Liquid−liquid systems research increasingly concentrates on computer simulations. However,
the possibility of adequately testing complex theoretical models against experiments is hindered
by a lack of reliable reproducibility data for laboratory and pilot-plant measurements. This
strongly limits meaningful evaluation of the increasingly complex process and equipment models/algorithms that are being developed. In this work, experimental data are obtained in a pilot-scale Kühni column, and model parameters and simulated data are generated using a drop
population balance model and algorithm. The results can be summarized as follows: (i) As
measured by the magnitude of careful random error and corresponding confidence limits
estimates, the simulation results exhibit excellent agreement with experimental drop-size
distributions and fair conformity with measured dispersed-phase hold-ups. (ii) Both experimental
and simulated results show that interdrop coalescence is always present within a column
extractor, even at low dispersed-phase hold-ups, and thus cannot be neglected in any physically
realistic and accurate modeling.
Liquid−liquid systems research increasingly concentrates on computer simulations. However,
the possibility of adequately testing complex theoretical models against experiments is hindered
by a lack of reliable reproducibility data for laboratory and pilot-plant measurements. This
strongly limits meaningful evaluation of the increasingly complex process and equipment models/algorithms that are being developed. In this work, experimental data are obtained in a pilot-scale Kühni column, and model parameters and simulated data are generated using a drop
population balance model and algorithm. The results can be summarized as follows: (i) As
measured by the magnitude of careful random error and corresponding confidence limits
estimates, the simulation results exhibit excellent agreement with experimental drop-size
distributions and fair conformity with measured dispersed-phase hold-ups. (ii) Both experimental
and simulated results show that interdrop coalescence is always present within a column
extractor, even at low dispersed-phase hold-ups, and thus cannot be neglected in any physically
realistic and accurate modeling.
“…In this scientific and technological field, experimentation still lags far behind our theoretical understanding of the underlying processes and mechanisms; as a result, the same happens with the practical implementation of dynamic models for design and online control algorithms. The theoretical and computational components of the latter aspect has advanced significantly with the contribution of the present authors, − but such development still needs to be further evaluated, adapted, and complemented by information and data accessible only by experiment, using typical liquid−liquid systems in specially designed and instrumented liquid−liquid contacting apparatuses . During the past decades, several drop or particle-size measurement techniques have been developed.…”
Section: Introductionmentioning
confidence: 99%
“…Their use is easily extended to the case of extraction columns, although at the price of much longer computation time. Industrial & Engineering Chemistry Research ARTICLE Ribeiro et al [3][4][5] published innovative algorithms for directly (numerically) solving the population balance equations (PBE) in three-dimensional phase space (drop volume, age, and solute concentration), with both breakage and coalescence. These enable the quick and accurate solution of both the transient and steady-state cases for a stirred vessel, under either batch or continuous conditions.…”
The highly dynamic behavior of liquid−liquid dispersions in reaction and separation operations still defies accurate and experimentally validated modeling. This behavior is characterized by simultaneous dropsize and operating conditions dependent drop breakage and coalescence, which strongly influence both the hydrodynamics and the reaction yield and selectivity, or separation performance, of such systems. This dynamic character of the behavior is present and of critical importance even at steady state, and not just during the transient evolution toward it or during disturbances in the operating conditions. This work addresses the measurement (by a noninvasive technique) and the optimization of kinetic liquid drop interaction parameters, duly taking into account the full and real complexity of the behavior, which is shown to require the inclusion and quantification of drop coalescence frequencies, no matter how lean and strongly agitated the dispersion may be. The analysis in this paper is limited to batch perfectly agitated vessels with lean dispersions at steady state and uses carefully collected experimental drop size distribution data and a very precise (with 50 logarithmic drop volume classes, to ensure uniform precision of drop size assignment) and fast coupled numerical dynamic simulation and nonlinear optimization algorithm, to quantify the drop breakage and coalescence kinetic parameters of drop interaction models. Significant physical insight has been gained on the interdependence of two (one for breakage and the other for coalescence) of the parameters and on the values of the others, in addition to an excellent agreement of the predicted and experimental drop size distributions at steady state. Further, and as expected, the need to always fully account for interdrop coalescence (in addition to breakage), whatever the operating conditions, by contrast to oversimplified modeling approaches, has also been clearly demonstrated.
“…The algorithm was implemented in C++, and the corresponding program has a friendly Windows interface for data entry. , In the interface, the user may choose…”
Given the difficulties normally associated with direct experimentation in liquid-liquid extraction processes, their direct computer simulation has acquired increased relevance and utility, especially when dealing with some of the details of the dispersed-phase hydrodynamics. The possibility of testing very complex theoretical models of such behavior is increasingly attractive to the researcher, as a result of both the power and the availability of personal computing resources. Experimental data obtained in a pilot-scale Ku ¨hni liquid-liquid extraction column and simulated data generated by means of a drop population-balance model and algorithm were used to describe and compute the local drop-size distributions and dispersed-phase holdup profiles. In this work, the applicability of this algorithm to describe the steady-state behavior of a Ku ¨hni liquid-liquid extraction column is illustrated. Data generated using this algorithm exhibit reasonable agreement with experimental data, with physically meaningful model parameter values.
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