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Research Papers

Low-Dimensional Modeling of Transient Two-Phase Flow in Pipelines

[+] Author and Article Information
Amine Meziou

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

Majdi Chaari

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

Matthew 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

Rafik Borji

FMC Technologies,
10600 Southdown Trace Trail,
Apt. #408,
Houston, TX 77034
e-mail: rafik.borji@fmcti.com

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

Associate 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 15, 2015; final manuscript received June 2, 2016; published online July 14, 2016. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 138(10), 101008 (Jul 14, 2016) (17 pages) Paper No: DS-15-1447; doi: 10.1115/1.4033865 History: Received September 15, 2015; Revised June 02, 2016

Presented are reduced-order models of one-dimensional transient two-phase gas–liquid flow in pipelines. The proposed model is comprised of a steady-state multiphase flow mechanistic model in series with a transient single-phase flow model in transmission lines. The steady-state model used in our formulation is a multiphase flow mechanistic model. This model captures the steady-state pressure drop and liquid holdup estimation for all pipe inclinations. Our implementation of this model will be validated against the Stanford University multiphase flow database. The transient portion of our model is based on a transmission line modal model. The model parameters are realized by developing equivalent fluid properties that are a function of the steady-state pressure gradient and liquid holdup identified through the mechanistic model. The model ability to reproduce the dynamics of multiphase flow in pipes is evaluated upon comparison to olga, a commercial multiphase flow dynamic code, using different gas volume fractions (GVF). The two models show a good agreement of the steady-state response and the frequency of oscillation indicating a similar estimation of the transmission line natural frequency. However, they present a discrepancy in the overshoot values and the settling time due to a difference in the calculated damping ratio. The utility of the developed low-dimensional model is the reduced computational burden of estimating transient multiphase flow in transmission lines, thereby enabling real-time estimation of pressure and flow rate.

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Figures

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Fig. 1

Modeling procedure

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Fig. 2

Two-phase flow patterns [47]

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Fig. 3

Flow pattern determination procedure in Ref. [31]

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Fig. 4

Flow pattern map for air/water system at 90 deg upward inclination: (a) Petalas and Aziz model [31] and (b) present work

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Fig. 5

(a) Predicted versus experimental pressure gradient and (b) predicted versus experimental liquid holdup

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Fig. 6

Modal approximation of 1/cosh(Γ): (a) uncorrected, (b) Hullender's correction, and (c) alternate correction

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Fig. 7

Modal approximation of Zc sinh(Γ)/cosh(Γ): (a) uncorrected, (b) Hullender's correction, and (c) alternate correction

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Fig. 8

Modal approximation of sinh(Γ)/Zc cosh(Γ): (a) uncorrected and (b) alternate approach

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Fig. 9

Distributed-parameter model with lumped turbulent resistance

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Fig. 10

Frequency response of the transfer function relating Pin to Pout and Qout to Qin for different Reynolds numbers

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Fig. 11

Frequency response of the transfer function relating Pin to Qin for different Reynolds numbers

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Fig. 12

Frequency response of the transfer function relating Qout to Pout for different Reynolds numbers

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Fig. 13

Frequency response of the transfer function relating: (a) Pin to Pout and Qout to Qin, (b) Pin to Qin, and (c) Qout to Pout

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Fig. 14

Simulation points

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Fig. 15

Four-mode frequency response for different GVF levels: (a) 1/cosh(Γ), (b) Zcsinh(Γ)/cosh(Γ), and (c) sinh(Γ)/Zccosh(Γ)

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Fig. 16

Inlet pressure time response to inlet flow rate step for different GVF levels

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Fig. 17

Inlet pressure time response to inlet flow rate step for different truncation orders

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Fig. 18

Computation time versus absolute relative error

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Fig. 19

Inlet pressure time response to inlet flow rate step: (a) laminar flow and (b) turbulent flow

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Fig. 20

Frequency response of the transfer function relating Pin to Qin: (a) laminar flow and (b) turbulent flow

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Fig. 21

Inlet pressure time response to inlet flow rate step for 10% GVF

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Fig. 22

Inlet pressure time response to inlet flow rate step for 20% GVF

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Fig. 23

Inlet pressure time response to inlet flow rate step for 30% GVF

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