Mathematical Model for “Bubble Gas-Stratified Oil” Flow in Horizontal Pipes

A one-dimensional, isothermal, transient model for bubble gas-stratified oil flow is presented. Bubble gas- stratified oil flow pattern of heavy oil, water and gas, in horizontal pipelines, consists of two regions: (1) a stratified region with a gross water layer in the bottom, an oil layer in the middle and a thin water layer in the top, (2) a region with a water layer in the bottom, an oil layer in the middle and a gas bubble in the top. The two-fluid mathematical model consists of mass, momentum and energy conservation equations for every phase, considering the hydrostatic gradient. The model takes into account: (1) wall shear stress, (2) interfacial shear stress, and (3) the non-Newtonian oil behavior. The model is able to predict pressure, volumetric fraction, temperature, and velocity profiles for every phase. The numerical solution is based on the finite difference technique in an implicit scheme. The model was validated using experimental data reported in literature, for a heavy crude oil (14 °API), and it was observed that the pressure drop calculated by the model was reasonably close to the experimental data.