Heat Transfer Coefficients in Mimicked Fischer-Tropsch Slurry Bubble

ARTICLE pubs.acs.org/IECR

Heat Transfer Coefficients in Mimicked Fischer-Tropsch Slurry Bubble Columns Chengtian Wu† and Muthanna Al-Dahhan*,‡ Department of Energy, Environmental & Chemical Engineering (EECE), Washington University, St. Louis, Missouri 63130, United States ABSTRACT: To provide more support for Fischer
Tropsch (FT) slurry bubble column reactor design, scale-up, and performance, the effects of operating conditions on the heat transfer coefficients were investigated in a mimicked FT cold flow system (compressed air:C9
C11:FT catalyst carrier). The studied operating conditions varied in superficial gas velocity (up to 0.3 m/s), pressure (up to 10 bar), and solids concentration (up to 25 vol %). The effects of these variables on heat transfer coefficients are discussed and analyzed. The increase in pressure tended to reduce the heat transfer coefficient, while the increase in solids loading enhanced the heat transfer coefficient, especially at high solids loading (25 vol %).

1. INTRODUCTION Among the alternative energy processes, Fischer
Tropsch (FT) synthesis for the conversion of synthesis gas (a mixture of CO and H2 produced from natural gas, coal, and/or biomass) to clean liquid fuels and chemicals has attracted significant interest from industry. In recent years, slurry bubble column reactors have become the reactors of choice for FT synthesis, because much higher productivities can be achieved in slurry bubble column reactors than in fixed bed FT reactors.1 High heat and mass transfer rates caused by the strong mixing interactions among phases are the main advantages of bubble column and slurry bubble column reactors. In addition, these reactors have many other advantages, such as low pressure drop, simple structure, easy operation, and low operating and maintenance costs. Therefore, bubble column and slurry bubble column reactors are widely employed in petrochemical, chemical, and biochemical industries, which involve oxidation, hydrogenation, chlorination, alkylation, and polymerization processes.2
4 Heat transfer rates and coefficients are among the important parameters required for proper design, operation, and understanding the performance of bubble and slurry bubble column reactors. However, the heat transfer characteristics in bubble and slurry bubble column reactors have not been fully studied or understood. In the past few decades, a number of studies have been performed on the heat transfer coefficient in bubble and slurry bubble columns.5
10 In general, the operating and design parameters of these reactors affect heat transfer coefficients through affecting related key parameters such as physical properties, gas holdup, bubble dynamics and intensity of liquid/slurry circulation.10 It has been reported that heat transfer coefficients increase as superficial gas velocity increases due to increased gas holdup, bubble size, bubble frequencies, and intensity of liquid/ slurry circulation, decrease as pressure increases due to reduction in bubble size, and enhances with the increase in solids loading due to formation of larger bubble.10,11 A tabulated summary of the available open literatures has already been addressed in our previous work,11 and the contributions of previous work were also discussed. In general, little research has been performed on r 2011 American Chemical Society

heat transfer coefficients under industrial conditions, and most of the studies have one or more of the following drawbacks: (1) using small diameter columns, (2) employing low superficial gas velocities, and (3) operating under ambient pressure. Therefore, the current available heat transfer information in open literature is not sufficient to confidently support the commercial reactor design, scale-up, and operation. Accordingly, the primary focus of this work is to advance the knowledge of the heat transfer in high pressure bubble columns and slurry bubble columns by extending the work of Wu et al.11 in which liquid hydrocarbon (C9
C11) that mimics at room temperature the physical properties of FT wax at FT conditions and FT catalyst carrier have been used. Compressed air at 8
10 bar and room temperature has been employed which mimics the density of the mixture of FT gases at FT conditions. Therefore, following the steps of Wu et al.,11 the effects of superficial gas velocity, pressure, liquid type, and catalyst content on heat transfer coefficients have been investigated experimentally using a cold-flow slurry bubble column system.

2. EXPERIMENTS The experiments were performed using a stainless steel column with an inner diameter of 0.162 m and a height of 2.5 m. Compressed air was used as the gas phase and was supplied by two compressors in parallel. As mentioned earlier, the density of air at 8
10 bar mimics the density of the mixture of FT gases at FT conditions. A C9
C11 n-paraffin mixture was selected as the liquid phase which was supplied by Sasol, South Africa, because its physical properties are close to those of the FT liquid at real reaction conditions.12,13 The composition of C9
C11 is as follows: C8 and less than C8 = 3.3%; C9 = 36.3%; C10 = 34.5%; C11 = 23.8%; greater than or equal to C12 = 1.9%. The liquid Special Issue: Nigam Issue Received: March 3, 2011 Accepted: August 2, 2011 Revised: July 26, 2011 Published: August 02, 2011 1543

dx.doi.org/10.1021/ie200431g | Ind. Eng. Chem. Res. 2012, 51, 1543–1548

Industrial & Engineering Chemistry Research

ARTICLE

mixture will be referred to as C9C11, and the physical properties are listed in Table 1 (Sasol, South Africa). FT catalyst carrier supplied by ConocoPhillips was chosen to be the solids phase. FT catalyst carrier is a suitable choice to mimic FT catalyst, because it has similar properties (size, density, heat capacity, thermal conductivity, and porosity) as the real catalyst but does not have the health concerns caused by the active metals. The porous FT catalyst carrier is an alumina-based skeleton with a mean size of about 75 μm will be mentioned as FT catalyst in the following sections. The compressed air passed through filters, a pressure regulator, and a rotameter system, which consisted of 4 rotameters of increasing range connected in parallel to adjust gas flow rate. The superficial gas velocity varied from 0.03 to 0.30 m/s in this study covering bubbly, transition, and churn-turbulent flow regimes. At room temperature, air was introduced at the bottom of the column through a perforated plate gas distributor with 163 holes (diameter = 1.32 mm) and an open area of 1.09%. During the experiments, the averaged dynamic liquid height was maintained at 1.80 m for all studied conditions by adjusting the amount of liquid and solids loaded in the column. In this way, the relative position of the probe could be kept the same, and a fair comparison of the effects of operating parameters could be achieved. The investigated pressure was up to 10 bar, and the selected solids loading were at 0, 9.1, and 25 vol %. A probe containing three thermocouples was used to measure the bulk temperature of the media in the column. The heat transfer probe of rod type was manufactured at Washington University and was a modified version of the probe proposed by Li and Prakash.9 More details about the setup and the resolution of the probe are available in the previous work of Wu et al.11,14 To investigate heat transfer coefficients in the fully developed zone, the rod type heat transfer probe was installed vertically to mimic the surface contact with the media to that encountered in heat exchanging tubes. The measurements were performed at an axial height (from the sparger to the heat flux sensor) to column diameter ratio (Z/D) equal to 5.1. The measured signals of the heat flux are in the range of microvolts, which are amplified before reaching the data acquisition (DAQ) system. The amplified heat flux signals and the signals from thermocouples were sampled at 50 Hz for more than 40 s. Therefore, the local instantaneous and averaged heat transfer coefficient can be estimated as follows. qi ð1Þ hi ¼ Tsi
Tbi have ¼

1 n qi n i ¼ 1 Tsi
Tbi

∑

ð2Þ

where hi is the instantaneous local heat transfer coefficient, qi is the heat flux through the sensor, Tbi is the instantaneous bulk temperature of the media, Tsi is the instantaneous surface temperature of the sensor, have is the time averaged heat transfer coefficient, and n is the total number of the samples. Since the solids are fine particles (75 μm), they form a pseudohomogeneous slurry. Hence, they follow the movement of the liquid phase. Thus, the probe would detect the effect of solids by realizing the slurry as a pseudoliquid with the physical properties equivalent to the apparent physical properties of the slurry.

3. RESULTS AND DISCUSSION The effects of operating parameters and the radial positions of the probe on the heat transfer coefficients are investigated. When

Table 1. Physical Properties of the Studied Liquids and Solid C9C11 (Sasol, parameters

South Africa)

catalyst carrier water (ConocoPhillips)

pressure, MPa

0.1

0.1

0.1

temperature, °C

25

25

25

density, kg/m3

728

998

1200

viscosity, Pa 3 s

0.00085

0.00099

surface tension, N/m

0.0232

0.072

thermal conductivity, W/m 3 K

0.135

0.597

5.38

heat capacity, J/kg 3 K

2197

4182

880

appropriate, the results of this work are also compared with those obtained in previous study of Wu, et al.,11 which was performed using the same setup but with an air
water system. To avoid replication, the results of Wu et al.11 are not reported again here. The measurements are reproducible with standard deviation of the repeated measurements varies within or less than 0.036
0.41 kW/ m2 3 K. For clarify of the figures, the error bars are not plotted on the data points. Also, broken lines are plotted to just demonstrate the expected trend. 3.1. Effect of Superficial Gas Velocity. Figure 1 shows the effect of superficial gas velocity on the time averaged heat transfer coefficients under both pressures (1 and 10 bar) and for the studied solids loading (0, 9.1, and 25 vol %). The addition of solids increases the apparent viscosity of the slurry which causes an increase in large bubble population that enhances turbulence. Hence heat transfer coefficients increase as discussed below. However, for all studied conditions in this work the, standard deviations of the shown data points are less than 0.036 kW/m2 3 K. The trend of the results is similar to those found earlier in the air
water system. The heat transfer coefficients in both the center and wall regions of the column initially increased with the superficial gas velocity, and then the increase rate slowed down at higher range of gas velocity. This is because at higher superficial gas velocity, large bubbles are formed which do not noticeably affect the energy transfer of the microscale levels where the heat transfer rate is controlled according to isotropic theory, and therefore, the heat transfer coefficients level off at high superficial gas velocity and as the velocity further increases.10 However, the heat transfer coefficients in the air
C9C11 system are much smaller than those obtained by Wu et al.11 in an air
water system. This is due to an overall effect of the liquid physical properties, bubble dynamics, and hydrodynamics, considering the same operating conditions. The higher thermal conductivity of water favors the heat transfer, which is an important reason for such larger heat transfer coefficients in the air
water system. Liquid surface tension and viscosity are closely related to bubble dynamics and hydrodynamics in gas
liquid system. Compared with water, the low surface tension and viscosity of C9C11 (Table 1) form smaller bubbles at the same conditions. Kumar et al.15 studied the effect of a single bubble, passing by the probe, on the local heat transfer coefficient, and found that a large bubble could cause a relatively larger heat transfer coefficient. After a movement of a bubble, the liquid that was around the bubble fills up the vacancy. Therefore, the larger the bubble, the stronger the turbulence causes in the bubble wake area. The strong turbulence reduces the thickness of the thermal boundary layer, which increases the heat transfer coefficient. Yang et al.10 used the mechanistic model developed by Wasan and Ahluwalia16 to analyze their heat transfer data obtain in high pressure and high temperature bubble/slurry 1544

dx.doi.org/10.1021/ie200431g |Ind. Eng. Chem. Res. 2012, 51, 1543–1548

Industrial & Engineering Chemistry Research

Figure 1. Effect of superficial gas velocity on the heat transfer coefficients: (a) no solids, 1 bar; (b) no solids, 10 bar; (c) solids loading at 9.1 vol %, 10 bar; and (d) solids loading at 25 vol %, 10 bar. Dashed lines represent the expected trend.

bubble column. The model is based on a consecutive film and surface renewal where a thin liquid/slurry film surrounds the heating surface and liquid/slurry elements are in contact with the outer surface of the film for short contact time due to the bubble motion and/or liquid/slurry turbulence. The liquid/slurry elements are replaced by fresh elements from the bulk fluid. The heat is transferred from the heating surface to the bulk via steady state conduction in the film and unsteady state conduction in the fluid elements. Accordingly, any of the following leads to higher heat transfer coefficients: shorter contact time obtained by larger bubbles; fast moving bubbles; high bubble frequency; intensity of circulation and turbulence; and a thinner film obtained as a result of physical properties (e.g., viscosity), bubble velocity, high bubble frequency, and turbulence intensity. Yang et al.10 demonstrated the ability of such a mechanistic approach in describing the effects of superficial gas velocity, pressure, and addition of solids to the liquid on the heat transfer coefficients in bubble/ slurry bubble columns. In an air
C9C11 system, the apparent bubble frequency is higher but the average bubble size is small.14 The effects of bubble frequency and bubble size on heat transfer coefficients counteract with each other. Hence, other parameters have to be considered to realize which one is stronger. Furthermore, it is claimed that axial liquid circulating velocity and turbulent kinetic energy are higher in the air
water system,13 which implies the potential thinner thermal boundary layer near the probe and higher heat transfer in air
water system. In both two-phase and three-phase systems, the heat transfer coefficients in the center are larger than those near the wall under the investigated pressures. It is worthwhile to mention that the differences at low superficial gas velocities are relatively small (3
5%), but at high superficial gas velocity, the differences become larger, reaching 8
11%. These effects can be explained

ARTICLE

by the variation in the hydrodynamics and bubble dynamics obtained at these conditions.17,18 At low superficial gas velocities, the bubbles with relatively small diameters are uniformly distributed across the column cross-section and slowly move along the column axis. With an increase in superficial gas velocity, large bubbles are formed, and most of them rise through the core region of the column at high frequency. The rapid bubble acceleration and the increased bubble velocity result in an increase in surface renewal and a decrease in the film thickness at the probe surface, which can significantly increase the heat transfer coefficient. On the other hand, small bubbles are still the main population in the wall region, where the direction of the liquid/slurry flow obtained by the radioactive particle tracking technique is downward.19,20 The rise of these small bubbles in this region is disturbed by the downward moving phase, and some of the bubbles may be carried by the liquid/slurry into downward movements. On average, these small bubbles in the wall region move at lower velocities than the bubbles in the center. Therefore, the abovementioned reasons cause the changes of the difference in heat transfer coefficients between the center and wall regions at increased superficial gas velocity. 3.2. Effect of Pressure. Figure 2 shows the effect of pressure on the heat transfer coefficients in the center of the column, and the standard deviations are less than 0.036 kW/m2 3 K. In general, decreases in heat transfer coefficients are observed with an elevated pressure. The decreases of the heat transfer coefficients at low superficial gas velocities (which are about 12
14% at low solids loading (no solid and 9.1 vol %) and 7% at high solids loading (25 vol %)) are larger than those at high superficial gas velocities, which are less than 2% at all solids loadings. As mentioned earlier,10,11 the overall decreasing trend of the heat transfer coefficient with increasing pressure is mainly due to the decrease of bubble size. Even though the average bubble size at high pressure is still smaller than that under atmospheric pressure, these small bubbles move much faster because of higher energy input at the inlet20,21 causing enhanced liquid/ slurry circulation.19,20 These bubbles provide larger driving forces for the liquid circulation, which decreases the thickness of the contact film between the probe and the bulk. As a result, the heat transfer coefficients increase to some extent and hence erase some of the effect of bubble size reduction. Hence, the differences, caused by elevated pressure, in the heat transfer coefficient at high superficial gas velocities are smaller than those at low superficial gas velocities. 3.3. Effect of Solids Loading. The effect of solids loading on the heat transfer coefficient under atmospheric pressure and high pressure (10 bar) is shown in Figure 3. When the solids loading rise from no solids to 9.1 vol %, the changes in heat transfer coefficients due to the addition of catalysts are slight under both atmospheric and high pressures and within about 2% on an average. However, with a further increase in solids loading to 25 vol %, the heat transfer coefficients increase noticeably. The increases range from 7% to 18%, and the large changes are obtained at low superficial gas velocities. In earlier studies, Deckwer et al.,7 Saxena et al.,22 and Yang et al.10 also reported increases in heat transfer coefficients with increasing solids loading. In all three studies, organic liquids were employed as the liquid phase. Deckwer et al.7 assumed that the increase was due to the independent motion of the particles, which lead to an increase in exchanging frequency of fluid elements at the heat surface area. Saxena et al.22 and Yang et al.10 thought the increase was mainly caused by the change 1545

dx.doi.org/10.1021/ie200431g |Ind. Eng. Chem. Res. 2012, 51, 1543–1548

Industrial & Engineering Chemistry Research

ARTICLE

Figure 2. Effect of pressure on the heat transfer coefficients in the column center at Ug = 0.30 m/s: (a) no solids; (b) solids loading at 9.1 vol %; and (c) solids loading at 25 vol %. Dashed lines represent the expected trend.

Figure 3. Effect of solids loading on the heat transfer coefficients in the center at Ug = 0.30 m/s: (a) 1 bar, center; (b) 10 bar, center; (c) 1 bar, wall; and (d) 10 bar, wall. Dashed lines represent the expected trend.

in viscosity of the suspension due to the addition of solids. However, Li and Prakash9 reported a decreased heat transfer coefficient with an increased slurry concentration, using water as the liquid phase. They claimed that the addition of solids damped the turbulence intensity in the bubble wake and, thus, further decreased heat transfer coefficient. It is noteworthy that Kantarci et al.23 observed an enhanced heat transfer coefficient with the addition of solids, applying the same probe developed by Li and Prakash.9 To evaluate the effect of solids, the apparent viscosity of the slurry system in this study is estimated based on the correlation proposed by Vand,24 μsl = μl exp[2.5ϕs/(1
0.609ϕs)], and the results are shown in Table 2. Here, μsl is the viscosity of the solid
liquid phase, μl is the viscosity of the liquid, and ϕs is the volume based solids loading. Compared with the viscosity of the pure liquid phase, the apparent viscosity of the slurry phase increases 22% at low solids loading (9.1 vol %) and increases significantly (111%) at high solids loading (25 vol %). Hence, the heat transfer behavior of the slurry system at low solids loading (9.1 vol %) is more likely to be close to that in a gas
liquid system. It is noteworthy that such analysis does not apply on the comparison between the heat transfer coefficients obtained in air
water system and those obtained in air
C9C11 where the change in viscosity is less than 22%. In such a case, the surface tension of C9C11 is much smaller than that of water (Table 1) where its effect is more dominant than the difference in viscosity causing smaller bubble size to form in C9C11. Therefore, the heat transfer coefficients in air
C9 C11 are smaller than those in air
water as discussed earlier where it has been reported that it is the overall effect of liquid/ slurry physical properties, bubble dynamics, and hydrodynamics that determines the magnitude change in heat transfer coefficients.

Table 2. Estimated Apparent Viscosity of the Slurry Suspension solids loading (vol %)

0

9.1

25

viscosity (Pa 3 s)

0.0009

0.0011

0.0019

Hence, at high solids loading (25 vol %), the heat transfer behaves differently than that in a gas
liquid system. The increase in the apparent viscosity of the slurry increases the bubble size.25 The bubble size changes are much obvious at high solids loading, especially at low superficial gas velocities.18 When the enhanced turbulence in the bubble wake appears close to the heat flux probe,15 the thickness of the liquid/slurry heat transfer film at the probe surface can be reduced dramatically, and hence, the measured heat transfer coefficient will increase sharply. Under our studied conditions, the addition of solids may damp the mixing in the bubble wake, but the effect is relatively small compared to the enhancement caused by the bubble size increase. Hence, the heat transfer coefficients at high solids loading in a slurry bubble column are higher than those in a two-phase system and those at low solids loading in a slurry system. 3.4. Radial Profile of the Heat Transfer Coefficient. Figure 4 shows the radial profiles of heat transfer coefficients in the studied system at several different operating conditions. The standard deviations at high solids loading (25 vol.%) are relatively larger than those at low solids loading (no solid and 9.1 vol. %). However, the standard deviation values are all still less than 0.41 kW/m2 3 K. The radial profiles of the heat transfer coefficients with no solids at low superficial gas velocities are more flat than those at high superficial gas velocities under both pressures. At the same superficial gas velocity, the radial profiles of the heat transfer coefficients with no solids become flatter with increasing 1546

dx.doi.org/10.1021/ie200431g |Ind. Eng. Chem. Res. 2012, 51, 1543–1548

Industrial & Engineering Chemistry Research

ARTICLE

Figure 5. Effect of solids loading on the heat transfer coefficient profile Ug = 0.30 m/s: (a), 1 bar and (b) 10 bar. Dashed lines represent the expected trend.

Figure 4. Effect of solids loading on heat transfer coefficients: (a) no solids and (b) solids loading at 25 vol %. Dashed lines represent the expected trend.

pressure (Figure 4a). As mentioned earlier, these phenomena are due to more uniformly distributed small bubbles and hence more uniformly distributed gas holdup across the column cross-section at low superficial gas velocity and/or at high pressure compared to that at high superficial gas velocity and/or at low pressure. However, with solids loading of 25 vol % and due to the formation of large bubbles which these usually favor the central region of the cross-section of the column, as discussed earlier, the radial profiles of high pressure seem less steep than those at low pressure (Figure 4b). This is because at higher pressure the bubbles distribution gets narrower but yet gas holdup radial profiles is not flatter as in the case within no solids. This is obvious in Figure 5 which shows the effect of solids loading on the heat transfer coefficient radial profile at Ug = 0.30 m/s under both pressure (1 bar and 10 bar). The trend of the profiles in a two phase system and that in a slurry system with low solids loading (9.1 vol %) are close. With a further increase in the solids loading (25 vol %), the increases in heat transfer coefficients are noticeable and the radial profiles become relatively steeper compared to low and/or no solids loading due to an enhanced large bubble population favoring the central region of the column and causing higher gas holdup in the center. This is because the apparent viscosity of the solid
liquid phase increases with the addition of fine catalysts as discussed earlier.

4. REMARKS The heat transfer coefficient has been studied under conditions that mimic FT reaction conditions in a high-pressure slurry bubble column. Air, C9C11, and FT catalyst carrier were employed as the gas, liquid, and solids phase, respectively. The effects of superficial gas velocity, pressure, and solids loading on

the heat transfer coefficients and the related radial profiles were investigated. The findings are summarized as follows: • The heat transfer coefficient increases with superficial gas velocity, although at higher velocities the rate of increasing slows. • When the operating conditions are maintained unchanged, the heat transfer coefficient in the center of the column is larger than those near the wall region, and the differences at low superficial gas velocities are smaller than those at high superficial gas velocities. • With an increase in pressure, the heat transfer coefficient decreases, although the differences at low superficial gas velocities are larger than those at high superficial gas velocities. • At low solids loading, the heat transfer in the slurry bubble column behaves like that in a two-phase system. However, with further increases in solids loading, an obvious increase of heat transfer coefficients has been observed. • The radial profile of heat transfer coefficients becomes flat with increasing pressure and relatively steeper with increasing solids loading. In actual FT operation, a large amount of internal coils or vertical tubes were applied to remove the heat generated by the reactions. Therefore, in the future, more efforts are encouraged to study the heat transfer coefficients in columns with heat exchanging internals.

’ AUTHOR INFORMATION Corresponding Author

*Mailing address: 143 Schrenk Hall, Missouri University of Science and Technology, Rolla, MO 65409-1230. Phone: (573) 341-7518. Fax: (573)341-4377. E-mail: [email protected]. Present Addresses †

ConocoPhillips Company, Ponca City Technology Center, OK 74604. ‡ Department of Chemical & Biological Engineering, Missouri University of Science and Technology, Rolla, MO 65409.

’ ACKNOWLEDGMENT This project was supported by the clean alternative energy using high pressure slurry bubble column consortium sponsored by ConocoPhillips (USA), Eni (Italy), Sasol (South Africa), and Statoil (Norway). Also, the authors acknowledge the effort of Rahman Abdulmohsin in finalizing this manuscript. 1547

dx.doi.org/10.1021/ie200431g |Ind. Eng. Chem. Res. 2012, 51, 1543–1548

Industrial & Engineering Chemistry Research

ARTICLE

’ REFERENCES (1) Krishna, R.; Sie, S. T. Selection, Design and Scale-Up aspects of Fischer
Tropsch reactors. Fuel Process. Technol. 2000, 64, 73–105. (2) Deckwer, W.-D.; Alper, E. Katalytische suspensions reacktoren. Chem. Eng. Technol. 1980, 52, 219–228. (3) Fan, L.-S. Gas-liquid-solid fluidization engineering; Butterworths Series in Chemical Engineering: Boston, MA, 1989. (4) Dudukovic, M. P.; Larachi, F.; Mills, P. L. Multiphase reactors
revised. Chem. Eng. Sci. 1999, 54, 1975–1995. (5) Fair, J. R.; Lambright, A. J.; Anderson, J. W. Heat transfer and gas holdup in a sparged contactor. Ind. Eng. Chem. Process Des. Dev. 1962, 1, 33–36. (6) Hart, W. F. Heat transfer in bubble-agitated systems. A general correlation. Ind. Eng. Chem. Res. 1976, 15, 109–114. (7) Deckwer, W.-D.; Louisi, Y.; Zaidi, A.; Ralek, M. Hydrodynamic properties of the Fischer
Tropsch slurry process. Ind. Eng. Chem. Res. 1980, 19, 699–708. (8) Saxena, S. C. Heat transfer from a cylindrical probe immersed in a bubble column. Chem. Eng. J. 1989, 41, 25–39. (9) Li, H.; Prakash, A. Heat transfer and hydrodynamics in a three-phase slurry bubble column. Ind. Eng. Chem. Res. 1997, 36, 4688–4694. (10) Yang, G. Q.; Luo, X.; Lau, R.; Fan, L.-S. Heat transfer characteristics in slurry bubble columns at elevated pressures and temperatures. Ind. Eng. Chem. Res. 2000, 39, 2568–2577. (11) Wu, C.; Al-Dahhan, M.; Prakash, A. Heat transfer coefficients in a high-pressure bubble column. Chem. Eng. Sci. 2007, 62 (1
2), 140–147. (12) Shaikh, A. Mixing and flow behavior in slurry bubble column reactors. D.Sc. dissertation, Washington University in Saint Louis, MO, 2007. (13) Han, L. Hydrodynamics, back-mixing, and mass transfer in a slurry bubble column reactor for Fischer
Tropsch alternative fuels. D. Sc. dissertation, Washington University in St. Louis, MO, 2007. (14) Wu, C. Heat Transfer and Bubble Dynamics in Slurry Bubble Columns for Fischer
Tropsch Clean Alternative Energy. D. Sc. dissertation, Washington University in St. Louis, MO, 2007. (15) Kumar, S.; Kusakabe, K.; Raghunathan, K.; Fan, L.-S. Mechanism of heat transfer in bubbly liquid and liquid-solid systems: single bubble injection. AIChE J. 1992, 38, 733–741. (16) Wasan, D.; Ahluwalia, M. Consecutive film and surface renewal mechanism for heat or mass transfer from a wall. Chem. Eng. Sci. 1969, 24, 1535–1542. (17) Xue, J.; Al-Dahhan, M.; Dudukovic, M. P.; Mudde, R. F. Bubble velocity, size, and interfacial area measurements in a bubble column by four-point optical probe. AIChE J. 2008, 54 (2), 350–363. (18) Wu, C.; Suddard, K.; Al-Dahhan, M. Bubble dynamics investigation in a slurry bubble column. AIChE J. 2008, 54 (4), 1203–1212. (19) Ong, B. C. Experimental Investigation of Bubble Column Hydrodynamics: Effect of Elevated Pressure and Superficial Gas Velocity. D. Sc. dissertation, Washington University in Saint Louis, MO, 2003. (20) Rados, N. Slurry bubble column hydrodynamics: experimentation and modeling. D. Sc. dissertation, Washington University in Saint Louis, MO, 2003. (21) Xue, J. Bubble velocity, size and interfacial area measurements in bubble columns. D. Sc. dissertation, Washington University in Saint Louis, MO, 2004. (22) Saxena, S. C.; Rao, N. S.; Yousuf, M. Heat-transfer and hydrodynamic investigations conducted in a bubble column with powders of small particles and viscous liquid. Chem. Eng. J. 1991, 47, 91–103. (23) Kantarci, N.; Ulgen, K. O.; Borak, F. A study on hydrodynamics and heat transfer in a bubble column reactor with yeast and bacterial cell suspensions. Can. J. Chem. Eng. 2005, 83, 764–773. (24) Vand, V. Viscosity of solutions and suspensions. J. Phys. Colloid Chem. 1948, 52 (2), 277–299. (25) Luo, X.; Lee, D. J.; Lau, R.; Yang, G. Q.; Fan, L. -S. Maximum stable bubble size and gas hold up in high-pressure slurry bubble column. AIChE J. 1999, 45, 665–680.

1548

dx.doi.org/10.1021/ie200431g |Ind. Eng. Chem. Res. 2012, 51, 1543–1548