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# Difference between revisions of "Homogeneous Two-Phase Flow"

(Created page with "== Introduction == In homogeneous two-phase flow, both phases are assumed to move at the same in-situ velocity. This assumption enables the simple calculation of liquid hold...") |
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The pressure gradient ''dp/dL'' of the "no-slip" flow is calculated from the momentum balance based on averaged fluid properties. E.g. the Mixture Density ''ρ''<sub>m</sub> is defined as follows, | The pressure gradient ''dp/dL'' of the "no-slip" flow is calculated from the momentum balance based on averaged fluid properties. E.g. the Mixture Density ''ρ''<sub>m</sub> is defined as follows, | ||

− | [[File: | + | [[File:Fig5.2HTPF.jpg|RTENOTITLE]]....................(5) |

Based on the same weighting approach, some authors define the "Mixture Viscosity" ''μ''<sub>m</sub> as follows, | Based on the same weighting approach, some authors define the "Mixture Viscosity" ''μ''<sub>m</sub> as follows, | ||

− | [[File: | + | [[File:Fig6.2HTPF.jpg|RTENOTITLE]]....................(6) |

+ | In the case of three-phase flow, the interfacial tension is of oil and water mixture is estimated as follows, | ||

+ | [[File:Fig7HTPF.jpg|RTENOTITLE]]....................(7) | ||

− | + | where ''f''<sub>w</sub> is the no-slip liquid holdup in the liquid phase and is defined, similar to ''λ'' as follows, | |

− | Torres, C. Modeling of oil-water flow in horizontal and near-horizontal pipes | + | [[File:Fig8HTPF.jpg|RTENOTITLE]]....................(8) |

+ | |||

+ | From the mass balance of the steady-state flow, the pressure gradient is then estimated as follows, | ||

+ | |||

+ | [[File:Fig9HTPF.jpg|RTENOTITLE]]....................(9) | ||

+ | |||

+ | where ''v''<sub>m</sub> is mixture velocity or the sum of the superficial velocities of the flow phases, while ''f''<sub>n</sub> is the no-slip friction factor calculated from the following definition of Reynolds number ''Re''<sub>n</sub>, | ||

+ | |||

+ | [[File:Fig10HTPF.jpg|RTENOTITLE]]....................(10) | ||

+ | |||

+ | == References == | ||

+ | |||

+ | Alsafran, M. and Brill J. 2017. Applied Multiphase Flow in Pipes and Flow Assurance. Society of Petroleum Engineers. | ||

+ | |||

+ | Shoham, O. 2006. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipes. Richardson, Texas: Society of Petroleum Engineers. | ||

+ | |||

+ | Trallero, J L, Intevep, S A, Sarica, C, and Brill, J P. 1996. A study of oil-water flow patterns in horizontal pipes. United States: N. p., Web. | ||

+ | |||

+ | Torres, C. 2005. Modeling of oil-water flow in horizontal and near-horizontal pipes. Ph.D Thesis, The University of Tulsa, Tulsa, OK. | ||

+ | |||

+ | Zhang, H. -Q., Wang, Q., Sarica, C. et al. 2003. Unified Model for Gas-Liquid Pipe Flow via Slug Dynamics—Part 1: Model Development. ASME J Energ Resour Tech 125 (4): 266-273. https://doi.org/10.1115/E1615246 |

## Latest revision as of 21:57, 12 September 2021

## Introduction

In homogeneous two-phase flow, both phases are assumed to move at the same in-situ velocity. This assumption enables the simple calculation of liquid holdup and pressure drop in pipes and wellbores. It was found experimentally that this assumption of homogeneous flow is representative in "Dispersed Flow" of gas-liquid (Shoham 2006) and liquid-liquid flow (Torres 2005) and in "Mist Flow" of gas-liquid. Moreover, It was found that it is a representative assumption for flow inside liquid slugs (Zhang et al. 2003).

## Derivation of Steady-State Homogeneous Two-Phase Flow Equations

The condition of homogeneous flow is called the "no-slip" condition, where the slip is the difference between gas and liquid in-situ velocities. The "no-slip" and "homogeneous" terminologies are used interchangeably in the literature and they refer to the same concept. Based on the "no-slip" conditions,

Based on the mass balance at steady-state conditions, the superficial phase velocity is linked to the in-situ phase velocity as follows,

where *ρ* is the phase density, *A* is the cross-sectional area of the pipe and *H*_{L} is the liquid holdup. Substituting Eqs. 2 and 3 into Eq. 1, the following expression for *H*_{L} is found as follows,

where *λ* becomes the liquid holdup at the "no-slip" conditions.
The pressure gradient *dp/dL* of the "no-slip" flow is calculated from the momentum balance based on averaged fluid properties. E.g. the Mixture Density *ρ*_{m} is defined as follows,

Based on the same weighting approach, some authors define the "Mixture Viscosity" *μ*_{m} as follows,

In the case of three-phase flow, the interfacial tension is of oil and water mixture is estimated as follows,

where *f*_{w} is the no-slip liquid holdup in the liquid phase and is defined, similar to *λ* as follows,

From the mass balance of the steady-state flow, the pressure gradient is then estimated as follows,

where *v*_{m} is mixture velocity or the sum of the superficial velocities of the flow phases, while *f*_{n} is the no-slip friction factor calculated from the following definition of Reynolds number *Re*_{n},

## References

Alsafran, M. and Brill J. 2017. Applied Multiphase Flow in Pipes and Flow Assurance. Society of Petroleum Engineers.

Shoham, O. 2006. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipes. Richardson, Texas: Society of Petroleum Engineers.

Trallero, J L, Intevep, S A, Sarica, C, and Brill, J P. 1996. A study of oil-water flow patterns in horizontal pipes. United States: N. p., Web.

Torres, C. 2005. Modeling of oil-water flow in horizontal and near-horizontal pipes. Ph.D Thesis, The University of Tulsa, Tulsa, OK.

Zhang, H. -Q., Wang, Q., Sarica, C. et al. 2003. Unified Model for Gas-Liquid Pipe Flow via Slug Dynamics—Part 1: Model Development. ASME J Energ Resour Tech 125 (4): 266-273. https://doi.org/10.1115/E1615246