Parameter optimisation and validation for droplet population balances

Abstract

Single droplet experiments in Kühni compartment for five different liquid systems were used to evaluate Schmidt breakage model parameters. Based on these optimised parameters, Coulaloglou and Tavlarides coalescence model parameters were obtained by an inverse solution of population balance model (PBM) using the extended fixed‐pivot technique. The estimated interaction parameters were used to study the hydrodynamics of a pilot Kühni column. For online prediction purposes the One Primary and One Secondary Particle Model (OPOSPM), which is essentially a reduced population balance model (PBM), was used as an alternative to the computational expensive detailed PBM. Different test systems and column geometries were used for steady and transient state validation where OPOSPM was found to produce remarkable good results.

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

“…Most authors in Table 4 investigated the drop size distribution in stirred vessels using various physical systems. Two authors studied different set-ups: Azizi and Taweel (2011) applied static mixers to create the liquid/liquid dispersion, and Jildeh et al (2014) determined parameters for Kühni extraction columns with several oil/water systems (using a different breakage model). The parameters from literature fit quite well to the parameter sets obtained in this study.…”

A pseudo-3D model with 3D accuracy and 2D cost for the CFD–PBM simulation of a pilot-scale rotating disc contactor

“…Attarakih et al (2004Attarakih et al ( , 2006aAttarakih et al ( , 2006bAttarakih et al ( , 2006cAttarakih et al ( , 2012Attarakih et al ( , 2013 developed the PBM codes, including the liquid-liquid extraction column module (LLECMOD) and the particulate population balance laboratory (PPLAB) for extraction columns, in which simplified hydrodynamic models were employed to solve population balance equations. The codes were successfully applied to simulate different extraction columns such as RDC, Kühni column and pulsed column Jaradat et al, 2010;Jaradat et al, 2011;Attarakih et al, 2012;Jildeh et al, 2013;Jildeh et al, 2014;Attarakih et al, 2015). Their results showed that the PBM codes are able to reasonably simulate the holdup profiles, droplet Sauter mean diameter and concentration profiles.…”

Online monitoring, simulation and prediction of multiphase flows

“…η x , ρ x are the continuous phase viscosity and density, respectively σ is the surface tension. The model contains the two adjustable parameters C 1 and C 2 which are dependent on the experimental system …”

“…To be able to predict the behaviour under different operating conditions the parameters of breakage and coalescence kernels have to be obtained from an offline optimisation and verified for the setup . In the brackets in Equation are the kernels with parameters as discussed previously . However, the OPOPSM model had to be modified for online optimisation using the fitting parameters K B for breakage and K C for coalescence to take into account the droplet interactions: Once the OPOSPM has learnt (its two parameters are optimised, the underlying mathematical optimisation problem is solved) with data from specified column operating conditions, it can be used to simulate droplet coalescence without significant loss of information .…”