Coupling of CFD with DPBM for an RDC extractor

Abstract

For the design of counter-current liquid–liquid extraction columns, there is a strong industrial demand for more straightforward, faster and money-saving simulation methods. One possibility in this direction that has a great potential is the coupling of computational fluid dynamics (CFD) with population balance models (PBM). Therefore, a combination of CFD and droplet population balance modelling (DPBM) is applied to simulate the drop size distributions and flow fields in a liquid–liquid RDC extractor. The simulations are carried out in the commercial CFD code Fluent. The liquid–liquid flow is modelled using a Reynolds averaged turbulence model in conjunction with the Eulerian two-fluid equations. Models for coalescence and breakup, from Luo and Svendsen [1996. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42, 1225–1233] Coulaloglou and Tavlarides [1977. Description of interaction processes in agitated liquid–liquid dispersions. Chemical Engineering Science 32, 1289–1297] and a mixed model [Martínez-Bazán, C., Montañés, J.L., Lasheras, J.C., 1999. On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency. Journal of Fluid Mechanics 401, 157–182; Prince, M.J., Blanch, H.W., 1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E Journal 36, 1485–1499] are implemented in the CFD code as user defined functions. For the solution of the PBM a classes method (CM) [Kumar, S., Ramkrishna, D., 1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332] and the quadrature method of moments (QMOM) [Marchisio, D.L., Pikturna, J.T., Fox, R.O., Vigil, R.D., Barresi, A.A., 2003a. Quadrature method of moments for population-balance equations. A.I.Ch.E. Journal 49, 1266–1276] are used. Simulated droplet distributions for the systems toluene–water and butyl acetate-water are compared to experimental measurements. The model of Luo and Svendsen was modified to predict the droplet size distribution. The mixed model allows the prediction of the Sauter mean diameter without any adjustable parameter. Pros and cons of the combined model as well as future needs and trends such as multi-fluid CFD–PBM models are discussed. The results show that the link of PBM and CFD is a suitable design tool which can significantly improve the layout of industrial columns.