In this study, the occurrence of multiple solutions in stratified flows was investigated. The model equations give multiple holdup solutions for certain flow regimes – in small angle upflows with low liquid velocity (low liquid loading) and with low to moderate gas velocity. We applied a steady state as well as a transient flow model, supplied with different closures, verifying the structural stability of different solutions. We compared our model results to observations in our own experiments for zero net liquid flow, and also with two experimental cases by other authors, who investigated the occurrence of hysteresis or holdup discontinuities in stratified flows.


Long gas/condensate pipelines follow the natural terrain and thus have an undulating profile. Since they operate in the low liquid loading regime, the flow pattern is predominantly stratified flow. In those parts of the pipeline which are slightly upwardly inclined, a steep change in holdup can be observed when the gas velocity is decreased. Under these same conditions, the standard stratified two-phase flow models predict the occurrence of multiple holdup solutions. It is our goal to investigate if we can reliably predict which holdup solution is going to happen in reality, and at which conditions the sudden change in holdup will take place. One of the first studies to point out the occurrence of multiple solutions under certain conditions in the original two-phase stratified flow model presented by Taitel and Dukler (1) was done by Baker and Gravestock (2). Landman (3, 4) and Ullmann et al. (5) showed that this was also the case when laminar gas/liquid flow in rectangular ducts was solved exactly. Further, Landman (3, 4) parameterized the multi-valued solutions, and did a stability analysis and dynamic simulations in order to see which of the solutions is likely to happen in reality.

This content is only available via PDF.
You can access this article if you purchase or spend a download.