# Multiphase Flows In Vertical Pipelines

2017-05

## Abstract

The modeling of fluid dynamics through pipelines requires a full understanding of the internal and external factors that influence its transients. The Navier-Stokes momentum equation represents a complete description of the forces acting on a fluid. The equation’s non-linear terms enable to take into account the complex environment that influence the fluid motion. However, for hundreds of years, scientists have not been able to fully solve the Navier-stokes equation in terms of uniqueness without the consideration of simplifying assumptions. In addition to the fluid momentum transient’s resolution, the problem becomes more complicated when introducing more phases to the fluid dynamics equations. Reduced order analytic and numerical models have been employed to model multiphase flow behavior and have been showing good agreement against experimental providing then a robust tool for the modeling of multiphase flows.

Throughout this dissertation, different techniques of two-phase flow modeling through vertical pipelines under varying flowrate and pressure boundary conditions are illustrated. Numerical modeling is elaborated by discretizing the space and time scale and evaluating the flow physical variables’ dynamics along the pipe. The employed quasisteady state momentum equation numerical resolution results in more than one root, known as the multiple root problem. A mathematical constraint, applied over the pipe and time discretization steps, is presented aiming to guarantee the existence of the momentum equation liquid phase holdup solution while insuring its uniqueness. While numerical models provide discretized solution over the pipe length, their implementation on complex systems presents a challenge limiting their applicability. Analytic models are investigated as an effective solution to this type of constraints. The reduced order transmission line model for one-phase flows is extended for inclined and vertical inclinations while taking into account fluid compressibility. The adaptation of the analytic one-phase flow model to two-phase flows is done using an equivalent flow procedure. Two industrial applications concerning the integration of multiphase flow models in complex systems are presented, namely pumping units’ production and safety optimization when two-phase flows (gas and oil) are encountered, and gas kick numerical modeling through the extension of the numerical model to fast transients’ regime.

## Keywords

Multiphase Flows, Vertical Flow, Oil, Gas, Gas kicks, Pumping Units, Numerical models, Analytical Modeling

## Citation

Portions of this document appear in: Omrani, Ala E., Matthew A. Franchek, Karolos Grigoriadis, and Reza Tafreshi. "Liquid Holdup Discretized Solution's Existence and Uniqueness Using a Simplified Averaged One-Dimensional Upward Two-Phase Flow Transient Model." Journal of Dynamic Systems, Measurement, and Control 139, no. 8 (2017): 081005. And in: Omrani, Ala E., Matthew A. Franchek, Behrouz Ebrahimi, Mete Mutlu, and Karolos Grigoriadis. "Low-Dimensional Modeling of a Pumping Unit to Cope With Multiphase Flow." Journal of Dynamic Systems, Measurement, and Control 139, no. 4 (2017): 041010.