Estimation of Coalescence Parameters in an Agitated Extraction Column Using a Hybrid Algorithm

A method based on a genetic algorithm (GA) combined with Levenberg‐Marquardt (LM) method applicable to the population balance model for coalescence parameter estimation in a liquid‐liquid biphasic system is presented. The toluene/water system in a rotating disk contactor was taken as an example. Estimation methods for such a problem are often based on deterministic optimization models that are rather instable and divergent around a local minimum. To overcome these limitations, the present study involves the introduction of a semi‐stochastic method that is able to provide at first the estimation of coalescence parameters from the GA based on an inverse approach, exploiting the principle of GA. The LM algorithm was applied to ensure that the results are not restricted to a local minimum.     

Comparison of the Hydrodynamic Performance of Pulsed Solvent Extraction Columns with Tenova Pulsed Column Kinetics Internals and Standard Disc and Doughnut Internals for Copper Extraction Using the LIX 84 System

The dispersed phase holdup and droplet size are important parameters for understanding the hydrodynamic performance of pulsed solvent extraction columns. This study provides a comparison of the hydrodynamic performance between a Tenova Pulsed Column with Kinetics Internals (TPC-KI) and a pulsed column with standard disc and doughnut internals. The TPC-KIs are designed to improve the performance of systems with slow reaction kinetics, such as copper extraction with LIX 84, which was the focus of the current study. Holdup and drop size have been measured as a function of pulsation intensity and phase velocities for both types of column internals. Lower holdup and larger drop sizes were obtained with the TPC-KI, which indicates a higher flood point and a higher throughput. Correlations have been developed to predict the performance of these internals over a range of operating conditions.     

Simulation of a Bubble Column by Computational Fluid Dynamics and Population Balance Equation Using the Cell Average Method

An axisymmetric computational fluid dynamics (CFD) simulation coupled with a population balance equation (PBE) has been applied in simulating the gas‐liquid flow in a bubble column with an in‐house code. The novel feature of this simulation is the application of the cell average method in a CFD‐PBE coupled model for the first time. The predicted results by this method are compared with those by the traditional fixed pivot method and experimental data. For both methods, the simulated results are in reasonable agreement with the reported experimentally measured values. However, the bubble size distributions determined by the cell average method are slightly better than those found by means of the fixed pivot method, i.e., the latter provides a smaller peak value and a wider bubble size distribution, and the probability density function of large bubbles is higher.     

Population balance modelling and H∞—controller design for a crystallization process

In this paper we consider the robustly stabilizing control of a 1000l draft tube baffled crystallizer. When operated at high fines dissolution rates, the crystallizer exhibits sustained oscillations. A detailed population balance model for the process can be found in the literature. Based on this detailed model we develop a simpler population balance model. This, in turn, permits the derivation of an irrational transfer function from manipulated to measured variable. An H_∞ mixed sensitivity minimization problem is formulated and solved using an infinite-dimensional version of H_∞ theory. Two different controllers are designed and compared in simulation studies.     

Population Balance Model (PBM) for flocculation process: Simulation and experimental studies of palm oil mill effluent (POME) pretreatment

The present study is intended for the first time to completely replace the inorganic coagulants with organic polymers in palm oil mill effluent (POME) pretreatment by using direct flocculation of single and dual polymer systems under applied shear. The efficiency of direct flocculation of POME was investigated by using the Population Balance Model (PBM) which considered the charge neutralization and bridging attraction under applied shear. The collision efficiency was calculated based on the Derjaguin Landau Verwey Overbeek (DLVO) theory which considered the effect of adsorbed polymer layers on van der Waals attraction and bridging attraction. This is the first attempt to correlate the floc size distribution from PBM to the indirect indicators of COD, suspended solids, oil and grease. The model predictions are in close agreement with the experimental results for both single and dual polymer systems. The interaction energy curves based on PBM shows that the flocculation using cationic polymer is by charge neutralization and bridging attraction whereas flocculation using anionic polymer is by only bridging attraction. At the optimum flocculation conditions, 99.66%, 55.79%, 99.74% and 80.78% of suspended solids, COD, oil and grease removal and water recovery are achieved, respectively. The direct flocculation process significantly reduced the treatment cost by a factor of 3.6 compared to the conventional coagulation–flocculation process.     

Holdup Profile in Multistage Stirred‐Cell Liquid‐Liquid Extraction Column Using Population Balance Model

The drop exit frequency model developed in the literature is modified and simplified to suit the practical situations. An adjusting factor is inserted in the exit frequency model to account for the simplification of the hydrodynamic pattern used in the analysis and the incorrect constants used in the rise velocity model. The holdup profiles calculated in the present analysis are compared with experimental and theoretical results in the literature to evaluate the model. The comparison shows good agreement between the present model and the experimental data. Even for the cases of poor agreement, the breakage and coalescence rates are adjusted, and the stages of quasi‐equilibrium state are determined to improve the results.     

Effect of Plate Wettability on Dispersed-Phase Holdup in a Pulsed Disc-and-Doughnut Solvent Extraction Column

The effect of plate wettability on the dispersed-phase holdup in a pulsed disc-and-doughnut solvent extraction column is presented. Teflon, nylon, and stainless steel plates have been used to simulate a change in the wetting characteristics of the plate material that can occur in an operating column due to ageing or deposits accumulating on the plate. Experimental holdup data have been measured over a range of operating conditions using a 1.0 m long glass column with an internal diameter of 72.5 mm containing alternating discs and doughnuts. The liquid-liquid system studied was tri-n-octylamine (TOA)-kerosene-water with sulphuric acid as the solute. Results show that there are noticeable changes in the characteristic velocity (determined from measured holdup) and operational regimes for the different plate materials, particularly at low pulsation intensities, when operating under dispersed aqueous conditions. Experimental holdup data from this study have also been compared to correlations from literature for predicting holdup. As none of these correlations for holdup incorporate plate wettability, a new correlation for predicting holdup has been proposed that incorporates the contact angle of the plate material to allow for changes in the wettability of the plate surface. This correlation is able to predict the holdup data from this study to within 10.5% for aqueous dispersed conditions.     

Modelling and Simulation of a Complete Supercritical Fluid Extraction Plant with Countercurrent Fractionation Column

The most complete dynamic model to date of a supercritical fluid extraction (SFE) plant is presented and experimentally validated. The SFE flowsheet is modularly organized into a set of detailed sub-models of the main unit operations, including the extraction packed column, the supercritical solvent heat exchanger, the product recovery and solvent regeneration column, and the solvent make-up. The modules are interconnected through appropriate boundary conditions that establish continuity of mass, momentum, and energy. The present model significantly improves our previous modeling efforts by, among other features, including the gas compressor unit, extending the operation of the whole plant to nonisothermal conditions, and upgrading the packed column model for reflux mode operation. The SFE model was validated against experimental data for the fractionation of edible oil mixtures by supercritical carbon dioxide. Good agreement was obtained between experimental and predicted results; moreover, the model correctly predicts the trends with different operating and design parameters.     

Population balance modeling of bubble size distributions in a direct-contact evaporator using a sparger model

The study of bubble size distributions in direct-contact evaporators was addressed both theoretically and experimentally. Recently developed models for calculating bubble coalescence and breakage frequencies in isothermal bubble columns were adapted to the population balance equation using the bubble mass as the internal coordinate which was discretized using an expansion of the number density function by impulse functions. A sparger model was developed based on experimental data for a non-coalescing system and using bubble formation models for isothermal and non-isothermal conditions. Bubble size distributions in a direct-contact evaporator operating in the quasi-steady-state regime for four different gas superficial velocities, including the homogeneous and heterogeneous regimes, together with the sparger model, were used for estimating the three empirical parameters from the population balance model, which were observed to be functions of the gas superficial velocity. In all cases considered, the population balance model fitted the experimental data rather well and the regressed parameters exhibit the physically expected behavior with changes in the gas superficial velocity.     

Towards a Complete Population Balance Model for Fluidized-Bed Spray Agglomeration

This article concerns the simultaneous processes of agglomeration and drying. In order to predict temperatures and moisture content in gas and particle phase, heat and mass transfer mechanism and particle size enlargement has been considered in one model. The model takes heat and mass transfer phenomena between particle phase, suspension gas, and bypass gas into account. The disperse phase is modeled by a three-dimensional population balance (PBE), which can be reduced to a set of three one-dimensional PBEs. The latter are coupled with heat and mass transfer balances of the gas phase. Furthermore, some simulation and experimental results are presented.     

Simulation von Extraktionskolonnen in der industriellen Praxis

The design of extraction columns is usually based on lab‐scale and pilot‐plant experiments. A new alternative design approach is based on lab‐scale experiments with single drops to quantify mass transfer and drop sedimentation. From these experiments, liquid‐liquid system specific parameters for the simulation of the extraction column are obtained. This approach has been successfully validated for standard‐test systems and shall now be established in industrial practice. As part of this, separation performance and flooding limits measured with pilot‐plant experiments are compared to simulation results that are obtained on the basis of single‐drop experiments. The challenges that come with the simulation of industrial systems are presented and discussed.     

Hydrodynamics and Mass Transfer in a Lab‐Scale Stirred‐Pulsed Extraction Column

An extraction column with energy input through simultaneous stirring and pulsation allows for efficient countercurrent extraction on lab‐scale. While stirring generates small droplets with a narrow droplet size distribution, pulsation supports the axial transport of the dispersed phase, enabling countercurrent flow on this small scale. By studying the influence of several operating parameters, fundamental mechanics and characteristics of the column are revealed. Increasing the stirrer speed leads to smaller droplets and higher extraction performance as well as lower maximum throughput. The maximum throughput is increased by raising the pulsation intensity.     

脉冲填料萃取塔的绿色设计

在用脉冲填料塔（以苯为溶剂）萃取硫酸铵水溶液中己内酰胺的过程中,由于设备正常操作时溶剂泄漏以及公用工程中锅炉燃油燃烧,部分苯和有害气体排放到大气中,对环境产生不可忽视的影响.今根据绿色设计思想,引入化学物质环境影响因子和化学物质边际环境损害的概念,将萃取塔和溶剂回收塔中泄漏的苯,以及锅炉燃烧排放的硫、氮氧化物、二氧化碳等化学物质引起的环境损害进行了量化,并综合考虑萃取过程的经济成本（设备和操作成本）和环境影响,提出了新的设计目标函数,优化确定了脉冲填料塔的绿色设计结果,并与传统设计结果作了比较.     

Process Design of a Multistage Drying Process via Flowsheet Simulation

Multistage drying processes including spray drying and fluidized bed unit operations are challenging to design due to the dependencies of the preceding process steps. Flowsheet simulation offers the possibility to simulate a complete process by the application of suitable short-cut models. In this contribution a novel model for a spray dryer based on a population balance approach is presented. Furthermore, a dynamic model for a fluidized bed dryer is introduced. Experimental data is used for validation and parameter optimization. The calibrated models are then used to design an industrial drying process of multiple drying stages.     

润滑油糠醛精制填料萃取塔的传质性能

针对润滑油精制工业装置技术改造的需求,选用低界面张力的润滑油－糠醛精制体系,在ф１００ｍｍ的填料萃取塔中对孔板纹填料和共轭环填料的萃取性能进行了实验研究。结果表明,共轭环填料用于低界面张力体系萃取过程时传质性能优于孔板波纹填料。     

Population balances for particulate processes—a volume approach

Population balance models have been used in chemical engineering since the 1960s and have evolved to become the most important tools for design and control of particulate processes. In this paper we show that the intrinsic particle parameter that determines changes in the process and should thus be included in the population balance is the particle volume. The basic population that is modeled should be the mass distribution, or the volume distribution if the density is constant. The population balance thus describes the change of the volume distribution of volume with time. Furthermore, we suggest that the “birth” and “death” terms that are often used to describe discrete events in particulate processes can almost always be replaced by a rate of change term.To design and control existing and future processes, a multi-dimensional population balance model is required. We propose a volume-based model in which the particle properties that are modeled are the volumes of solid, liquid, and air, respectively. In the most general case the model will consist of a properties vector and a distribution tensor. Depending on the complexity of the process, one or more of the properties may be omitted from the model. This is shown in three examples of increasing complexity: comminution, sintering, and granulation.     

搅拌萃取塔引入气体后滞液率和气含率的研究

本文在搅拌萃取塔中,对气-液-液三相体系的流体力学进行了研究,讨论了气速与液速对分散相滞液率和气含率的影响,提出了分散相滞液率和表观液速、表观气速及气含率间的关系式。在给定的实验条件下,得到了气含率的关联式。根据实验确定的临界转速,将塔的操作区分为区域Ⅰ和区域Ⅱ,从而为工程放大设计提供理论依据。     

Solution of the droplet breakage equation for interacting liquid-liquid dispersions: a conservative discretization approach

A conservative discretization approach for the population balance equation (PBE) with only droplet breakage describing the hydrodynamics of a continuously interacting liquid-liquid dispersion is presented. The approach is conservative in the sense that it conserves any two integral properties associated with the number droplet distribution and thus it is considered internally consistent. The discrete set of equations is laid down through applying the subdomain method where it is shown that this set of discrete equations is only internally consistent with respect to one integral property. The internal consistency is enforced by introducing a set of two auxiliary functions that are uniquely determined by matching the integral properties obtainable from the discrete set against those from the continuous PBE. However, it is shown that this conservation of integral properties is not exact for all the subdomains and hence it results in what we call the intrinsic discretization error (IDE). This IDE is not only associated with this approach, but also it is found inherently existing in the fixed-pivot (FP) technique of Kumar and Ramkrishna (Chem. Eng. Sci. 51 (1996a) 1333). The derived equations of the IDE for the present discretization approach and the FP technique generalized to continuous flow systems show that the present approach enjoys a small value of the IDE. To validate the discretization approach, two analytical solutions for the continuous PBE are presented, where good agreement is found between the predicted and the analytical solutions. To assess the reliability of the present discretization approach two experimentally validated breakage frequency functions describing droplet breakage in a turbulent continuous phase as well as two daughter droplet distributions are considered. The convergence characteristics show that the present discretization approach has an identical convergence rate as that of the FP technique, and in some cases it is superior to it. This rate of convergence is found approximately proportional to the square of the inverse of the number of subdomains.     

Population balance modelling for a flow induced phase inversion based granulation in a two-dimensional rotating agglomerator

A novel two-dimensional rotating agglomerator was developed to carry out the flow induced phase inversion (FIPI) based granulation. The process in this agglomerator shows that a continuous paste flow (mixed with liquid binder and primary particles) is extruded into the interstice of two relatively rotating disks, as the paste becomes solidified due to the loss of heat to the disks, it is then broken into granules by the shearing force imposed by the rotating disk. Experimental measurements have shown that the size of these granules is enlarged along the positive radial direction of the disks. It is also found that these granules contain approximately the same quantity of binder in terms of its volume fraction. The paper thus proposes a population balance (PB) model to describe the growth of the granules by considering a size independent agglomeration kernel. The PB simulated results are found to be well capable of describing the change of the particle size distribution (PSD) of the granules in the radial direction. This study also proposes a velocity profile for the paste flow and attempts to establish a quantitative relationship between the granulation rate and the deformation rate as this would help us understand the mechanism of the agglomeration. It is hoped that this study would be used to improve the design of the agglomerator and to assure the control of the process and the granular product quality.