Solution of Inverse Problem with the One Primary and One Secondary Particle Model (OPOSPM) Coupled with Computational Fluid Dynamics (CFD)

AbstractThe reduced one group population balance (PBE) model, the One Primary and One Secondary Particle Model (OPOSPM) is developed for a liquid extraction column. It is used because of its simplicity and the ability to reproducemost of the information contained in the PBE. It is usedto estimate the optimum droplet breakage and coalescence parameters using steady state experimental data. The data is obtained from a pilot plant liquid extraction column of 80mm diameter and 4.4 m height for toluene-acetone-water chemical test system as recommended by the European Federation of Chemical Engineering (EFCE). In this contribution Coulaloglou and Tavlarides (1977)breakage and coalescence model is studied to obtain the parameters by solving a population balance inverse problem. The estimated droplet parameters are used as input parameters for the CFD simulation and in the simulation program PPBLAB.The optimized values were found to predict accurately the mean dispersed phase holdup, mean droplet diameter and the concentration profile for the continuous and dispersed phase along the extraction column height

Applications of He’s methods to the steady-state population balance equation in continuous flow systems

The population balance equation has numerous applications in physical and engineering sciences, where one of the phases is discrete in nature. Such applications include crystallization, bubble column reactors, bioreactors, microbial cell populations, aerosols, powders, polymers and more. This contribution presents a comprehensive investigation of the semi- analytical solutions of the population balance equation (PBE) for continuous flow particulate processes. The general PBE was analytically solved using homotopy perturbation method (HPM) and variational iteration method (VIM) for particulate processes where breakage, growth, aggregation, and simultaneous breakage and aggregation take place. These semi-analytical methods overcome the crucial difficulties of numerical discretization and stability that often characterize previous solutions of the PBEs. It was found that the series solutions converged exactly to available analytical steady-state solutions of the PBE using these two methods

The normalized quadrature method of moments coupled with finite pointset method

This work reports the numerical performance of the Normalized Quadrature Method of Moments (NQMOM) involving more than one quadrature node (secondary particle) for dispersed phase flows coupled with the Finite Pointset Method (FPM). At first, the model used for the dispersed phase acting in a continuous environment is discussed briefly, followed by a theoretical discussion of NQMOM and FPM. Further sections report the numerical performance for test problems with increasing difficulty

The normalized quadrature method of moments coupled with finite pointset method

This work reports the numerical performance of the Normalized Quadrature Method of Moments (NQMOM) involving more than one quadrature node (secondary particle) for dispersed phase flows coupled with the Finite Pointset Method (FPM). At first, the model used for the dispersed phase acting in a continuous environment is discussed briefly, followed by a theoretical discussion of NQMOM and FPM. Further sections report the numerical performance for test problems with increasing difficulty

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Crystal morphology is known to be of great importance to the end-use properties of crystal products, and to affect down-stream processing such as filtration and drying. However, it has been previously regarded as too challenging to achieve automatic closed-loop control. Previous work has focused on controlling the crystal size distribution, where the size of a crystal is often defined as the diameter of a sphere that has the same volume as the crystal. This paper reviews the new advances in morphological population balance models for modelling and simulating the crystal shape distribution (CShD), measuring and estimating crystal facet growth kinetics, and two- and three-dimensional imaging for on-line characterisation of the crystal morphology and CShD. A framework is presented that integrates the various components to achieve the ultimate objective of model-based closed-loop control of the CShD. The knowledge gaps and challenges that require further research are also identified