Optimization of Breakage and Coalescence Model Parameters in a Steady-State Batch Agitated Dispersion

Abstract

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.

From single drop coalescence to droplet swarms – Scale-up considering the influence of collision velocity and drop size on coalescence probability

“…/j.ces.2016.08.028 21 simulations using the adapted parameter sets of Coulaloglou and Tavlarides (1977) and Kamp and Kraume (2015) result in nearly identical steady states of 32 although the parameters 1 and 1 vary by several orders of magnitude. But the ratio between the parameters 1 / 1 and the value of 2 do not vary considerably which confirms the findings of Ribeiro et al (2011).…”

“…Numerical parameters are needed to apply the population balance equation to a specific system. In literature a broad variety of parameter sets can be found (Maaß, 2011;Ribeiro et al, 2011) because interdependencies between the numerical parameters exist (Ribeiro et al, 2011). For that reason, different parameter combinations can lead to the same ratio between drop breakage and coalescence rate which results in identical simulations (at least in steady state).…”

“…For that reason, different parameter combinations can lead to the same ratio between drop breakage and coalescence rate which results in identical simulations (at least in steady state). Ribeiro et al (2011) discussed the proportional dependency between the preexponential parameters 1 and 1 for steady state simulations in detail. As drop breakage is not in the focus of this work but inevitable to simulate a stirred vessel, appropriate parameters ( 1 , 2 ) from the literature were used and compared (see Table 4): the original parameters of Coulaloglou and Tavlarides (1977), 1 and 2 from an earlier publication (Kamp and Kraume, 2015) and breakage parameters estimated from single drop experiments by Maaß and Kraume (2012).…”

Mean drop size correlations and population balance models for liquid—liquid dispersion

“…The different might be attributed by the different approaches in determining the parameters although most of the approaches have been based on trial and error attempts to reproduce experimental results. Ribeiro et al, (2011) developed an optimization tool which was tested on the determination of constants in the models of Coulaloglou and Tavlarides (1977) . The work showed that the constants values obtained by the authors are in agreement with the older values reported in literature.…”

“…Drop coalescence is one of the processes that is responsible for the evolution of drop sizes and without coalescence, real steady state could not be achieved . The relative motion between drops result in collisions which lead to coalescence .…”