Transition between stratified and non-stratified horizontal oil–water flows. Part I: Stability analysis

Abstract

The characteristics of waves at the interface of oil–water stratified flow and at the onset of entrainment, where drops of one phase appear into the other, were studied. Theoretically a model was developed based on Kelvin–Helmholtz instability to predict the critical wave amplitude at which the waves become unstable for a specific wavelength. According to the model, waves become unstable in stratified flow when at a particular wavelength they exceed a critical amplitude, which decreases with increasing wavelength until it acquires an almost constant value. The model predictions showed that for low-viscosity oils the maximum critical amplitude appears at slip velocity close to zero, while for high-viscosity oils, the maximum amplitude appears for water velocity higher than that of the oil. Also the required entrainment wavelength over the pipe diameter, calculated using literature experimental onset conditions, was found to decrease as the viscosity of the oil increased. Experimentally, wave characteristics before and at the onset of entrainment were investigated by measuring the instantaneous fluctuations of the interface between oil (5.5 mPa s, 828 kg / m 3 ) and water in a 0.038 m ID stainless steel horizontal pipe using a conductivity probe. The formation of drops and the onset of entrainment were identified using a high-speed video camera. At the onset of entrainment, wave characteristics were above the stability lines predicted by the model. Using a semi-empirical characteristic amplitude and wavelength in the model, it was possible to predict the onset of entrainment and transition from stratified to other mixed flow patterns reported in a number of studies.