1302
Ind. Eng. Chem. Res. 2004, 43, 1302-1311
Gas-Liquid Mass Transfer in High-Pressure Bubble Columns R. Lau, W. Peng, L. G. Velazquez-Vargas, G. Q. Yang, and L.-S. Fan* Department of Chemical Engineering, The Ohio State University, 140 West 19th Avenue, Columbus, Ohio 43210
Volumetric gas-liquid mass-transfer coefficients are investigated in bubble columns under highpressure and moderate-temperature conditions by utilizing an oxygen desorption method. The oxygen concentration in the liquid phase, water or Paratherm NF heat-transfer fluid, is monitored with a high-pressure optical fiber oxygen probe. The study covers operating conditions up to pressures of 4.24 MPa and up to temperatures of 92 °C. The superficial gas and liquid velocities vary up to 40 and 0.89 cm/s, respectively. Experimental results show that system pressure, temperature, gas and liquid velocities, liquid properties, and column dimensions are major factors affecting mass transfer. The mass-transfer coefficient increases with both pressure and temperature. Both gas and liquid velocities improve mass transfer due to higher turbulence at high-velocity conditions. Liquid properties and column dimensions also have significant effects on mass transfer. The effect of liquid velocity on kla is mainly due to the change in kl, while other variables affect kla mainly through the change in gas holdup, which directly affect the interfacial area, a. A consideration of the dispersion term on the determination of kla gives results similar to those of the continuous stirred tank reactor model, which was used to determine kla in this study. Introduction Bubble and slurry bubble column reactors are widely used for industrial processes such as Fischer-Tropsch synthesis, coal liquefaction, and methanol synthesis. The design and scale-up of these reactors require knowledge of the hydrodynamics and the mass- transfer behavior of three-phase fluidized beds at high pressures. Although the hydrodynamics of bubble and slurry bubble columns have been widely studied, mass-transfer studies have been limited to ambient conditions in airwater systems and little has been reported on highpressure conditions with relevant industrial processes. Pressure is known to have a significant effect on the hydrodynamics of slurry bubble columns.1 The bubble size decreases and gas holdup increases with increasing pressure. Because the mass-transfer behavior depends heavily on the hydrodynamics, it is expected that pressure affects the mass-transfer phenomena. Previous mass-transfer studies in the literature were commonly conducted with oxygen absorption or the desorption method using either air or oxygen as the gas phase.2,3 Studies under atmospheric conditions are extensive, especially for air-water systems, and a list of some literature studies on gas-liquid mass transfer is shown in Table 1. Calderbank and Moo-Young found that kl is lower for smaller bubble sizes. Because an increase in pressure decreases the bubble size, these findings would suggest that the liquid-phase masstransfer coefficient decreases with increasing pressure.4 Deckwer et al. found that both desorption and adsorption methods resulted in similar kla values and that different gas sparger designs can affect kla values up to a factor of 2.2,5 Lewis and Davidson measured the volumetric mass-transfer coefficient in a 0.45-m-diameter column and found that the mass-transfer rates were enhanced by bubble breakup, but the effect was small * To whom correspondence should be addressed.
because of the rapid coalescence of small bubbles.6 Sada et al. found that the type of suspended particles employed and the electrolyte concentration insignificantly influence kla. The increase of kla in a low concentration of fine particles was due to an increase of the interfacial area, a.7 Ozturk et al. determined the volumetric mass-transfer coefficient in a 0.095-mdiameter glass column with different gases and organic liquids. The gas holdup and kla were found to increase with gas density, but kla in liquid mixtures does not correlate with high gas holdup. They suggested that small bubbles were entrapped in the liquid, which do not contribute to the mass transfer but only circulate.8 Tang and Fan used a steady-state axial dispersion model to determine the volumetric mass-transfer coefficient and found that kla decreases with increasing solids concentration and particle terminal velocity. An increase in the liquid velocity significantly increases kla but only slightly increases the gas holdup.9 For mass-transfer studies at elevated pressure conditions, only a handful of studies are available in the literature. A list of literature studies is shown in Table 2. Wilkinson et al. used the uncatalyzed oxidation of sodium sulfite method to determine the volumetric mass-transfer coefficient at pressures up to 0.4 MPa in a 0.158-m bubble column. Their experimental results showed that both the interfacial area and the volumetric mass-transfer coefficient increase with pressure. They also argued that the increase in kla is partly limited to the higher gas-phase mass-transfer resistance and a decrease in the liquid-phase volume.10 Linek et al. developed a method by implementing a small sudden change in the system pressure and then monitoring the resulting oxygen concentration change in the liquid phase to measure kla.11 The method was further improved by incorporating a nonideal step change in pressure while monitoring the subsequent change of pressure and oxygen concentration simultaneously.12 Letzel et al. applied this pressure step method to
10.1021/ie030416w CCC: $27.50 © 2004 American Chemical Society Published on Web 01/31/2004
Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004 1303 Table 1. List of Literature Studies of the Gas-Liquid Mass-Transfer Coefficient under Ambient Conditions ref Akita and
system
Yoshida25
Deckwer et al.2
Hikita et al.27
Lewis and Davidson6 Patwari et al.28 Sada et al.7
Kawase et al.29 Ozturk et al.8 Schumpe et al.30 Tang and Fan9 Kim and Kim31
operating conditions
Dc ) 0.15 m, H ) 4.0 m, oxygen-nitrogen-water, glycerol solution, methanol, Na2SO3 solution Dc ) 0.2 m, H ) 7.23 m, and Dc ) 0.15 m, H ) 4.4 m, air-tap water and solutions of salts and molasses Dc ) 0.10 m, H ) 1.5 m and Dc ) 0.19 m, H ) 2.4 m, air, O2, H2, CH4, CO2-water, sucrose, n-butanol, methanol Dc ) 0.45 m, air-water Dc ) 0.14 m, H ) 2.65 m, glass beads-glycerol solution, CMC solution-oxygen Dc ) 0.078 m, CO2-aqueous calcium hydroxide saturated solution-aluminum oxide, calcium hydroxide, calcium carbonate Dc ) 0.23 m, H ) 1.22 m and Dc ) 0.76 m, H ) 3.21 m Dc ) 0.095 m, air, N2, CO2, He, H2-organic liquids Dc ) 0.14 m, 2.65 m in height, glass beads-glycerol solution, CMC solution-oxygen Dc ) 0.0762 m, polystyrene, acrylic, acetate, nylon-air-water Dc ) 0.142 m, 2.0 m in height, glass beads-air-water Dc ) 0.29 m, O2/air-distilled water and aqueous Na2SO4 Dc ) 0.285 m, H ) 4.1 m, air-water
Linek et al.12 Zheng et al.32 Terasaka et al.3 Peeva et al.33
Dc ) 0.06 and 0.114 m, N2/O2-tap water, solutions of microbial polysaccharides xanthan or gellan Dc ) 0.087 m, H ) 0.54 m, silicon oil-n-decane
measurement method
T ) 293 K, P ) 0.1 MPa, Ug up to 0.33 m/s
oxygen absorption
T ) 298 K, P ) 0.1 MPa, Ug up to 0.15 m/s
oxygen absorption and desorption
T ) 283-303 K, P ) 0.1 MPa, Ug up to 0.39 m/s
oxygen absorption and desorption
T ) 293 K, P ) 0.1 MPa, Ug up to 0.23 m/s, Ul up to 0.68 m/s T ) 298 K, P ) 0.1 MPa, Ul ) 3.0-8.1 cm/s, Ug ) 1.7-11.4 cm/s T ) 293 K, P ) 0.1 MPa, Ug up to 0.2 m/s
oxygen absorption
T ) 298 K, P ) 0.1 MPa, Ug ) 0.6 m/s T ) 293 K, P ) 0.1 MPa, Ug up to 0.1 m/s T ) 298 K, P ) 0.1 MPa, Ul up to 12 cm/s, Ug up to 12 cm/s T ) 298 K, P ) 0.1 MPa, Ug up to 4.14 cm/s T ) 298 K, P ) 0.1 MPa, Ul ) 0.02-0.1 m/s, Ug ) 0.02-0.2 m/s T ) 293 K, P ) 0.1 MPa, Ug ) 0.004 m/s T ) 298 K, P ) 0.1 MPa, Ug up to 11 cm/s T ) 292 K, P ) 0.1 MPa, Ug up to 0.15 m/s
dynamic CO2 gas analysis method oxygen absorption
T ) 298 K, P ) 0.1 MPa, Ug ) 0.018 m/s
decane absorption into emulsion and decane concentration determined by gas chromatography
oxygen electrode oxygen absorption
oxygen absorption, oxygen electrode oxygen absorption oxygen absorption oxygen absorption oxygen absorption oxygen absorption
Table 2. List of Literature Studies of the Gas-Liquid Mass-Transfer Coefficient at Elevated Pressure Conditions ref Wilkinson et
system al.10
Kojima et al.14
Letzel et al.13 Yang et al.15 Jordan et al.34 Behkish et al.16
Dc ) 0.158 m, 0.8 mol/L sodium sulfite deionized water solution-air Dc ) 0.045 m column, N2/O2-tap water, aqueous buffered solution, aqueous enzyme solution Dc ) 0.15 m, N2/O2-demineralized water Dc ) 0.037 m, H2/CO, N2-liquid paraffin-134 µm silica gel powder Dc ) 0.115 m, 1.37-m height, O2-water, ethanol, 1-butanol (96%), toluene Dc ) 0.316 m, H ) 2.8-m height, H2, CO, N2, and CH4-Isopar M and hexanes mixture
measure the volumetric mass-transfer coefficient in a 0.15-m-i.d. bubble column with an air-water system. They found that an increase in kla with increasing pressure is due to the increase in gas holdup and the ratio of kla/g was determined to be approximately 0.5 for all pressure conditions.13 Kojima et al. used a discontinuous switch from nitrogen to a nitrogen-
operating conditions
measurement method
T ) 293 K, P ) 0.1-0.4 MPa, Ug up to 0.15 m/s
uncatalyzed oxidation of sodium sulfite
T ) 293 K, P ) 0.1-1.1 MPa, Ug up to 0.15 m/s
oxygen absorption
T ) 293 K, P ) 0.1-1.3 MPa, tindUg up to 0.3 m/s T ) 293-523 K, P ) 1.0-5.0 MPa, s ) 5-20%, Ug up to 0.02 m/s
oxygen absorption
T ) 293 K, P ) 0.1-1.0 MPa, Ug ) 0.15 m/s
oxygen absorption
T ) 293 K, P ) 0.17-0.8 MPa, Ug ) 0.08-0.2 m/s
gas absorption in a closed circulating system
gas adsorption
oxygen mixture in a 45-mm-i.d. bubble column to measure the volumetric mass-transfer coefficient. Both the gas holdup and volumetric mass-transfer coefficient were found to increase with pressure. Furthermore, the effect of pressure on gas holdup and kla became significant at higher superficial gas velocities for single-nozzle gas distributors.14 A gas adsorption method was em-
1304 Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004
Figure 1. Schematic diagram of the experimental setup.
ployed by Yang et al. to estimate the volumetric liquidside mass-transfer coefficient in a slurry system. There is little variation in kl values with superficial gas velocity in the range of their study (up to 2 cm/s). The interfacial area, a, was found to increase with increasing pressure and superficial gas velocity but decrease with increasing temperature and solids concentration.15 In a more recent study, Behkish et al. used the transient physical gas absorption technique to determine the volumetric mass-transfer coefficient in a 0.316-m-i.d. column. The mass-transfer behavior of H2, CO, N2, and CH4 in Isopar-M and hexane mixtures was studied with and without iron oxide catalysts and glass beads. The volumetric mass-transfer coefficient was found to increase with pressure and gas velocity but decrease dramatically with increasing solids concentration. In addition, they suggested that the mass transfer in the fully developed, churn-turbulent flow regime with high solids concentration was controlled by the gas-liquid interfacial area.16 The objective of this study is to examine the volumetric gas-liquid mass-transfer coefficient under a wide range of operating conditions, especially under high pressures and in systems of industrial relevance. Experimental Section The gas-liquid mass-transfer experiments are conducted in two stainless steel high-pressure columns with inner diameters of 5.08 and 10.16 cm, respectively. There are three pairs of quartz windows 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. The windows cover the entire test section. A perforated plate is used as the gas distributor, with 120 square-pitched holes of 1.5-mm diameter. The system pressure is controlled by a back-pressure regulator installed at the outlet of the column. Both columns can be operated up to 22 MPa and 250 °C. The schematic of the experimental setup is shown in Figure 1. The gas-liquid mass-transfer coefficient is measured using the oxygen desorption method with a discontinuous switch from air to nitrogen. An optical fiber oxygen probe is utilized to measure the liquid oxygen concentration at high pressures. A 470-nm light source is used to activate the fluorescence dye coated on the tip of the probe. When the fluorescence gel is excited, it emits a 590-nm-wavelength light. As oxygen molecules collide with the excited fluorescence dye, energy is transferred to the oxygen molecule (fluorescence quenching). The energy transfer is proportional to the collision number
frequency between the oxygen molecules and the fluorescence dye. Therefore, the light intensity can be translated into partial pressure or concentration of oxygen. A two-point calibration of the optical fiber oxygen probe is performed by applying atmospheric air and an aqueous solution of sodium dithionite. The addition of sodium dithionite to water chemically removes the dissolved oxygen to generate a zero-oxygen environment. At the beginning of each test trial, the liquid is saturated with air initially. The air flow is then shut down so that all bubbles escape from the liquid. Then, nitrogen is fed into the column while, simultaneously, the oxygen concentration in the liquid is monitored. In this study, nitrogen and air are used as the gas phase and Paratherm NF heat-transfer fluid is used as the liquid phase. 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.17 The liquid is operated in continuous mode, and the superficial liquid velocity varies from 0.08 to 0.89 cm/s. The superficial gas velocity varies up to 40 cm/s, which covers both the homogeneous bubbling and churnturbulent regimes. The operating pressures and temperatures are up to 4.24 MPa and 92 °C, respectively. Mass-Transfer Model The mass-transfer coefficient is determined by assuming that the liquid is perfectly mixed in the radial direction; therefore, the dissolved oxygen concentration can then be described by the equation
V(1 - g)
dC ) klaV(1 - g)(Ceq - C) + Q(C0 - C) dt (1)
where V is the reactor volume, g is the gas holdup, kla is the gas-liquid mass-transfer coefficient, C is the liquid-phase oxygen concentration, C0 is the inlet liquid oxygen concentration, and Ceq is the equilibrium oxygen concentration. Assuming that Ceq is negligible for all pressure conditions and the inlet liquid has no oxygen content, eq 1 can be integrated with the boundary condition that, at t ) t0, C ) Ci. The solution of the above equation becomes
C(t) ) Cie-Pt
(2)
where
P)
klaV(1 - g) + Q V(1 - g)
Therefore
ln C(t) ) -Pt + constant
(3)
The oxygen concentration in the liquid phase can be normalized by the air-saturated and nitrogen-equilibrated points
Cnorm(t) )
C(t) - Cmin Cmax - Cmin
(4)
where Cmax is the measured signal when the liquid is saturated by air and Cmin is the signal at which oxygen
Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004 1305
is completely desorbed to the nitrogen stream. Some initial data points from the response curve are not used for the kla calculation in order to take into account the nonideal step change of the gas flow rate. To account for the effect of axial dispersion of the liquid, eq 1 can be rewritten as
∂C ∂C ∂2C )D 2 -U + kla(Ceq - C) ∂t ∂z ∂z
(5)
where D is the axial dispersion coefficient and U is the interstitial liquid velocity. The dispersion coefficients in air-water and nitrogen-Paratherm systems at different pressures were determined in a previous study.18 The initial condition for eq 5 is
C(z,t)0) ) Ci
(6)
The boundary conditions used are
(-D ∂C∂z + UC)
z)0
) UC0(z)0,t)
(7)
and
∂C (z)0,t) ) 0 ∂z
(8)
The above partial differential equation can be solved analytically by a Laplace transform,19 and the solution is as follows:
C(z,t) ) C0A(z,t) + B(z,t)
(9)
where
[ [
] [ ] ] [ ] ( ) [ ] { [ ] ( ) ) [ ] ( ( ) [ ]}
(U - v)z z - vt U exp erfc + A(z,t) ) U+v 2D 2xDt (U + v)z z + vt U exp erfc + U-v 2D 2xDt Uz z + Ut U2 exp - klat erfc (10) 2klaD D 2xDt 1 z - Ut U 2 1/2 erfc + × 2 πD 2xDt (z - Ut)2 1 Uz U 2t exp + - 1+ × 4Dt 2 D D Uz z + Ut erfc [-Ci exp(-klat)] + exp D 2xDt Ci exp(-klat) (11)
B(z,t) )
and
(
v)U 1+
)
4klaD U2
Figure 2. Comparison of the oxygen concentrations computed by the dispersion and CSTR models at (a) 0.1 MPa and (b) 4.24 MPa.
continuous stirred tank reactor (CSTR) model. Therefore, a larger section of the initial data point needs to be truncated in order to ensure the constant-gas-flow condition. A comparison of the oxygen concentration computed by the dispersion and CSTR models is shown in Figure 2. It is observed that the dispersion model provides a better fit to the experimental data than the CSTR model at all pressures. The mass-transfer coefficient, kla, determined by both the CSTR model and the dispersion model are compared in Figure 3. With the incorporation of the dispersion coefficient, kla found is slightly smaller than that determined by the CSTR model. Studies also showed that the values of kla are almost independent of axial dispersion coefficients.5,9 The CSTR model is employed to estimate kla because of the fact that dispersion coefficients at different conditions in different systems may not be available.
1/2
(12)
The mass-transfer coefficient, kla, is then solved by optimizing the objective function:
error ) (Cexp - Ccal)2
(13)
Optimization is performed for a number of cases using the algorithm described. The dispersion model is more sensitive to the variation of the gas flow rate than the
Results and Discussion Dissolved Oxygen Concentration. Figure 4 shows the logarithmic plot of oxygen concentration signals versus time. As seen from the figure, the logarithm of oxygen concentration versus time formed a straight line for both ambient and high-pressure conditions. Therefore, it is reasonable to use the CSTR model to determine the mass-transfer coefficient. Comparison with Literature Data. The measurement technique has been verified in an air-water
1306 Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004
Figure 3. Comparison of the mass-transfer coefficients determined by the dispersion and CSTR models at (a) 0.1 MPa and (b) 2.86 MPa.
system under ambient conditions, and the measured mass-transfer coefficients are comparable with the literature data. The measured mass-transfer coefficient in the air-water system under ambient conditions is shown in Figure 5. In general, kla increases as the gas velocity increases, but there is a significant variation in the mass-transfer coefficient among available literature data. The large deviation in the literature results is probably due to the difference in gas distributor designs and experimental temperatures. Most experimental studies conducted at ambient temperatures did not indicate the actual system temperature. In this study, it is found that a several degree Celsius difference in the system temperature can result in a substantial difference in the mass-transfer coefficient. The effect of the system temperature on mass transfer will be discussed in a later section. Effect of the System Pressure. The system pressure plays a major role in dictating the mass-transfer behavior mainly through its influence of the masstransfer interfacial area. The interfacial area, a, depends on the bubble size and number of bubbles in the system and can be expressed by the following equation:
a ) 6g/db
(14)
Accurate bubble-size measurements in the multiphase flow systems are difficult to obtain. Therefore, the gas holdup alone is used to provide a qualitative analysis
Figure 4. Sample logarithmic plot of concentration versus time: (a) 0.1 MPa; (b) 2.86 MPa.
Figure 5. Effects of gas velocities on the mass-transfer coefficient in the air-water system under ambient conditions.
of the pressure effect on the mass-transfer interfacial area. As shown in Figure 6, the effect of pressure on the overall gas holdup is more significant in the coalesced bubble regime than in the dispersed bubble regime. The transition velocities from the dispersed bubble regime to the coalesced bubble regime indicated in the figure are identified based on the drift-flux model.20 For gas-liquid flows, the drift flux is defined as the volumetric flux of the gas phase relative to a surface moving at the average velocity of gas-liquid systems. This flux can be expressed using the relative velocity between the gas and liquid phases as
Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004 1307
Figure 8. Effect of the system temperature on the mass-transfer coefficient in a 10.16-cm-i.d. column. Figure 6. Effect of the pressure on the overall gas holdup in a 10.16-cm-i.d. column.
Figure 7. Effect of the system pressure on the mass-transfer coefficient in a 10.16-cm-i.d. column: (a) Ul ) 0.17 cm/s; (b) Ul ) 0.26 cm/s.
(
jgl ) g(1 - g)
)
Ug Ul g l
(15)
At low gas holdups, the drift flux increases linearly with the gas holdup, indicating the presence of small, dispersed bubbles. As the gas holdup or gas velocity increases to a certain point, the drift flux increases with the gas holdup at a high rate, which indicates the existence of large coalesced bubbles. The point at which a sudden change in the drift flux against gas holdup occurs indicates the gas holdup value at transition, and
the gas velocity corresponds to the fact that the specific gas holdup is the transition velocity. The higher gas holdup at elevated pressures is partially due to the change in liquid properties. For example, as the pressure increases, the liquid viscosity increases and the surface tension decreases, leading to the formation of smaller bubbles. Higher gas density at elevated pressures also enhances bubble breakup and suppresses bubble coalescence, which further promotes the formation of smaller bubbles. The smaller bubble size is the major contributor to the increase in gas holdup in the churn-turbulent regime and, in turn, a factor in the dramatic increase in the interfacial mass-transfer area. The effect of pressure on the mass-transfer coefficient in the 10.16-cm column for the air-Paratherm system is shown in Figure 7. kla increases significantly when the pressure is increased from ambient pressure to 4.24 MPa. The pressure effect is more noticeable at high gas velocities. For example, at a gas velocity of 10 cm/s and a liquid velocity of 0.17 cm/s, when the pressure increases from 0.1 to 2.86 MPa, kla increases from 0.01 to 0.023 s-1 (a 130% increase), while at a gas velocity of 20 cm/s and the same liquid velocity, kla increases from 0.015 to 0.043 s-1 (a 187% increase). A similar pressure effect was also observed by other researchers.10,13,16 The more pronounced effect of the pressure at high gas velocities is probably due to the higher bubble breakup rate in the churn-turbulent regime than in the dispersed bubble regime. The higher gas density also enhances mass transfer, as indicated by a number of studies using different gas sources.8,16 Effect of the System Temperature. The system temperature has a considerable effect on the masstransfer coefficient by directly affecting the liquid diffusivity and thereby kl. Temperature also affects the physical properties of the liquid phase. An increase in the temperature reduces both the viscosity and surface tension of the liquid phase. A lower viscosity and smaller surface tension favors the formation of smaller bubbles. Therefore, the mass-transfer interfacial area increases with increasing temperature. In addition, because kl is inversely proportional to the liquid viscosity,4 the decrease in the viscosity would therefore increase kl. Conversely, according to Higbie, the masstransfer coefficient is inversely proportional to the square root of the contact time.21 The smaller surface tension at higher temperatures would reduce the liquid flow over the surfaces of rising gas bubbles, resulting in a reduction of the bubble rise velocity and a longer
1308 Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004
Figure 9. Effect of the system temperature on the overall gas holdup in a 10.16-cm-i.d. column.
contact time between the liquid and bubbles.22 As a result, kl would be smaller at higher temperatures because of the surface tension effect. The effects of the liquid surface tension and viscosity have competing effects on kl. From Figure 8, an increase in the system temperature increases kla significantly. The increase in the interfacial area, a, and kl is much stronger than the decrease of kl at high temperatures. To have a better understanding of the effect of the temperature on mass transfer, it is necessary to compare gas holdup at elevated temperatures as shown in Figure 9. For example, at a superficial gas velocity of 20 cm/s, kla increases from 0.03 to 0.17 s-1 (a 470% increase) when the temperature increases from 25 to 92 °C. As for the corresponding gas holdup, it only increases from 0.24 to 0.30 (a 25% increase). The rate of increase of kla is much higher than the rate of increase of gas holdup. Therefore, it can be surmised that the favorable effect of temperature on kl due to the higher liquid diffusivity may play an important role in determining the masstransfer behavior at high temperatures. Effect of the Gas and Liquid Velocities. The superficial gas and liquid velocities have a crucial influence on the operation of bubble and slurry bubble columns. The regime of operation is directly affected by the gas and liquid flow into the reactor. The effect of the liquid velocity on gas holdup is shown in Figure 10. It can be seen from the figure that, as the liquid velocity increases, the gas holdup decreases because of the higher bubble rise velocity exerted by upward liquid flow. However, the effect of the liquid velocity on the gas holdup is marginal for the range studied. Therefore, little change in the mass-transfer interfacial area can be expected. Figure 11 shows the effect of the gas and liquid velocities on the gas-liquid mass-transfer coefficient. An increase in the liquid velocity increases kla, especially at high gas velocities. Because the variation in the mass-transfer interfacial area is small at different liquid velocities, the increase in kla is mainly due to the increase in kl at higher liquid velocities. Figure 12 shows the effect of liquid velocities on kla at different pressures. The effect of the liquid velocity on kla becomes more pronounced at high pressures. For example, at 2.86 MPa, increasing the liquid velocity from 0.17 to 0.26 cm/s increases the mass-transfer coefficient by as much as 30%. The enhancement of mass transfer at higher liquid velocity is probably due to the turbulence induced by the liquid flow. Changes in kla due to gas velocity are believed to have resulted mainly from an increase in the interfacial area.
Figure 10. Effect of the liquid velocity on the overall gas holdup in a 10.16-cm-i.d. column: (a) P ) 0.1 MPa; (b) P ) 4.24 MPa.
Figure 11. Effect of gas and liquid velocities on the mass-transfer coefficient in a 10.16-cm-i.d. column.
As the gas velocity increases, the mean bubble diameter decreases. However, the bubble size decreases up to a certain point and then remains constant even if the gas velocity is increased further. Thus, the increase in the interfacial area can be explained mainly as a result of the higher gas holdup at high gas velocity. An increase in the gas velocity also enhances the turbulence induced by the gas flow, which increases kl. The increase in the interfacial area and kl at high gas velocities predominates over the decrease in the mass-transfer coefficient because of shorter gas-liquid contacting time and results in an increase in kla. Effect of the Column Size. The volumetric masstransfer coefficient has been determined in an air-
Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004 1309 Table 3. Physical Properties of Water and Paratherm at 25 °C and 0.1 MPa physical properties
water
Paratherm
density (kg/m3) viscosity (Pa‚s) surface tension (dyn/cm)
999 0.001 72
870 0.0317 29.5
Figure 12. Effect of liquid velocities and pressure on the masstransfer coefficient in a 10.16-cm-i.d. column.
Figure 15. Effect of liquid properties on the mass-transfer coefficient.
Figure 13. Effect of the column diameter on the mass transfer in an air-nitrogen-water system.
Figure 16. Effect of liquid properties on the gas holdup.
Figure 14. Effect of the column diameter on the overall gas holdup in an air-nitrogen-water system.
nitrogen-water system for both 5.08- and 10.16-cm-i.d. columns. The results are shown in Figure 13. kla values are generally lower in the 10.16-cm-i.d. column than in the 5.08-cm-i.d. column. Mass transfer strongly depends on the liquid-phase turbulence and large-scale liquid internal circulation, both of which are column size dependent. As shown in Figure 14, the gas holdup in the 5.08-cm column is higher than that in the 10.16-cm column. The difference is more prominent in the churnturbulent flow regime. The higher gas holdup in the smaller column is mainly due to wall effects on the bubble characteristics. In a small column, the bubble size is limited by the column size; therefore, a higher
gas holdup is observed in smaller columns. When the column size is larger than 0.1-0.15 m, the wall effect on gas holdup becomes negligible.23,24 Thus, the bubble size becomes independent of the column dimension and is governed by the rates of bubble coalescence and breakup. Effect of Liquid Properties. Two liquids, water and paratherm NF heat-transfer fluid, are used for the experiments. The physical properties of the two liquids at ambient pressure and temperature are shown in Table 3. Paratherm properties at high pressure and temperature can be found in work by Lin et al.17 As shown in Figure 15, kla values at ambient pressure and temperature are higher in water than in Paratherm. The gas holdup comparison in Figure 16 reveals that the water gives only slightly lower gas holdup values than Paratherm under ambient pressure and temperature. Therefore, the difference in the mass-transfer interfacial area for both liquids would be small. The difference in kla between water and Paratherm would then be solely because of the difference in kl, which is influenced by the liquid properties. Both the higher viscosity and the lower surface tension of Paratherm in relation to water contribute to the lower kla in Paratherm than observed in water.
1310 Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004 Table 4. Applicable Range of the Mass-Transfer Coefficient Correlation parameter (units)
range
parameter (units)
range
Fl (kg/m3) µl (Pa‚s) σl (N/m) Fg (kg/m3)
790-1580 0.00036-0.0383 0.0233-0.0726 0.97-33.4
Ug (m/s) Ul (m/s) Dc (m) H/Dc
0.028-0.678 0-0.00089 0.045-0.45 >5
Yoshida, Koide et al., and Wilkinson et al.10,25,26 The applicability of the correlation is shown in Table 4. Concluding Remarks
Figure 17. Correlation for the mass-transfer coefficient.
Model Correlation. An empirical correlation is developed to predict kla values for different liquids under various operating conditions:
kla ) 1.77σ-0.22e1.65Ul-65.3µlg1.2
(16)
where σ is the liquid surface tension in dyn/cm, Ul is the liquid velocity in cm/s, µl is the liquid viscosity in Pa‚s, and g is the gas holdup. The gas holdup in a slurry bubble column at elevated pressures can be calculated by using the empirical correlation developed by Luo et al.:1
( )( )
2.9
R
Ug4Fg σg
g ) 1 - g [cosh(Mo
Fg Fm
)]
Acknowledgment
β
0.054 4.1
m
(17)
where Mom is the modified Morton number for the slurry phase, (ξµl)4g/Fmσ3, and
R ) 0.21Mom0.0079
and
An oxygen desorption method is used to determine the kla of the liquid phase in bubble columns under high-pressure and high-temperature conditions. The liquid-phase oxygen concentration is measured by a high-pressure optical oxygen probe. The study covers a pressure operating range up to 4.24 MPa and temperatures up to 92 °C. The superficial gas and liquid velocities of the study are up to 40 and 0.89 cm/s, respectively. Experimental results show that kla increases with both pressure and temperature. Both gas and liquid velocities have a significant effect on the improvement of mass transfer because of higher turbulence at high-velocity conditions. Liquid properties and column dimensions also have significant effects on mass transfer. Liquid velocities have a direct influence on kl, while other factors generally change the interfacial area. An empirical correlation, which takes into consideration the experimental data obtained from this study and in the literature, is developed to estimate kla in high-pressure and moderate-temperature bubble columns.
β ) 0.096Mom-0.011 (18)
ξ is a correction factor that accounts for the effect of particles on the slurry viscosity:
ln ξ ) 4.6s{5.7s0.58 sinh[-0.71 exp(-5.8s) ln Mo0.22] + 1} (19) where Mo is the Morton number of the liquid, gµl4/Flσ3. For bubble columns, ξ goes to 1. Therefore, Mom is reduced to Mo and Fm is reduced to Fl. This correlation is obtained based on various experimental data of the gas holdup in high-pressure systems. The experimental data of the gas holdup have been given by Luo et al.,1 and the correlation can accurately predict the gas holdup at high pressures including the conditions of this study. Figure 17 shows the parity plot for the model correlation for the experimental data obtained in this study. The average error of the predictions is 16.2%. The correlation has a power of 1.2 for the gas holdup. It agrees well with the correlations developed by Akita and
This was supported in part by U.S. Department of Energy Grant DE-FC2295PC95051 and National Science Foundation Grant CTS-0207068. Notation a ) interfacial area per unit volume C ) oxygen concentration in the liquid phase C0 ) inlet oxygen concentration of the liquid phase Ccal ) oxygen concentration in the liquid phase determined by the axial dispersion model Cexp ) oxygen concentration in the liquid phase determined by experiments Ceq ) equilibrium oxygen concentration at the gas-liquid interface Ci ) oxygen concentration in the liquid phase at the start of the experiment Cmax ) oxygen concentration in the liquid phase when saturated with air Cmin ) oxygen concentration in the liquid phase when in equilibrium with nitrogen gas Cnorm ) normalized oxygen concentration Cprobe ) direct oxygen concentration reading from an optical fiber oxygen probe D ) axial dispersion coefficient Dc ) column diameter db ) average bubble diameter H ) column height kl ) gas-liquid mass-transfer coefficient P ) system pressure Q ) volumetric liquid flow rate T ) system temperature
Ind. Eng. Chem. Res., Vol. 43, No. 5, 2004 1311 t ) time U ) interstitial liquid velocity Ul ) superficial liquid velocity Ug ) superficial gas velocity V ) reactor volume g ) gas holdup s ) solids holdup Fg ) gas density Fl ) liquid density µl ) liquid viscosity Fm ) slurry density in gas-free slurry σ ) surface tension
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Received for review May 14, 2003 Revised manuscript received September 30, 2003 Accepted September 30, 2003 IE030416W
