Dynamic 1-D-PBM simulation of droplet size evolution with directly-measured kernel functions in pulsed extraction column

A rigours mathematical model based on the bivariate population balance frame work (the base of LLECMOD “Liquid-Liquid Extraction Column Module”) for the steady state and dynamic simulation of pulsed liquid-liquid extraction columns is developed. The model simulates the coupled hydrodynamic and mass transfer for pulsed (packed and sieve plate) extraction columns. It is implemented using visual digital FORTRAN and then integrated into the LLECMOD program. Experimental validated correlations are used for the estimation of the droplet terminal velocity in extraction columns based on single and swarm droplet experiments in laboratory scale devices. Additionally, recently published correlations for turbulent energy dissipation, droplet breakage and coalescence frequencies are discussed as being used in this version of LLECMOD. In a case study, LLECMOD is used here to simulate the steady state performance of pulsed extraction columns with two chemical test systems recommended by the European Federation of Chemical Engineering (water- acetone-n-butyl acetate and water-acetone-toluene) and an industrial test system. Model predictions are successfully validated against steady state and transient experimental data, where good agreements are achieved. The simulated results (holdup, mean droplet diameter and mass transfer profiles) compared to the experimental data show that LLECMOD is a powerful simulation tool, which can efficiently predict the dynamic and steady state performance of pulsed extraction columns.

The relationship between the holdup of the dispersed phase and the velocity at which drops move in the continuous phase, as well as the concept of characteristic velocity, has been valuable in the design and operation of liquid–liquid extraction (LLE) columns. At the flooding point, the maximum-phase throughput (Qd and Qc) and phase velocities can be reached. This point is known as the hydrodynamic loading limit, beyond which the phase flow rate becomes disorganized. Several significant research papers in the literature utilize pulsed or agitated extraction columns to investigate characteristic/slip velocities and flooding conditions. Numerous studies have examined various correlations, but there are inconsistencies in designing LLE columns accurately. The aim of this study is to examine existing literature comprehensively regarding hydrodynamic velocities and flooding characteristics in commercial pulsed and agitated extraction columns. Established correlations for predicting slip velocities, characteristic velocities, and flooding conditions are carefully evaluated. Furthermore, past studies on how key parameters affect hydrodynamic velocities and flooding characteristics are summarized in this manuscript.

Pressure drop in pulsed extraction columns with internals of discs and doughnuts

A study has been made of the dynamic behaviour of a nuclear fuel reprocessing plant utilising pulsed solvent extraction columns. A flowsheet is presented and the choice of an extraction device is discussed. The plant is described by a series of modules each module representing an item of equipment. Each module consists of a series of differential equations describing the dynamic behaviour of the equipment. The model is written in PMSP, a language developed for dynamic simulation models. The differential equations are solved to predict plant behaviour with time. The dynamic response of the plant to a range of disturbances has been assessed. The interactions between pulsed columns have been demonstrated and illustrated. The importance of auxillary items of equipment to plant performance is demonstrated. Control of the reprocessing plant is considered and the effect of control parameters on performance assessed.

Etude de la dispersion longitudinale dans les colonnes d'extraction liquide-liquide

Solvent extraction process is frequently used to obtain chemical compounds used in the nuclear field. In order to make nuclear energy a safe, clean and cheap energy source, one has resorted to the identification of new, innovative methods in the immediate transfer of the laboratory results to an industrial scale. A method is described for the design of liquid extraction columns by scaling up from the results of small scale plant tests. Such a method was applied for scaling up a pulsed column with sieve trays using the dimensions of an experimental model column. The scale-up method is based on the assumption that the height of the column is independent of column diameter, and that increased backmixing accounts entirely for differences in performance on small and large scales. This paper uses the results obtained on an experimental model column for the purpose of designing a high capacity column. The final result consists in determining the diameter and height of a scaled up column by using like parameter the number of transfer units corresponding to a compartment, a value that will stay the same for the laboratory-scale column and for the large-scale (pilot or industrial) column.

Acid-Thorex flowsheets using tributyl phosphate (TBP) to process feed which simulated that from HTGR fuels were tested in pulsed solvent extraction columns. Tests were performed to study the effects of solvent degradation and solids in the feed and decontamination performance using tracer Zr-95. Equipment recommendations for each process step are made. The Acid-Thorex process is expected to provide relatively trouble-free operation in commercial reprocessing of HTGR fuel. (auth)

Simulation of hydrodynamics in RDC extraction columns using the simulation tool “ReDrop”

The slip velocity, the dispersed‐phase hold‐up, and the characteristic velocities of the phases in a horizontal pulsed extraction column were investigated under no‐mass transfer conditions using four binary systems: kerosene‐water, toluene‐water, n‐butyl acetate‐water, and butanol‐water. The effects of the pulsation intensity, the dispersed‐ and continuous‐phase flow rates, and the interfacial tension on the dispersed‐phase hold‐up and slip velocity of the phases were investigated. Based on the obtained results, a semi‐empirical correlation for estimating the slip velocity and the characteristic velocity was established, which proved to be in good agreement with the experimental findings.

High-efficient CFD-based framework for the comprehensive hydrodynamic evaluation of pulsed extraction columns

Pulsed columns are one of the most important extraction columns that have extensive application in different industries. Obtaining the solute concentration in different heights of the column has a great influence on achieving the physical property changes of the phases along the column. An experimental work of mass transfer in a pilot pulsed sieve plate extraction column at different operating conditions is carried out in this research, and the solute concentration in different heights of the column is obtained for two different systems with medium and high interfacial tensions. The solute concentration changes along the column are calculated using previous models in the literature and the model presented for achieving the effective diffusivity in a previous work of the present authors. Comparison of the experimental results and the models is made and the best one is suggested.

This paper presents the real-time application of the learning control theory to the control of a chemical pilot plant: a pulsed liquid-liquid extraction column. The behaviour of an agitated liquid-liquid extraction column can be related to random mechanisms such as the phenomena of droplets breakage and coalescence. Previous studies on hydrodynamic and mass transfer aspects showed that a pulsed liquid-liquid extraction column had an optimal behaviour for operating conditions close to flooding. These results led to choose the following strategy to control the column in its optimal behaviour zone: - the measure of the conductivity of the liquid medium below the distributor which gives a good information about flooding, is the controlled variable -the pulse frequency is the control action. The learning control algorithm is based on a multilevel system of automata which operates in a random environment. By means of an evaluation unit of the performances of the column which generates either penalty (inaction) ...

Modeling of a two-phase countercurrent pulsed sieve plate extraction column—A hybrid CFD and radiotracer RTD analysis approach

The present contribution reports on a new method for the simulation of the dispersed phase behaviour in liquid‐liquid extraction columns. The fluid dynamic description is based on a mathematical model which explicitly takes into account drop transport, break‐up and coalescence mechanisms, via a drop population balance along the column. Application of the model requires some simple measurements on single drops in order to determine transport and break‐up laws, which are required by the model, and possibly also coalescence parameters. In this study the model is applied to pulsed sieve plate columns. The specific example considered here is based on systematic studies on the determination of break‐up rates from the corresponding probabilities of break‐up and the generated daughter drop size distributions by means of high‐speed photography. The validity of the model was subsequently tested by comparison with some experimental results from studies on two different pulsed columns 80 and 225 mm in diameter for the water/toluene system without mass transfer. The satisfactory agreement between the results justifies the use of such a method for the description of the behaviour of liquid‐liquid extraction columns in a wide range of operating conditions. Furthermore, application of the model may help to dispense with long and expensive pilot tests.

Some critical computations in pole-placement design and in that of many model reference adaptive systems are described. These numerical problems are associated with the resolution of the diophantine equation. They occur when the assumption of no common poles and zeros is violated. Regularization techniques which cope with ill-conditioning are presented. The resulting algorithm combines a standard indirect pole-placement adaptive control algorithm and a dimension-free regularization procedure of the design equations, thus avoiding the pole-zero cancellation problem and yet retaining the other properties of the algorithm. The application of this control scheme in a pulsed liquid-liquid extraction column is described. The control objective is to optimize the column behaviour. Extraction columns are subject to changes in feed compositions, feed flow-rates, physical properties of the solvent (the extractor) and the solute (liquid mixture) and various disturbances. The column exhibits highly non-linear and time-varying dynamics. The conductivity measured at a specific place in the column and the pulse frequency have been selected as control variables. Experimental results demonstrate the usefulness and the robustness of this regularized pole-placement adaptive control algorithm.