Justification of the drift-flux model for two-phase flow in a circular pipe

A flow of a gas-liquid dispersed mixture in a circular pipe with a variable inclination to the horizon, as applied to oil and gas flows in wells, is considered. Within the framework of a multi- fluid approach, the equations of an asymptotic drift-flux model, which contains an algebraic relation between the phase velocities and one momentum equation for the volume-averaged velocity of the mixture, are derived. It is shown that the drift-flux model in this formulation strictly follows from the balance laws under assumption of inertialess velocity slip of the phases in case of validity of one of the following conditions: (i) the dispersed-phase volume fraction is small; (ii) the phase velocity slip may be neglected; or (iii) the flow regime is inertialess and the acceleration of the mixture can be neglected. A numerical algorithm based on the SIMPLE method is implemented for solving the obtained equations of the drift-flux model. The possibility of modeling the gravitational segregation and the pressure buildup in a shut-in well and transient slug flows is demonstrated.