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.
Experiments for air-water flow with and without added foamers were performed in a 50 mm diameter 12 m long vertical pipe at ambient pressure. It was observed that adding foamers to water will lead to a lower pressure drop at superficial gas velocities below the transition limit from annular flow to churn annular flow (which is around 15 m/s) and at superficial liquid velocities between 0.5 and 2 cm/s. Visualisation of the flow with a high speed camera indicates that the decrease in the pressure drop is due to the more regular nature of the flow when the water is foaming: churning of the flow is suppressed by the foam. This is confirmed by the decrease of the pressure oscillations in the presence of foamers. These experiments give insight into why and how liquid loading in gas wells is prevented by the addition of foamers.
In a gas well, both liquids – in the form of water and gas condensate – and gas are produced. If the reservoir pressure is high, the gas velocity in the well tubing is sufficient to drag the liquids to the surface. However, near the end of field life when the reservoir pressure has depleted, the gas velocity becomes too low to transport the liquids through the well. The minimum gas velocity required to lift the liquids is called the critical velocity. When the gas velocity becomes lower than the critical velocity, liquid will start accumulating at the bottom of the well. This will generate a large hydrostatic pressure in the well, which severely limits the gas production. This process is called liquid loading (1). Most foamers used in gas wells foam only the water (2), but there also exist some condensate foamers (3). In this work, only a water-based foamer has been considered.