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

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.