Three-phase flows of gas and two liquid phases () often occur during production of oil. A typical oil and gas reservoir contains gas, oil and water. As oil is extracted from the reservoir, the formation water beneath may flow into the well, due to its easier motion through the rock pores. In many cases, water is pumped into the reservoir, through water injection wells, to help boost production (See Enhanced Oil Recovery). Eventually this water will find its way to the production well, which will from that point produce oil with a progressively larger water fraction (“water cut”).
As the North Sea oil fields mature, production of water with the oil is becoming increasingly important. A good understanding of the effects of the water phase on the flow behaviour of multiphase mixtures in pipelines can have a significant bearing on the economics of oil recovery at high water cuts.
This is reflected in the growing research interest in the subject of three-phase flows over the last few years as highlighted in recent publications by Hall (1992, 1993), Lahey et al. (1992), Stapelberg et al. (1991), and Lunde et al. (1993).
In a vertical or inclined pipe, the greater density of the water phase compared to the oil phase means that there is a greater hydrostatic pressure drop. This is particularly noticeable in fields, where water injection is used to boost output. Once injection water breakthrough occurs, the larger pressure drop in the well causes a fall in production rate.
In a horizontal pipe, due to the effect of gravity, the water will tend to settle to the bottom of the pipe. While this may considerably reduce the frictional component of the pressure gradient if the oil is very viscous, the separate water layer may cause corrosion of the pipe.
At higher gas flow rates there may be sufficient mixing, particularly in the slug flow regime for one of the liquids to be dispersed in the other. If the oil is the continuous phase, the dispersion of water in it can cause a large increase in the effective viscosity and consequent increase in frictional pressure gradient. If the continuous phase is water, the pressure gradient may be much less, but the pipe walls will be continuously water-wet. These effects will influence the sizing of pipelines to give the most economic design and operation.
At ceitain flow-rates it may be possible that the water settles into a separate layer in the intervals between liquid slugs. In this case, parts of the pipe walls would experience a variation in wetting with time, with implications for the distribution of corrosion inhibitors, for example.
With the growing interest in three-phase flows in recent years, a number of useful experimental investigations have been reported. Hall et al. (1993) performed experiments using the high pressure multiphase flow facility at Imperial College, London, with air, water and a lubricating oil of viscosity approximately 40 mPas. The main test pipeline had an internal diameter of 78 mm and a length of 40 m and had a visualisation section towards the end. In addition to observing flow patterns the pressure drop, holdup and slug frequency were measured.
Lahey et al. (1992) investigated three-phase flows of air, water, and mineral oil (viscosity 116.4 mPas at 25°C) in a pipe of 19 mm internal diameter. The main objective of the experiments reported was to observe flow patterns and to measure the oil and water holdup. The small diameter may have had a significant effect on the flow patterns in this system; for example, the region of stratified flow was found to be very restricted.
Nuland et al. (1991) developed a dual-energy gamma densitometer for the measurement of holdup in three-phase flow. This was compared with the quick-closing valve method for measurement of holdup for a three-phase air/oil/water flow in a 32 mm internal diameter pipe, the oil viscosity in these experiments was 175 mPas at 20°C. Reasonable agreement was obtained between the phase fractions obtained using the gamma densitometer and those using the quick-closing valves.
In those cases where significant discrepancies occurred the disagreement was due to the assumption of a Stratified Flow geometry for the calculation of holdup from the gamma densitometer readings, when the interfaces were in reality curved. More recent experiments at the same institution have been focused on the study of three-phase gas-condensate flows in an uphill inclined pipe, as described by Lunde et al. (1993).
Stapelberg et al. (1991) studied the flow of gas, water and a white mineral oil of viscosity 31 mPas in a test loop with diameters 23.8 mm and 59.0 mm. The flows were in the stratified and Slug Flow regimes and results were obtained for pressure gradient and slug characteristics (slug length, frequency, etc.). Some measurements were also reported of holdup and information given on flow visualization. These experiments have provided new data and physical information and have demonstrated the inadequacy of current methods for calculating a pressure gradient, particularly in stratified three-phase flows. Further experiments reported by Nadler and Mewes (1993) have extended these experiments by using oils with a range of viscosities from 14 mPas to 37 mPas and increased liquid and gas flow-rates. Results for the characteristic of three-phase slug flows have been obtained and compared with measurements for oil-air and water-air flows.
The work by Lahey et al. (1992) demonstrated the difficulty of classification of flow patterns in three-phase flows. In addition to the well-known descriptions for the flow patterns in gas-liquid flows (stratified, slug, annular, etc.), the distribution of the two liquid phases needs to be taken into account. The two liquids may be either dispersed, in which case either the water or the oil may form the continuous phase or they may flow separately.
Hall (1992, 1993) concentrated on the stratified and slug flow regimes. Both stratified and slug flows may exist where the oil and water are completely separate, are partially mixed or are fully mixed. In the case where the two fluids are fully mixed, either the oil or the water can form the continuous phase, depending on the volume ratio of the two liquids and theinversion point.
The modelling of the transition between stratified and slug flow is very strongly influenced by the distribution of the two liquid phases. If the oil and water are fully mixed then the flow behaves almost as if it were gas-liquid flow, where the liquid phase has the physical properties of the combined oil and water phases. The density is given by a volume fraction average of the oil and water densities:
where φ and ρdisp are the volume fraction and density of the dispersed phase and is the density of the continuous phase. A volume fraction average must not be used for the effective viscosity because it is observed in practice that the viscosity of a dispersion of one liquid in another can be significantly higher than the viscosity of the pure liquid, as shown by Woelflin (1942). A suitable equation to use is that of Brinkman (1952):
where ηcont is the viscosity of the continuous phase.
These effective liquid properties may then be used in a two-phase gas-liquid transition prediction, for example that given by Taitel and Dukler (1976).
When the two liquids are not completely mixed, it is necessary to model the flow in greater detail. Since neither phase forms the continuous phase, it is difficult to define meaningful mixture physical properties. The approach suggested by Hall (1992) was to model the three-phase stratified flow using a three-fluid model (in a similar way to the Taitel and Dukler two-fluid method for gas-liquid flow) and to use the holdup obtained from this method to calculate the stratified to slug transition. However, comparison with experimental data showed that the transition occurred at much higher gas velocities than those predicted by this method. This was believed to be because the oil layer, although being more viscous than the water, is travelling at a higher mean velocity because its lower interface is in contact with a moving water layer rather than a fixed wall. Hence a second approach was tried, based on modifying the linear stability analysis of Lin and Hanratty (1986) to allow a second liquid phase. This was reported by Hall and Hewitt (1992).
This approach was found to work for both slug flows where a separate water layer was present continuously and for those flows where a separate water layer only formed in the film region between liquid slugs. Hall et al. (1993) presented a simple criterion to determine whether or not this separate water layer forms. This is based on a comparison of the time taken for drops of the dispersed phase (which are formed in the slug body) to settle and the interval between liquid slugs. If the drops take longer to settle than the slug interval, then there is not enough time for a separate layer to form. This criterion showed good agreement with experimental observations from the Imperial College loop, but further development is really required for more general application.
There is very little information on methods for calculation of pressure gradient and holdup in three-phase flows, and in most cases the available methods for two-phase flows must be used, with suitable modifications for the physical properties of the combined liquid phases. The correct method is very dependent on the flow pattern, and it is therefore essential to make the best estimate possible of the likely flow pattern, using the guidelines in the previous section, or any available observations of the system under investigation.
If the flow is stratified and the oil and water form separate layers, then the most reliable estimate of pressure gradient and holdup (of both the oil and the water phases) is probably to use a three-fluid model for the stratified flow, as described by Hall (1992).
If the flow is stratified and the oil and water are mixed, then the flow may be treated as a two-phase flow of gas and oil-water mixture and methods such as Taitel and Dukler (1976) may be used for the stratified flow holdup. It is important to be able to determine which liquid forms the continuous phase in order to calculate the correct effective liquid viscosity. Prediction of the inversion point (between oil-continuous and water-continuous) is difficult, since it depends on a number of factors, in particular the interfacial chemistry of the oil-water mixture. The best approach is to determine the inversion point from experimental measurements of viscosity at various water fractions. In slug flows, the pressure gradient can almost always be reasonably accurately calculated by using the density and viscosity of an oil/water mixture as given earlier. This will remain true even in cases where a separate water layer forms between slugs (because the largest contribution to the pressure gradient is the frictional resistance of the liquid slug, where the two liquids are well-mixed).
Either a two-phase frictional pressure correlation, e.g. Beggs and Brill (1973) or a slug flow model, e.g. Dukler and Hubbard (1975) was shown to give good agreement with experimental observations by Hall et al. (1993); the slug flow model of Dukler and Hubbard also gives the holdup. In the less common case where a separate water layer may persist throughout the slug, this approach may not be appropriate. However, further work is required before making any recommendations.
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