Evolution of the droplet size distribution during a two-phase flow through a porous media: Population balance studies Wojciech Orciuch, Lukasz Makowski, Arkadiusz Moskal, Leon Gradon ´ n Warsaw University of Technology, Faculty of Chemical and Process Engineering, Warynskiego 1, Warsaw 00-645, Poland article info Article history: Received 5 June 2011 Received in revised form 23 August 2011 Accepted 18 September 2011 Available online 24 September 2011 Keywords: Coalescer Coalescence Breakage Suspension Droplets size distribution Separation abstract Fibrous-bed coalescers are frequently used for separation of the suspension. The effectiveness of the process depends on the flow condition through the packed bed and its structure. The population balance equation was used for analysis of the evolution of the distribution of droplet diameter in the raw suspension due to the coalescence and breakage of droplets passing different sequences of the coalescer structures distinguished by the packing density of fibers in the layers of the coalescers. The results of calculations show the values of particular parameters, like droplet concentration, the mean diameter of the droplet and droplet size distribution in the population as the results of the process. The proposed model can be useful for the designing of the coalescer structures for their particular applications. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Separation of the two-phase systems, including dispersed and continuum liquids is a big challenge in advanced technologies. Liquid–liquid separations may require the use of special equip- ment when the drop sizes are small, typically in the range of 1–50 mm in size. These fluid systems are classified as stable emulsions, and often conventional bulk separators with mist pads or plate-type internals will not be effective. High-efficiency liquid– liquid coalescers have been developed to break these emulsions and provide improved separations (Mokhtab et al., 2006). Coalescers are typically manufactured as either pads or cartridge fibrous filters that have been designed especially to take small drops in an emulsion and grow them into large drops that are separated more easily. The use of fiber-bed coalescers is getting increasingly attractive in the chemical and automotive industries due to their high efficiency and their rather simple construction (Speth et al., 2002). However, their layout is still based on detailed experimental data and experience (Shin et al., 2005). There is a lack of comprehensive theoretical studies on the process of coalescence. The effectiveness of the process is highly dependent on the characteristic properties of dispersion, two- phase flow through a porous media performance and the topology of the coalescer structure, which is the basis for the entire process. We will consider in our paper the evolution of the distribution of droplet size, using the population balance equation (PBE). Water-in-fuel emulsion separation will be considered as the example for calculation. We have selected this system as impor- tant to the petroleum and chemical industries to remove the dispersed liquid for safety, ecologic and economic reasons. 2. Topology of a porous media It is difficult to describe in detail the geometry of a porous media made of fibers or grains. Very often, it is not necessary to do it if another useful description can be used for rendering of the main phenomenon under consideration. The concepts of network models fulfill such expectations. The idea is to avoid detailed geometric description of the pore space (which is essentially impossible in a real porous media) in favor of idealized descriptions that preserve the macroscopic properties of the media. The pore space may be represented by a network of interconnected pipes with equal or random radii, assigned according to a log-normal probability distribution. The physics of individual pipes and junctions that connected them (‘‘nodes’’) can be referred to as the microscale, and were examined as the ‘‘constricted tubes’’ model. We can distinguish now three main areas in the ‘‘network’’ model approach: 1) Determination of the net topology. 2) Prediction of the flow physics in the net. 3) Development of the drops transport model. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2011.09.034 n Corresponding author. Tel.: þ48 22 234 62 79. E-mail address: L.Gradon@ichip.pw.edu.pl (L. Gradon ´ ). Chemical Engineering Science 68 (2012) 227–235