Flow regime independent, high resolution multi-field modelling of near-horizontal gas-liquid flows in pipelines

For fully-developed two-phase flows, maps that correlate experimental and semi-empirical expressions for flow regimes are widely used. For calculations of the various important two-phase flow parameters, this in turn requires correlations for various interfacial and wall interaction effects that are flow regime dependent. For many systems of practical interest, however, the evolution of flow regimes (such as slug flow in oil–gas pipelines) is of interest because the development lengths are long and flow regimes may change in regions where pipeline inclination changes due to the terrain. It is shown here that for slow transients in near-horizontal pipes, the one-dimensional multi-field model, when solved with sufficient resolution, does not require flow regimes to be specified or flow regime dependent closure relationships. The formulation predicts the development of flow regimes and various flow parameters without the need for maps, or the need to change closure relationships. To accomplish this, the model includes four fields, i.e. continuous and dispersed liquid, continuous and dispersed gas, as well as a set of appropriate closure relationships from the literature. For the main application considered here, i.e. slow transients in oil–gas pipelines, order of magnitude analyses indicate that certain inertial terms in the model are very small and can be neglected in comparison to the others. Advantage is taken of this to simplify both the structure of the mathematical problem and the solution procedure, which is sufficiently accurate that mass is conserved for each of the four fields. Furthermore, the calculations require high spatial resolution, so a fast, easily-parallelizable numerical procedure has been applied. The results indicate that the development of certain flow regimes, including transitions from bubbly to stratified flow and vice versa, slug flow including slug frequency and length, and the evolution of these parameters along a pipeline are well predicted by the model when compared to experimental data. As part of the validation it is also shown that the model predicts, without need to change closure relationships, flow regimes in fully-developed near-horizontal two-phase flows in good agreement with existing flow regime maps. This suggests that for slow transients in flows for which one-dimensional effects dominate, predictions can be made without requirements for flow regime maps and closure relationships that depend on them.