Lagrangian approach to modeling unsteady gas-liquid flow in a well

Abstract

The purpose of this paper is to develop a numerical method of solving the problem of evolution of the finite gas volume that entered in a liquid flow at a set flow rate. The drift- flux model is used as gas-liquid mixture equations. The velocities of both phases, mixture and gas, are related by the Zuber-Findlay equation which coefficients depend on flow regime and gas void fraction. Lagrangian coordinates are used to simplify the initial equations. The numerical solution scheme is proposed. The numerical solution of the Riemann problem is verified by comparison with the exact self-similar solution. The model and numerical method efficiency is illustrated by examples of gas kick calculations in a vertical well.