Calculation of gas-liquid flow with mass transfer between phases

Analysis of two-phase flow taking into account mass transfer (boiling/condensation) may be performed for pipelines of various structures without recycles. Individual branches are analyzed using direct calculation method, long pipes are subdivided into parts with slight change of calculated parameters, if necessary ([1], pp.22-23).

Change of flow temperature and phase composition for this type of flow is calculated using full energy balance equation. First change of fluid enthalpy is determined, then phase equilibrium on the basis of enthalpy and pressure is calculated and finally fluid temperature and phase composition are obtained.  

If positive flow quality is entered in the beginning of pipeline, then the input temperature is ignored. In this case at calculating phase equilibrium fluid temperature in the start node is determined using flow quality and pressure values.  

To analyze flow with mass transfer in unbranched pipeline one may enter pressure in the end node of a branch. In this case the fluid temperature is also interpreted as being entered in the end node and the “upstream” calculation is performed that obtains initial flow parameters (quality, temperature, pressure).

The analysis determines where in the pipeline the fluid state changes to one phase (liquid or gas). In these points the automatic switch to one-phase methods is performed. Similarly the reverse transition is recognized (the beginning of boiling up or condensation) with switching to two-phase methods.

For the “upstream” calculation of two-phase flow in unbranched pipelines Hydrosystem determines where the choked flow occurs in the pipeline which is characterized by Mach number equal to 1, flow discontinuity and shock waves.  These points are pipe exits, reducers, abrupt expansions and endings of straight pipes (the cases of choked flow calculation inside the orifices and valves is currently not implemented in software). At “upstream” analysis the program uses iterations based on energy and material balance equations to determine fluid properties before shock wave. A specific algorithm is used to analyze straight pipes with Mach number close to 1 and pressure, temperature and other parameters changing very fast along the pipe. Such flow is simulated using a system of ordinary differential equations which is solved by Runge-Kutta method and quadrature formulas (see [2]). For two-phase flows in branched pipelines, as well as other (in addition to the "upstream" calculation) cases of calculating unbranched pipelines, the calculation of the choked and near-choked flow has not yet been implemented.

References

1. Shoham O. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipes. Socienty of Petroleum Engineers. 2006.

2. L.B. Korelshteyn. On One Form of Equations of Chocked Flow in Pipes (in Russian). Industrial service, N3(44), 2012, pp. 29-36.