Ind. Eng. Chem. Res. 2007, 46, 3153-3156
3153
Particle Fluidization with Supercritical Carbon Dioxide: Experiments and Theory Fenghui Niu and Bala Subramaniam* Center for EnVironmentally Beneficial Catalysis, Department of Chemical & Petroleum Engineering, UniVersity of Kansas, Lawrence, Kansas 66045
Glass and Amberlite particles ranging in size from 0.18 to 1.0 mm were fluidized by supercritical CO2. For a given material in a narrow size range, the volume of the random packing increases exponentially with CO2 mass flow rate. In the supercritical region investigated (35-55 °C, 83-124 bar), the bed expansion has relatively weak temperature and pressure dependences due to the counteracting effects of the density and viscosity variations of supercritical CO2. Consistent with conventional particle fluidization correlations, the minimum fluidization velocity (umf) values obtained experimentally depend only on the packing material, size, and fluidization conditions (pressure and temperature). A plot (log u vs log ε) of the Richardson-Zaki correlation is nearly linear with the value of the exponent (∼2.6) being in the range of values reported for spherical particles. The umf values and terminal velocity (ut) predicted with conventional correlations bracket those obtained from experiments, confirming that such correlations may be used for designing CO2-based fluidization processes. Introduction The pressure-tunable density and transport properties of compressed carbon dioxide (Pc ) 73.8 bar; Tc ) 31.1 °C), in either its liquid state or its supercritical state, have been exploited in unit operations such as extraction, chromatography, crystallization, and reactions as summarized elsewhere.1-5 The liquidlike densities and heat capacities along with the gaslike transport properties make supercritical fluids attractive media for fluidization applications.6-9 In recent years, compressed CO2 has been investigated as a medium for fluidizing and coating particles used in pharmaceutical applications.10-14 Poletto et al.7 and Marzocchella et al.8 studied the fluidization of spherical particles in the 0.095-0.45 mm diameter range with CO2 at pressures from ambient to near-critical pressures (up to 80 bar). They showed that the bed expansion followed the R-Z equation and reported n values ranging from 2.4 to 4.6. To rationally develop and design CO2-based fluidized bed processes, correlations are needed that predict bed minimum fluidization and terminal velocities under supercritical conditions as a function of the operating parameters. Specifically, the following question of practical significance has not been fully addressed in earlier work: Are conventional correlations reliable for predicting the minimum fluidization and terminal velocities at supercritical conditions? The experimental data reported in the previous literature are not adequate (actually not designed) to clearly address this question. This paper presents experimental investigations aimed at investigating whether conventional correlations for minimum fluidization velocities are valid when fluidizing particles with supercritical CO2, which possess a combination of gaslike and liquidlike properties. Fluidization experiments with dense phase CO2 (ranging from 69 to 124 bar and 35-55 °C) were performed with different types of substrates (glass and Amberlite beads) ranging in diameter from 0.18 to 1.0 mm. Thus, our study explores a wider range of supercritical pressures compared to the previous studies.7,8 A fixed bed of these substrates was loaded in a Jerguson gage and fluidized with dense CO2. The movement of the particles and extent of bed expansion were observed. The effects of * To whom correspondence should be addressed. Tel.: 785-8642903. Fax: 785-864-6051.
[email protected].
parameters such as temperature, pressure, flow rate, particle density, and particle size on bed expansion were investigated. The minimum fluidization velocity (umf) was experimentally determined in each case and compared with predictions made using conventional fluidization correlations. Similarly, the terminal velocity (ut) obtained from the intercept of the R-Z plot and the slope (n) of the R-Z plot, an important empirical parameter, are compared with literature values.7 All of these comparisons are in close agreement. Experimental Section A schematic of the experimental unit for fluidization studies is shown in Figure 1. Glass tubes (i.d. ranging from 4.95 to 11.0 mm) with porous metal mesh to retain the particles were used as fluidization columns. The height of the randomly packed particles inside these columns ranged from 18 to 36 mm. For a given experiment, one of the glass tubes was placed vertically inside the Jerguson gage such that the CO2 flows through the porous frit and the column of particles. A linear scale (0.5 mm accuracy) on the window of the Jerguson gage allowed measurement of the bed height. An ISCO (model 260D) syringe pump was used to pump CO2 as a liquid. The pressures at the pump inlet and in the cell were monitored with Validyne transducers. The CO2 mass flow rate was calculated based on the CO2 density estimated using the correlation available at webbook.nist.gov (available free of charge). CO2 was preheated by flowing through a 6 ft long, 1/16 in. OD copper coil and then led to the Jerguson gage. Both the coil as well as the Jerguson gage were placed in a constant temperature water bath whose temperature was controlled from ambient to 60 °C. The pressure in the Jerguson gage (and therefore in the fluidized bed) was controlled by a metering valve regulated by a computer-controlled, stepper-motor assembly. The metering valve and the lines downstream were heated to prevent CO2 freezing upon expansion. For a typical fluidization experiment using glass beads, the initial bed height was set at approximately 18 mm. Dense CO2 was pumped through the particle bed at several different flow rates (from 5.4 to 84.3 g/min). The height of the expanded bed was recorded at each CO2 flow rate. The flow rate corresponding to the initial fluidization of particles
10.1021/ie0606789 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/14/2006
3154
Ind. Eng. Chem. Res., Vol. 46, No. 10, 2007
Figure 1. Schematic of experimental setup.
(i.e., the minimum fluidization velocity) was obtained by extrapolating the bed expansion curve to the zero bed expansion.
Figure 2. Effect of CO2 mass flow rate on the expansion of randomly packed glass beads (0.18-0.25 mm) at 103 bar (i.d. of the glass tube ) 4.95 mm). Trend line is shown.
Theory The minimum fluidization velocity was predicted using the following empirical correlations.15-17 For small particles
umf )
dp2(Fp - FL) g, valid for Rep () dpumfFL/µ) < 20 1650µ
(1)
For large particles
umf2 )
dp(Fp - FL) g, valid for Rep > 1000 24.5FL
(2) Figure 3. Effect of CO2 flow rates on the expansion of randomly packed Amberlite IRA-96 (0.29-1.0 mm) particles at various cell temperatures (i.d. of glass tube ) 8.0 mm; cell pressure ) 103 bar). Trend lines connect experimental data.
For 20 e Rep e 1000, the following equation was used
umf ) 0.0093
dp1.82(Fp - FL)0.94 µ0.88FL0.06
(3)
The terminal velocity was estimated from the following equations15
[
]
(Fp - FL)2g2 1/3 dp, ut ) (4/225) F Lµ valid in the following domain: 0.4 < Rep < 500 (4)
[
]
3.1dp(Fp - FL)g , FL valid in the following domain: 500 < Rep < 200 000 (5)
ut )
1/2
The density and viscosity of supercritical CO2 at the cell pressure and temperature were obtained from correlations available at webbook.nist.gov (free of charge). The Richardson and Zaki18 correlation is given by
u ) n ut
(6)
where u, ut, and ε represent the superficial velocity of the fluidizing medium, terminal velocity, and bed voidage, respectively. In general, the exponent n is a function of Reynolds’ number and the ratio of the particle to tube diameter (dp/D). For 1< Rep >200, the following empirical correlation is valid
(
n ) 4.45 + 18
)
dp Rep-0.1 D
(7)
For Rep > 500, n is independent of both dp/D and Rep with a value of approximately 2.4. The bed voidage at a given fluidized state is obtained from the volume of the fluidized bed and of the solid particles19
)
VT - VP ) 1 - HP/HT VT
(8)
The HT of the solid particles is obtained from experiments, while the volume of the solid particles (and thus HP) is obtained using eq 6 from the bed voidage corresponding to minimum fluidization. Results and Discussion Influence of CO2 Mass Flow Rate and Cell Temperature. Figure 2 shows the expansion of glass beads (diameter in the 0.18-0.25 mm range) with CO2 mass flow rate at a cell pressure of 103 bar and various cell temperatures. The repeated 35 °C data are from experiments performed using different pump temperatures. The bed expands exponentially with CO2 mass flow rate. Because the mass flow rate is independent of pump temperature, the scatter around the trend line reflects the range of experimental error. From Figure 2 it can be seen that the cell temperature has almost no effect on bed expansion in the 35-45 °C range. Figure 3 shows the effect of CO2 flow rate on the expansion of Amberlite IRA-96 (0.29-1.0 mm) particles at a cell pressure of 103 bar and at different cell temperatures. Again, the bed expands exponentially with increasing CO2 mass flow rates. The
Ind. Eng. Chem. Res., Vol. 46, No. 10, 2007 3155
Figure 4. Effect of cell pressure on the expansion of randomly packed glass beads (0.42-0.59 mm) at various CO2 mass flow rates and 35 °C (i.d. of glass tube ) 8.0 mm). Trend lines connect experimental data.
cell temperature has a relatively minor effect, with bed expansion being slightly lower at higher cell temperatures. The rather weak temperature dependence seen in Figures 2 and 3 is attributed to the opposing effects of density and viscosity on bed expansion. The CO2 density decreases significantly with temperature (0.72 g/mL at 35 °C, 0.54 g/mL at 45 °C, and 0.35 g/mL at 55 °C at 103 bar). The lower densities at higher temperatures result in increased linear fluidization velocities that favor bed expansion. Similarly, the CO2 viscosity also decreases significantly with temperature at 103 bar (591.2 µp at 35 °C, 393.8 µp at 45 °C, and 266.4 µp at 55 °C). The lower viscosities at higher temperatures hinder bed expansion, thereby countering the density effect and yielding relatively weak temperature dependence. Influence of Cell Pressure. Figure 4 demonstrates that randomly packed glass beads (diameter in the 0.42-0.59 mm range) expand approximately linearly with CO2 mass flow rates at a fixed cell temperature (35 °C) and various cell pressures. While the cell pressure has no significant effect on bed expansion at supercritical pressures (83-124 bar), the bed is more easily expanded in the near critical region (69 bar). At 35 °C, the CO2 density increases nearly 3-fold in the 6983 bar range and only about 35% in the 83-124 bar range (0.21 g/mL at 69 bar, 0.57 g/mL at 83 bar, 0.72 g/mL at 103 bar, and 0.77 g/mL at 124 bar, all at 35 °C). Lower CO2 densities result in higher linear fluidization velocities that favor bed expansion. However, the CO2 viscosity also increases significantly with pressure (195.1 µp at 69 bar, 421.3 µp at 83 bar, 591.2 µp at 103 bar, and 667.6 µp at 124 bar, all at 35 °C). The lower viscosities hinder bed expansion, thereby counteracting the density effects and mitigating bed expansion. Influence of Particle Size and Material. As can be inferred from Figure 5, the expansion of glass beads depends strongly on the particle size. As expected, smaller beads are more easily expanded than larger beads of the same material. The exponential variation of bed expansion with the CO2 mass flow rate, observed subtly with the larger beads, is seen more clearly with the smaller beads over a wider expansion range. For similar sizes, the lower density material (Amberlite with Fa ) 1.04 g/mL) is more easily expanded than the higher density material (glass with Fg ) 2.46 g/mL). R-Z Plot. On the basis of the Richardson and Zaki correlation (eq 6), a logarithmic plot of the superficial velocity and the bed voidage should be linear if the exponent n is constant. As shown in Figure 6, the R-Z plot corresponding to fluidization of spherical beads (0.18-0.25 mm diameter range) at supercritical conditions (T ) 35 °C; P ) 103 bar) in a 4.95 mm i.d. tube is linear. The terminal velocity (10.8 cm/s)
Figure 5. Fluidization of randomly packed particles of various materials by CO2 at 103 bar and 35 °C (i.d. of glass tube ) 8.0 mm). Trend lines connect experimental data.
Figure 6. Richardson-Zaki plot for fluidization experiments at 103 bar and 35°C (i.d. of glass tube ) 4.95 mm; 0.18-0.25 mm glass beads).
estimated from the plot is in close agreement with the value (10.5 cm/s) predicted using eq 4. The n value (2.56) obtained from the slope of Figure 6 is also in the range reported previously.7 Comparison of the Experimental Minimum Fluidization Velocities with Predicted Values. On the basis of the experimental data represented in Figures 2-5, the minimum fluidization velocities were estimated for various combinations of operating variables such as particle size, packing material, CO2 mass flow rate, inner tube dimensions, cell pressure, and cell temperature. The visual observation of incipient fluidization is subject to uncertainties. Hence, the “experimental” umf values were estimated from the CO2 mass flow rate corresponding to the intersection of the extrapolated expansion curves and the abscissa. Reliable estimates are possible following this procedure because the bed expansion curves following incipient fluidization tend to be linear for smaller values (typically up to at least 10%). Table 1 compares the experimental umf values with those predicted using the correlations in eqs 1-3. The experimental umf values in Table 1 represent average values for particles in the noted size ranges. Consistent with the correlations, the experimental umf values are nearly constant for a given particle material, size, and fluidization conditions (pressure and temperature). As inferred from Table 1, the predicted umf values for particles in a given size range bracket those obtained experimentally, suggesting that conventional correlations are also valid for fluidization with compressed CO2 and may indeed be used to reliably predict umf values. To verify whether terminal velocities may also be predicted by conventional correlations, the 0.18-0.25 mm glass beads were fluidized at higher CO2 flow rates at the following conditions: glass tube i.d. ) 4.95 mm; cell temperature ) 35
3156
Ind. Eng. Chem. Res., Vol. 46, No. 10, 2007
Table 1. Comparison of Experimental Fluidization Velocities with Predicted Valuesa size range of glass beads, mm
i.d. of inner glass tube, mm
experimental umf, cm/s
predicted umf, cm/s
0.18-0.25
4.95 8.0 10.1 11.0 4.95 5.16 6.92 8.0 10.1 6.92 8.0
0.61 0.76 0.64 0.56 1.66 1.61 1.75 1.82 1.63 1.98 2.11
0.53-0.79
0.42-0.59
0.59-0.85
1.49-1.75
1.75-2.17
a Material, glass beads; fluidization pressure, 103 bar; fluidization temperature, 35 °C.
Pc ) critical pressure, bar Rep ) Reynolds’ number Tc ) critical temperature, °C VT ) volume of the fluidized bed Vp ) volume of the solid particles u ) superficial velocity, m/s in R-Z plot umf ) minimum fluidization velocity, cm/s ut ) terminal velocity, cm/s ) bed voidage µ ) viscosity of fluid, µp Fa ) density of Amberlite beads, g/mL Fg ) density of glass beads, g/mL FL ) density of fluid, g/mL Fp ) density of particles, g/mL Literature Cited
°C; cell pressure ) 103 bar; CO2 mass flow rate ) 83 g/min. At this flow rate a few glass beads (presumably at the lower end of the size range) were entrained out of the inner tube, implying attainment of terminal velocity. Using a particle size of 0.18 mm, the terminal velocity predicted using eq 4 is 8.89 cm/s. The corresponding linear CO2 flow velocity based on the aforementioned experimental conditions is approximately 9.94 cm/s, suggesting that the empirical correlation is also valid for predicting terminal velocities during fluidization with supercritical carbon dioxide. Terminal velocities could not be attained with the larger particles due to constraints on the pumping capacity of CO2 and on the tube size. Conclusions Nearly spherical glass and Amberlite particles ranging in size from 0.18 to 1.0 mm were successfully fluidized by supercritical CO2. For a given packing material, the length of the expanded bed varies exponentially with CO2 mass flow rate. In the supercritical region investigated (35-55 °C, 83-124 bar), the bed expansion has relatively weak temperature and pressure dependences. This is attributed to opposing effects of density and viscosity changes of the fluidizing medium on the bed expansion. Consistent with the correlations, the experimental umf values depend only on the particle material, size, and fluidization conditions (pressure and temperature). The predicted umf and ut values bracket those obtained from experiments. A logarithmic plot (R-Z plot) of u and ε yields a linear correlation with the ut (intercept) and n (slope) values in close agreement to literature values. Our results prove that conventional correlations may be used for designing CO2-based fluidization processes. Acknowledgment It is a distinct pleasure to be able to contribute to this special issue honoring Professor M. M. Sharma. This work was partially supported by the NSF-ERC program (NSF-EEC 0310689) and partially by the Kansas Technology Enterprise Corporation’s Centers of Excellence Program. Notations dp ) diameter of particles, mm D ) tube diameter, mm g ) gravitational acceleration, m/s2 HT ) height of total fluidization bed, mm Hp ) height of particles, mm n ) parameter in R-Z equation
(1) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice; Butterworth Publishing: Boston, 1986. (2) King, J. W. Supercritical Fluid Extraction: Present Status and Prospects. Grasas y Aceites (SeVilla, Spain) 2002, 53, 8. (3) Perrut, M.; Clavier, J. Y. Supercritical Fluid Formulation: Process Choice and Scale-up. Ind. Eng. Chem. Res. 2003, 42, 6375. (4) Ikariya, T.; Noyori, R. Carbon Dioxide as a Reactant and Solvent in Catalysis. In Green Chemistry Using Liquid and Supercritical Carbon Dioxide; DeSimone, J. M., Tumas, W., Eds.; Oxford University Press: New York, 2003; p 48. (5) Wai, C. M.; Gopalan, A. S.; Jacobs, H. K. An Introduction to Separations and Processes Using Supercritical Carbon Dioxide; ACS Symposium Series 860; American Chemical Society: Washington, DC, 2003; p 2. (6) Crowther, M. E.; Whitehead, J. C. Fluidization of Fine Particles at Elevated Pressure. In Fluidization; Davidson, J. F., Kearns, D. L. Eds.; Cambridge University Press: London, 1978; p 65. (7) Poletto, M.; Salatino, P.; Massimilla, L. Fluidization of Solids with CO2 at Pressures and Temperatures Ranging from Ambient to Nearly Critical Conditions. Chem. Eng. Sci. 1993, 48, 617. (8) Marzocchella, A.; Salatino, P. The Dynamics of Fluidized Beds under Pressure, In Progress in Fluidization and Fluid Particle Systems; AIChE Symp. Ser. 313; American Institute of Chemical Engineers: New York, 1996; p 25. (9) Marzocchella, A.; Salatino, P. Fluidization of Solids with CO2 at Pressures from Ambient to Supercritical. AIChE J. 2000, 46, 901. (10) Subramaniam, B.; Saim, S.; Rajewski, R. A.; Stella, V. J. Green Process Concepts for the Pharmaceutical Industry. In Green Engineering; Anastas, P. T., Heine, L. G., Williamson, T. C., Eds.; ACS Symposium Series 766; Washington, DC, 2000; p 96. (11) Schreiber, R.; Reinke, B.; Vogt, C.; Werther, J.; Brunner, G. Highpressure Fluidized Bed Coating Utilizing Supercritical Carbon Dioxide. Powder Technol. 2003, 138, 31. (12) Kroeber, H.; Teipel, U. Microencapsulation of Fine Particles in a Supercritical Fluidized Bed. Chem. Ing. Tech. 2002, 74, 1715. (13) Vogt, C.; Schreiber, R.; Werther, J.; Brunner, G. Coating of Particles in Fluidized Beds Operated with Supercritical Fluids. Chem. Ing. Tech. 2003, 75, 693. (14) Matsumura, Y.; Minowa, T. Fundamental Design of a Continuous Biomass Gasification Process Using a Supercritical Water Fluidized Bed. Int. J. Hydrogen Energy 2004, 29, 701. (15) Cheremisinoff, N. P.; Cheremisinoff, P. N. Hydrodynamics of GasSolids Fluidization; Gulf Publishing Co.: Houston, Texas, 1984. (16) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd ed.; Butterworth-Heinemann: Boston, 1991. (17) Leva, M. Fluidization; McGraw-Hill Book Co.: New York, 1959. (18) Richardson, J. F.; Zaki, W. N. Sedimentation and Fluidization: Part I. Trans. 1nst. Chem. Eng. 1954, 13, 35-53. (19) Davidson, J. F.; Clift, R.; Harrison, D. Fluidization, 2nd ed.; Academic Press: New York, 1985.
ReceiVed for reView May 28, 2006 ReVised manuscript receiVed August 28, 2006 Accepted September 1, 2006 IE0606789
