Numerical method for determining the coefficient of hydraulic resistance two-phase flow in a gas lift well

Abstract

The process of stationary movement of a gas-liquid mixture in the lifting pipe of a gas-lift well is considered. To describe this two-phase flow, a mathematical model is proposed that includes the equation of flow motion and the continuity equation for each phase. The presented model is transformed to a single nonlinear ordinary differential equation with respect to pressure. Within the framework of the obtained model, the task is set to determine the hydraulic resistance coefficient of a two-phase flow according to an additionally specified condition with respect to pressure. An additional condition, presented in the form of a nonlinear algebraic equation, is transformed into an ordinary differential equation with respect to an unknown coefficient of hydraulic resistance by applying the method of differentiation by parameter. The solution of the resulting Cauchy problem is determined by the finite difference method. Based on the proposed computational algorithm, numerical experiments were carried out for model data. Keywords: gas lift; two-phase flow; hydraulic resistance coefficient; parameter differentiation method; finite difference method.