Numerical modelling of two-phase oil–water flow patterns in a subsea pipeline
Introduction
The flow of two immiscible liquids is encountered in a diverse range of processes, such as those of the petroleum industry. The simultaneous flow of oil and water in pipelines is a common occurrence in offshore oil production systems. In the early stages of a well’s lifetime the amount of water is negligible. However, as the well ages the water production increases. Furthermore, water injection for enhanced oil recovery is commonly used to maintain the reservoir pressure. In contrast to the early days of the offhore oil industry, when the amount of produced water was negligible, these days many wells are mature and are producing large amounts of water. From an economical point of view, operation of a well might be reasonable even for water cuts as high as 90% (Elseth, 2001, Kumara et al., 2009). The internal structure of the oil–water flow, known as the flow pattern, and the distribution of water have a great influence on the design of the pipeline. The distribution of oil and water in the pipeline significantly affects the corrosion rate, the pressure drop, wax deposition, etc. An effective design can be made only if the flow pattern and the phase distributions under different conditions are known. (Xu, 2007).
Liquid–liquid flows in a horizontal pipeline can be classified into two major groups and several sub-groups, based on the interface structure. At relatively low velocities two immiscible liquids are separated by a clearly defined interface. This flow regime is referred to as a stratified flow pattern. However, at relatively high velocities there is no clear interface and one fluid is in the form of drops in the continuum of the other. This flow pattern is usually called a dispersed flow. At intermediate velocities a combination of the dispersed and stratified flow patterns is observed, where both phases retain their continuity at the top and bottom of the pipe, with a dispersed region present in the middle of the pipe cross section. Apart from these, formation of slug flow and annular flow was reported by several investigators. Experimental studies showed that by increasing the oil viscosity the extent of core annular flow increases. The transition boundaries among these flow patterns depend on many factors. A great deal of effort has gone into studying flow patterns under different conditions. Various experimental studies have been carried out to get reliable flow pattern maps through which we can identify the flow regime inside the pipe. However, because of the diversity of the oil properties, the available flow pattern maps lack a general agreement. Previous experimental studies show that the observed flow patterns and the phase distribution critically depend on the fluid properties, mixture velocity, inlet water cut,and the geometry (diameter and inclination angle) as well as wetting property of pipe (Arirachakaran et al., 1989, Angeli and Hewitt, 2000a; Lovick and Angeli, 2004a; Xu, 2007; Kumara et al., 2009, Strazza et al., 2011, Yusuf et al., 2012, Hanafizadeh et al., 2015).
As mentioned earlier, the prediction of the flow pattern and phase distribution is essential for the proper design of the wells and the pipeline. Prior knowledge of the type of flow pattern is needed to choose an appropriate method for predicting the pressure drop (Xu, 2007). In addition, predicting phase distribution is essential for wax deposition management in subsea pipelines, because wax deposition is a flow pattern-dependent phenomenon (Matzain et al., 2002, Sarica and Panacharoensawad, 2012). Furthermore, predicting the distribution of water inside the pipe is of the utmost importance when modelling sweet corrosion. Corrosion problems are associated with the continuous water phase being in contact with the wall at the bottom of the pipe. Hence, it is crucial to predict whether a free water layer exists at the bottom of the pipe (water wetting) or the oil is a continuous phase (oil wetting) containing water drops. The incorrect prediction of water distribution leads to significant mistakes in predicting the corrosion rate. Furthermore, it may lead to use of the wrong type of inhibitor, a larger amount of inhibitor, or the use of corrosion resistant material, thereby, increasing the operational and capital costs (Nyborge, 2005, Nesic, 2007, Cai et al., 2012).
The computational fluid dynamics (CFD) technique is a powerful tool for simulating flow-field characteristics in a multiphase pipeline. Using CFD we can gain a deeper insight into the underlying physics and thus foster an understanding of the different phenomena. In addition, CFD can provide phase distribution and velocity profiles with high resolution, which can significantly reduce uncertainty at the design stage. However, extensive evaluation with experimental results is essential before using the model predictions for scale-up and optimisation of facilities.
Thus far, few numerical studies have been reported on predicting the hold-up distribution in oil–water flow. Parvini et al. (2010) used the Eulerian–Eulerian approach to model dispersed oil in water flow in vertical pipes. Their results suggested that the interfacial lift force is more important than the turbulent dispersion and virtual mass forces. Hamad et al. (2013) also investigated dispersed oil–water flow in vertical pipes and there was a good agreement with the experimental data. Recently, Burlutsky and Turangan (2015) used the Eulerian–Lagrangian approach to model dispersed oil–water flow in vertical pipes. Their numerical results also indicated that lift force has a dominant effect on distribution of the dispersed phase.
Due to the influence of gravity on horizontal pipelines, predicting the flow pattern and phase distribution is even more complex than that of vertical pipes. Limited numerical studies have been carried out on modelling oil–water flows in horizontal pipes, with prior knowledge of the type of flow pattern. Walvekar et al. (2009) used the Eulerian–Eulerian model to study the oil in water dispersion through horizontal pipes. The model was able to predict the water volume fraction distribution at high velocities, but it failed to predict the distribution at low velocities where the effect of gravity becomes important. Monzon (2006) carried out a numerical simulation using Fluent 6.2. He used the Eulerian–Eulerian method for a dispersed oil–water flow in horizontal pipes and the numerical results of the distribution of phase fraction agreed fairly well with the experiment. Gao et al. (2003) used the volume of fluid (VOF) model to investigate the stratified oil–water flow in a horizontal pipe. The results agreed well with the experimental data. However, the application of such interface tracking methods is limited to flows with sharp interfaces that do not develop to the dispersed flow pattern. Generally, when modelling the oil–water flow there is a lack of prior knowledge of the type of flow pattern. As a matter of fact the type of flow pattern itself is one of the unknowns that should be predicted before design. Hence, a more general model is required to predict the flow pattern and phase volume distribution. Two-fluid models are capable of simulating all types of two-phase flows, ranging from those with large interfacial lengths, such as stratified flows, to dispersed flows with very small interfacial length scales. These models have been successfully applied to simulation of stratified and dispersed gas–liquid flows (Yao et al., 2004, Prosperetti and Tryggvason, 2007). The capability of the two-fluid model to identify different flow patterns in liquid–liquid flow has also been reported (Sathe et al., 2010).
In the present study, numerical modelling of oil–water flow through a horizontal pipeline was carried out using the Eulerian–Eulerian approach. The two-fluid and standard k–epsilon models were used to predict the flow pattern and water distribution under comparatively wide operating conditions, ranging from low to high velocities and low to high water cuts. Furthermore, numerical results predicting the flow pattern and the distribution of the water volume fraction were compared with the corresponding experimental data.
Section snippets
Eulerian–Eulerian approach
In the Euler–Euler approach, each phase is assumed to coexist at every point in space in the form of interpenetrating continua. It solves all the phases present and coupling between the phases is obtained through the pressure and interphase exchange coefficients (Guha et al., 2008). For each phase k, the conservation equation is written as a function of the volume fraction of the phase αk. In this method, both the phases can be averaged over a fixed volume. The volume fraction of each phase is
Experiment
In the present study the experimental study of Elseth (2001) was used to examine the capability of CFD model in predicting the type of flow patterns. A schematic layout of the test pipe is shown in Fig. 1a.
The test pipe had an outer diameter of 60.3 mm and an inner diameter of 56.3 mm. The test pipe consisted of one entry section and two different sections for flow field measurements, one section for Laser Doppler Anemometry (LDA) measurements and another one for gamma densitometer. Except for a
Geometry and boundary conditions
In this study, we present the numerical results of oil–water turbulent flow in a horizontal pipe. The numerical simulations were performed for different water cuts and mixture velocities, to examine the capability of the used CFD model in predicting the flow patterns and local water volume fraction distributions inside the pipe. The density and viscosity of the oil were 790 kg/m3 and 1.64 cp, respectively. A brief description of the property of fluids and the used geometry is presented in Table 1
Results and discussions
Fig. 3(a) shows the numerical results and the experimental data for the vertical distribution of the water volume fraction across the pipe cross-section for a low mixture velocity of 1 m/s. The input water cut for this case is 0.1. Both the numerical results and experimental data show a dispersed water-in-oil flow pattern. Fig. 3(b) shows the contours of the water volume fraction obtained using the CFD model. For this condition, a continuous oil flow with a zero water volume fraction at the top,
Conclusions
Numerical modelling of two-phase oil–water flow through a horizontal pipeline was carried out using a two-fluid model and the standard k–epsilon turbulence model. The used CFD model and closure laws were presented, accordingly.
The CFD model was used for modelling oil–water flow in comparatively wide operating conditions, ranging from low to high velocities and low to high water cuts.
Comparison of the CFD results with the corresponding experimental data revealed the capability of the CFD model
Acknowledgements
This research was conducted under the project to establish the foundations of industrial technology which is funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) (Grant no.: N0000003, N0001154).
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