Modelling of liquid-liquid extraction columns: Use of published model correlations in design

Design of several liquid-liquid extraction columns — packed, pulsed-packed, pulsed-plate, Oldshue-Rushton columns and the rotating disc contactor — was attempted utilizing available correlations for drop size, holdup of dispersed phase, flooding velocities, mass transfer coefficients and axial mixing coefficients. Correlations in many cases were vaguely defined and often based on very limited data. Results indicated that for given flow rates and extraction efficiency, the height of a packed or Oldshue-Rushton column must be considerably greater than the predicted minimum heights of the other three columns, which were comparable considering the limited data utilized in the developed correlations. A critical evaluation of the correlations should be carried out to guide the further experimental effort required to confirm the utility of the axial dispersion model in liquid-liquid extraction column design. Extension of the theory to include drop size variation is highly desirable.     

Inline Measurement of the Residence Time Distribution in High-Pressure Extraction Columns

Axial backmixing lowers the efficiency of packed countercurrent high-pressure extraction columns. To quantify backmixing, a method of measuring the residence time distribution and calculating the axial dispersion coefficient in high-pressure extraction columns is introduced. Using a design of experiments, the effect of supercritical and liquid mass flow rates as well as the pressure at a constant temperature on the mean residence time and the axial dispersion coefficient are evaluated for the system water/supercritical CO₂. The experimental data is correlated to the Reynolds and Schmidt number.     

萃取塔数学模型及过程强化的若干研究进展

萃取塔因生产能力大、占地面积小、密闭性好等优点,在石油、化工、生物、医药和环境工程等多领域被广泛应用。本文从以下几个方面介绍了萃取塔近些年的研究进展：综述了传统萃取塔（脉冲萃取塔、转盘塔与Kühni塔等）的水力学、轴向扩散与传质模型的发展,分析比较了表面张力、传质方向、放大效应等因素对模型的影响;介绍了计算流体动力学（CFD）在萃取塔中单液滴、单相流模拟、液-液两相流模拟、外加能量模拟、与群体平衡模型（PBM）耦合模拟中的应用进展;介绍了国内外设计开发的新型萃取塔,包括改变传统塔的内构件和引入多种外场能量等方式来强化相间传质。研究表明,将先进实验研究方法、准确经验模型和可靠理论计算相结合,将会是萃取塔研究的重要手段和方向。     

New Approach in the Prediction of RDC Liquid‐Liquid Extraction Column Parameters

The liquid‐liquid extraction process is well‐known for its complexity and often entails intensive modeling and computational efforts to simulate its dynamic behavior. This paper presents a new application of the Genetic Algorithm (GA) to predict the modeling parameters of a chemical pilot plant involving a rotating disc liquid‐liquid extraction contactor (RDC). In this process, the droplet behavior of the dispersed phase has a strong influence on the mass transfer performance of the column. The mass transfer mechanism inside the drops of the dispersed phase was modeled by the Handlos‐Baron circulating drop model with consideration of the effect of forward mixing. Using the Genetic Algorithm method and the Numerical Analysis Group (NAG) software, the mass transfer and axial dispersion coefficients in the continuous phase in these columns were optimized. In order to obtain the RDC column parameters, a least‐square function of differences between the simulated and experimental concentration profiles (SSD) and 95 % confidence limit in the plug flow number of the transfer unit prediction were considered. The minus 95 % confidence limit and sum of square deviations for the GA method justified it as a successful method for optimization of the mass transfer and axial dispersion coefficients of liquid‐liquid extraction columns.     

Settling velocities of particles in bubbly gas-liquid mixtures

The axial dispersion-sedimentation model is commonly used to describe the axial concentrations of solids in three phase bubble columns at low liquid velocities. When the two parameters of this model, the particle settling velocity and the solids axial dispersion coefficient, are uncoupled by the use of various assumptions, physically unrealistic values of these parameters often result. Direct experimental measurements of solids settling rates in bubbly gas-liquid mixtures were carried out. The measured mean settling velocities decreased slightly with gas flow rate and were equal to or slightly less than the single particle free settling velocity in the liquid alone. Solids axial dispersion coefficients were also obtained from the solids settling rate distribution data, and gave values considerably less than the experimental liquid axial dispersion coefficient.     

Modelling churn-turbulent bubble columns—I. Liquid-phase mixing

A new two-region phenomenological model for liquid-phase mixing in churn-turbulent bubble columns has been proposed. A gas-rich region rises rapidly through the column transporting liquid to various points in the system while a relatively stagnant, gas-lean region is vigorously agitated by the passage of the gas-rich region. Estimation of most of the model parameters by physical reasoning reduces the proposed model to a one-parameter model. This unknown parameter, which describes liquid exchange between the gas-rich and gas-lean regions, can be obtained by matching the model predictions to the experimentally measured tracer response. The comparison of the proposed model's tracer response and that of the axial dispersion model also allows this exchange parameter to be calculated from the available axial dispersion coefficient correlations. The proposed model is computationally much superior to the axial dispersion model.     

Axial dispersion in a rectangular bubble column

This paper presents the results of an experimental study on the gas holdup and the liquid phase axial dispersion coefficient in a narrow packed and unpacked rectangular bubble column. In both cases the gas and liquid flow rates were varied and the data were obtained by employing standard tracer technique. The gas holdup and the axial dispersion coefficient for both the packed and unpacked columns were found to be dependent on the gas and liquid flow rates. For given gas and liquid velocities and a given packing size in the case of the packed column, the rectangular column gave significantly higher dispersion coefficients than a cylindrical column of the equivalent cross sectional area. This result agrees very well with the one predicted by the velocity distribution model. The correlations for the Peclet number, the axial dispersion coefficient, and the fluid holdup for both the unpacked and packed bubble columns are presented.     

The Droplet Population Balance Model – Estimation of Breakage and Coalescence

A droplet population balance model is employed in order to describe the hydrodynamic behavior of solvent extraction columns. This model describes the axial change of local column holdup and local droplet size distributions due to the basic phenomena, like droplet rising, axial dispersion, droplet breakage and coalescence. In order to reduce experimental efforts, single and swarm droplet experiments in small lab‐scale devices were performed. For this, a rotating disc contactor (RDC) with one compartment and a Venturi tube were used to investigate droplet breakage and droplet coalescence. In case of breakage the experiments were made for different droplet sizes at different rotor speeds for the EFCE system toluene/water, whereas the investigations of the coalescence phenomena depending on droplet size and holdup were done with the EFCE system n‐butylacetate/water.     

Calculation of flow fields in two and three-phase bubble columns considering mass transfer

The dimension of bubble column reactors is often based on empirical correlations. Very popular is the axial dispersion model. However, the applicability of these models is limited to the experimental conditions for which the dispersion coefficients are measured, because backmixing depends strongly on the columns dimension and the flow regime. This paper presents a numerical method for the calculation of the three-dimensional flow fields in bubble columns based on a multi-fluid model. Therefore, the local bubble size distribution is considered by a transport equation for the mean bubble volume, which is obtained from the population balance equation. For comparison with experimental results, the axial dispersion coefficients in the liquid and gas phase are calculated from the instationary, three-dimensional concentration fields of a tracer. The model is then extended to include mass transfer between the gas and liquid phase. Increasing mass transfer rates significantly influence the flow pattern. For several applications, a dispersed solid phase is added. For the calculation of three-phase gas-liquid-solid flow, the solid phase is considered numerically by an additional Eulerian phase.     

Exact Analysis of Field-Flow Fractionation

Abstract

A rigorous convective diffusion theory is formulated for the predictive modeling of field-flow fractionation (FFF) columns used for the separation of colloidal mixtures. The theory is developed for simulating the behavior of a colloid introduced into fluid in time-dependent flow in a parallel plate channel across which a transverse field is applied. The methodology of generalized dispersion theory is used to solve the model equations. The theoretical results show that the cross-sectional average concentration of the colloid satisfies a dispersion equation with time-dependent coefficients. The results of this work, in principle, are valid for all values of time since the introduction of the colloid. It is shown that these results asymptotically approach those of the nonequilibrium theory formulated by Giddings for large values of time.

Illustrative numerical results are obtained for the case of steady laminar flow and a uniform initial distribution. The behavior of the coefficients in the dispersion equation is explained on physical grounds. Of particular interest is the fact that at large values of the transverse Peclet number P, Taylor dispersion in the FFF column is very small. Under these conditions, axial molecular diffusion as well as Taylor dispersion in the connecting tubing could make a substantial contribution to the axial dispersion observed in practical FFF columns.

The theoretical predictions are compared with the experimental data of Caldwell et al. and Kesner et al. on electrical FFF columns. The comparisons indicate that the theory has potential in predicting the performance of such systems.     

脉冲萃取塔径向扩散系数的测定方法

引　言对于脉冲筛板萃取塔或脉冲填料萃取塔中的轴向混合 ,已有许多人用轴向扩散模型作了研究[1,2 ].但是 ,在脉冲萃取塔工业放大设计的过程中 ,径向混合程度是个不可忽略的重要因素 .然而 ,这方面的研究尚未见报道 .萃取塔中的混合情况会直接影响液液两相传质推动力的大小 .通常 ,希望塔内连续相出现尽可能小的轴向混合 ,使连续相的流形接近活塞流 ,以获得最大的传质推动力 .而对于连续相的径向混合 ,其混合程度越大越有利于径向浓度的均匀 ,有利于获得最大的传质推动力 .因此 ,径向扩散系数大小的确定 ,对于工业规模脉冲萃取塔的设计具有…     

Determining axial dispersion coefficients of pilot-scale annular pulsed disc and doughnut columns

In this study, a computational fluid dynamics(CFD) method was adopted to calculate axial dispersion coefficients of annular pulsed disc and doughnut columns(APDDCs). Passive tracer was uniformly injected by pulse input at the continuous phase inlet, and its concentration governing equation was solved in liquid–liquidtwo-phase flow fields. The residence time distributions(RTDs) were obtained using the surface monitoring technique. The adopted RTD–CFD method was verified by comparing the axial dispersion coefficient between simulation and experimental results in the literature. However, in pilot-scale APDDCs, the axial dispersion coefficients predicted by the CFD–RTD method were approximately three times larger than experimental results determined by the steady-state concentration profile method. This experimental method was demonstrated to be insensitive to the variation of the axial dispersion coefficient. The CFD–RTD method was more recommended to determine the axial dispersion coefficient. It was found that the axial dispersion coefficient increased with an increase in pulsation intensity, column diameter, and plate spacing, but was little affected by the throughput.     

A Critical Review of the Application of Drop-Population Balances for the Design of Solvent Extraction Columns: I. Concept of Solving Drop-Population Balances and Modelling Breakage and Coalescence

Population-balances are a powerful method to predict the population behavior of drops in chemical-engineering equipment such as solvent extraction columns. In such columns a complex interaction of different phenomena, namely drop sedimentation, mass transfer, drop breakage and coalescence as well as axial dispersion occurs. In this article the concept of drop-population balances is discussed in detail as well as possible solution methods. Also, a critical review of existing models accounting for breakage and coalescence taking place in extraction columns is presented. Future parts of this series will be devoted to modelling mass-transfer and sedimentation as well as on application of single-drop based modelling.     

短塔技术的研究现状

本文介绍了近年发展起来的短塔技术以及应用短转盘塔和振动筛板槽进行的有关液滴运动、轴向混合、传质性能、液液分散特性等方面的研究工作。     

EXERGETIC CRITERIA FOR THE DEVELOPMENT OF ABSORPTION HEAT PUMPS

Lumped parameter mass transfer models based upon a tanks-in-series representation of fixed bed adsorption columns are derived. The effects of external and internal diffusion and axial dispersion are incorporated in the model for both single and multisolute (competitive) adsorption. The advantages of this type of model as compared with distributed parameter models are discussed. The model is validated against experimental data for both the single solute and bi-solute adsorption.     

Axial Mixing and Mass Transfer Performance of an Annular Pulsed Disc-and-Doughnut Column

The annular pulsed disc-and-doughnut column (APDDC) is an important type of extraction equipment in the PUREX process, which has been used in several commercial reprocessing plants. As there are few mass transfer experimental results reported in the literature, the axial mixing and mass transfer performance of an APDDC was studied for both extraction and stripping processes in the present work. Two parameters in the axial dispersion model (ADM), namely, the axial dispersion coefficient of the continuous phase and the number of mass transfer units, were regressed by correlating ADM with experimental concentration profiles. The influence of flow rate and pulsation intensity on these parameters was also investigated. Models developed for the PDDC were tested for correlation with APDDC experimental data and suitable models and conditions were determined. The height of a mass transfer unit was also calculated, which highlights the impact of axial mixing on mass transfer performance. Moreover, the influence of internal wettability on mass transfer performance was discussed.     

A study on flow characteristics in a rotating screen blade extraction column

Studies have been carried out on the axial dispersion in the continuous phase and the hold-up of dispersed phase in a rotating screen-blade extraction column, by employing an axial dispersion model. Experiments on both single and two phase operations have been conducted with the plate spacing, the mesh size, the impeller speed (RPM), and the superficial velocities as the system parameters. By regression analysis of experimental data, empirical equations correlating the dispersion coefficients and the fractional hold-up of dispersed phase with the system parameters were obtained.     

Flüssigphase-Rückvermischung in gepackten Blasensäulen

Liquid phase backmixing in packed bubble columns . Correlations for the axial liquid phase dispersion coefficient in bubble columns packed with metal Raschig rings and Pall rings are given as Pe_g = f (Ga, Re_g, H/D). The dependencies on physical and operational properties are discussed in detail with the aid of diagrams. Pall rings are not able to completely suppress greater turbulences and backmixing in columns of diameters D > 20 cm. A rule of thumb is also given for the apparent dispersion coefficient in this range. Raschig rings, however, are well suited for suppressing backmixing. The problems of adequate fulfilling of the model and undisturbed measurement of the backmixing behaviour are dealt with in detail.     

LUMPED PARAMETER MODELS OF ADSORPTION KINETICS IN FIXED BEDS

Lumped parameter mass transfer models based upon a tanks-in-series representation of fixed bed adsorption columns are derived. The effects of external and internal diffusion and axial dispersion are incorporated in the model for both single and multisolute (competitive) adsorption. The advantages of this type of model as compared with distributed parameter models are discussed. The model is validated against experimental data for both the single solute and bi-solute adsorption.     

Prediction of Concentration Profiles in an L‐Shaped Pulsed Extraction Column

The L‐shaped extraction pulsed plate column is believed to be able to perform under operating conditions between those of the vertical and the horizontal pulsed plate columns. It has an extraction efficiency similar to the vertical pulsed plate column. Here, the mass transfer performance of this novel column type was investigated and the application of three different models, i.e., the plug flow, the axial dispersion, and the back flow models, was evaluated to predict the solute concentration profile along the column length. The water‐acetone‐n‐butyl acetate and the water‐acetone‐toluene systems were used. The influence of the operational parameters on the height of the mass transfer unit and the back flow coefficients was evaluated using the back flow model. New correlations were proposed to predict the height of the mass transfer unit along with the back flow coefficients in each phase, which were in satisfactory agreement with the experimental data.