(177d) One-Equation Population Balance Modeling of Liquid-Liquid Extraction Processes

Scale up of Counter-current liquid-liquid extraction columns requires pilot plant experiments. Simulations using computational fluid dynamics (CFD) along with population balance modeling (PBM) has been a useful tool in predicting the hydrodynamics, turbulence and size distributions inside the agitator.

CFD in conjunction with PBM has been used several engineering disciplines such as fermentation, bubble columns, and crystallization.

Population balance methods involve solving equations for particle sizes (bin method) or equations for particle moments (moment method) to track the distribution of droplets produced by breakage and coalescence mechanisms.

 The extra equations that are solved increases the computational effort. To reduce the computational effort,  a one equation population balance model that conserves either the total area or total number density of the dispersed phase is used in this work.  The results from the model are compared against the quadrature moments (QMOM) model and experiments for a pilot-plant extraction column.

The speed and the accuracy of the one-equation model is also discussed.