(155e) Prediction of Phase Inversion in Oil-Water Systems

Two immiscible liquids (for instance, oil and water) flowing at high velocity through a pipe mix due to turbulence may form a dispersed mixture, where one liquid is present in the other one in the form of drops. Which liquid is the continuous phase and which the dispersed one depends on many parameters, such as the viscosities and densities of the liquids, the presence of a surfactant, the 'history' of the experiment, the wetting properties of the pipe wall, etc. At a certain condition the continuous phase might become the dispersed one, and vice versa. This phenomenon is called phase inversion. Phase inversion has been studied for many years, but there are still many questions about it.

Two types of phase-inversion experiments are reported in the literature: continuous experiments and direct experiments. During a continuous experiment the dispersed phase is gradually added to the continuous phase and so the volume fraction of the dispersed phase increases with time. During a direct experiment the two liquids are mixed from the start at certain values of the phase-volume fraction for the two phases, which remain constant with time. We carried out continuous and direct experiments in a pipe (for details see our previous papers - Piela et al. (2006, 2008)). In our experiments we paid attention to the region between the maximum and minimum value of the dispersed phase-volume fraction where phase inversion can take place (for a certain set of conditions). During the continuous experiments we found that the critical volume fraction of the dispersed phase at the point of inversion does not depend on the Reynolds number, Froude number and Weber number of the mixture flow and also not on the injection velocity of the dispersed phase, as long as the mixture velocity is sufficiently large (> 2 m/s). However, we found that the injection phase-volume fraction (ratio of the rate of injection of the dispersed phase and the rate of the mixture flow through the pipe) had a significant influence on the critical volume fraction. Starting experiments with water flow and injecting oil leads to a different critical concentration than starting with oil flow and injecting water. The difference between these two is called ambivalence region. We observed that ambivalence region decreases with increasing injection phase-volume fraction. The direct experiment can be considered as the limiting case of a continuous experiment, with a large injection rate of the dispersed phase and with inversion taking place before one cycle through the pipe is completed. The injected phase-volume fraction is then equal to the ratio of the rate of injection of one of the two phases and the rate of the mixture flow through the pipe. The phase with the lowest injection rate is considered as the injected dispersed phase. Most of the experiments described in the literature, are in fact direct experiments where the influence of different parameters (viscosity ratio, density ratio, wetting properties, etc.) on inversion have been observed. Based on these observations a number of modelling approaches have been developed. In each of them a certain phenomenon plays a crucial role:

1) Coalescence. Under steady state conditions the break-up and coalescence of drops are in equilibrium. However, when the conditions change the coalescence rate may increases and exceed the break-up rate, leading to inversion (Yeo et al.(2002), Brauner et al.(2002)).

2) Formation of multiple drops. Small parts of the continuous phase are trapped inside the dispersed phase. So the drops (forming the dispersed phase) grow, coalesce and finally form the new continuous phase (Pacek et al (1994,1995), Pal (1993), Sajjadi et al (2000, 2002, 2003), Liu et al. (2005, 2006), Jahanzad et al. (2009)).

3) Dissipation rate. Inversion occurs when the effective viscosity of the oil-in-water mixture and the water-in-oil mixture are the same (Poesio et al. (2008), Ngan et al (2009)).

None of the proposed models predicts phase inversion accurately. Models based on coalescence rate, formation of multiple drops and dissipation rate do not take into account ?history' of the experiment, which in many cases leads to wide ambivalence range. Ginzburg-Landau model can be used to describe ambivalence region in an oil-water mixture. This is due to the close similarity between the hysteresis region for first-order phase transitions and the ambivalence region for phase inversion between two liquids in a dispersed flow. According to our measurements, the ambivalence region is unique for a specific water-oil mixture. For such a mixture the ambivalence region depends on the injected phase-volume fraction. It is independent of the Reynolds, Froude, and Weber numbers and also independent of the injection rate, as long as the mixture velocity is large enough. Of course, when the oil type is changed or when a surfactant is added, the ambivalence region will change.

In many practical applications viscosity difference between oil and water phase is high. Reaching mixture velocity required to ensure that results are independent of the injection rate is in many applications impossible. At lower velocities, more viscous liquid will always tend to become dispersed phase. That of course has an impact on inversion map. In many experiments described in the literature, it was noted that increasing oil viscosity shifts inversion point towards lower oil volume fractions. We modified our Ginzburg-Landau model to extend it to systems with high viscosity ratio. In Ginzburg-Landau model phase inversion is predicted based on two parameters: injected phase volume fraction and friction factor. Friction factor represents energy dissipation. When two liquids have similar viscosities energy dissipation is almost the same for oil continuous and water continuous systems (system is symmetrical). Increasing oil viscosity leads to high increase in dissipation energy for oil continuous system, which affects the symmetry of the inversion map. Modification of the model to take into account high viscosity ratios allow us to extend model predictions to more viscous (practical) systems.

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