### Abstract

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.

Original language | English |
---|---|

Article number | 081005 |

Journal | Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME |

Volume | 139 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Aug 2017 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Information Systems
- Instrumentation
- Mechanical Engineering
- Computer Science Applications

### Cite this

*Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME*,

*139*(8), [081005]. https://doi.org/10.1115/1.4035901

**Liquid holdup discretized solution's existence and uniqueness using a simplified averaged one-dimensional upward two-phase flow transient model.** / Omrani, Ala E.; Franchek, Matthew A.; Grigoriadis, Karolos; Tafreshi, Reza.

Research output: Contribution to journal › Article

*Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME*, vol. 139, no. 8, 081005. https://doi.org/10.1115/1.4035901

}

TY - JOUR

T1 - Liquid holdup discretized solution's existence and uniqueness using a simplified averaged one-dimensional upward two-phase flow transient model

AU - Omrani, Ala E.

AU - Franchek, Matthew A.

AU - Grigoriadis, Karolos

AU - Tafreshi, Reza

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85012290025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012290025&partnerID=8YFLogxK

U2 - 10.1115/1.4035901

DO - 10.1115/1.4035901

M3 - Article

VL - 139

JO - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

JF - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

SN - 0022-0434

IS - 8

M1 - 081005

ER -