Two-Phase Flow Governing Equations for Transient Geothermal Well and Pipeline Simulation

Abstract

Governing equations for transient gas-liquid flow as a result of the sequential spatialtemporal averaging procedure are presented. This set of equations forms the basis for the elaboration of the friction losses calculation technique and one-dimensional models for transient two-phase flow in geothermal wellbores and pipelines for bubbly, slug and churn-turbulent flow patterns. These models comprise two transient partial differential mass conservation equations for each phase and a momentum equation for gas-liquid mixture. The algebraic slip velocity and the perfect gas state equation are added to complete the model. The friction losses are represented by using the concept of turbulent boundary layer with vanishing viscosity with only a single additional empirical coefficient.