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research-article

LIQUID HOLDUP DISCRETIZED SOLUTION’S EXISTENCE AND UNIQUENESS USING A SIMPLIFIED AVERAGED 1D UPWARD TWO-PHASE FLOW TRANSIENT MODEL

[+] Author and Article Information
Ala Eddine Omrani

Department of Mechanical Engineering, University of Houston 4726 Calhoun Rd, N285 Engineering Building 1, Houston, TX 77204
aomrani@uh.edu

Matthew A. Franchek

Department of Mechanical Engineering, University of Houston 4726 Calhoun Rd, W214 Engineering Building 2, Houston, TX 77204
mfranchek@central.uh.edu

Karolos Grigoriadis

Department of Mechanical Engineering, University of Houston 4726 Calhoun Rd, W212 Engineering Building 2, Houston, TX 77204
karolos@uh.edu

Reza Tafreshi

Department of Mechanical Engineering Texas A&M University at Qatar Doha, Qatar
Reza.tafreshi@qatar.tamu.edu

1Corresponding author.

ASME doi:10.1115/1.4035901 History: Received September 09, 2015; Revised January 21, 2017

Abstract

Presented is a one-dimensional (1D) numerical model for vertical upward multiphase flow dynamics in a pipeline. A quasi-steady-state condition is used for the gas phase as well as liquid and gas momentum equations. A second-order polynomial for homogeneous flows and a sixth-order polynomial for separated flows are derived to determine the two-phase flow dynamics, assuming that the gas flow mass is conserved. The polynomials are formulated based on the homogenous and separate flows’ momentum equation and the homogeneous flows’ rise velocity equation and their zeros are the flow actual liquid holdup. The modeling polynomial approach enables the study of the polynomial liquid holdup zeros existence and uniqueness and as a result the design of a stable numerical model in terms of its outputs. The 1D solution of the flow for the case of slug and bubble flow is proven to exist and to be unique when the ratio of the pipe node length to the time step is inferior to a specific limit. For the annular flow case, constraints on the inlet gas superficial velocity and liquid to gas density ratio show that the existence is insured while the uniqueness may be violated. Simulations of inlet pressure under transient condition are provided to illustrate the numerical model predictions. The model steady-state results are validated against experimental measurements and previously developed and validated multiphase flow mechanistic model.

Copyright (c) 2017 by ASME
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