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Effect of pipe rotation on flow pattern and pressure drop of horizontal two-phase flow
International Journal of Multiphase Flow 111 (2019) 101–111
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International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow
Effect of pipe rotation on flow pattern and pressure drop of horizontal two-phase flow Yosef Baghernejad a,b, Ebrahim Hajidavalloo a,b,∗, Seyed Mohsen Hashem Zadeh a,b, Morteza Behbahani-Nejad a a b
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 61355 Iran Drilling Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran
a r t i c l e
i n f o
Article history: Received 1 April 2018 Revised 2 November 2018 Accepted 24 November 2018 Available online 24 November 2018 Keywords: Flow pattern map Horizontal and inclined pipe Pipe rotation Two-phase flow Pressure drop
a b s t r a c t In this paper, the effect of pipe rotation on two-phase flow patterns and pressure drop of a horizontal pipe is experimentally investigated. To obtain two-phase flow patterns and related transition boundaries, a unique experimental set-up was constructed to measure flow patterns under different pipe rotational speeds. A Plexiglas pipe, with 40 0 0 mm length and 25.4 mm ID was used in experiments to allow direct observation of flow pattern. For rotation of the pipe, an electromotor coupled with gearbox was used to allow different rotational speeds. The set-up also supports up to ±25° inclination. Air and water were used as the gas and liquid phase, respectively. Over 3800 experiments were conducted to draw flow pattern maps at six different rotational speeds of 0, 50, 10 0, 20 0, 30 0 and 400 rpm in both horizontal and 10° inclined pipe. To validate the results, experimental findings were compared with previous research for a horizontal fixed pipe case. Results show that pipe rotation has a significant effect on the flow pattern map and the transition boundaries. It was found that in horizontal pipe case, the stratified smooth flow regime decreases as the pipe rotation increases and disappears at high revolution speeds. Moreover, the annular regime enlarges with increasing pipe rotational speed. For a 10° inclined pipe, the stratified wavy region appears as the pipe rotation speeds up. It was observed that for both horizontal and inclined pipe, pressure drop considerably increases as the pipe rotational speed increases. Furthermore, the effect of pipe inclination on the pressure drop is reduced as the rotational speed increases. © 2018 Elsevier Ltd. All rights reserved.
1. Introduction Gas-liquid two-phase flows are very common in various industrial application such as drilling, boiling heat transfer, nuclear reactors, cooling circuits of power plants and pipeline flow in petroleum industries. Due to different interactions between the phases such as interfacial transfer, entrainment, deposition, and flooding, two-phase gas-liquid pipe flow is in fact a complex phenomenon. Moreover, two-phase flow can appear in different geometrical and operational forms that are very important to determine the properties of the system (Ghanbarzadeh et al., 2012). Simultaneous flow of two fluid phases with different physical properties, different flow patterns can be observed in the pipe. As significant engineering design parameters such as heat transfer and pressure drop are closely related to the type of two-phase flow regime (De Schepper et al., 2008), correct flow pattern predic-
∗ Corresponding author at: Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Golestan St., Ahvaz, 61355 Iran. E-mail address: [email protected] (E. Hajidavalloo).
https://doi.org/10.1016/j.ijmultiphaseflow.2018.11.012 0301-9322/© 2018 Elsevier Ltd. All rights reserved.
tion at different conditions of pipe flow is one of the most important parts of two-phase flow analysis. An engineering application of two-phase flow is when the pipe is rotating either in horizontal or vertical conditions. For instance, under-balanced drilling (UBD) of oil and gas wells requires prediction of two-phase flow patterns in horizontal and vertical pipes for precise calculation of bottomhole pressure to prevent kicking of the well or collapsing the wall (Khezrian et al., 2015). Although there is great amount of literature about behavior and properties of two-phase flow in pipes, but the effect of pipe rotation in a horizontal case was not studied yet. A few studies have examined flow patterns in an annular space with a rotating inner tube. Taitel and Dukler (1976) proposed mechanistic models for determining flow regime transitions in horizontal and near horizontal two-phase gas-liquid flow and presented a generalized flow regime map. Weisman et al. (1979) examined the effect of pipe diameters and fluid properties on two-phase flow patterns in horizontal pipes. They used air-water and air-glycerin as two-phase systems with the pipe diameters varies from 1.2 to 5.1 cm. They
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Fig. 1. Schematic of the experimental set-up.
present non-dimensional correlations from curve fitting for transition boundaries. Ozbayoglu and Ozbayoglu (2007) studied flow patterns and frictional pressure loss in two-phase flow through a horizontal annulus with a rotating inner pipe using Artificial Neural Networks (ANN) rather than proposing a mechanistic model. They compared their results with experimental data and showed that the ANN could estimate flow patterns with a high accuracy (error is less than ±5%). Hernandez Perez (2008) conducted experimental study of airwater two-phase flow in inclined pipes. His test pipes were 6.5 m long with two diameters, namely 38 mm and 67 mm. He measured time series of liquid holdup (using capacitance probes) and pressure drop (differential pressure transducer) and used a high speed video system in order to obtain image sequences of the flow conditions. Finally, he showed that increasing pipe diameter displaces the bubbly-slug transition to the right hand side on the flow pattern map for inclined flow, and for horizontal pipe the stratifiedslug transition is moved up. Shannak (2008) examined frictional pressure loss of vertical and horizontal smooth and relatively rough pipes and demonstrated that the frictional pressure drop increases with increasing relative roughness of the pipe; although the influence of the relative roughness becomes more evident at higher gas void fraction and higher mass flux. He proposed a new prediction model for frictional pressure drop of two-phase flow in pipes which includes a new definition of the Reynolds number and the friction factor of two-phase flow. The mentioned model is sufficiently accurate for engineering purposes. Shiomi et al. (1993) conducted an experimental study of twophase flow in a concentric annulus with inner cylinder rotation and showed that at relatively low rotational speed, the buoyancy effect of bubbles dominated the flow field and a dispersed bubbly flow was formed. On the other hand, at high rotational speed, the
vortex motion induced by the rotation dominated the flow field and ring-form and spiral flows were formed. Sorgun et al. (2011) studied the effect of cuttings and inner pipe rotation in horizontal/highly-inclined wellbores on friction factors and pressure loss, experimentally. They showed that the existence of cuttings increases the pressure drop due to decrease in flow area inside the wellbore. Dewangan and Sinha (2016) investigated the effect of the eccentricity and presence of the secondary solid phases in the flow instability (transition from laminar to turbulent flow) for the fully developed horizontal annular flow and showed that radius ratio, eccentricity and presence of the secondary phase have the most dramatic impact on transition from laminar to turbulent flow. Hasan and Kabir (1992) investigated inclined annular space and estimated the void fraction during upward concurrent two-phase flow in annuli using a drift-flux approach to model the slip between phases and the transition between regimes. De Schepper et al. (2008) investigated gas/vapor–liquid twophase co-current horizontal flow regimes numerically, using VOF model that uses a Piecewise Linear Interface Calculation (PLIC) interface reconstruction method in each computational cell and compared them with experimental data, taken from the Baker chart (Baker, 1953). They showed that all horizontal flow regimes appearing in the Baker chart can thus be calculated using CFD. Raeiszadeh et al. (2016) constructed an experimental setup to study the effect of pipe rotation on downward co-current air–water flow in a vertical pipe. They used a transparent vertical pipe with a diameter of 50 mm and an aspect ratio (L/d) of 80 to obtain flow maps at revolutions of 0, 60, 120, 180, 240, 300, 400 and 500 rpm by changing the air and water velocities at these revolutions. Using image processing, they showed that pipe rotation has major effect on flow patterns map and their transitions boundaries. They found increasing pipe rotation cause slug and annular flow start at lower VSG . As discussed by Raeiszadeh et al. (2016), although different
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Fig. 2. Photos of different flow patterns in horizontal two-phase flow.
methods have been used for flow pattern prediction in two-phase flow, but direct observation is common. As mentioned earlier, horizontal and inclined two-phase flows in pipes with rotation are used in various industries. Until now, fixed pipe relations are used for design purposes such as gas and oil well drilling and revolution of pipe is totally neglected, whereas it seems to be inaccurate. Therefore, investigation on the effect of pipe rotation on the pressure loss and related flow pattern in horizontal case is required. In this paper, gas-liquid two-phase flow in a rotating pipe in horizontal and inclined condition is studied using experimental approach. A high speed videometry system is used to capture twophase flow pattern through the pipe. Flow pattern map can then be discovered by direct analysis of the photography. 2. Experimental set-up In order to demonstrate the behavior of horizontal and inclined two-phase flow, an experimental set-up was designed and constructed. The experimental apparatus is shown schematically in Fig. 1. The main pipe ID is 25.4 mm and has an L/D of 157.48 (L = 40 0 0 mm), composed of Plexiglas to allow direct observation
of flow patterns. The temperature of the air and water were held constant under ambient conditions. Air and water were used as the gas and liquid phases in all experiments. Water from a tank is pumped through the pipe using a centrifugal pump and a rotameter, an absorber, a mixer and several ball valves are used after the pump as shown in Fig. 1. The rotameter (range 0–400 L/min with 1.0 L/min resolution) was frequently calibrated by comparing with the direct flow measurement using a pre-calibrated measuring tank in the laboratory. To control the inlet water flow rate, a by-pass system is considered after the pump. The compressed air at maximum 10 bar was fed continuously from a large reservoir which is connected to the compressor using a ball valve, three air rotameters and two check valves. One rotameter measures ranges of 0–10 L/min with 0.2 L/min resolution, the second measures ranges 5–100 L/min with 1.0 L/min resolution. For gas flow rate higher than measurement range of the first and second rotameters, a third rotameter (range from 1–40 m3 /h with 0.2 m3 /h resolution) is used. The calibration curves supplied by the manufacturer were used to calibrate the air rotameters. As shown in Fig. 1, the test section is located at the end part of the pipe (at about L/D of 138) to ensure the fully developed flow condition.
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Fig. 3. Present flow pattern maps compared with Taitel and Dukler (1976) (a) horizontal and (b) 10° upward inclined pipe (0 rpm).
Fig. 4. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (50 rpm).
To generate two-phase flow, air and water were mixed in the mixer which is a cylindrical aquarium bubble stone and connected to the inlet air pipe, inserted inside the water pipe, as it was done by Raeiszadeh et al. (2016). Two-phase air-water flow then entered the main pipe and after passing it drained into the main tank, using return pipe flow. It should be noted that the return pipe flow is installed in proper height to ensure air and water separation take place naturally. Moreover, a baffle was used to divide the inlet and outlet of water storage tank to prevent turbulence and air entrance in the suction side of the pipe. The pipe section was designed to have up to ±25° inclination by using a pivot. The pipe can also rotate about its axis at different revolutions using an electric motor and gearbox. Using several
bushings and bearing to support the pipe, the set-up had no important vibration except for revolutions above 500 rpm. A high-tech camera with 1/40 0 0 shutter speed (EOS 650D, Canon) was used for flow regime determination and flow pattern recording. A differential pressure gauge from WIKA with 1.0 bar range and 0.02 bar resolution was used for measuring pressure drop along the pipe (at the L/D of 0 and 157.48). Note that for the cases with low pressure drop, two pressure gauges from WIKA with 250 mbar range and 5 mbar resolution was used at both ends of the pipe (L/D of 0 and 157.48) to record pressure drop with higher resolution. The differential pressure gauge and the pressure gauges were accurately calibrated by a standard buoyancy ball pressure meter. Fig. 2 shows the photo of different flow patterns observed in the experiments.
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Fig. 5. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (100 rpm).
Fig. 6. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (200 rpm).
A detailed error analysis has been done to evaluate the maximum values of uncertainties in measured pipe dimensions and other measurements made by the instruments (Cacuci et al., 2005): 5.7% for the liquid superficial velocity, 13.6% for the gas superficial velocity and 10.3% for pressure drop data for pressure drops higher than 1.0 kPa/m. A uniform instruction was used during all experiments. Initially, stationary pipe tests were run, in which each run was started by setting the water flow rate a constant value using appropriate control valve, then the gas valve was opened and gas flow rate was increased step by step. The superficial air velocities were between 0.048 and 32.094 m/s (20 steps). After recording the results for a fixed water flow rate and different gas flow rates, then, the superficial water velocity was increased and the tests continue. The super-
ficial water velocities were between 0.048 and 4.815 m/s (16 steps). Moreover, experiments were conducted in 0, 50, 100, 200, 300 and 400 rpm both at horizontal and 10° inclination of pipe, which totals 3840 experimental runs. There was at least 5 min waiting time initially and between every two steps to ensure steady state condition in the pipe, and after that, the flow regime was recorded and the pictures were captured. After stationary tests completed, the experiments were repeated again for rotational case of the pipe.
3. Results and discussion Flow visualization was used to capture flow regimes in horizontal and 10° inclined air–water two-phase flow, in which, the following flow patterns were observed:
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Fig. 7. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (300 rpm).
Fig. 8. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (400 rpm).
Stratified smooth flow (only in horizontal pipe case) (SS): Pattern in which the liquid flows along the pipe bottom and the gas flows above water while their interface is smooth. Stratified wavy flow (SW): Pattern which is similar to the stratified flow, but due to higher velocity of gas, the interface is disturbed by waves in the flow direction. Bubble flow (BL): Pattern in which gas bubbles move along the upper part of the pipe at approximately the same velocity of the liquid. Elongated bubble flow (Plug flow) (EB): Pattern in which plugs of liquid and gas move in sequence along the upper part of the pipe. Slug flow (SL): Pattern in which a wave is picked up periodically by the more rapidly moving gas to form a frothy slug which
passes through the pipe at a much greater velocity than the average liquid velocity. Annular flow (A): Pattern in which the liquid phase forms a film on the pipe wall while the gas phase flows in the core at a higher velocity.
In the present study, air and water superficial velocities were used as coordinates of flow pattern maps (VSG = QG /AP and VSL = QL /AP respectively). As mentioned before, experiments were conducted in both stationary and rotating pipe conditions, each in horizontal and 10° inclined pipe. Therefore, the results of stationary pipe are first compared with previous researchers and then the rotating pipe cases are presented.
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Fig. 9. Effect of pipe rotation on the transition from bubble to slug flow (a) horizontal and (b) 10° upward inclined pipe.
3.1. Flow pattern maps for fixed pipe Fig. 3(a) and (b) show flow pattern map of present study in horizontal and 10° inclined pipe and compares them with Taitel and Dukler (1976) results. Comparison of the results shows that, although there are small differences on transition boundaries for each flow pattern, the results of present study are consistent with Taitel and Dukler (1976) results.
3.2. Effect of pipe rotation on flow pattern map Flow pattern maps of two-phase flow in horizontal and 10° upward inclined pipe at different rotational speeds (50, 10 0, 20 0, 30 0 and 400 rpm) are shown in Figs. 4–8. As seen in Fig. 4, pipe rotation at 50 rpm has no special impact on the flow map, but increasing revolution to 100 rpm leads to small changes in the flow map (Fig. 5). As shown in Fig. 5(a), stratified wavy and annular regime appears earlier (at VSG = 0.04 m/s and VSG = 2.0 m/s, respectively). Moreover, direct transition appears between elongated bubble and annular regime for rotational speeds over than 100 rpm at small range of superficial water velocity. This direct transition starts at lower gas superficial velocity as the rotational speed increases (VSG = 1.541 m/s at 100 rpm, VSG = 1.059 m/s at 200 rpm, VSG = 0.578 m/s at 300 rpm, VSG = 0.578 m/s at 400 rpm). On the other hand, Fig. 5(b) shows that stratified wavy flow appears for low values of VSL in pipe revolution of 100 rpm. In addition, slug to annular transition starts at lower values of VSG . Figs. 6(a)–8(a) shows that at 200 rpm and higher revolution speeds, stratified smooth region totally disappears. In addition, stratified wavy area reduces and annular region enlarges as the rotational speed increases. For 10° upward inclined pipe, as shown in Figs. 6(b)–8(b), stratified wavy and annular region grows with increasing pipe revolution speed. Effect of pipe rotation on different flow pattern transition boundaries are shown in Figs. 9–13. Note that symbols in these figures refers to the fixed pipe case. As shown in Fig. 9(a) and (b), increasing revolution has no great impact on disperse bubble to slug transition boundary.
Fig. 10. Effect of pipe rotation on the transition from stratified smooth to stratified wavy flow (horizontal pipe).
Fig. 10 depicts stratified smooth to stratified wavy transition boundary in horizontal case. It can be stated that by increasing pipe rotational speed, centrifugal force increases and move transition boundary from the stratified smooth regime to stratified wavy happen at lower gas and liquid superficial velocities. This effect is quite considerable in somehow that stratified smooth regime totally disappears for revolutions higher than 100 rpm. Fig. 11(a) shows that as the pipe rotation increases in horizontal case, stratified wavy flow region decreases and annular region enlarges. The phenomenon can be explained as follows: As the revolution speed increases, centrifugal dynamic force rises, and finally dominates the gravitational force, which results in moving the stratified wavy to annular transition boundary toward lower VSG . In contrast with horizontal case, for a 10° upward inclined
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Fig. 11. Effect of pipe rotation on the boundary of stratified wavy flow (a) horizontal and (b) 10° upward inclined pipe.
Fig. 12. Effect of pipe rotation on the transition from slug to annular flow (a) horizontal and (b) 10° upward inclined pipe.
pipe, stratified wavy area increases with increasing pipe revolution speed as shown in Fig. 11(b). It can be concluded that component of centrifugal force helps the gravitational force. Fig. 12 illustrates the transition lines between slug and annular regime in horizontal and inclined cases. As seen, by increasing rotational speed the area of annular regime increases. In other words, by increasing rotational speed, Taylor bubbles in slug regime collapses earlier, which causes annular regime starts at lower VSG . In order to compare the effect of different pipe rotation on the flow pattern maps with each other, all transition lines are shown in Fig. 13. As can be seen, flow pattern maps are significantly affected by pipe rotation both in horizontal and inclined cases. The main influence of pipe revolution is on the annular region, which enlarges it as the pipe rotation increases. On the other hand, strat-
ified smooth region decreases and totally disappears in high pipe rotational speed.
3.3. Pressure drop calculation Pressure drop data was recorded during each experiment. Because of oscillating nature of pressure in two-phase flow, an average pressure drop based on calculating pressure difference between inlet and outlet of the pipe in several times was reported. Neglecting accelerational component of the total pressure drop, Chisholm prediction model for the frictional component of pressure drop (Chisholm, 1967) and Homogeneous No-Slip model for the gravitational component (Shoham, 2006) were taken into account. Total pressure drop can then be calculated by adding these
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Fig. 13. Flow pattern maps of two phase flow at different rotation speeds (a) horizontal and (b) 10° upward inclined pipe.
Fig. 14. Effect of gas flow rate on pressure drop in a horizontal fixed pipe.
Fig. 15. Effect of pipe inclination on pressure drop (VSL = 0.578 m/s, 0 rpm).
two values. Finally, the total predicted pressure drops are used to compare with experimental pressure drop data. Fig. 14 depicts the effect of increasing gas flow rate on the pressure drop for two different values of VSL in the case of fixed horizontal pipe and compares experimental results with results of model predictions. Different flow regimes taking place by increasing VSG as it is clear in Fig. 14. Because mechanistic models ignore most of complications and interactions between the phases, deviation between measured and predicted results are always inevitable. Moreover, most of the prediction models are based on limited ranges of experimental data, therefore their predications might be inconsistent to use for wide ranges of gas flow rates (Xu et al., 2012). Although there are some discrepancies, but the overall magnitude of pressure drop for both experiment and model results are in the same order. Pressure drop increases as the VSG is
raised due to increasing frictional force. Moreover, pressure drop is much higher as the liquid flow rate increases (VSL = 4.237). In contrast with predicted mechanistic model results at high VSG range, the experimental pressure drops do not increase rapidly as VSG increases for high liquid flow rate, as was previously reported by Nicholson et al. (1978). It should be mentioned that by increasing VSG , the flow pattern changes from Disperse bubble (DB) to Slug (SL). Fig. 15 compares the effect of pipe inclination on the pressure drop in the case of fixed pipe condition for both experimental and model prediction results. As expected, due to gravitational force, pressure drop in 10° upward inclined pipe is higher than the horizontal case. As both the results of experiment and model show, difference between horizontal and inclined pipe pressure drop diminish as the superficial gas velocity increases. This is due to the
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Fig. 16. Effect of pipe revolution speed on (a) pressure drop (b) normalized pressure drop with fixed pipe case, in a horizontal and 10° upward inclined pipe (VSL = 0.966 m/s and VSG = 9.628 m/s).
fact that by increasing VSG , the frictional share of pressure drop enhances, leads to the dominance of frictional pressure drop at high values of gas flow rates. Effect of pipe rotational speed on the pressure drop and normalized pressure drop for horizontal and 10° upward inclined pipe is shown in Fig. 16. It is seen that pressure drop increases considerably as the pipe rotation speeds up. Moreover, as discussed earlier, due to gravitational effect, pressure drop for inclined pipe is more than horizontal pipe in low revolution speeds (Fig. 16a). The results show as the revolution increases the effect of gravitational pressure drop decreases leading to smaller difference between pressure drops of two cases. To compare the effect of pipe rotation and inclination of the pipe, the measured data for both horizontal and inclined pipe are normalized by their values in the case of fixed pipe (0 rpm). Normalized pressure drop results show that the effects of pipe rotation decreases with inclination of the pipe (Fig. 16b). On the other hand, as symbols illustrate, the flow pattern changes from slug (SL) to annular (A) as the pipe rotation increases. For both horizontal and 10 inclined pipe, the pressure drop exhibits a rapid increase for the revolutions between 100 and 260 rpm. This can be explained considering transition effects of flow pattern on the frictional forces acting on the pipe wall. 4. Conclusions In the present paper, the effect of pipe rotation on two-phase flow patterns and pressure drop was investigated through experiments using a direct observation method. For this purpose, an experimental set-up was designed and constructed and extensive tests were conducted to draw flow pattern maps under different pipe rotational speeds at two different angles, horizontal and 10° upward inclined. Results showed that flow pattern maps and the transition boundaries between flow regimes change considerably as the pipe rotational speeds increases. The following conclusions may also be drawn: 1- In a horizontal pipe, as the pipe rotation increases, the stratified smooth flow regime decreases and finally disappears (for revolutions higher than 100 rpm). Moreover, stratified wavy region
2-
3-
4-
5-
starts at lower gas superficial velocities. In contrast with a horizontal pipe, in a 10° inclined pipe, the stratified wavy region appears and enlarges as the pipe rotation increases. A flow regime transition line appears between elongated bubble and annular regime for rotational speeds over than 100 rpm and it starts at lower gas superficial velocity as the rotation speed increases (in a horizontal pipe). Taylor bubbles in the slug regime collapse earlier as the pipe rotational speed increases which leads the slug to annular transition boundary moving toward lower VSG . The pressure drop in horizontal pipe raises as the VSG raises due to the frictional force effect. Pressure drop is much higher for higher liquid flow rates. Moreover, the pressure drop in the 10° upward inclined pipe is more than the horizontal one due to the gravitational force. Moreover, the effect of pipe inclination decreases as the gas flow rate increases due to dominance of the frictional relative to gravitational pressure drop. The pressure drop increases as the pipe rotational speed increases. Moreover, due to the gravitational effects, pressure drop for the inclined pipe is more than the horizontal pipe at low rotation speeds. By increasing the rotational speeds, the difference in pressure drop for horizontal and inclined pipes decrease. Furthermore, effect of pipe rotation on pressure drop decreases with inclination of the pipe.
Acknowledgment The authors thank Shahid Chamran University of Ahvaz for its financial support to this project (Grant number: 96/3/02/16670). References Baker, O., 1953. Design of pipelines for the simultaneous flow of oil and gas. Soc. Petrol. Eng. 53, 185–195. Cacuci, D.G., Ionescu-Bujor, M., Navon, I.M., 2005. Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems. CRC Press, Boca Raton, United States. Chisholm, D., 1967. A theoretical basis for the Lockhart-Martinelli correlation for two-phase flow. Int. J. Heat Mass Transf. 10, 1767–1778. De Schepper, S.C., Heynderickx, G.J., Marin, G.B., 2008. CFD modeling of all gas–liquid and vapor–liquid flow regimes predicted by the Baker chart. Chem. Eng. J. 138, 349–357.
Y. Baghernejad, E. Hajidavalloo and S.M. Hashem Zadeh et al. / International Journal of Multiphase Flow 111 (2019) 101–111 Dewangan, S.K., Sinha, S.L., 2016. On the effect of eccentricity and presence of multiphase on flow instability of fully developed flow through an annulus. J. Non-Newton. Fluid Mech. 236, 35–49. Ghanbarzadeh, S., Hanafizadeh, P., Hassan Saidi, M., 2012. Intelligent image-based gas-liquid two-phase flow regime recognition. J. Fluids Eng. 134 061302-061302-061310. Hasan, A.R., Kabir, C.S., 1992. Two-phase flow in vertical and inclined annuli. Int. J. Multiph. Flow 18, 279–293. Hernandez Perez, V., 2008. Gas-liquid Two-Phase Flow in Inclined Pipes. University of Nottingham, United Kingdom (PhD Thesis). Khezrian, M., Hajidavalloo, E., Shekari, Y., 2015. Modeling and simulation of under-balanced drilling operation using two-fluid model of two-phase flow. Chem. Eng. Res. Des. 93, 30–37. Nicholson, M.K., Aziz, K., Gregory, G.A., 1978. Intermittent two phase flow in horizontal pipes: Predictive models. Can. J. Chem. Eng. 56, 653–663. Ozbayoglu, M.E., Ozbayoglu, M.A., 2007. Flow Pattern and Frictional-Pressure-Loss Estimation Using Neural Networks for UBD Operations, IADC/SPE Managed Pressure Drilling & Underbalanced Operations Conference and Exhibition. Society of Petroleum Engineers, Galveston, Texas. Raeiszadeh, F., Hajidavalloo, E., Behbahaninejad, M., Hanafizadeh, P., 2016. Effect of pipe rotation on downward co-current air–water flow in a vertical pipe. Int. J. Multiph. Flow 81, 1–14.
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Contents lists available at ScienceDirect
International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow
Effect of pipe rotation on flow pattern and pressure drop of horizontal two-phase flow Yosef Baghernejad a,b, Ebrahim Hajidavalloo a,b,∗, Seyed Mohsen Hashem Zadeh a,b, Morteza Behbahani-Nejad a a b
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 61355 Iran Drilling Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran
a r t i c l e
i n f o
Article history: Received 1 April 2018 Revised 2 November 2018 Accepted 24 November 2018 Available online 24 November 2018 Keywords: Flow pattern map Horizontal and inclined pipe Pipe rotation Two-phase flow Pressure drop
a b s t r a c t In this paper, the effect of pipe rotation on two-phase flow patterns and pressure drop of a horizontal pipe is experimentally investigated. To obtain two-phase flow patterns and related transition boundaries, a unique experimental set-up was constructed to measure flow patterns under different pipe rotational speeds. A Plexiglas pipe, with 40 0 0 mm length and 25.4 mm ID was used in experiments to allow direct observation of flow pattern. For rotation of the pipe, an electromotor coupled with gearbox was used to allow different rotational speeds. The set-up also supports up to ±25° inclination. Air and water were used as the gas and liquid phase, respectively. Over 3800 experiments were conducted to draw flow pattern maps at six different rotational speeds of 0, 50, 10 0, 20 0, 30 0 and 400 rpm in both horizontal and 10° inclined pipe. To validate the results, experimental findings were compared with previous research for a horizontal fixed pipe case. Results show that pipe rotation has a significant effect on the flow pattern map and the transition boundaries. It was found that in horizontal pipe case, the stratified smooth flow regime decreases as the pipe rotation increases and disappears at high revolution speeds. Moreover, the annular regime enlarges with increasing pipe rotational speed. For a 10° inclined pipe, the stratified wavy region appears as the pipe rotation speeds up. It was observed that for both horizontal and inclined pipe, pressure drop considerably increases as the pipe rotational speed increases. Furthermore, the effect of pipe inclination on the pressure drop is reduced as the rotational speed increases. © 2018 Elsevier Ltd. All rights reserved.
1. Introduction Gas-liquid two-phase flows are very common in various industrial application such as drilling, boiling heat transfer, nuclear reactors, cooling circuits of power plants and pipeline flow in petroleum industries. Due to different interactions between the phases such as interfacial transfer, entrainment, deposition, and flooding, two-phase gas-liquid pipe flow is in fact a complex phenomenon. Moreover, two-phase flow can appear in different geometrical and operational forms that are very important to determine the properties of the system (Ghanbarzadeh et al., 2012). Simultaneous flow of two fluid phases with different physical properties, different flow patterns can be observed in the pipe. As significant engineering design parameters such as heat transfer and pressure drop are closely related to the type of two-phase flow regime (De Schepper et al., 2008), correct flow pattern predic-
∗ Corresponding author at: Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Golestan St., Ahvaz, 61355 Iran. E-mail address: [email protected] (E. Hajidavalloo).
https://doi.org/10.1016/j.ijmultiphaseflow.2018.11.012 0301-9322/© 2018 Elsevier Ltd. All rights reserved.
tion at different conditions of pipe flow is one of the most important parts of two-phase flow analysis. An engineering application of two-phase flow is when the pipe is rotating either in horizontal or vertical conditions. For instance, under-balanced drilling (UBD) of oil and gas wells requires prediction of two-phase flow patterns in horizontal and vertical pipes for precise calculation of bottomhole pressure to prevent kicking of the well or collapsing the wall (Khezrian et al., 2015). Although there is great amount of literature about behavior and properties of two-phase flow in pipes, but the effect of pipe rotation in a horizontal case was not studied yet. A few studies have examined flow patterns in an annular space with a rotating inner tube. Taitel and Dukler (1976) proposed mechanistic models for determining flow regime transitions in horizontal and near horizontal two-phase gas-liquid flow and presented a generalized flow regime map. Weisman et al. (1979) examined the effect of pipe diameters and fluid properties on two-phase flow patterns in horizontal pipes. They used air-water and air-glycerin as two-phase systems with the pipe diameters varies from 1.2 to 5.1 cm. They
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Fig. 1. Schematic of the experimental set-up.
present non-dimensional correlations from curve fitting for transition boundaries. Ozbayoglu and Ozbayoglu (2007) studied flow patterns and frictional pressure loss in two-phase flow through a horizontal annulus with a rotating inner pipe using Artificial Neural Networks (ANN) rather than proposing a mechanistic model. They compared their results with experimental data and showed that the ANN could estimate flow patterns with a high accuracy (error is less than ±5%). Hernandez Perez (2008) conducted experimental study of airwater two-phase flow in inclined pipes. His test pipes were 6.5 m long with two diameters, namely 38 mm and 67 mm. He measured time series of liquid holdup (using capacitance probes) and pressure drop (differential pressure transducer) and used a high speed video system in order to obtain image sequences of the flow conditions. Finally, he showed that increasing pipe diameter displaces the bubbly-slug transition to the right hand side on the flow pattern map for inclined flow, and for horizontal pipe the stratifiedslug transition is moved up. Shannak (2008) examined frictional pressure loss of vertical and horizontal smooth and relatively rough pipes and demonstrated that the frictional pressure drop increases with increasing relative roughness of the pipe; although the influence of the relative roughness becomes more evident at higher gas void fraction and higher mass flux. He proposed a new prediction model for frictional pressure drop of two-phase flow in pipes which includes a new definition of the Reynolds number and the friction factor of two-phase flow. The mentioned model is sufficiently accurate for engineering purposes. Shiomi et al. (1993) conducted an experimental study of twophase flow in a concentric annulus with inner cylinder rotation and showed that at relatively low rotational speed, the buoyancy effect of bubbles dominated the flow field and a dispersed bubbly flow was formed. On the other hand, at high rotational speed, the
vortex motion induced by the rotation dominated the flow field and ring-form and spiral flows were formed. Sorgun et al. (2011) studied the effect of cuttings and inner pipe rotation in horizontal/highly-inclined wellbores on friction factors and pressure loss, experimentally. They showed that the existence of cuttings increases the pressure drop due to decrease in flow area inside the wellbore. Dewangan and Sinha (2016) investigated the effect of the eccentricity and presence of the secondary solid phases in the flow instability (transition from laminar to turbulent flow) for the fully developed horizontal annular flow and showed that radius ratio, eccentricity and presence of the secondary phase have the most dramatic impact on transition from laminar to turbulent flow. Hasan and Kabir (1992) investigated inclined annular space and estimated the void fraction during upward concurrent two-phase flow in annuli using a drift-flux approach to model the slip between phases and the transition between regimes. De Schepper et al. (2008) investigated gas/vapor–liquid twophase co-current horizontal flow regimes numerically, using VOF model that uses a Piecewise Linear Interface Calculation (PLIC) interface reconstruction method in each computational cell and compared them with experimental data, taken from the Baker chart (Baker, 1953). They showed that all horizontal flow regimes appearing in the Baker chart can thus be calculated using CFD. Raeiszadeh et al. (2016) constructed an experimental setup to study the effect of pipe rotation on downward co-current air–water flow in a vertical pipe. They used a transparent vertical pipe with a diameter of 50 mm and an aspect ratio (L/d) of 80 to obtain flow maps at revolutions of 0, 60, 120, 180, 240, 300, 400 and 500 rpm by changing the air and water velocities at these revolutions. Using image processing, they showed that pipe rotation has major effect on flow patterns map and their transitions boundaries. They found increasing pipe rotation cause slug and annular flow start at lower VSG . As discussed by Raeiszadeh et al. (2016), although different
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Fig. 2. Photos of different flow patterns in horizontal two-phase flow.
methods have been used for flow pattern prediction in two-phase flow, but direct observation is common. As mentioned earlier, horizontal and inclined two-phase flows in pipes with rotation are used in various industries. Until now, fixed pipe relations are used for design purposes such as gas and oil well drilling and revolution of pipe is totally neglected, whereas it seems to be inaccurate. Therefore, investigation on the effect of pipe rotation on the pressure loss and related flow pattern in horizontal case is required. In this paper, gas-liquid two-phase flow in a rotating pipe in horizontal and inclined condition is studied using experimental approach. A high speed videometry system is used to capture twophase flow pattern through the pipe. Flow pattern map can then be discovered by direct analysis of the photography. 2. Experimental set-up In order to demonstrate the behavior of horizontal and inclined two-phase flow, an experimental set-up was designed and constructed. The experimental apparatus is shown schematically in Fig. 1. The main pipe ID is 25.4 mm and has an L/D of 157.48 (L = 40 0 0 mm), composed of Plexiglas to allow direct observation
of flow patterns. The temperature of the air and water were held constant under ambient conditions. Air and water were used as the gas and liquid phases in all experiments. Water from a tank is pumped through the pipe using a centrifugal pump and a rotameter, an absorber, a mixer and several ball valves are used after the pump as shown in Fig. 1. The rotameter (range 0–400 L/min with 1.0 L/min resolution) was frequently calibrated by comparing with the direct flow measurement using a pre-calibrated measuring tank in the laboratory. To control the inlet water flow rate, a by-pass system is considered after the pump. The compressed air at maximum 10 bar was fed continuously from a large reservoir which is connected to the compressor using a ball valve, three air rotameters and two check valves. One rotameter measures ranges of 0–10 L/min with 0.2 L/min resolution, the second measures ranges 5–100 L/min with 1.0 L/min resolution. For gas flow rate higher than measurement range of the first and second rotameters, a third rotameter (range from 1–40 m3 /h with 0.2 m3 /h resolution) is used. The calibration curves supplied by the manufacturer were used to calibrate the air rotameters. As shown in Fig. 1, the test section is located at the end part of the pipe (at about L/D of 138) to ensure the fully developed flow condition.
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Fig. 3. Present flow pattern maps compared with Taitel and Dukler (1976) (a) horizontal and (b) 10° upward inclined pipe (0 rpm).
Fig. 4. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (50 rpm).
To generate two-phase flow, air and water were mixed in the mixer which is a cylindrical aquarium bubble stone and connected to the inlet air pipe, inserted inside the water pipe, as it was done by Raeiszadeh et al. (2016). Two-phase air-water flow then entered the main pipe and after passing it drained into the main tank, using return pipe flow. It should be noted that the return pipe flow is installed in proper height to ensure air and water separation take place naturally. Moreover, a baffle was used to divide the inlet and outlet of water storage tank to prevent turbulence and air entrance in the suction side of the pipe. The pipe section was designed to have up to ±25° inclination by using a pivot. The pipe can also rotate about its axis at different revolutions using an electric motor and gearbox. Using several
bushings and bearing to support the pipe, the set-up had no important vibration except for revolutions above 500 rpm. A high-tech camera with 1/40 0 0 shutter speed (EOS 650D, Canon) was used for flow regime determination and flow pattern recording. A differential pressure gauge from WIKA with 1.0 bar range and 0.02 bar resolution was used for measuring pressure drop along the pipe (at the L/D of 0 and 157.48). Note that for the cases with low pressure drop, two pressure gauges from WIKA with 250 mbar range and 5 mbar resolution was used at both ends of the pipe (L/D of 0 and 157.48) to record pressure drop with higher resolution. The differential pressure gauge and the pressure gauges were accurately calibrated by a standard buoyancy ball pressure meter. Fig. 2 shows the photo of different flow patterns observed in the experiments.
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Fig. 5. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (100 rpm).
Fig. 6. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (200 rpm).
A detailed error analysis has been done to evaluate the maximum values of uncertainties in measured pipe dimensions and other measurements made by the instruments (Cacuci et al., 2005): 5.7% for the liquid superficial velocity, 13.6% for the gas superficial velocity and 10.3% for pressure drop data for pressure drops higher than 1.0 kPa/m. A uniform instruction was used during all experiments. Initially, stationary pipe tests were run, in which each run was started by setting the water flow rate a constant value using appropriate control valve, then the gas valve was opened and gas flow rate was increased step by step. The superficial air velocities were between 0.048 and 32.094 m/s (20 steps). After recording the results for a fixed water flow rate and different gas flow rates, then, the superficial water velocity was increased and the tests continue. The super-
ficial water velocities were between 0.048 and 4.815 m/s (16 steps). Moreover, experiments were conducted in 0, 50, 100, 200, 300 and 400 rpm both at horizontal and 10° inclination of pipe, which totals 3840 experimental runs. There was at least 5 min waiting time initially and between every two steps to ensure steady state condition in the pipe, and after that, the flow regime was recorded and the pictures were captured. After stationary tests completed, the experiments were repeated again for rotational case of the pipe.
3. Results and discussion Flow visualization was used to capture flow regimes in horizontal and 10° inclined air–water two-phase flow, in which, the following flow patterns were observed:
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Fig. 7. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (300 rpm).
Fig. 8. Flow pattern maps of two-phase flow (a) horizontal and (b) 10° upward inclined pipe (400 rpm).
Stratified smooth flow (only in horizontal pipe case) (SS): Pattern in which the liquid flows along the pipe bottom and the gas flows above water while their interface is smooth. Stratified wavy flow (SW): Pattern which is similar to the stratified flow, but due to higher velocity of gas, the interface is disturbed by waves in the flow direction. Bubble flow (BL): Pattern in which gas bubbles move along the upper part of the pipe at approximately the same velocity of the liquid. Elongated bubble flow (Plug flow) (EB): Pattern in which plugs of liquid and gas move in sequence along the upper part of the pipe. Slug flow (SL): Pattern in which a wave is picked up periodically by the more rapidly moving gas to form a frothy slug which
passes through the pipe at a much greater velocity than the average liquid velocity. Annular flow (A): Pattern in which the liquid phase forms a film on the pipe wall while the gas phase flows in the core at a higher velocity.
In the present study, air and water superficial velocities were used as coordinates of flow pattern maps (VSG = QG /AP and VSL = QL /AP respectively). As mentioned before, experiments were conducted in both stationary and rotating pipe conditions, each in horizontal and 10° inclined pipe. Therefore, the results of stationary pipe are first compared with previous researchers and then the rotating pipe cases are presented.
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Fig. 9. Effect of pipe rotation on the transition from bubble to slug flow (a) horizontal and (b) 10° upward inclined pipe.
3.1. Flow pattern maps for fixed pipe Fig. 3(a) and (b) show flow pattern map of present study in horizontal and 10° inclined pipe and compares them with Taitel and Dukler (1976) results. Comparison of the results shows that, although there are small differences on transition boundaries for each flow pattern, the results of present study are consistent with Taitel and Dukler (1976) results.
3.2. Effect of pipe rotation on flow pattern map Flow pattern maps of two-phase flow in horizontal and 10° upward inclined pipe at different rotational speeds (50, 10 0, 20 0, 30 0 and 400 rpm) are shown in Figs. 4–8. As seen in Fig. 4, pipe rotation at 50 rpm has no special impact on the flow map, but increasing revolution to 100 rpm leads to small changes in the flow map (Fig. 5). As shown in Fig. 5(a), stratified wavy and annular regime appears earlier (at VSG = 0.04 m/s and VSG = 2.0 m/s, respectively). Moreover, direct transition appears between elongated bubble and annular regime for rotational speeds over than 100 rpm at small range of superficial water velocity. This direct transition starts at lower gas superficial velocity as the rotational speed increases (VSG = 1.541 m/s at 100 rpm, VSG = 1.059 m/s at 200 rpm, VSG = 0.578 m/s at 300 rpm, VSG = 0.578 m/s at 400 rpm). On the other hand, Fig. 5(b) shows that stratified wavy flow appears for low values of VSL in pipe revolution of 100 rpm. In addition, slug to annular transition starts at lower values of VSG . Figs. 6(a)–8(a) shows that at 200 rpm and higher revolution speeds, stratified smooth region totally disappears. In addition, stratified wavy area reduces and annular region enlarges as the rotational speed increases. For 10° upward inclined pipe, as shown in Figs. 6(b)–8(b), stratified wavy and annular region grows with increasing pipe revolution speed. Effect of pipe rotation on different flow pattern transition boundaries are shown in Figs. 9–13. Note that symbols in these figures refers to the fixed pipe case. As shown in Fig. 9(a) and (b), increasing revolution has no great impact on disperse bubble to slug transition boundary.
Fig. 10. Effect of pipe rotation on the transition from stratified smooth to stratified wavy flow (horizontal pipe).
Fig. 10 depicts stratified smooth to stratified wavy transition boundary in horizontal case. It can be stated that by increasing pipe rotational speed, centrifugal force increases and move transition boundary from the stratified smooth regime to stratified wavy happen at lower gas and liquid superficial velocities. This effect is quite considerable in somehow that stratified smooth regime totally disappears for revolutions higher than 100 rpm. Fig. 11(a) shows that as the pipe rotation increases in horizontal case, stratified wavy flow region decreases and annular region enlarges. The phenomenon can be explained as follows: As the revolution speed increases, centrifugal dynamic force rises, and finally dominates the gravitational force, which results in moving the stratified wavy to annular transition boundary toward lower VSG . In contrast with horizontal case, for a 10° upward inclined
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Fig. 11. Effect of pipe rotation on the boundary of stratified wavy flow (a) horizontal and (b) 10° upward inclined pipe.
Fig. 12. Effect of pipe rotation on the transition from slug to annular flow (a) horizontal and (b) 10° upward inclined pipe.
pipe, stratified wavy area increases with increasing pipe revolution speed as shown in Fig. 11(b). It can be concluded that component of centrifugal force helps the gravitational force. Fig. 12 illustrates the transition lines between slug and annular regime in horizontal and inclined cases. As seen, by increasing rotational speed the area of annular regime increases. In other words, by increasing rotational speed, Taylor bubbles in slug regime collapses earlier, which causes annular regime starts at lower VSG . In order to compare the effect of different pipe rotation on the flow pattern maps with each other, all transition lines are shown in Fig. 13. As can be seen, flow pattern maps are significantly affected by pipe rotation both in horizontal and inclined cases. The main influence of pipe revolution is on the annular region, which enlarges it as the pipe rotation increases. On the other hand, strat-
ified smooth region decreases and totally disappears in high pipe rotational speed.
3.3. Pressure drop calculation Pressure drop data was recorded during each experiment. Because of oscillating nature of pressure in two-phase flow, an average pressure drop based on calculating pressure difference between inlet and outlet of the pipe in several times was reported. Neglecting accelerational component of the total pressure drop, Chisholm prediction model for the frictional component of pressure drop (Chisholm, 1967) and Homogeneous No-Slip model for the gravitational component (Shoham, 2006) were taken into account. Total pressure drop can then be calculated by adding these
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Fig. 13. Flow pattern maps of two phase flow at different rotation speeds (a) horizontal and (b) 10° upward inclined pipe.
Fig. 14. Effect of gas flow rate on pressure drop in a horizontal fixed pipe.
Fig. 15. Effect of pipe inclination on pressure drop (VSL = 0.578 m/s, 0 rpm).
two values. Finally, the total predicted pressure drops are used to compare with experimental pressure drop data. Fig. 14 depicts the effect of increasing gas flow rate on the pressure drop for two different values of VSL in the case of fixed horizontal pipe and compares experimental results with results of model predictions. Different flow regimes taking place by increasing VSG as it is clear in Fig. 14. Because mechanistic models ignore most of complications and interactions between the phases, deviation between measured and predicted results are always inevitable. Moreover, most of the prediction models are based on limited ranges of experimental data, therefore their predications might be inconsistent to use for wide ranges of gas flow rates (Xu et al., 2012). Although there are some discrepancies, but the overall magnitude of pressure drop for both experiment and model results are in the same order. Pressure drop increases as the VSG is
raised due to increasing frictional force. Moreover, pressure drop is much higher as the liquid flow rate increases (VSL = 4.237). In contrast with predicted mechanistic model results at high VSG range, the experimental pressure drops do not increase rapidly as VSG increases for high liquid flow rate, as was previously reported by Nicholson et al. (1978). It should be mentioned that by increasing VSG , the flow pattern changes from Disperse bubble (DB) to Slug (SL). Fig. 15 compares the effect of pipe inclination on the pressure drop in the case of fixed pipe condition for both experimental and model prediction results. As expected, due to gravitational force, pressure drop in 10° upward inclined pipe is higher than the horizontal case. As both the results of experiment and model show, difference between horizontal and inclined pipe pressure drop diminish as the superficial gas velocity increases. This is due to the
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Fig. 16. Effect of pipe revolution speed on (a) pressure drop (b) normalized pressure drop with fixed pipe case, in a horizontal and 10° upward inclined pipe (VSL = 0.966 m/s and VSG = 9.628 m/s).
fact that by increasing VSG , the frictional share of pressure drop enhances, leads to the dominance of frictional pressure drop at high values of gas flow rates. Effect of pipe rotational speed on the pressure drop and normalized pressure drop for horizontal and 10° upward inclined pipe is shown in Fig. 16. It is seen that pressure drop increases considerably as the pipe rotation speeds up. Moreover, as discussed earlier, due to gravitational effect, pressure drop for inclined pipe is more than horizontal pipe in low revolution speeds (Fig. 16a). The results show as the revolution increases the effect of gravitational pressure drop decreases leading to smaller difference between pressure drops of two cases. To compare the effect of pipe rotation and inclination of the pipe, the measured data for both horizontal and inclined pipe are normalized by their values in the case of fixed pipe (0 rpm). Normalized pressure drop results show that the effects of pipe rotation decreases with inclination of the pipe (Fig. 16b). On the other hand, as symbols illustrate, the flow pattern changes from slug (SL) to annular (A) as the pipe rotation increases. For both horizontal and 10 inclined pipe, the pressure drop exhibits a rapid increase for the revolutions between 100 and 260 rpm. This can be explained considering transition effects of flow pattern on the frictional forces acting on the pipe wall. 4. Conclusions In the present paper, the effect of pipe rotation on two-phase flow patterns and pressure drop was investigated through experiments using a direct observation method. For this purpose, an experimental set-up was designed and constructed and extensive tests were conducted to draw flow pattern maps under different pipe rotational speeds at two different angles, horizontal and 10° upward inclined. Results showed that flow pattern maps and the transition boundaries between flow regimes change considerably as the pipe rotational speeds increases. The following conclusions may also be drawn: 1- In a horizontal pipe, as the pipe rotation increases, the stratified smooth flow regime decreases and finally disappears (for revolutions higher than 100 rpm). Moreover, stratified wavy region
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starts at lower gas superficial velocities. In contrast with a horizontal pipe, in a 10° inclined pipe, the stratified wavy region appears and enlarges as the pipe rotation increases. A flow regime transition line appears between elongated bubble and annular regime for rotational speeds over than 100 rpm and it starts at lower gas superficial velocity as the rotation speed increases (in a horizontal pipe). Taylor bubbles in the slug regime collapse earlier as the pipe rotational speed increases which leads the slug to annular transition boundary moving toward lower VSG . The pressure drop in horizontal pipe raises as the VSG raises due to the frictional force effect. Pressure drop is much higher for higher liquid flow rates. Moreover, the pressure drop in the 10° upward inclined pipe is more than the horizontal one due to the gravitational force. Moreover, the effect of pipe inclination decreases as the gas flow rate increases due to dominance of the frictional relative to gravitational pressure drop. The pressure drop increases as the pipe rotational speed increases. Moreover, due to the gravitational effects, pressure drop for the inclined pipe is more than the horizontal pipe at low rotation speeds. By increasing the rotational speeds, the difference in pressure drop for horizontal and inclined pipes decrease. Furthermore, effect of pipe rotation on pressure drop decreases with inclination of the pipe.
Acknowledgment The authors thank Shahid Chamran University of Ahvaz for its financial support to this project (Grant number: 96/3/02/16670). References Baker, O., 1953. Design of pipelines for the simultaneous flow of oil and gas. Soc. Petrol. Eng. 53, 185–195. Cacuci, D.G., Ionescu-Bujor, M., Navon, I.M., 2005. Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems. CRC Press, Boca Raton, United States. Chisholm, D., 1967. A theoretical basis for the Lockhart-Martinelli correlation for two-phase flow. Int. J. Heat Mass Transf. 10, 1767–1778. De Schepper, S.C., Heynderickx, G.J., Marin, G.B., 2008. CFD modeling of all gas–liquid and vapor–liquid flow regimes predicted by the Baker chart. Chem. Eng. J. 138, 349–357.
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