Liquid-liquid flow pattern prediction using relevant dimensionless parameter groups

Accurate predictions of flow patterns in liquid-liquid flow are critical to the successful design and operation of industrial and geo-energy systems where two liquids are jointly transported. Unfortunately, there is no unified flow pattern map, because all published maps are based on limited ranges of dimensional parameters. Dimensional analysis was performed on oil-water horizontal flows, to obtain some relevant dimensionless parameter groups (DPG) for constructing flow pattern maps (FPM). The following combinations of DPG were used: (i) the ratio of mixture Reynolds number to Eötvös number versus water fraction, (ii) the ratio of Weber number to Eötvös number versus water fraction, (iii) the mixture Froude number versus water fraction, (iv) the water Froude number versus oil Froude number, (v) the ratio of gravity force to viscous force versus water fraction. From twelve published experimental studies, 2696 data points were gathered and analysed covering a variety of flow patterns including stratified, stratified mixed, dispersed oil in water, dispersed water in oil, annular and slug flows. Based on the performed analysis, it was found that flow patterns could occupy more than one isolated region on the DPG-based flow pattern map. None of the combinations of DPG can mark out all the considered flow patterns, however, some combinations of DPG are particularly suitable for marking out the regions associated with some flow patterns