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# Numerical Study of Two-Phase Flow in a Horizontal Pipeline Using an Unconditionally Hyperbolic Two-Fluid Model

[+] Author Affiliations
Raphael V. N. de Freitas, Carina N. Sondermann, Rodrigo A. C. Patricio, Aline B. Figueiredo, Gustavo C. R. Bodstein

Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

Felipe B. F. Rachid

Fluminense Federal University, Niterói, Brazil

Renan M. Baptista

PETROBRAS R&D Center, Rio de Janeiro, Brazil

Paper No. IMECE2018-87571, pp. V007T09A012; 10 pages
doi:10.1115/IMECE2018-87571
From:
• ASME 2018 International Mechanical Engineering Congress and Exposition
• Volume 7: Fluids Engineering
• Pittsburgh, Pennsylvania, USA, November 9–15, 2018
• ISBN: 978-0-7918-5210-1

## abstract

Numerical simulation is a very useful tool for the prediction of physical quantities in two-phase flows. One important application is the study of oil-gas flows in pipelines, which is necessary for the proper selection of the equipment connected to the line during the pipeline design stage and also during the pipeline operation stage. The understanding of the phenomena present in this type of flow is more crucial under the occurrence of undesired effects in the duct, such as hydrate formation, fluid leakage, PIG passage, and valve shutdown. An efficient manner to model two-phase flows in long pipelines regarding a compromise between numerical accuracy and cost is the use of a one-dimensional two-fluid model, discretized with an appropriate numerical method. A two-fluid model consists of a system of non-linear partial differential equations that represent the mass, momentum and energy conservation principles, written for each phase. Depending on the two-fluid model employed, the system of equations may lose hyperbolicity and render the initial-boundary-value problem illposed. This paper uses an unconditionally hyperbolic two-fluid model for solving two-phase flows in pipelines in order to guarantee that the solution presents physical consistency. The mathematical model here referred to as the 5E2P (five equations and two pressures) comprises two equations of continuity and two momentum conservation equations, one for each phase, and one equation for the transport of the volume fraction. A priori this model considers two distinct pressures, one for each phase, and correlates them through a pressure relaxation procedure. This paper presents simulation cases for stratified two-phase flows in horizontal pipelines solved with the 5E2P coupled with the flux corrected transport method. The objective is to evaluate the numerical model capacity to adequately describe the velocities, pressures and volume fraction distributions along the duct.

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