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Research Papers

Liquid Holdup Discretized Solution's Existence and Uniqueness Using a Simplified Averaged One-Dimensional Upward Two-Phase Flow Transient Model

[+] Author and Article Information
Ala E. Omrani

Department of Mechanical Engineering,
University of Houston,
4726 Calhoun Road,
N285 Engineering Building 1,
Houston, TX 77204
e-mail: aomrani@uh.edu

Matthew A. Franchek

Professor
Department of Mechanical Engineering,
University of Houston,
4726 Calhoun Road,
W214 Engineering Building 2,
Houston, TX 77204
e-mail: mfranchek@central.uh.edu

Karolos Grigoriadis

Professor
Department of Mechanical Engineering,
University of Houston,
4726 Calhoun Road,
W212 Engineering Building 2,
Houston, TX 77204
e-mail: karolos@uh.edu

Reza Tafreshi

Professor
Department of Mechanical Engineering,
Texas A&M University at Qatar,
P.O. Box 23874,
Doha, Qatar
e-mail: reza.tafreshi@qatar.tamu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 9, 2015; final manuscript received January 21, 2017; published online May 24, 2017. Assoc. Editor: Kevin Fite.

J. Dyn. Sys., Meas., Control 139(8), 081005 (May 24, 2017) (14 pages) Paper No: DS-15-1431; doi: 10.1115/1.4035901 History: Received September 09, 2015; Revised January 21, 2017

This article presents a one-dimensional 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 one-dimensional 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 ensured 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.

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References

Figures

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Fig. 1

Two-phase vertical flow patterns

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Fig. 2

Two-phase upward vertical flow pattern map

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Fig. 3

Two-phase upward vertical flow computational flowchart

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Fig. 5

Bubble flow numerical model liquid holdup validation against experimental data

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Fig. 6

Slug flow numerical model liquid holdup validation against experimental data

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Fig. 7

Bubble flow numerical model liquid holdup validation against Petelas and Ghajar models

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Fig. 8

Slug flow numerical model liquid holdup validation against Petelas and Ghajar models

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Fig. 9

Annular flow numerical model liquid holdup validation against experimental data

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Fig. 10

Annular flow numerical model liquid holdup validation against Petelas and Ghajar models

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Fig. 11

Flow pattern change with the inlet flow rates

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Fig. 12

Pipe inlet pressure transient responses

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Fig. 13

Bubble flow liquid holdup pipe distribution transients

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Fig. 14

Slug flow liquid holdup pipe distribution transients

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Fig. 15

Annular flow liquid holdup pipe distribution transients

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Fig. 16

Uniqueness condition simulation

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