C:\Users\raoh\Desktop\Paper_6.xps The Journal of Engineering Research Vol. 8 No 2 (2011) 49-58 deformable interfaces requires various characteristdis- tributions called flow regimes or flow patterns (Hewitt 1982). Understanding the transition from stratified flow to slug flow is important in hydrocarbon trans- portation systems, and has constantly stimulated the research in this direction (Valluri et al. 2008). Slug flow is a commonly observed pattern in horizontal and 1. Introduction Liquid-liquid flows appear in various industrial processes and in the petroleum industry in particular, where mixture of gas with associated liquids (oil, con- densate and/or water) are produced and transported together. During their co-current flow in a pipe the _______________________________________ *Corresponding author’s e-mail: lakehal@ascomp.ch Transition of Gas-Liquid Stratified Flow in Oil Transport Pipes D. Lakehal*a, M. Laboisa, D. Caviezela, and B. Belhouachib aASCOMP GmbH, Technoparkstr. 1, Zurich, CH 8005, Switzerland bImperial College London, Prince Consort Road, London SW7 2BY, UK Received 17 April 2011; accepted 23 September 2011 Abstract: Large-Scale Simulation results of the transition of a gas-liquid stratified flow to slug flow regime in circular 3D oil transport pipes under turbulent flow conditions expressed. Free surface flow in the pipe is treated using the Level Set method. Turbulence is approached via the LES and VLES method- ologies extended to interfacial two-phase flows. It is shown that only with the Level Set method the flow transition can be accurately predicted, better than with the two-fluid phase-average model. The transi- tion from stratified to slug flow is found to be subsequent to the merging of the secondary wave modes created by the action of gas shear (short waves) with the first wave mode (high amplitude long wave). The model is capable of predicting global flow features like the onset of slugging and slug speed. In the second test case, the model predicts different kinds of slugs, the so-called operating slugs formed upstream that fill entirely the pipe with water slugs of length scales of the order of 2-4 D, and lower size (1-1.5 D) disturbance slugs, featuring lower hold-up (0.8-0.9). The model predicts well the frequency of slugs. The simulations revealed important parameter effects on the results, such as two-dimensionality, pipe length, and water holdup. Keywords: Stratified flow, Two-phase flow, Level-set method slug 50 D. Lakehal, M. Labois, D. Caviezel and B. Belhouachi near horizontal gas liquid flows. It is the regime with large coherent disturbances, causing large pressure fluctuations and variations in the flow rates that can affect process equipment. It is also characterized by intermittent appearance of aerated liquid masses that entirely fill the pipe cross-section and travel down- stream at a large velocity. Earlier techniques for the prediction of slugs were based on various linear stabil- ity theories. The transition from stratified to slug flow regime has often been associated with the sudden growth of interfacial waves due to the Kelvin- Helmholtz instability. The onset of this instability for long waves has early been determined analytically assuming a continuous growth of a small-amplitude long wave into a slug, driven by Kelvin-Helmholtz instabilities (Taitel and Dukler 1976). Wall shear and interfacial stress were later accounted for, but the long- wave assumption was retained, facilitating an integral momentum balance. Although the criteria for linear instability obtained in these early theoretical studies show good agreement with experimental conditions at the onset of slug formation, the underlying assump- tions have been increasingly undermined by subse- quent work and now seem unlikely to be justifiable. Other authors (Valluri et al. 2008) report observations invalidating the assumption that a single long wave develops continuously into a slug (Lin and Hanratty 1986). This slug formation subject is addressed here by means of large scale simulation using the CMFD code (TransAT of ASCOMP GmbH, 2010), combining the Level Set method for interface tracking and LES/VLES for turbulence. This model combination of ITM and LES/VLES is referred to as LEIS, short for Large Eddy and Interface Simulation (Lakehal 2010). We discuss the 3D results of flow transition to slug in two different pipe configurations under turbulent flow conditions. Turbulence is approached via the LES and V-LES methodologies extended recently (Liovic and Lakehal 2007) to interfacial two-phase flows. The sim- ulations were conducted 3D. 2. The Mathematical Model In TransAT, the incompressible two-fluid flows are represented by a single equation by a technique known as the Interface Tracking Method (ITM). For more details, the reader can refer to (Lakehal et al. 2002). The equations are of the form: where u stands for the fluid velocity and p for the pressure, is the density, and is the viscosity. The source terms in the RHS of the momentum equation represents the body force, Fb, the wall shear, Fw, and the surface tension, Fs. Material properties are updat- ed locally based on a phase marker field, denoted here by the level-set function (Sussman et al. 1994). is a distance function, whose value represents the distance to the interface. The interface itself has a value of zero, is positive on one side and negative on the other. Other material properties like viscosity, thermal conductivity and heat capacity are also updat- ed in the same way. TransAT uses the Immersed Surfaces Technology (IST), whereby the wall shear (Fw) appears explicitly in the equations based on the solid level-set function s that defines solid obstacles (in addition to the gas-liquid function ). To track the interface and update material properties, a topology equation is solved for the level-set function : (2) Conceptually, ITMs are capable of capturing the topology of interfaces and resolving accurately the interfacial boundary layers, independently from the Reynolds number. But since full DNS resolving all turbulence and interface motions is practically elusive, one is forced to solve the flow using statistical models like RANS, or LES, solving directly for super-grid scale and modelling unresolved or sub-grid scales (SGS). For turbulent interfacial flows, use should be made of the filtered form of the equations above (Lakehal 2010; Liovic and Lakehal 2007). This is now known as the LEIS, short for Large Eddy & Interface Simulation, in which turbulent scales and interface deformations larger than the grid size are directly solved, whereas sub-scales are modelled (Lakehal 2010; Liovic and Lakehal 2007). Because statistically steady-state flow conditions are difficult to attain in 3D, recourse is made here of the V-LES (instead of LES), where the flow-dependent cut-off fil- ter is larger and independent from the grid. Although contradictory in terms of scale separation, one actual- ly could resort to RANS closure models to deal with turbulence as well, at the expense of affecting the degree of interface topology resolution; higher eddy viscosity levels at the interface could hamper the high- frequency surface motions, i.e. wrinkling. Be it as it may, advancing the RANS form of the above system of equation in time is referred to as URANS. 3. The Numerical Approach The CMFD code (TransAT 2010) developed at (1) 51 Transition of Gas-Liquid Stratified Flow in Oil Transport Pipes ASCOMP is a multi-physics, finite-volume code based on solving multi-fluid Navier-Stokes equations. The code uses structured meshes, though allowing for mul- tiple blocks to be set together. MPI and OpenMP par- allel based algorithms are used in connection with multi-blocking. The grid arrangement is collocated and can thus handle more easily curvilinear skewed grids. The solver is pressure based (Projection Type), corrected using the Karki-Patankar technique for sub- sonic to supersonic compressible flows. High-order time marching and convection schemes can be employed; up to third order Monotone schemes in space. Multiphase flows can be tackled using (i) inter- face tracking techniques for both laminar and turbulent flows (Level Set, VOF with interface reconstruction, and Phase Field), (ii) N-phase, phase-averaged mix- ture model with Algebraic Slip, and (iii) Lagrangian particle tracking (one-to-four way coupling). As to the level set, use is made of the 3rd order Quick scheme for convection, and 3rd order WENO for re-distancing. Mass conservation is enforced using global and local mass-conserving schemes (Lakehal et al 2002). To mesh complex geometries, use is made of the Immersed Surfaces Technology (IST) developed by implemented in the code (Labois and Lakehal 2011). 4. Slug Formation In Condensation-Indu- ced Waterhammer 4.1 Problem Description The experiment of Martin et al. (2005) was designed for the purpose of investigating the phenom- enon of condensation-induced waterhammer in an ammonia refrigeration system. Waterhammer was ini- tiated by introducing warm ammonia gas over static subcooled ammonia liquid placed in a horizontal car- bon steel pipe 6.0 m in length. The only data used for comparison with the simulation include the isothermal subsonic case, with no condensation. The apparatus was designed to simulate an industrial environment whereby ammonia liquid is standing in a partially- filled horizontal pipe in thermal equilibrium with ammonia gas above it. The essential elements of the test setup consist of a horizontal pipe and a high pres- sure tank containing warm ammonia gas, as shown in Fig. 1. The test pipe has a nominal diameter of 150 mm and length of 6 m, made of 80 carbon steel, hav- ing internal diameter of 146.3 mm, and wall thickness 11.0 mm. The pressure tank contains warm ammonia gas on top of liquid in thermal equilibrium at ambient conditions inasmuch as the entire test facility was out- doors. Between the pressure tank and the test pipe were three valves and a metering orifice. The angle valve remained fully open, while flow was initiated by a solenoid valve for a given position of the throttle valve. The ammonia in the insulated test pipe was introduced from an ancillary system containing a com- pressor, an auxiliary tank, and another tank for purging non-condensable gases. For each test, care was exer- cised to transfer ammonia liquid to or from the test pipe to establish the desired depth and equilibrium temperature. Instrumentation consisted of an orifice meter to determine the transient mass flow rate utilizing both upstream P0 and differential pressure transducers P . In order to calculate the mass flow rate through the ori- fice, which was calibrated with water, the upstream temperature was monitored by RTD1. Another pres- sure transducer (PD) was located in the downcomer. The initial liquid temperature within the test pipe was recorded by RTD2, mounted on the bottom of the pipe. For the measurement of waterhammer or shock pres- sures four piezoelectric pressure transducers - PCB1, PCB2, PCB3, and PCB4 - were mounted as shown. The first three piezoelectric transducers were on the bottom of the pipe, while PCB4 was mounted on the pipe centerline at the end cap. In order to determine the gas pressure within the test section during the transient event four diaphragm differential pressure transducers - labeled PACE1, PACE2, PACE3, and PACE4 were mounted on the top of the pipe, as shown in Fig. 1. By maintaining one side of the diaphragm open to the atmosphere and the other side connected to the top of the pipe gage pressures were measured during the test. The test procedure consisted of reducing the liquid and gas temperature within the test pipe to the desired value by means of a compressor. 4.2 Simulation Setup A full 3D computational domain is considered in these simulations. A portion of the grid is shown in Fig. 2. The pipe length is 6.3m, and the diameter is 0.14 m. The multi-block grid strategy is used to cover the domain with adjacent sub-domains (coloured dif- ferently). Here boundary fitted grids were used rather than the IST. The blocks are distributed between 12 processors for MPI parallel execution. The results pre- sented here were obtained for a grid composed by 360,000 curvilinear cells distributed over 12 blocks. The LEIS approach was employed here, relying on the Level-Set technique for interface tracking. Sub-grid scale (SGS) modelling was achieved using the MILES approach (Lakehal 2010), where the diffusive effects of unresolved turbulence motion is left to the scheme. The inflow boundary conditions involve fixing the superficial gas and liquid velocities and the void frac- tion as specified in the experiments. The right-end of the cap was left open now since we deal with the non- phase case; pressure boundary conditions were used, in combination with a special scheme for the void frac- tion to control global and phase-specific volume con- servation. Specifically at the inflow, we have set the 52 D. Lakehal, M. Labois, D. Caviezel and B. Belhouachi 53 Transition of Gas-Liquid Stratified Flow in Oil Transport Pipes that is the formation of vortex shedding past the slug, immediately after sealing. This observation is corrob- orated by all three instantaneous velocity- component contours, in particular w'. The mechanism is similar to what may be expected in flows past fixed blunt bodies; the slug plays somehow the same role, as it travels with a lower velocity than the gas after sealing. The breaking of the free surface after slug sealing is also perfectly illustrated in Fig. 4. Again, the panels com- bine free-surface and velocity iso-contours. The figure shows the vigorous plunging of the breaker after seal- ing, pretty much similar to what we observe in plung- ing breakers. The third panel shows the impact of the breaker over the stratified liquid surface, a region characterized by a very high level of turbulence pro- duction. Vortex shedding is again visible as in the pre- vious panels, though the breaker seems to have affect- ed the coherence of their motion. The slug tail and centre speeds are discussed in Fig. 5 below, displaying the position of the slug versus time. A linear dependency is revealed, which is in agreement with the measurements of Martin et al. (2005), who obtained an average slug speed of Us = 9.4 m/s, under these conditions. The slug speed is rather constant, as it has been found in the earlier 2D simulations (results not shown here). In case of the hydrodynamic slugging, the slug velocity can be cal- culated from gas and liquid flow rates if the void frac- tion is known, in horizontal lines the mean velocity of the liquid in the body of the slug is approximately equal to the mixture velocity, or can be estimated ana- lytically Collins et al. (1978) using: (3) where Um stands for the mixture velocity. The result shown in Fig. 5 reveal that our LEIS simulation pre- dicts the slug speed (tail and centre) in accord with the Figure 3. Surface displacements at various time instants Figure 4. Vortex shedding past the slug coloured by velocity fluctuations, highlighting wave breaking 1.201 0.532 / 1 1.2 1.4 t (s) 6 5 4 3 2 Slug center (9.8t - 8.33) Slug tail (8.46t - 6.82 Collins 1978 (vs = 9.33 m/s) Linear fits Figure 5. Slug speed (tail and centre): LEIS vs. analytical solution 54 D. Lakehal, M. Labois, D. Caviezel and B. Belhouachi theory (3), which gives Us=9.33 m/s, and experiment of (Martin et al. 2005) (Us=9.4 m/s). This is an inter- esting result for practical applications, which shows that although a coarse grid has been used, the LEIS concept is capable to predict one of the most important flow features of pipe flows. 5. Slug Formation at the Wasp Facility 5.1 Problem Description The experiments were performed at the Imperial College WASP facility with the test section mounted horizontally. Gas and water were fed from two differ- ent entries perpendicular to the main pipe (Fig. 6). Slugs were monitored from close to the point where they were first initiated until they decayed or exited the pipe. Twin-wire holdup probes were used to mon- itor the liquid level at a series of locations along the pipe. Slugs were discriminated from large waves by measuring the velocity using cross correlation of the outputs of successive probes (the waves travel at a lesser velocity that that of the mixture and slugs travel at a velocity higher than that of the mixture). The length of the stainless steel test section is 37 m and its diameter is 77.92 mm, the pressure at the outlet is 1 atm, and the temperature is 25oC. The liquid water is introduced below a stratification plate at the bottom of the test-line and the gas is introduced above it. The superficial velocities of the two phases (air and water) are: UsL = 0.611 m/s and UsG = 4.64 m/s, respectively. 5.2 Simulation Setup Use was made here of the IST technique to mesh the pipe. The pipe CAD file was created using Rhinoceros software, and immersed into a Cartesian grid, as shown in Fig. 6. The 2D simulations were per- formed in a pipe of length 17 m. The 3D simulations were performed in a shorter domain of 8m, consisting of 715.0 cells, then in a longer one of 16 m, consisting of 1.200.000 cells. The simulation time for the 8 m pipe simulation was 10 days on a low bandwidth Dell PC (2 nodes x 4 cores; Open MP parallel protocol) for 20s real time, and 53H on a high bandwidth 18 nodes IBM multicore computer (OpenMP protocol). The LEIS approach was employed here, with a filter width of 0.1D, combined with the Level-Set technique for interface tracking. Subscale modelling of turbulence was achieved with the k- model with filter width set equal to 0.1D (Labois, Lakehal 2011). The inflow boundary conditions involve fixing the superficial velocities and the void fraction, as specified in the experiment. Specifically at the inflow, we have set the following values for the turbulent flow conditions: gas superficial velocity UsG = 4.64 m/s; liquid superficial velocity UsL = 0.611 m/s; void fraction = 50%. 5.3 Simulation Results (2D) Figure 7 shows the measured liquid hold-up at dif- ferent probe locations along the axis: 5.01 m, 5.69 m, 6.99 m and 13.32 m. The signals display distinct large- wave structures developing along the pipe that could in fact be considered as slug-structures (Ujang 2003). While a traditional slug is a structure blocking the cross section of the pipe completely, large-wave struc- tures with a length scale larger than the pipe diameter can also be termed as 'slugs'. The 3D simulations dis- cussed next will help make the distinction between the different structures. Slugs or large-wave structures are captured around location x = 3 m and beyond (results not shown here). The periodicity of slug occurrence is clearly visible from these locations (x > 5 m). Figure 8 depicts the calculated water holdup in 2D at differ- ent probe locations along the axis, from 5.65 to 15 m. While the signal is qualitatively similar to the meas- ured one in terms of slug or large-wave structures intermittency, it is unclear whether slugs were indeed captured; various locations exhibit water holdup of about hL/D = 0.8-0.9. Be it as it may, large surface per- turbations were already captured upstream close to the inflow, at x = 0.76m, while the experiment there shows liquid hold-up not exceeding hL/D = 0.2. For the locations considered, the data and CFD provide a similar picture as to wave frequency. Figure 6. Computational IST grid. The CAD file is immersed in a cartesian grid 55 Transition of Gas-Liquid Stratified Flow in Oil Transport Pipes 5.4 Simulation Results (3D) To address the effect of pipe length the flow was reproduced in pipes with different lengths: 8 m and 16 m, using the same flow conditions. Figure 9 shows the development structures at different probe locations along the axis, at 5.01m, 5.695m and 6.995m. These were obtained from 3D simulations in the short pipe (L = 8 m). The distinct patterns at different locations show the variations in the slug frequencies. Slug fre- quency decays as the location of the probe is moved further downstream. Slugs or large-wave structures are predicted at downstream locations close to the pipe end: x = 7 m, in contrast to the experiment and longer- pipe simulations, both indicating a shorter position for the early slugs. Further, in contrast to the 2D results discussed earlier, slugs or large disturbances of the surfaces are not predicted upstream close to the inflow, but downstream. These results are interpreted later on in terms of slug frequency, and compared to the longer pipe results. Turning now to the 16m long pipe, the formation of the different types of slugs is well illustrated in Fig. 10. The first panel exhibits a 'large-scale slug', which, in the experiments is often referred to as 'operation slug'. This slug is formed upstream (x < 3 m) and fills entirely the pipe (hL/D = 1) with an average size of the order of 2-4 D. Although the lower panels do not show a 100% water holdup filling the pipe as in the first one, the liquid structures are travelling at a higher speed than the mean flow, which makes them 'slugs'. Here one observes that gas bubbles are caught inside the slug, which explains that the measured liquid hold up hL/D is less than unity (usually hL/D is between 0.80 and 0.95). Figure 7. Measured liquid holdup for UsL = 0.61 m/s and UsG = 4.64 m/s Figure 8. Simulated liquid holdup for UsL = 0.611 m/s and UsG = 4.64 m/s 56 D. Lakehal, M. Labois, D. Caviezel and B. Belhouachi The slug- or large-wave structures frequency results shown in Fig. 11 are qualitatively similar to the struc- tures observed in the experiment. The lines in green correspond to the 16m pipe simulations; the red ones to the 8m simulations; both in 3D. The shift in the fre- quency peak observed for the two simulations is clear- ly due to the difference in pipe length, as the outflow boundary condition has an important impact on the flow. The frequency of the slugs is measured as a function of the abscissa. In the 16 m case, better Figure 9. Water holdup for the 3D simulation (short pipe: 8 m) Figure 10. The formation of different kinds of slugs (long pipe: 16 m) 57 Transition of Gas-Liquid Stratified Flow in Oil Transport Pipes results are obtained as a peak frequency around 3.5 m can be seen, which is almost equal to the measured value. There is however a difference in terms of inter- pretation, when the frequency of slugs is evaluated based on hL/D of 0.8 or 0.85. It is clear the simulation and measurement agree best for hL/D = 0.85. Moreover, the evolution of the slug frequency along the axis of the pipe is in good agreement with the data, although the result suggests that the simulation time was not enough to acquire all the slugs with lower fre- quency (0.3 Slug/s). We thus conclude that the data. Conclusions The development of large-wave structures in gas- liquid 3D pipe flows has been examined using detailed CMFD simulations combining the Level-Set approach for interface tracking and VLES for turbulence model- ling. The investigation complements earlier ones (Lakehal 2008) which had shown that the approach predicts more details of the flow as compared to the Eulerian two-fluid model, even if it is computational- ly expensive. Our predictions show that the ITM approach can be used for a one mile pipeline, using five million cells, which require a week of simulation on a 128 CPU cluster. The 3D turbulent flows simula- tions clearly provide a better picture of the flow, in particular regarding the onset of slug formation and frequency, the latter being predicted in accord with the experiment. From a practical standpoint, the results show that oil transport in a portion of pipelines can be approached more rigorously. The information from detailed 3D simulations could actually be employed to calibrate coarse-grained 1D lumped parameter models, which fail under other conditions than straight pipes. These detailed simulations should be ultimately cou- pled with a 1D code like OLGA; it could then be acti- vated in fixed critical regions (e.g. over a hill). Acknowledgments This research has been undertaken within the Joint Project on Transient Multiphase Flows and Flow Assurance. 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