Predictive model of the entrained fraction in horizontal oil-water flows

Knowledge of entrained fraction of one phase into the other during dual continuous liquid-liquid flows, where both phases retain their continuity at the top and bottom of the pipe but there is dispersion of one phase into the other, is important for predicting pressure drop and hold up in this pattern. However, there is only limited amount of experimental information available on entrained fractions and almost no modelling attempts for their evaluation. In this paper, a semi-empirical model is proposed for predicting the entrainment of one phase into the other in dual continuous horizontal oil-water flows based on the balance between drop entrainment and drop deposition rates and assuming no slip between dispersed and continuous phases. Drop entrainment occurs when the detaching drag force on the waves of stratified wavy flow overcomes the attaching surface tension force. A force balance on the wave developed by Al-Wahaibi et al. [2007. Transition between stratified and non-stratified horizontal oil-water flows: part 11 (mechanism of drop formation). Chem. Eng. Sci. 62, 2929-2940] is used to predict the drop volume that entrains into the opposite phase. For the calculation of the drop deposition rate a correlation developed for gas-liquid systems was initially used. However, improved predictions are obtained with a new deposition rate constant that was developed from available data on entrained fraction in oil-water flows. The model with the new deposition rate constant is able to predict reasonably well experimental data available in the literature on entrained fraction in different oil-water flow systems. (C) 2009 Elsevier Ltd. All rights reserved.