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Liquid Entrainment in High-Pressure Bubble Columns Raymond Lau, Zhe Cui, and Liang-Shih Fan* Chemical and Biomolecular Engineering, The Ohio State University, 140 West 19th Avenue, Columbus, Ohio 43210
The liquid entrainment in bubble columns is experimentally studied under high-pressure conditions. Water and Paratherm NF heat-transfer fluid are used as the liquid phase, with nitrogen and air as the gas phase. Operating pressures and superficial gas velocities vary by up to 3.13 MPa and 33 cm/s, respectively. Parameters include the droplet size and droplet velocity, and local and total entrainment rates are examined. The study indicates that the entrainment rate increases with system pressures and superficial gas velocities. The maximum droplet velocity is found to be located between the center and wall regions at low pressures and low superficial gas velocities; the specific location shifts toward the center as the pressure and superficial gas velocity increase. The distributions of the droplet velocity and droplet size are narrower at locations further away from the entrainment surface. The droplet velocity of water at a given location and operating condition is found to be higher than that of paratherm, which has a higher viscosity and larger droplet size compared to water. Introduction The entrainment in gas-liquid flows has been studied extensively in the last few decades. The liquid entrainment is generally described as the carryover of liquid droplets by gas or bubbles. The liquid entrainment commonly occurs in processes where the gas and liquid are in contact, and a mist may be formed. Liquid entrainment can create operational problems such as loss of reactants and products and contamination of the outlet stream. Additional units for purification will be required for the contaminated outlet stream, which increases the capital and operating costs. There are two main types of droplet entrainments. The first type of droplet entrainment occurs when a gas flows over a thin liquid film. A typical example of this type would be in the annular two-phase-flow regime. In the annular flow regime, the formation of liquid droplets is dominated by the Rayleigh-Taylor instability of the shear on the liquid surface. The second type of droplet entrainment is due to the flow of gas bubbles in a liquid pool. Liquid droplets are formed from the bubble breakup at the liquid surface in the dispersedbubble and churn-turbulent regimes. Liquid droplets can also be ejected from the bubble nose or roof. Although there are different mechanisms in the formation of liquid droplets, as the upward gas velocity exceeds the terminal velocity of the liquid droplets, entrainment of liquid will be observed. In the annular flow regime, Ishii and Grolmes1 illustrated different entrainment mechanisms, which include roll wave, wave undercut, bubble burst, liquid impingement, and liquid bulge disintegration. A number of correlations have been proposed for the onset of droplet entrainment2,3 and entrainment and deposition rates.4-10 In general, no liquid entrainment is observed below a critical gas velocity, and the critical gas velocity continuously decreases as the liquid Reynolds number increases.2 The entrainment rate is proportional to the liquid Reynolds number and Weber number.6 The * To whom correspondence should be addressed. E-mail:
[email protected].
distribution of the entrained liquid droplet flow rate at the gas core is found to be sensitive to the flow configuration in annular flow. The droplet flow rate in the gas core is smaller than that of the vertical upward flow.3 Liquid entrainment studies in other areas such as hypothetical core disruptive accidents11,12 and in capillary-driven heat pipes13 have been conducted. During the expansion process in a hypothetical core disruptive accident, it is found that liquid entrainment is dominated by the Rayleigh-Taylor instability.11 At high fluid velocities, the Kelvin-Helmholtz mechanism is faster than the Taylor acceleration mechanism.12 It is also found that different modes of liquid entrainment can be observed in different systems. For example, in capillary-driven heat pipes, the wave-induced entrainment, pulsation entrainment, and intermediate entrainment are the dominating entrainment mechanisms.13 Little work has been conducted on the droplet entrainment due to the flow of bubbles. Thus, the objective of this work is to experimentally investigate the liquid entrainment due to the flow of gas bubbles on the liquid surface. Specifically, the effects of pressure on the liquid entrainment phenomena in bubble columns are probed. In this study, experiments are conducted to measure the entrainment rate at pressures up to 3.13 MPa and at gas velocities up to 33 cm/s. The Laser Doppler Velocimetry (LDV) technique is applied to examine the droplet size distribution and droplet flow characteristics. An empirical correlation is developed to account for the entrainment rate in high-pressure bubble columns. Experimental Section High-Pressure Multiphase-Flow Visualization System. All liquid entrainment experiments are conducted in a stainless steel high-pressure column with an inner diameter of 10.16 and a height of 91.44 cm in the straight section. The column has an expanded section that serves to reduce the superficial liquid velocity before the liquid exits the column. The expanded section is 30.48 cm in height with an inner
10.1021/ie0491847 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/12/2005
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Figure 1. Schematic diagram of the experimental setup.
diameter of the upper part of the section of 15.24 cm. Note that all liquid entrainment data in this study with the exception of those in Figure 14 are taken from the straight section of the column. Three pairs of quartz windows are installed on the front and rear sides of the column to allow direct visualization of bubble characteristics and flow phenomena under high-pressure and high-temperature conditions. Each window is 12.7 mm in width and 93 mm in height. These windows cover the entire test section. A perforated plate with 120 squarepitched holes of 1.5-mm diameter is used as the gas distributor. The system pressure is controlled by a backpressure regulator installed at the outlet of the bubble column. The high-pressure column can be operated under conditions up to 22 MPa and 250 °C. The schematic of the experimental setup is shown in Figure 1. A gas-liquid separator of 5.08 cm is connected to the outlet of the bubble column. The separator consists of two chambers, one for the inflow and one for the outflow of exiting gas from the bubble column. At the outlet of the separator, a porous plate of 10-µm pore sizes is installed to remove the liquid droplets from the outlet stream. The total volume of the removed liquid droplet collected at the bottom of the separator over a period of time represents the entrainment rate. A local entrainment rate is also measured by using nonisokinetic probes in the bubble column. Experimental results are compared between an isokinetic probe and a nonisokinetic probe. Both the isokinetic and non-isokinetic probes have the same construction. The isokinetic probe has a 0.76-hp vacuum pump at the outlet of the filter and a needle valve to adjust the suction velocity. The probe is an L-shaped tube, with an inner radius of 3.5 mm, bent to permit a smooth flow of droplets down the length of the probe. As droplets pass through the liquid filter, droplets can be trapped in the gas chamber while gas passes through. Over a long period of time, the liquid is collected and drained. The local droplet flux is then measured. The local droplet flux is measured at distances of 3, 11, and 20 cm above the liquid surface
and 0, 2.3, and 4 cm from the center of the column to determine the axial and radial distributions of the droplet flux in the column. LDV System. A two-dimensional LDV/Phase Doppler Particle Analyzer (PDPA) system is used in the backscattering mode for the measurement of the liquid droplet velocity and size. The LDV/PDPA system consists of a 300-mW air-cooled argon-ion laser system and a beam separator. They are used to generate two pairs of beams of known wavelengths of 514.5 and 480 nm. The light is transmitted through a fiber-optic cable and a probe with a 25-cm focal-length lens. This configuration yields 48 fringes with fringe spaces of 3.40 and 3.22 µm, yielding measurement volumes of 0.164 × 0.164 × 2.162 and 0.156 × 0.156 × 2.05 mm for the 514.5- and 480-nm wavelengths, respectively. The scattered light is collected through the same probe (backscattering mode) as the detector and processed with a signal processor. All LDV measurements are taken in the 10.16-cmi.d. columns. Distortion of the laser beams does not occur through the cylindrical column because of the flat quartz window on the cylindrical column. All measurements in this study are sampled between 600 and 3000 s based on different sampling rates. The sampling rate ranges from 10 to 100 Hz. The sampling rate is relatively low because of the system limitation, e.g., the low power source of the laser system and the thick visualization window of the high-pressure column. In this study, nitrogen and air are used as the gas phase; Paratherm NF heat-transfer fluid is used as the liquid phase. Paratherm NF heat-transfer fluid has a vapor pressure of less than 1 mmHg at 70 °F; therefore, the liquid loss due to vaporization can be neglected. The physical properties of Paratherm NF heat-transfer fluid (Fl ) 870 kg/m3, µl ) 0.032 Pa‚s, and σ ) 0.029 N/m at 25 °C and 0.1 MPa) at different pressures and temperatures are given by Lin et al.14 Water is also used as the liquid phase for comparison. The liquid is operated in a batch mode. The superficial gas velocity varies up to 33 cm/s, which covers both the homogeneous bubbling and churn-turbulent regimes. Results and Discussion Droplet Formation Mechanism. Figure 2 presents a series of photos, taken by a high-speed video camera with a frame rate of 240 frames/s, showing the mechanism of the entrained droplet formation during bubble bursting at the gas-liquid interface. As the gas bubble rises to the liquid surface, the liquid drains from the dome top (Figure 2a,b). The bubble dome becomes weakened and then bursts, giving rise to small droplets and leaving a crater at the interface (Figure 2c,d). As the crater fills in, the inflow of the liquid forms a jet at the center of the crater (Figure 2e). At high velocities, the top of the jet may detach, which would form additional droplets. The jet then retracts, and the liquid surface returns to the original condition (Figure 2f). The droplets formed by the bubble bursting are smaller than those formed by the inflow of liquid.15 Droplet Velocity. The droplet size and droplet velocity profile are measured using the LDV/PDPA system. The average droplet velocity is obtained from the LDV measurements by ensemble averaging, 〈u〉 ) N u(i), where u is the axial droplet velocity and (1/N)∑i)1 N is the total number of samples. In Figure 3, the droplet velocity profiles for two different superficial gas velocities in the air-paratherm system at a pressure
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Figure 4. Effect of the pressure on the vertical droplet velocity at various radial directions in the air-paratherm system.
Figure 2. Bubble-bursting mechanism in water at ambient pressure.
Figure 5. Effect of the liquid on the vertical droplet velocity at various radial directions at ambient pressure and a superficial gas velocity of 33 cm/s.
Figure 3. Effect of the superficial gas velocity on the vertical droplet velocity at various radial directions in the air-paratherm system.
of 0.584 MPa are shown. The velocity profile is more evenly distributed in the central region at the superficial gas velocity of 15 cm/s as compared to the superficial gas velocity of 33 cm/s. For both superficial gas velocities, the droplet velocity profile is flat near the centerline and reaches a maximum at r/R of 0.78 at the superficial gas velocity of 15 cm/s and at r/R of 0.5 at the superficial gas velocity of 33 cm/s. The presence of the maximum is due to the underdeveloped flow field resulting from the discharge of liquid droplets during the bubble breakup at the liquid surface. As the axial distance increases, the location for the maximum droplet velocity shifts toward the centerline at the superficial gas velocity of 33 cm/s while the location for the maximum droplet velocity at the superficial gas velocity of 15 cm/s remains unchanged. The change in the location for the maximum droplet velocity occurs because of the fact that, as the gas flow emends to be uniform at a higher
axial position, the flow pattern becomes fully developed. Figure 4 shows the effect of the pressure on the droplet velocity in the air-paratherm system. The profile is measured at the superficial gas velocity of 33 cm/s and pressures of 0.101 and 0.584 MPa. The maximum droplet velocity is located closer to the wall at a low pressure as compared to that at a high pressure. Measurements of the droplet velocity in an air-water system are also performed. A comparison of the measured droplet velocity profiles in the air-water and airparatherm systems is given in Figure 5. The droplet velocity profile in the air-water system is almost independent of the axial position and shows a parabolic profile along the radial direction. Both observations indicate a shorter developing distance in an air-water system than in an air-paratherm system. The droplet velocity of paratherm near the centerline is also found to be lower than that of water. One explanation is that, because of the higher viscosity of paratherm, more kinetic energy is required to break the droplets. The larger paratherm droplets thus lead to lower droplet velocities than those for water. The response time of larger paratherm droplets is also longer compared to the smaller water droplets. The droplet velocity distribution is determined using a minimum of 600 samples. Figure 6 shows the comparison of the droplet velocity at different axial positions. A normal distribution of the droplet velocity can be observed at r/R ) 0 and 0.4, while the droplet velocity
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Figure 7. Effect of the superficial gas velocity on the droplet velocity distribution in the air-paratherm system.
Figure 6. Effect of the axial location on the droplet velocity distribution in the air-paratherm system.
distribution at r/R ) 1 is skewed to the left. This behavior denotes the fact that a lower gas velocity in the boundary layer near the wall due to viscous effects and the backflow of droplets is more significant than that of the upward flow at the wall region. The collision of the droplet and the wall forms a liquid film along the wall, which also contributes to the lower gas velocity near the wall region. A longer left tail for the droplet velocity distribution at r/R ) 1 is also observed as the axial distance increases. At a low axial position, the burst of bubbles provides upward inertia to the droplets. This effect of inertia dampens with increasing axial distance. Thus, as the axial distance increases, the amount of the droplet backflow at the wall region increases. Figure 7 shows the effect of the superficial gas velocity on the droplet velocity distribution. The droplet velocity distribution broadens and shows more variations in the radial positions with an increase in the superficial gas velocity. A high gas velocity gives a large disturbance in the flow field than a low gas velocity and requires a longer developing distance. Therefore, a broader and nonuniform droplet velocity distribution in the radial position is observed. The effect of the pressure on the droplet velocity distribution is illustrated in Figure 8. The droplet velocity distribution is very similar for the ambient pressure and elevated pressures. The higher gas density at an elevated pressure provides a larger drag force to the liquid droplets; thus, the average droplet velocity is higher at an elevated pressure. Figure 9 shows the comparison of the droplet velocity distribution in both air-paratherm and air-water systems. The droplet velocity in the air-
Figure 8. Effect of the pressure on the droplet velocity distribution in the air-paratherm system.
paratherm system shows a wider distribution than that in the air-water system, and a higher average droplet velocity is found in the air-water system. There is also more backflow present in the air-paratherm system than in the air-water system. Droplet Size. The droplet size measurement with the PDPA system requires two laser sensors to be positioned perpendicularly to each other. With the window layout in the high-pressure column, the PDPA measurement cannot be conducted. Thus, the measurement of the droplet size is made only for the Plexiglas column under ambient pressure and temperature conditions. Figure 10 shows the effect of the superficial gas velocity and the axial position on the droplet size in air-water systems. A larger droplet size is measured at a super-
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Figure 9. Effect of the liquid on the droplet velocity distribution.
Figure 11. Effect of the axial location on the droplet size distribution in the air-water system.
Figure 10. Effect of the superficial gas velocity on the droplet size at various radial directions in the air-water system.
ficial gas velocity of 15 cm/s than at a superficial gas velocity of 33 cm/s. Even though larger droplets are formed from the bursts of large bubbles formed at a higher superficial gas velocity compared to those formed by the burst of small bubbles formed at a lower superficial gas velocity, these large droplets quickly drop back to the liquid bed because they cannot be supported by the upward gas flow. As shown in Figure 11, the droplet size distribution at a superficial gas velocity of 33 cm/s is found to be wider at a low axial distance as compared to that at a high axial distance. The droplet sizes close to the wall are generally smaller than those near the centerline. This result is consistent with the parabolic velocity profile of gas flow through a tube. The droplet size at a high axial position shows a relatively uniform distribution throughout the radial plane, while at low axial positions, some variations of the droplet size distribution in the radial position can be observed. The effect of the superficial gas velocity on the droplet size is shown in Figure 12. The droplet size measured at a low superficial
Figure 12. Effect of the superficial gas velocity on the droplet size distribution in the air-water system.
gas velocity shows a larger droplet size near the centerline and then becomes smaller closer to the wall. Because of the smaller boundary layer at high gas velocity, the droplet size measured shows a uniform distribution along the radial direction. Local Droplet Flux. The radial and axial profiles of local time-averaged droplet flux are measured using
Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3781 Table 1. Comparison of the Droplet Flux between Isokinetic and Non-isokinetic Probe Measurements at the Center 30 cm above the Liquid Surface droplet flux (×106 cm/s) superficial gas velocity (cm/s)
isokinetic probe
non-isokinetic probe
24.3 34.0
2.63 3.15
2.58 3.00
nonisokinetic sampling probes. The time-averaged mass flux measurement is found to be the same for both isokinetic and non-isokinetic probes.16-18 Because the sampling points are far away from the entrance region, the use of nonisokinetic probes is subject to a minimal error.19 As shown in Table 1, the difference in the droplet flux for this study between an isokinetic probe and a non-isokinetic probe is less than 5%, indicating the validity of the non-isokinetic sampling. Radial and axial profiles of the local time-averaged droplet flux measurement in the air-paratherm system are shown in Figure 13. In the range of the superficial gas velocity shown, there is no significant difference in the measurement of the droplet flux at different axial positions. The radial variation of the droplet flux is also relatively flat in the central region; it then decreases when approaching the column wall. The measurement of the timeaveraged droplet flux at higher pressures is limited to the total gas consumed during the sampling process. Total Droplet Entrainment Rate. The total liquid entrainment rate in a nitrogen-paratherm system at various pressures is measured at the outlet of the reactor. The location of the outlet is over 700 mm above the liquid surface. On the basis of the LDV and PDPA measurements, this distance well exceeds the transport disengaging height. In a comparison of the low-pressure results in Figures 13 and 14, the local entrainment rate measured in the straight section and the total entrainment rate measured at the outlet of the expanded section are comparable. This comparison indicates that the entrained droplets are small enough so that the effect of the expanded section of the column is negligible. As shown in Figure 14, the results clearly indicate the positive effect of the pressure on the total entrainment rate. Similar to the higher droplet velocity at high pressures, a higher gas density at elevated pressure yields a larger drag force. The higher gas density at elevated pressure enhances bubble breakup and sup-
Figure 14. Total liquid entrainment rate in the nitrogenparatherm system at various pressures. Table 2. Applicable Range of the Droplet Entrainment Correlation in a Batch Liquid System parameter (units)
range
parameter (units)
range
Fl (kg/m3) µl (Pa‚s) σl (N/m) Fg (kg/m3)
868-872 0.0322-0.0374 0.0269-0.0293 1.13-35.49
Ug (m/s) H/Dc We Re
0.061-0.259 >5 1.89 × 10-3-0.32 703-6413
presses bubble coalescence, which promotes the formation of smaller bubbles. With the combination of the smaller droplet formation and higher upward drag, more liquid is entrained at high pressures. Correlation for Liquid Entrainment. An empirical correlation is developed to account for the total entrainment rate in a high-pressure bubble column given as
E0/AUgFg ) 0.79Re1.5We0.88
(1)
where E0 is the total entrainment rate, A is the crosssectional area of the outlet, Ug is the superficial gas velocity, Fg is the gas density, Re is the Reynolds number defined as Re ) FgUtDd/µg, and We is the Weber number defined as We ) FlUg2Db/σ. As can be seen from Figure 14, the correlation matches reasonably well with the entrainment rate data for all pressures. The applicable operating ranges of the correlation are shown in Table 2. Concluding Remarks
Figure 13. Local droplet entrainment flux in the air-paratherm system.
The liquid entrainment phenomenon in bubble columns can be described by the bubble-rupture mechanism. Large bubbles instigate the formation of large liquid droplets. Experimental results obtained in this study indicate that the entrainment rate increases with the system pressure and the superficial gas velocity. The maximum droplet velocity is found to be located between the central and wall regions at low pressures and low superficial gas velocities; the specific location shifts toward the center as the pressure and superficial gas velocity increase. The droplet velocity and droplet size distributions are narrower at a location further away from the entrainment surface. The droplet velocity of water is found to be larger than that of paratherm, which has a higher viscosity and hence a larger droplet. An empirical correlation that accounts for the total
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entrainment rate at various pressures can be expressed in terms of the Reynolds and Weber numbers. Acknowledgment This work was supported by National Science Foundation Grant CTS-0207068. Notation A ) cross-sectional area D ) column diameter Db ) average bubble diameter Dd ) droplet size E0 ) total entrainment rate g ) effective acceleration L ) column height N ) total number of samples P ) system pressure r ) radial coordinate of a column with the center denoted as zero R ) column radius Re ) Reynolds number ()FgUtDd/µg) u ) axial droplet velocity 〈u〉 ) time-averaged velocity Ud ) droplet velocity Ug ) superficial gas velocity Ut ) terminal velocity v ) entrainment velocity We ) Weber number ()FlUg2Db/σ) Fg ) gas density Fl ) liquid density µg ) gas viscosity µl ) liquid viscosity σ ) surface tension
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(6) Kataoka, I.; Ishii, M.; Nakayama, A. Entrainment and deposition rates of droplets in annular two-phase flow. Int. J. Heat Mass Transfer 2000, 43, 1573. (7) Maier, M. R.; Soliman, H. M.; Sims, G. E.; Armstrong, K. F. Onsets of entrainment during dual discharge from a stratified two-phase region through horizontal branches with centrelines falling in an inclined plane: Part 1sAnalysis of liquid entrainment. Int. J. Multiphase Flow 2001, 27, 1011. (8) Maier, M. R.; Soliman, H. M.; Sims, G. E. Onsets of entrainment during dual discharge from a stratified two-phase region through horizontal branches with centrelines falling in an inclined plane: Part 2sExperiments on gas and liquid entrainment. Int. J. Multiphase Flow 2001, 27, 1029. (9) Okawa, T.; Kitahara, T.; Yoshida, K.; Mastumoto, T.; Kataoka, I. New entrainment rate correlation in annular twophase flow applicable to wide range of flow condition. Int. J. Heat Mass Transfer 2002, 45, 87. (10) Holowach, M. J.; Hochreiter, L. E.; Cheung, F. B. A model for droplet entrainment in heated annular flow. Int. J. Heat Fluid Flow 2002, 23, 807. (11) Tan, M. J.; Delhaye, J. M. An experimental study of liquid entrainment by expanding gas. J. Fluids Eng. 1987, 109, 436. (12) Epstein, M.; Fauske, H. K.; Kubo, S.; Nakamura, T.; Koyama, K. Liquid entrainment by an expanding core disruptive accident bubblesa Kelvin/Helmholtz phenomenon. Nucl. Eng. Des. 2001, 210, 53. (13) Kim, B. H.; Peterson, G. P. Analysis of the critical Weber number at the onset of liquid entrainment in capillary-driven heat pipes. Int. J. Heat Mass Transfer 1995, 38, 1427. (14) Lin, T.-J.; Tsuchiya, K.; Fan, L.-S. Bubble flow characteristics in bubble columns at elevated pressure and temperature. AIChE J. 1998, 44, 545. (15) Newitt, D. M.; Dombrowski, N.; Knelman, F. H. Liquid entrainment. I. Mechanism of drop formation from gas or vapor bubbles. Trans. Inst. Chem. Eng. 1954, 32, 244. (16) Leckner, B.; Golriz, M.; Zhang, W.; Andersson, B. A.; Johnsson, F. Boundary layerssfirst measurements in the 12 MW CFB research plant at Chalmers University. Proc. Int. Conf. Fluid Bed Combust. 1991, 2, 771. (17) Aguillon, J.; Shakourzadeh, K.; Guigon, P. Comparative study of nonisokinetic sampling probes for solids flux measurement in circulating fluidized beds. Powder Technol. 1995, 83, 79. (18) Issangya, A. S.; Bai, D. R.; Grace, J. R. Solids flux profiles in a high-density circulating fluidized bed riser. Fluidization IX 1998, 197. (19) Ball, J. S.; Zhu, J.-X. A preliminary study into the local solids fluxes in a downer reactor. Powder Technol. 2001, 114, 96.
Received for review August 31, 2004 Revised manuscript received December 7, 2004 Accepted March 1, 2005 IE0491847
