The stability of core-annular flow (CAF) in pipes is analysed using the linear theory of stability. Attention is confined to the potentially stable case of lubricated pipelining with the less viscous liquid, say water, in the annulus. The effects of surface tension and density are included, but gravity is excluded. We find upper and lower branches of the neutral curve in a Reynolds number (ℝ) vs. wavenumber (α) plane. A window of parameters is identified in which CAF is stable to small disturbances. When ℝ is below the lower critical value, CAF is destabilized by surface tension and long waves break up into slugs and bubbles. The sizes of slugs and bubbles of oil in water observed by Charles, Govier & Hodgson (1961) are given by the wavelength of the fastest growing long wave. This long-wave instability is a capillary instability, modified by shear, which reduces to Rayleigh's instability in the appropriate limit. At higher ℝ, the capillary instability is stabilized by shear. At yet higher ℝ, above the upper critical value, the flow is unstable to generally shorter waves which leads to emulsification, water droplets in oil. The theory agrees with experiments. The analysis seems to be applicable to the design of lubricated pipelines; for example, there is an optimum viscosity ratio for stability, greater stability can be obtained by using heavy liquid as a lubricant when the flow is unstable to capillary modes on the lower branch and by using light liquids when the flow is unstable to emulsifying disturbances on the upper branch.

Lubricated pipelining: Stability of core-annular flow

Pressure gradient in horizontal liquid-liquid flows

Results are given for experiments on water-lubricated pipelining of 6.01 P cylinder oil in a vertical apparatus in up- and downflow in regimes of modest flow rates, less than 3 ft/s. Measured values of the flow rates, holdup ratios, pressure gradients and flow types are presented and compared with theoretical predictions based on ideal laminar flow and on the predictions of the linear theory of stability. New flow types, not achieved in horizontal flows, are observed: bamboo waves in upflow and corkscrew waves in downflow. Nearly perfect core–annular flows are observed in downflows and these are nearly optimally efficient with values close to the ideal. The holdup ratio in upflow and fast downflow is a constant independent of the value and the ratio of values of the flow rates of oil and water. A vanishing holdup ratio can be achieved by fluidizing a long lubricated column of oil in the downflow of water. The results of experiments are compared with computations from ideal theory for perfect core–annular flow and from the linear theory of stability. Satisfactory agreements are achieved for the celerity and diagnosis of flow type. The wave is shown to be nearly stationary, convected with the oil core in this oil and all oils of relatively high viscosity. These results are robust with respect to moderate changes in the values of viscosity and surface tension. The computed wavelengths are somewhat smaller than the average length of the bamboo waves which are observed. This is explained by stretching effects of buoyancy and lubrication forces induced by the wave. Other points of agreement and disagreement are reviewed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112092000041

Lubricated pipelining: Stability of core—annular flow. Part 5. Experiments and comparison with theory

Using a mechanistic approach, equations are developed to describe the stratified cocurrent flow of gas-liquid mixtures in horizontal pipes. An iterative method is suggested for their solution.

Experimental data were collected using air-oil mixtures in a one inch 1. D. by 101 ft. long acrylic pipe. Pressure drop and average in situ liquid volume fraction are presented as a function of the superficial gas velocity and are compared with predicted results from this study and other models reported in the literature.

Visual observation of flow patterns and their transitions are indicated on the tentative flow pattern map of Govier and Aziz(1).

An analysis of horizontal stratified two phase flow in pipes

Study on oil-water two-phase flow in horizontal pipelines

The parameters introduced by Lockhart and Martinelli to correlate pressure gradients accompanying the flow of gas-liquid mixtures in horizontal pipes have been found to be useful in correlating data for the stratified flow of two immiscible liquids in the laminar-turbulent regime. Curves through liquid-liquid data available from three different sets of experiments, though being significantly displaced from the Lockhart-Martinelli curves for gas-liquid systems, represent the data with a maximum deviation of approximately 24%.



Les parametres introduits par Lockhart et Martinelli pour obtenir une correlation des gradients de pression qui accompagnent l'ecoulement de melanges gaz-liquides dans des tuyaux horizontauz ont ete utilises avec avantage pour obtenir une correlation des donnees obtenues avec avantage pour obtenir une correlation des donnees obtenues avec l'ecoulement stratifie de deux liquires immiscibles. Bien qu'elles soient deplacees appreciablement des courbes Lockhart-Martinelli pour des systemes gaz-liquide, les courbes obtenues avec les donnees liquide-liquide pour trois differentes series d'experience accusent une deviation maximum d'environ 24%.

L. V. Lilleleht

Papers

Correlation of pressure gradients for the stratified laminar‐turbulent pipeline flow of two immiscible liquids