Thermodynamique de l'écoulement diphasique compressible à deux constituants de Fanno

Abstract

The behaviour of an adiabatic two-phase gas-liquid flow through a duct with a constant cross-sectional area is studied from a thermodynamics point of view. By assuming the two-phase mixture as homogeneous, the treatment of the physical conservation laws makes it possible to obtain an analytical equation of the fluid evolution which expresses the difference between the Fanno and the isothermal evolutions. On the basis of its differential form and the second principle of thermodynamic, the properties of this flow are discussed. The determination of the Fanno limit shows the existence of a maximum length of the duct. For a length greater than this maximum one, the flow is no more possible. One shows that this maximum length is a function of the mass quality as well as the initial conditions, i.e. the inlet state variables and the inlet velocity. The results are systematically verified by considering the limit of a single phase ideal gas flow. The theory allows to understand and to justify the existence of the so-called multichoked flow. It is applied to the two-phase flow through discharge lines involving geometrical singularities (sudden enlargement for example). The proposed model is validated on the basis of experimental data obtained for quasi steady-state discharges of pure nitrogen and water-nitrogen mixture through a complex pressure relief line involving several abrupt enlargements. The critical configuration and the maximum mass flowrate as well as the variables of the flow (pressure and temperature) predicted from the model are in good agreement with the experimental results. copyright C 1998, Institut Français du Pétrole.