffusion Column

Abstract

A more precise equation of separation applicable to the whole concentration range in a continuous thermal diffusion column with the feed introduced from any position has been derived. The results are also represented graphically and compared with those obtained by Powers in which he, as well as almost all previous investigators, considered the concentration at the feed position of the column to be approximately the feed concentration.     

Dynamic behavior of reciprocating-plate columns

The unsteady-state behaviour of a reciprocating plate column in which adjacent plates move out of phase with each other has been studied experimentally by determining responses to step changes. The one-dimensional, two-parameter model developed, leading to a system of differential equations with time-dependent coefficients, was simplified to allow parameter estimation in the Laplace domain. Special features of the experimental technique for obtaining instantaneous values of the tracer concentration which closely approximate to the average for a column cross section are described; the limitations of parameter estimation in the Laplace domain are discussed.     

A Novel Continuous Rotating Annular Liquid Chromatograph with a Multichannel Peristaltic Pump for Variable Eluent Withdrawal

Abstract

A novel continuous rotating annular chromatograph is proposed and used for the separation of amino acids. The system is equipped with a multichannel peristaltic pump to withdraw the eluent and to easily regulate its flow rate. The inlet of the annular chromatographic packed bed is divided into a number of chambers to prevent circumferential dispersion of the sample. The mass transfer characteristics of the apparatus were theoretically analyzed by using a two-dimensional transport model. The experimental results for solute elution are well simulated by the transport model. Solute dispersion in the annular column was found to be negligible. A shallower liquid depth in the inlet chamber gave sharper concentration peaks. An increase in the number of feed nozzles and the installation of inlet chambers were found to be preferable for multicomponent separation.     

Extraction Chromatography Versus Solvent Extraction: How Similar are They?

Abstract

Over the last decade, extraction chromatography (EXC) has emerged as a versatile and effective method for the separation and preconcentration of a number of metal ions. Frequently, EXC is described as a technique that combines the selectivity of solvent extraction (SX) with the ease of operation of chromatographic methods. Despite this, the extent to which EXC actually provides the selectivity of SX and to which solvent extraction data can be used for the quantitative prediction of the retention of metal ions on an EXC column has remained unclear. To address these questions, the extraction chromatographic and solvent extraction behavior of lanthanides using three different acidic organophosphorus extractants bis‐(2‐ethylhexyl) phosphoric acid (HDEHP), 2‐ethylhexyl 2‐ethylhexylphosphonic acid (HEH[EHP]), and bis‐(2,4,4 trimethylpentyl)phosphinic acid (H[DTMPeP])) have been compared. Specifically, the rate and extent of uptake of selected lanthanides by the three extractants have been examined. In addition, the relationship between the volume distribution ratios obtained in the chromatographic and liquid–liquid extraction modes have been compared and their utility in predicting the chromatographic parameter, k′, the number of free column volumes to peak maximum determined.     

Analysis and Application OF Luikov's Heat,Mass, and Pressure Transfer Model to a Capillary Porous Media

ABSTRACT

Luikov's system of partial differential equations for heat, mass and pressure transfer war applied to describe the drying process in a capillary porous body. A two dimensional finite element model were formulated to solve the system of equations. The simulated results agreed     

Probabilistic Approach to Digital Simulation of Chromatographic Processes

Abstract

A unique system has been developed for the digital simulation of chromatographic processes. This system is based on a probabilistic approach to the discrete events of adsorption and desorption rather than using a continuous solution of the differential equations used to describe the rates of adsorption and desorption. The simulation system has been developed using a threaded code technique of programming which allows the user to interact with the high speed, microcoded internal portions of the system through a very high level specific language. The utility of the system for studying both linear and nonlinear chromatographic processes is demonstrated.     

新型多组分连续制备色谱系统--阵列式柱色谱

本文介绍了一种新型多组分连续制备色谱系统———阵列式柱色谱。该系统是在综合了模拟移动床色谱和旋转环状色谱的工作原理的基础上开发出来的 ,主要由控制部分、流体输送部分、分离部分、检测部分和收集部分所组成。在分离部分中 ,本系统用色谱柱阵列代替了旋转环状色谱的环形填料层 ,即避免了溶质横向扩散和动密封问题 ,又可以根据实际生产需要增减色谱柱数目 ;在收集部分中 ,使用了专门为本系统设计的收集器实现了所有色谱柱流出液的集中收集 ;本系统采用将试验和生产一体化的设计 ,通过将单柱模式下的使用在线检测得出的优化分离条件应用到多柱模式中 ,实现了系统的柔性设计 ,降低了设备成本 ;用户可以通过使用装有系统控制软件的上位机与系统进行实时交互 ,大大提高了系统运行自动化程度 ,简化了操作。具有上述优点的本系统必将有着广泛的应用前景     

连续环状色谱柱分离性能的模拟

连续环状色谱柱是有机物稀溶液及生物制品纯化的重要制备手段,为深入认识连续环状色谱柱的性能,开展了连续环状色谱柱分离性能模拟计算的研究。提出了二维空间网格差分的模拟计算方法,并采用文献报道的木糖-山梨糖分离的实验结果进行验证,模拟计算结果与实验数据基本吻合,证明了模拟计算方法的可行性。同时考察了单组分体系下进料流量、床层旋转速度、相间总传质系数、吸附平衡常数对流出曲线的影响;以木糖为分离关键组分,以木糖的收率和纯度为目标函数,对双组分体系下进料流量、床层旋转速度、床层高度、选择性系数对分离效果的影响进行了计算和讨论,结果表明,选择性系数是决定性因素,适当提高床层旋转速度或床层高度可以增大木糖的纯度。     

Theory of Adsorption by Activated Carbon. II. Continuous Flow Columns

Abstract

A lumped parameter model for solute adsorption by activated carbon is used to model the operation of continuous flow activated carbon columns. A Langmuir adsorption isotherm is used, and the kinetics leading to the Langmuir isotherm are included in the continuity and mass balance equations representing the system. Two different approaches for the numerical integration of these equations are employed and compared. The effects of system parameters on column performance are explored.     

Theory of Adsorption by Activated Carbon. IV. High-Speed Modeling of Continuous Flow Columns

Abstract

An algorithm is developed for integrating the differential equations modeling the operation of a continuous flow activated carbon column. This algorithm is more than an order of magnitude faster in computation than the direct numerical integration of the differential equations, and appears to be just as accurate. Computer memory requirements are small. Results are presented showing the dependence of the breakthrough curves on the parameters of the Langmuir adsorption isotherm, flow rate, influent concentrations, mass transfer rate parameter, and other quantities appearing in the model. The theory is extended to the case of several solutes competing for adsorption sites.     

Unified Analysis of Compressive Packed Beds,Filter Cakes,and Thickeners

Abstract

Fluid—particle systems are widely used throughout industry. Using an ad hoc approach to model a particular fluid—solid process lacks generality. A unified approach using continuum theory for multiphase systems is applied here to evaluate a packed bed, filter cake, and continuous gravity thickener. The unified approach has the advantage that the governing equations are obtained by simplifying the generalized continuum equations. The simplifying assumptions are obvious from the equations and do not require intuitive understanding as does the ad hoc approach. Also, for similar localized conditions the same constitutive relations can be applied when the same material is used in several processes. In the packed bed, filter cake, and thickener modeled here, a compressible solid matrix behavior is represented by a truncated Taylor series expansion for the solid phase stress. The packed bed and filter cake behaviors are evaluated for a range of pump powers and bed masses or cake heights. The thickener behavior is evaluated for a range of feed and sludge discharge concentrations.     

Numerical approximation of nonlinear and non-equilibrium two-dimensional model of chromatography

This article is concerned with the numerical approximation of a nonlinear model describing the two-dimensional non-equilibrium transport of multi-component mixtures in a chromatographic column of cylindrical geometry. In contrast to previous studies, the work includes joint analysis of deviations from equilibrium and the possibility that radial concentration profiles can develop. The considered radial gradients are typically ignored, which can be problematic in the case of non perfect injections. The model consists of nonlinear convection-diffusion partial differential equations coupled with some differential and algebraic equations. A high resolution finite volume scheme is applied to solve the model equations numerically. The considered case studies include single-component, two-component and three-component elution on fixed (non-movable) beds of liquid chromatography. The developed numerical algorithm is an efficient tool to study the effects of mass transfer kinetics on the elution profiles.     

A Plate Model for Moving Feed-Injection Chromatography. I. Simulation Results

Abstract

The plate model was used to clarify the characteristics of a moving feed-injection system. The selected sample system was gas-liquid chromatography for the separation of close-boiling components such as diethyl ether and dichloro-methane. The solution of the model for the moving feed-injection system with simplified assumptions was obtained by summing up a series of solutions for a single pulse of feed. The results of the simulation showed that the efficiency of a chromatographic column could be improved by using the moving feed-injection system: the system had narrower bandwidths, higher outlet concentrations, and better resolutions when these were compared to those of preparative chromatography. Moreover, the system had much flexibility in its operation so that the retention times and the bandwidths of the components to be separated could be controlled by changing the feed port velocities. The velocity had optimum values; beyond the optimum value, the resolution became worse. An increased number of ports for feed-injection improved the resolution.     

Electrical Aspects of Adsorbing Colloid Flotation. IV. Stripping Column Operation

Abstract

The operation of a continuous flow foam flotation column in the stripping mode is analyzed under steady-state conditions. The effects of diffusive mixing, nonlinear adsorption isotherms, and finite rate of mass transport between the surface and bulk phases are taken into account in the differential equations from which column efficiencies are calculated. Adsorption isotherms are calculated by means of statistical mechanics for systems having coulombic interactions.