Developing a new approach for evaluating a de-oiling hydrocyclone efficiency Sina Amini b , Dariush Mowla a, b, ⁎, Mahdi Golkar b a Environmental Research Centre in Petroleum and Petrochemical Industries, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran b School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran abstract article info Article history: Received 4 May 2011 Received in revised form 30 August 2011 Accepted 29 September 2011 Available online 29 October 2011 Keywords: Hydrocyclone Mathematical model Efficiency De-oiling In this study, a new mathematical approach for evaluating of a de-oiling hydrocyclone efficiency has been developed. This new model uses the flow pattern of disperse phase and the boundary layer separation theory. In the present model unlike the other existing models, it is assumed that the droplet concentration in the radial direction is not uniform within the hydrocyclone. The hydrocyclone separation efficiency is calculated considering the droplet size distribution of the feed and the boundary layer thickness. The present approach considers the effects of droplet load, hydrocyclone geometry, mean droplet size and flow rate on the efficien- cy. The model is validated by comparison of the calculated separation efficiency with several previous experimental studies. © 2011 Elsevier B.V. All rights reserved. 1. Introduction For many years hydrocyclones have been used in different indus- tries such as pulp and paper production, food processing, chemical industries, power generation, metal working, as well as oil and mining industries. Both solid–liquid and liquid–liquid separation processes are possible with this technology. Most of the available reports on hydrocyclones within literature are focused on solid–liquid separa- tion. Since the 1980s, liquid–liquid separation has become popular due to the relevant application area in the oil industry. The hydrocyclone employs the centrifugal force to separate the dispersed phase from the continuous fluid. The swirling motion is produced by the tangential injection of pressurized fluid into the hydrocyclone body. The flow pattern consists of a spiral within another spiral moving in the same circular direction [1]. There is a forced vortex in the region close to the Liquid-Liquid Hydrocyclone (LLHC) axis and a free-like vortex in the outer region. The outer vortex moves down- ward to the underflow outlet while the inner vortex flows in reverse direction to the overflow outlet. Moreover, there is some recirculation zones associated with the high swirl intensity at the inlet. These zones, with a long residence time and very low axial velocity, have been found to be diminished as the flow enters the low angle tapered sec- tion from extensive experimental tests. Colman and Thew [2], devel- oped some correlations to predict the migration probability curve, which defines the separation efficiency for a particular droplet size in a similar way that the grade efficiency does. Later, it was found that the optimized correlation used in this work was erroneous [3]. However, useful conclusions can be extracted from this study. For in- stance, the separation efficiency is independent of the split ratio in the range of 0.5 to 10%. Seyda and Petty [1] evaluated the separation potential of the cylindrical tail pipe section. A semi-empirical model for prediction of the velocity field in a cylindrical chamber was devel- oped. This model is able to calculate the particle trajectories, and con- sequently, the grade efficiency. In the proposed model, the axial velocity was assumed to be independent of the axial location and a constant eddy viscosity was taken into consideration. The theoretical results showed an optimum split ratio which is opposed to the previ- ously reported results. Also, the relevant results illustrated an incre- ment in the LLHC efficiency when the feed flow rate was increased. Estimation of LLHC efficiency based on a droplet trajectory was the target of Wolbert et al. [4] work. The velocity distribution in the ta- pered section of Colman and Thew's design [2] was modelled. This was achieved considering a modified Helmholtz law for the tangential velocity, a polynomial correlation for the axial component, as well as the continuity equation and boundary conditions for the radial veloc- ity [5]. The importance of the tail pipe section to the LLHC separation efficiency was confirmed by comparing the model with experimental results. This fact was elaborated for liquid–liquid hydrocylone by Mo- raes et al. [6]. The modification takes into account the difference in the split ratio for liquid–liquid and liquid–solid hydrocyclones. Although, this model is sophisticated, results shown by the authors, disagree with existing data for sections with no reverse flow in the parallel sec- tion. Jinyu Jiao et al. [7] developed a multi-region model for determin- ing the cyclone efficiency. The multi-region model used the flow field data from recent experimental studies and applied a more accurate po- sition for the interface between the downward and the upward flows. Desalination 285 (2012) 131–137 ⁎ Corresponding author at: Environmental Research Centre in Petroleum and Petrochemical Industries, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran. Tel.: +98 711 2303071; fax: +98 711 6287294. E-mail address: dmowla@shirazu.ac.ir (D. Mowla). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.09.044 Contents lists available at SciVerse ScienceDirect Desalination journal homepage: www.elsevier.com/locate/desal