Analytical model for interfacial waves in vertical core flow

The vertical annular pipe flow of two immiscible liquids with very different viscosities provides an efficient and low cost method for producing heavy oils in vertical wells using water as a lubricant. The core flow pattern is becoming attractive in the current Brazilian deep water production scenario. Understanding interfacial phenomena present in this flow pattern is crucial for appropriate design of the production system. Assuming that in this axisymmetric flow there is no net force associated with interfacial tension, a differential equation governing the shape of the liquid–liquid interface is derived. An analytical solution is proposed for the prediction of the wave geometry, which depends only on pipe geometry, physical properties and flow rates of the fluids. The comparison between the model predictions and recent experimental data shows a reasonable agreement.