IV. -‘.-.4 ......,‘,V» ”4.1 I! 3’. .. I - \ - I ‘ " -\ .7 . ' ~ ‘ ~- Jun» 4 g l , ~ 31'.» “4.4.171. . ‘ .7 " a «A» u.“ r. L .. . .., > .. . _, . a, “0i w , A .., .1 up“ .r-wLi n. . — ‘0‘ ‘ . ‘. . ,V _ n: t ~25, ' .‘3..'.";'. ..._:' . . a. MICHIGAN STATEU H l’ W! NIH”!!!WIIHIHIIIHWNW 3 129 00877 0236 I! This is to certify that the dissertation entitled Hydrodynamic Aspects of a Three-Phase Fluidized Bed Reactor presented by Michael John Bly has been accepted towards fulfillment of the requirements for Ph.D.‘ degree in Chem. 319?. W 77% WW Major professor Date May 22, 1992 MSU is an Affirmative Action/Equal Opportunity Institution 042771 1* LIBRARY 4 Michigan State Univeniiy PLACE lN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before due due. DATE DUE DATEDUE DATE DUE l i—Tl I! MSU I. An Afflnnetive Action/Equal Opportunity iratnution WM? ,, “—* HYDRODYNAMIC ASPECTS OF A THREE-PHASE FLUIDIZED BED REACTOR BY Michael John Bly A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1992 ABSTRACT HYDRODYNAMIC ASPECTS OF A FLUIDIZED BED REACTOR by Michael John Bly The purpose of this investigation was to examine some hydrodynamic aspects of three-phase fluidized beds with emphasis on bioreactor conditions. The effects of system parameters on the gas holdup in a three-phase fluidized bed reactor were examined. A valve technique was used to measure the average gas hold-up in the reactor. Polysaccharide biocatalyst support beads and glass beads were used as the solid phase. Gas hold-up was found to be strongly affected by fluid superficial velocities, bead size and density, electrolyte concentration, type of gas sparger, and temperature. Quantitative and qualitative observations were made regarding the differences between conventional glass particle systems and low density gel particle systems. Most notably, the degree of bubble coalescence and mode of fluidization were highly dependent on each system. The effects of solids density and void fraction on the bubble rise velocity of distorted spherical and circular cap bubbles in two and three-dimensional liquid-solid fluidized beds have also been examined. Specific gravities of the solid phase ranged from 1.02 to 2.50, and the equivalent bubble diameters varied from 0.07 to 2.0 cm. Bubble rise velocities were found to decrease with increasing solids fraction and density and to increase with bubble size. The reduction in the bubble rise velocity due to the presence of the solid phase was semi-empirically modeled for bubble diameters greater than 0.20 cm using a virial expansion in the solids fraction. Smaller bubbles seemed to be influenced by local liquid flow patterns. The semi- empirical correlation was found to fit experimental results and literature values for solids fractions up to 0.43. iv DEDICATION This work is dedicated to my Dad whom I never knew, and those that helped me find him, and to my Mom. ACKNOWLEDGMENTS I want to thank two guiding lights in my scientific career, Joseph Steepleton and R.C. Seagrave. I would like to thank my committee, especially R. Mark Worden for their guidance and helpful suggestions. Thanks to Ram, Bharath, Alec Scranton, Martin Hawley, Craig, Robert Buxbaum, and Ponnam for their influence and challenging suggestions. Personal thanks to (thanks know no order) Amanda, Ram, Bharath, Rob H., Linda and Pat and Co., Steve and Lynn and Co., Paul, Rajesh, Dirk, Colleen, Arvind, Greg, Ali, Steve, Dave Guy, Julie, Sandy, Kelly, Andy, Bob, Julie, Usmeda, Kelly, Craig, Craig, Beth, Faith, Julie, Lora Mae, Rick, Himanshu, Henry, Roe, Schaeffer, Stanley, Michelle, Brian, Ken, Perry, Shelly, Jen, Impressions 5, and M.B.I. vi TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES NOMENCLATURE Chapter 1: INTRODUCTION Chapter 2: GAS HOLD-UP Summary Literature Review Experimental Results Discussion Conclusion Chapter 3: BUBBLE RISE VELOCITY Summary Introduction Literature Review Gas-Liquid Systems Gas-Liquid-Solid Systems Purpose Experimental Correlation Development Results Model Comparisons Conclusion Chapter 4: RECOMMENDATIONS BIBLIOGRAPHY vii page viii ix xii 100 120 123 127 LI ST OF TABLES page Table 3.1. Particle properties. 83 viii Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. LIST OF FIGURES page 1.1. A Simplified representation of a three-phase fluidized bed reactor. 2 2.1. Gas hold—up experimental system. (1. column; 2. Tank; 3. fluid measurement; 4. air humidified; 5. pumps; 6. fluid distributions; 7. liquid calming section; 8. three-way valve; 9. gate valve; 10. flowmeters; 11. heaters; 12. catch basin; 13. manometers; 14. air trap). 20 2.2. Rubber sparger. ' 24 2.3. The effects of glass bead size on gas hold-up (distilled water, T = 30°C). a.) dp = 1.30 mm. b.) dp = 3.03 mm c.)ao Small gel beads Medium gel beads Large gel beads Small gel beads Medium gel beads Large gel beads A 0.000 0.200 0.400 0.500 0.1500 1.000 1.200 1.400 Gas Velocity (cm/s) 2.10. The effects of gel bead size on gas hold- up in a non-coalescing medium (0.2 M CaClz, U, = 0.525 cm/s, T = 30°C Glass frit sparger). a.) three-phase. 51 -— No beads - - Small gel beads O'IOO' -- Medium gel beads -—-ngegdtnmk 0000- O. i’ P. 0.060- O 32 m D (D 0090- 0020- 0000, , 0.000 0.200 0.400 0.600 0.500 1.000 1.200 1.400 Gas Velocity (cm/s) b.) two- and three-phase. 52 system and approached those of the 2.59 and 3.84 mm bead systems. Finally, the effects of temperature on gas hold-up are shown in Fig. 2.11a - c and Fig. 2.12a - b. Here, 0.2M CaCl2 was used as the liquid phase along with the glass frit sparger. Small gel beads were used as the solid phase. Fig. 2.11a - c compare the two and three-phase results at 30°C, 45°C, and 60°C respectively. In general, three-phase values were slightly larger than two-phase values below a gas velocity of 0.4 cm/s. In Fig. 2.12a, three-phase values are compared for all three temperatures at the same liquid velocity. An increase in gas hold-up with increasing temperature was apparent. The effect of temperature on two-phase hold-up values is illustrated in Fig. 2.12b. Once again, increasing temperature caused an increase in gas hold-up. Discussion With the large number of parameters involved in the study of fluidized beds, comparison with literature values is difficult. For example, at given liquid and gas superficial velocities, gas hold-up values may greatly vary depending upon such factors as sparger type, liquid phase, column diameter, and solids loading. This deviation is illustrated in Fig. 2.9a with the sparger comparison. Gas hold-up values were found to vary by a factor of two. Even though the deviation between hold-up values of individual 53 mom)" 0 Small gel heads a No beads -- Small gel beads - No beads 00°60- / Gas Hold-up 0.000 0.200 0.400 0.600 0.600 1.000 Gas Velocity (cm/s) Fig. 2.11. The effects of temperature on gas hold-up (d, = 1.15 mm, 0.2 M CaClz, U, = 0.372 cm/s). a.) T = 30°C. 54 a Small gel beads 13 No beads 0:100' — Small gel beads - No beads 13 / / 0.080- a 2” / / O. / m 1’ / 2 0.060“ / O I o: c O 0.040- 0.020- l 0.000 I j I I —I ‘1 I 0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 Gos‘Vekxfig/(cnm/s) b.) T = 45°C. 55 a Small gel beads 11 No beads 040°“ — Small 9.1 beads - No beads 0.080- 0.060“ Gas Hold-up 0.040- 0.020- 0.000 0.000 0.200 0.400 0.600 0.500 1.600 1.200 1.400 Gas Velocity (cm/s) c.) T = 60°C. Fig. 56 o Tit-300 1: 7-450 0400" 1 rasoc -- 1:300 -- T-450 00BOJ 0.060- Gas Hold-up 0004‘0'll 0.02 - 0.000 0.000 0.200 0.400 0.300 0.600 1.600 1.200 1.400 Gas Velocity (cm/s) 2.12. The effects of temperature on gas hold-up (0.2 M CaClz, U, = 0.372 cm/s, Glass frit sparger). a.) dp = 1.15 mm. 57 00100- 00080"l A . 00060.ll ” Gas Hold—up \\ \ ‘OIMO- I osmo- ”g 0.0004 0.000 0.200 0.400 0.400 0.600 1.000 1.200 Gas Velocity (cm/s) b.) no beads. 58 researchers may be large, comparison of general hydrodynamic trends can still be made. These trends may include whether the system is bubble coalescing or disintegrating and how much three-phase values differ from two-phase (gas-liquid) results. The range of gas and liquid throughputs utilized in the conventional study with glass ballotini as the solid phase were generally smaller than other literature values. For example, using 6 mm particles, Michelsen and Ostergaard (1970) used gas velocities and liquid velocities ranging from 0 - 15 cm/s and 10 - 20 cm/s respectively. Here, for the large glass beads, fluid flow values ranged from 0 - 1 cm/s for the gas phase and 8 - 11 cm/s for the liquid phase. As a result, the flow patterns were not observed at high gas superficial velocities where differences between two and three-phase values as well as the effects of liquid superficial velocity are most notable. Even so, comparison of experimental trends with literature values is excellent. Bubble coalescence was apparent for beds of 1.30 and 3.03 mm particles under most conditions. Large, coalesced bubbles were observed exiting the column and three-phase hold-up values were generally less than those from two-phase (gas-liquid) flow. For the 5.99 mm particles, a lack of bubble coalescence was observed. The effect of liquid superficial velocity on gas hold-up agrees with the results of other researchers (Michelsen and Ostergaard, 1970; Dhanuka and Stepanek, 1978). Namely, the effect of liquid 59 velocity on column behavior was dependent upon the bead size. Gas hold-up was independent of liquid flow for the 1.30 mm glass beads. For the 3.03 and 5.99 mm particles, increasing the liquid superficial velocity decreased the gas hold—up but increased the gas velocity that could be utilized before slugging occurred. Hydrodynamic trends for the low density biocatalyst support particle systems were significantly different than those observed for the conventional glass ballotini system. Most notably, bubble coalescence was observed under all operating conditions. The degree of coalescence was dependent upon system properties such as bead size and liquid type. While bubble coalescence was expected for the 1.15 and 2.59 mm particles, the effect of the larger 3.03 mm neutral density particles on reactor operation was unknown. Apparently, the reactor conditions (ie., the particle terminal velocity and the solids fraction) were not sufficient to inhibit bubble coalescence. There is a major difference between the experimental results and literature findings concerning the comparison between two and three—phase gas hold-up values. The addition of a light solid phase (alginate or polystyrene beads) generally has reduced gas hold-up and, consequently, the gas-liquid mass transfer coefficient. Typical experimental systems have utilized a solids loading of less than 20% in three-phase bubble or airlift-loop columns. The addition of particles increased bubble coalescence, thus 60 decreasing gas hold-up. Quantitative studies of the behavior of low density particles on gas hold-up in fluidized bed bioreactors are scarce.‘ In this study, while an increase in bubble coalescence was observed relative to gas-liquid flow conditions, three-phase gas hold-up values were sometimes larger than corresponding two-phase values. This effect is illustrated, for example, in Fig. 2.4a and Fig. 2.6a for the 1.15 mm gel beads in the coalescing and non-coalescing liquids. The difference between two and' three-phase gas hold-up values was highly dependent upon the liquid type as well as other system parameters. An explanation for the larger hold—up values for three-phase than two-phase operation is that at low solids concentrations used by other researchers (less than 10%), the negative effect of the particles may be attributed to a decrease in the cross sectional area to flow and thus increase bubble collision frequency and the rate of coalescence. This effect is most notable for larger particles (3.84 mm). Smaller particles (1.15 mm) were thought to increase bubble coalescence by increasing the apparent viscosity of the pseudohomogeneous (liquid-solid) phase. Either way, an increased rate of bubble coalescence leads to a decrease in gas hold-up. In this study, an average solids hold-up of 30% was used, which is higher than was used in previous studies. At this solids concentration, the hold-up enhancement due to bubble-particle collisions apparently exceeds the hold-up reduction due to increased 61 coalescence. However, the net effect of the solids varied greatly with bubble and particle sizes. Consequently, different trends were observed for different liquid types and gel bead sizes. The effects of temperature observed in this study agree with the results of Smith et al. (1986) but differ from those obtained by Grover et al. (1986). In the present study, gas hold-up increased with increasing temperature for both two and three-phase systems for all gas velocities. Grover et al. (1986), working with a two-phase bubble column, noticed an increase in hold-up with increasing temperature at low gas velocities but found a decrease in the transition gas velocity between churn-turbulent and slug flow. Smith et al. (1986) found an increase in gas hold-up with increasing temperature at low gas velocities (less than 2.5 cm/s) in gas-liquid bubble columns. Another significant finding of the temperature studies was that the gelrite/alginate bead composition appeared to be suitable for thermophilic fermentations (Worden et al., 1991). (Alginate alone was not suitable for column operation at 60°C.) While not quantitatively measured, the degree of solids movement was found to vary significantly with the system parameters. The small gel beads were influenced most by the addition of gas to the liquid-solid bed. The particle mixing appeared to decrease with increasing bead diameter. The largest gel beads stratified axially within the reactor, 62 as was observed for the 3.03 and 5.99 mm glass beads. The degree of solids mixing may affect the reactor performance by increasing the liquid axial dispersion and by subjecting the biocatalyst support particle to large changes in substrate concentration. It should be emphasized that average hold-up values were measured. Axial variations in phase hold-ups did exist. Bubble coalescence produced a gradient in the gas hold-up along the column. In addition, the solids hold-up varied from a maximum in the sparger distribution area (for large particles) to a minimum at the top of the column. Even so, the results clearly show some important hydrodynamic relationships between the system parameters and the average gas hold-up. The quality of the experimental data, as indicated by the small degree of variance in the gas hold-up vs. gas velocity plots appears to be excellent. However, sources of error do exist. The major source of error was probably the outlet gas flow rate measurement. At flow rates less than 1000 ml/min, the air/water displacement system was used. At low gas flow rates (less than 300 ml/min), an oscillation in the release of gas into the graduated cylinder displacement meaSurement system was noticed. The effect of this oscillation was minimized by taking measurements over several cycle times (two minutes, for example). Another source of error is that, when the glass ballotini was used, gas remained entrapped within the bed after the fluid flows 63 were stopped. This effect was most apparent for small bed expansions. The majority of gas could be released by applying a pulse of liquid. This condition was not observed for the gel beads because of the extent of bed expansion and the low particle density. Finally, experimental error was caused by the gas entering the reactor at a lower temperature than the liquid. For instance, when the liquid entered the column at 30°C, the gas phase entered the column saturated with water at room temperature. This temperature and humidity difference between phases may have affected the bubble properties axially within the column. The effect is least significant for column operation at 30°C but may have been more important at higher temperatures. Conclusion Gas hold-up was found to be strongly affected by fluid superficial velocities, bead size and density, electrolyte concentration, type of gas sparger, and temperature. Hold- up values differed by up to a factor of two, depending on the gas sparger and the liquid type used. In addition, it was shown that low density particle systems behaved much differently than conventional glass particle systems. Most notably, the degree of coalescence and mode of fluidization were highly dependent on each system. The model system for fluidized bed reactor studies has typically involved the use of glass ballotini as the solid phase. Upon the addition of the gas phase, bubble 64 coalescence was generally observed for the beds of 1.30 and 3.03 mm particles. A lack of bubble coalescence relative to the two—phase system was noticed for beds of 5.99 mm particles. However, since the bubbles leaving the sparger (observed visually for gas-liquid flow) were approximately the same size as those exiting the 5.99 mm beds, the systems can not really be described as bubble disintegrating. The effect of liquid velocity on column behavior was dependent upon the bead size. Gas hold-up was independent of liquid flow for the 1.30 mm glass beads. For the 3.03 and 5.99 mm particles, increasing the liquid superficial velocity decreased the gas hold-up but increased the gas velocity that could be utilized before slugging occurred. Fluidized bed operation with the biocatalyst support as the solid phase greatly differed from the conventional system. Upon addition of the gas phase, a non-distinct bed height and solids gradient was visually observed along the reactor. This effect was dependent upon the bead size, liquid type (coalescing or non-coalescing) and gas flowrate. Another prominent feature of the gel bead systems was that bubble coalescence was observed under all circumstances, the degree of which depended upon the system parameters. Coalescence, in the form of large bubbles or bubble swarms, was even apparent for the 0.2 M CaCl2 non-coalescing medium. Finally, relative to the conventional systems, solids movement was observed. This effect, observed visually, was most pronounced for the 65 smallest gel beads and decreased as the gel head size increased. Parameters varied with the biocatalyst gel bead as the solid phase included bead size, liquid and gas superficial velocities, liquid composition, sparger type, and temperature. Changing the solid bead size had an affect on both the gas hold-up as well as solids movement. The effect on gas hold-up is shown in Fig. 2.12b. and Fig. 2.10a. Flow properties were dependent upon the sparger type used. Using the ring sparger, the largest hold-up values were obtained for the 3.84 mm gel beads. With the glass frit sparger, gas hold-up values for the 2.59 and 3.84 mm gel beads were similar. The solids movement was not quantitatively measured. However, it was visually noticed that the small gel beads circulated along the column. The effects of changing the gas flow on the gas hold-up is illustrated in Fig. 2.10a. Depending upon the flow regime, increasing the gas flow lead to an increase in gas hold-up and an increase in bubble coalescence. In addition, increasing the gas throughput caused an increase in solids movement. In general, increasing the liquid superficial velocity lead to an increase in the bed expansion and an increase in the gas velocity that could be utilized before gas slugging was observed (Fig. 2.6a.). However, increasing the liquid flowrate may decrease gas hold-up by increasing the bubble 66 rise velocity. This affect is illustrated in Fig. 2.5 two-phase flow conditions. (Bubble rise velocity was not measured.) Another property that greatly affected bioreactor operation was the type of liquid used (coalescing or non-coalescing). As is shown in Fig. 2.7b. for the medium gel beads, liquid characterization is essential in determining phase hold-ups and transitions between flow regimes. Larger gas hold-up values as well as an increase in the applied gas velocity before gas slugging occurred were found for the non-coalescing liquid. The effects of the sparger type on column operation were examined (Fig. 2.9a.). As can be seen, the glass frit produced significantly larger hold-up values relative to the flexible rubber sparger. Finally, the effects of temperature on gas hold-up were examined. An increase in temperature lead to an increase in gas hold-up. Also, column temperature had no noticeable effect on the transition from churn-turbulent to slug flow as indicated from the gas velocity/gas hold-up relationship., Chapter 3: BUBBLE RISE VELOCITY Summary The effects of solids density and void fraction on the bubble rise velocity of distorted spherical and circular cap bubbles in two and three-dimensional liquid-solid fluidized beds have been examined. Specific gravities of the solid phase ranged from 1.02 to 2.50, and the equivalent bubble diameter varied from 0.07 to 2.0 cm. Bubble rise velocities were found to decrease with increasing solids fraction and density and to increase with bubble size. The reduction in the bubble rise velocity due to the presence of the solid phase was semi-empirically modeled for bubble diameters greater than 0.20 cm using a virial expansion in the solids fraction. Smaller bubbles seemed to be influenced by local liquid flow patterns. The semi-empirical correlation was found to fit experimental results and literature values for solids fractions up to 0.43. 67 68 Introduction Knowledge of how system properties affect the rise velocity of a bubble through liquid and liquid-solid regions of a fluidized bed is essential for reactor design. Study of the bubble terminal velocity is fundamental to the understanding of the bubble and wake dynamics.. The bubble rise velocity is an integral part of dimensionless groups that describe two- and three-phase reactors (ie., Re, We, and CD). In addition, bubble rise velocities affect both the axial dispersion of the liquid phase and the gas-liquid mass transfer rate. As a result, prediction of the bubble rise velocity is fundamental to reactor design (Fan, 1990). Due to the change of bubble shape with size, the bubble rise velocity in liquid systems has traditionally been broken up into different regimes. Theories to describe these regimes range from Stokes’ law (Stokes, 1851) for small, spherical bubbles to the theory of Mendelson (1967) for large, spherical cap bubbles.~ Only recently has an attempt been made to unify these correlations in liquid systems (Fan, 1990). Few attempts have been made to model the bubble rise velocity characteristics in liquid-solid systems (Fan, 1990). Correlations have been semi-empirical at best and usually utilize dense glass particles as the solid phase (Darton and Harrison, 1974; Jean and Fan, 1990; Jang, 1989; Tsuchiya et al., 1990; Darton, 1985). Here, theories have ranged from treating the liquid-solid phase as a pseudo- 69 homogeneous liquid of a higher density and viscosity (Darton and Harrison, 1974) to taking into account the impaction of solid particles with the bubble roof (Jean and Fan, 1990). This fundamental study examined the effects of solids density and void fraction on bubble rise velocities in liquid-solid fluidized beds. The general hypothesis was that increasing the solids density or solids fraction would cause a corresponding decrease in the bubble rise velocity. Results from bubble-particle interaction studies were used to formulate a semi-empirical correlation with analogy towards the hindered settling of a sphere. Literature Review: Gas-Liquid Systems The relationship between the terminal bubble rise velocity and equivalent bubble diameter ( in 3-D, the spherical diameter of the bubble; in 2-D, the diameter of a circle having the same area as the bubble) in water is shown in Fig. 3.1 (Haberman and Morton, 1953). Small bubbles (de < 0.04 cm) are spherical and closely follow the theories of Stokes (1851) for an immobile gas-liquid interface or Hadamard-Rybczynski (Hadamard, 1911; Rybczynski, 1911) for a mobile interface. At larger diameters (0.04 < d, < 0.1 cm), the distorted spherical bubbles are affected by internal circulation. Shear stresses are reduced relative to the Stokes' law case (Mendelson, 1967). As a result, the bubble terminal velocity is greater than that predicted by Stokes’ law. Levich (1962), through the use of boundary layer Fig. 3. Corrected Bubble Velocity (cm/s) 1. 70 100 I 1 o Distilled Water a Taplwahu' 0.01 U I 1 '1‘00 1 0.10 Iv—“I—‘jj100| 1 .00 1 1T‘1“I 1 0.00 Equivalent Bubble Diameter (cm) The relationship between equivalent bubble diameter and bubble rise velocity for air bubbles in water at 18 - 22°C (Haberman and Morton, 1953). 71 theory, obtained an expression for a strictly spherical bubble in a pure liquid (no surface-active agents) in this region (50 < Re < 800): = 91ng b1 36.11 (3.1) In this regime, the bubble motion is highly dependent upon traces of impurities. Between 0.1‘<’0.5 cm in water) in fluidized beds of small particles 01,< 1 mm) was found to be similar to the rise velocity of a bubble in a higher viscosity fluid (containing no solids). Massimilla et al. (1961) measured the rise velocity of single bubbles in beds of sand (0.22 mm diameter), glass beads (0.79 and 1.09 mm) and iron sand (0.26 mm diameter) fluidized by water. Bubble rise velocities increased with increasing bed expansion. In addition, the dependence of the bubble rise velocity on the bubble radius of curvature approximately followed that for large bubbles in an inviscid liquid 76 (Davies and Taylor, 1950): U. = 2/319R)“ (3.9) but with a different proportionality constant. eqn. 3.9 is the well known relationship of Davies and Taylor. Henrickson and Ostergaard (1974) measured bubble rise velocities in liquids of different viscosities as well as water fluidized beds of 0.2, 1 and 3 mm diameter glass beads. Bubble rise velocities were proportional to the square root of the radius of curvature of the bubble: Ub = K1(gR)o’5 ' (3°10) where the constant, K, depended upon the bed porosity. An apparent bed viscosity was estimated to vary between 0.12 and 3.10 Poise. Darton and Harrison (1974) studied the bubble rise velocities of 0.5 to 2.5 cm diameter air bubbles in beds of water fluidized sand particles (0.5 and 1.0 mm diameter). The data were well fit to the relationship (Kojima et al., 1968; Jones, 1965) CD = 2.7 + Kz/Re (3.11) which is valid for large bubbles rising in viscous liquids. As a result, an apparent bed viscosity was found, which 77 varied with bed expansion and particle size in the range of 2 to 22 Poise. Subsequently, Darton (1985) fit these results as well as other literature data (for e,>’0.2) to the empirical equation: p.‘ = p,exp(36.15e§'5) (3.12) In addition, a pseudo-homogeneous liquid phase density can be taken as: p, =pses+plel (3.13) As shown by Fan (1990), eqns. (3.12) and (3.13) apply only under limited circumstances. For example, the apparent bed homogeneity theory does not apply for small bubbles at large and low bed expansions and for the larger particle size used (1 mm) in the Darton and Harrison (1974) study. De Oliveira Mendes and Qassim (1984) also used a Davies-Taylor type relationship (eqn. (3.9)) to explain the rise of large bubbles in fluidized beds of small particles. Jean and Fan (1990) developed a theory to explain the effect of solids on the bubble rise velocity by considering the collision of particles with the bubble roof. A steady- state force balance was applied to a spherical cap bubble accounting for the impaction force due to solid particles. Here, literature data analyzed used glass bead particle diameters ranging from 0.2 to 1.0 mm. This theory predicted the bubble rise velocity for large spherical capped bubbles 78 “L > 1.5 cm) and small particles (dp1< 0.5 mm). Thus, the theory applies only under limited bubble size and shape conditions. The most recent study on bubble rise velocities in a liquid—solid medium has been conducted by Jang (1989). A wide range of glass bead and bubble sizes (0.163 s dp:s 2.0 mm, 0.2 s d, s 2.4 cm) was utilized. In general, ‘ significant reduction in the bubble terminal velocity was found for d,;z 460 pm at a bed voidage (liquid fraction) of 0.48. At a bed voidage of 0.58, however, the terminal velocity was dependent upon both the bubble and particle sizes. For an equivalent bubble diameter greater than 0.7 cm, bubble rise velocities were a weak function of particle diameter. An empirical correlation, similar to eqn. 3.5, developed for liquid systems, was obtained: - 20 9d :9 Li U= Kd2”+—+ “’2“ 3.14 b [(bse) (91d. 2)1 ( ) where, (430e, — 211))x(190 — iggtan“(1.23 x 106x (3,15) (d,D - 3.11 x10“))) and n is correlated graphically with the glass bead particle diameter,ld and er Thus, the constants Km and n are pl 79 empirical functions of the solid void fraction and the glass particle properties. The predicted variations of U, with d, were quite good except for small bubbles (0.3 .<_ d, s 0.5 cm), and large particles 01,= 2.0 mm). The prediction was found to be within 30% for the water-glass bead systems. A similar theory to that given in eqn. 3.14 has been developed (Tsuchiya et al., 1990). The effect of glass beads (dp==774 pm) on the rise velocity of 1.2 to 3.0 cm equivalent diameter bubbles was examined. For these experimental conditions, provided U,< 2 cm/s, there was no significant difference in U, between the presence and absence of particles. A best fit to the data yielded the following semi-empirical equation: + 36.1, K2 plde 2 d?- d ;1 Ub=l(K,p1g°)‘1+i(2° 9°) 21-1 (3.16) where K, and K2 are empirical parameters that are functions of the particle properties: K,(U, , £5) = %(% 1 tan’1(2|U,eg'S - 1.9e;°“|1°°) (3.17) where the positive/negative sign applies when Ugf” - 1.96,")-4 is negative/positive respectively, and K2(Uc I 68) = 0.88 _ 0.01372 (exp(7.Zeg - 1) 3.18 .4125 +tan‘1((U,.-4.5)3/2)) ( ) 80 Purpose The purpose of this investigation was to examine the effects of particle density (1.02 s (S.G.) s 2.5) and solids void fraction (0 s q,s 0.42) on the average bubble rise velocities of distorted spherical and circular cap bubbles (0.07 s d, s 2.0 cm). Water fluidized two- and three-dimensional beds were utilized. The particle size was approximately constant at 3 mm. Experimental: Bubble Rise Velocities: The bubble rise velocities of single bubbles were measured in both a 2 inch diameter three-dimensional fluidized bed and a two-dimensional fluidized bed. Experimental details of the three-dimensional reactor have been given previously (Bly and Worden, 1990) (as given in Chapter 2). In this reactor, the bubbles (d,<:0.55 cm) were injected 23.5 cm above the column base at a radial position, r/R = 0.37, with hypodermic syringes. An initial solids loading of 500 ml was used. The two-dimensional column is shown in Fig. 3.3. It had a gap thickness of 1.64 cm and a width of 23.7 cm. Supports were placed at intervals of approximately 20 cm to prevent bowing of the reactor. The liquid calming area consisted of two levels of lead shot (10 cm of 2.9 mm diameter shot followed above by 2.5 cm of 2.0 mm diameter Fig. 3.3. 81 O 0 0 0 0 0 O O O O O 9 O O O O O O O 0 0 0 0 O 0 O 0 0 O 0 0 O O 0 0 0.0.0.0...0.0.0.....0.0.0.0.0.0.0.0.0.0 O 0.0.0.0...0.0.0.0.0.0.0'0‘; O O O O O O O O O O O O O 0 O O O O O O O O O O O 0 O O O O O O O .0 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O O 0 O O O O O 0 O O O O O O O I O O O O O O O O O O O O O O O 0 .4 0 O O 9 O 9 O O O 0 O O O O O 0 O O O O O O 0 O O 0 O O O 0 0 O 0 0 a O O C O O O O O O 0 0 O 0 O O O O O O O O 0 0 O O O O O O O O 0 O O 0 0 O O 0 O O O O O 0 O O 0 O 0 O O 0 O O 0 0 O O O O O 0 O O 0 O 0' 0.0.0.0...0.0.0.0.C.0.0'0‘..0.0.0...0.0...0.0.0.0.0.0.0.0.0...0.0.0.0. O I O O O O ..... O 6 O O O O 0 O O O O O O O O O O O O O O O O O 02. The two-dimensional fluidized bed (Gap thickness = 1.64 cm, width = 23.7 cm, fluidized height = 56 .cm). 1. Liquid distribution; 2. Bubble injection site; 3. Liquid calming regions; 4. Column supports; 5. Liquid outlet. 82 shot). Solids loading was varied to maintain a fluidized height of between 36 and 56 cm (generally 56 cm). Bubbles «L > 0.55 cm) were injected 8 cm above the liquid distribution area with hypodermic syringes. The hypodermic needle and syringe were chosen so as to minimize bubble satellite formation in both reactors. The bubble diameters for bubbles smaller than dt== 0.55 cm were calculated based on the bubble shape of a sphere. The diameters of larger bubbles were calculated as the equivalent diameter of a circle having the same two-dimensional area as the injected bubble (Fan, 1990). Properties of the solid phase are given in Table 3.1. The liquid phase consisted of partially purified water (conductivity of 7 - 14 umhos (relative to 25°C)) at 18 - 22 °C. The average bubble rise velocity was calculated from the time necessary for the bubble to exit the liquid-solid fluidized region. The bubble rise velocity was corrected for the liquid rise component by the following relationship (Darton and Harrison, 1974; Tsuchiya et al., 1990): The two-dimensional bubble rise velocities were multiplied by a correction factor to account for wall effects. A correction accounting for the presence of solids in a two-dimensional reactor is not available. However, a 83 Particle Diameter (nun) Specific Gravity 11, (011115) Glass Bead 3.03 1 0.06 2.50 33.41 1 1.17 _ ca Bead 3.12 :1; 0.17 1.23 t 0.01 12.711 :1: 0.77 061 Bead . 259 t 0.14 1.015 t 0.004 1.86 :1; 0.28 061 Bend 3.18 1 0.14 1.46 1 0.03 18.79 :1: 0.82 Table 3.1. Particle properties. 84 correction factor was approximated by the ratio of the solids-free bubble rise velocity in a 45 cm I.D. tank to the solids-free two-dimensional bubble rise velocity. The correction factor ranged from 1.01 for the 0.62 cm diameter bubble to 1.16 for the 2.0 cm diameter bubble. Bubble-Particle Interactions: Bubble-particle interactions were analyzed using a two- dimensional fluidized bed and video camera system (Tsuchiya et al., 1990). The two-dimensional fluidized bed is shown in Fig. 3.3. Following the injection of a single gas bubble (volume of 0.5 - 3.0 cm“, particle trajectories of colored tracer particles were monitored using a stationary camcorder (Magnavox VR82808K02), a digital tracking VCR (Mitsubishi HSU 31), and a monitor (Philco). Correlation Development: The proposed correlation (eqn. 3.23) is patterned after the hindered settling of a sphere. Experimental results from the bubble-particle interaction studies (given below) indicated that bubble rise velocities may be represented by an analogy to the hindered settling of a sphere. Particle trajectories are shown in Fig. 3.4 for d,== 0.6 cm, a, = 0.3 cm, and 6, = 0.40. Each frame represents the bubble and the particle positions at 1/60 5 intervals. Three particles are shown. Here, the bubble size and Fig. 3.4. 150! 85 5 O 1' 5 (:) (:) a=BuHme 15.! 1e 0 o =Solid F-i 6ann O 1 Bubble-particle interactions are illustrated (d, = 0.6 cm, = 0.3 cm, 6, = 0.4, S.G. = 1.02) The distorted spherical bubble is approximated by a circle. The frames, representing 1/60 s, are numbered for the bubble and solids. 86 particle size were such that the system could be considered heterogeneous (Fan, 1990). As can be seen from the figure, the bubble interacted with particles within its path. Also, particles away from the bubble were held stationary by the fluidized medium and particle-particle interactions. These particles were relatively unaffected by the rising bubble. The bubble rise velocity was related to the solids-free rise velocity as follows: IL = Um,f(system properties) (3.20) the corrected bubble rise velocity in the C‘. or II liquid-solid system Um,==the corrected bubble rise velocity in liquid (solids-free). The second term on the right hand side accounts for the effects of system properties such as particle density and solids fraction. One limiting case of the presence of the solids would be to view the liquidesolid suspension as a packed bed. The solids are held stationary by the fluidizing liquid phase, and the bubble travels around the solids. Thus, the effect of the solid phase would be to provide a tortuous path for the bubble. Qualitatively, the f(system properties) would only be dependent upon the area available for flow of the bubble (1 - EJ. The term would not be dependent upon the 87 density of the solids, since the solids are assumed to be held stationary by the fluidizing liquid, and the bubble flows around the solids. In addition to the tortuousity effect, bubble-particle interactions may be important. As a result, the bubble rise velocity would be dependent upon the solids fraction, solids density, bubble size, and the flow fields in the vicinity of the bubble. Such a system is represented by Fig. 3.5. This representation of the bubble rising through the liquid-solid region is similar to the bubble-particle interactions shown in Fig. 3.4. A bubble rising in a liquid-solid suspension was patterned after the hindered settling of a sphere at Re << 1. Hindered settling refers to the effects of the presence of a suspension on the motion (settling or rising) of a sphere. Flow field interactions and particle properties are taken into account. This theoretical analysis has been used to extend the Stokes-Einstein diffusional relationship for dilute solutions of solutes in a solvent medium to more concentrated solutions by modifying the frictional coefficient between solutes (Cussler, 1984). Batchelor (1972) determined that the hindered settling velocity of a sphere, correct to order 6“ is U = U0(1 - 6.556,) ~ (3.21) where, E5 is the velocity of a single sphere in unbounded 88 0 = solid 0 = bubble Fig. 3.5. Representation of a bubble rising through a liquid-solid region. 89 fluid. Reid (1980) explicitly solved for the hindered settling velocity in terms of properties of the system (for example, hydrodynamic interaction parameters, particle and fluid densities, and the potential energy between particles). In addition, an expansion of the form U = U0(1 + 6,6s + a212,2 + ) (3.22) was recommended for more concentrated solutions. The above theoretical results are not directly applicable to a fluidized bed since the inertia of the solid and gas phases cannot generally be neglected (Re >> 1). As a result, a general form of eqn. 3.22 was utilized and the constants solved for empirically: U, = Ub,,(1 + (1,6, + (126,2) (3.23) The bubble rise velocity in the absence of solids was found from a modified Mendelson equation (eqn. (3.3)). The normalized bubble rise velocity (aunn,) was plotted versus the solids fraction. A quadratic fit to the data was made using Plotit (Copyright, 1987, Scott P. Eisensmith) with an alpha value for T statistics of 0.9. The parameters a, and 022 were represented as functions of the bubble diameters and solids density (alternatively, the particle terminal velocity). Experimental values and optimized fits are shown in Fig. 3.6 and 3.7 for a, and 0:2 90 AIphol - I l U. - 33.3 cm/s -4.50- A U. - 18.8 cm/s - D U.-1238cm/s ' O U. I- 1.86 cm/s ‘5-50 I V 1 ' 1 I ‘ 0 DO 0 40 0.80 1.20 1 60 2.00 de (cm) Fig. 3.6. Experimental and optimized fits for 01,. 91 Alph02 l" O O l 33.3 cm/s 18.8 cm/s 12.78 cm/s 1.88 cm/s 009' .9 1111 Fig. 3.7. Experimental and optimized fits for 02. 92 respectively. Optimized fits are shown graphically in Fig. 3.8 and 3.9 as a function of the particle terminal velocity. Optimized fits were obtained by an extrapolation of the experimental values given in Fig. 3.6 and 3.7. The asymptotic values of a, and (12 for U, = 18.8 cm/s at d, > 0.8 cm were estimated from Jang (1989). Results: The experimentally measured corrected bubble rise velocities are given as a function of bubble diameters for the solids-free system in Fig. 3.10. They lie within the range of the results of Haberman and Morton (1953). Experimental results for the liquid-solid systems are shown in the following figures. Generally, the bubble rise velocity decreased with increasing solids fractions and particle density except for d, = 0.07 cm. The normalized bubble rise velocity is plotted versus the solids fraction for d,==0.07 cm in Fig. 3.11a - d. The lines represent quadratic fits to the experimental data obtained from Plotit (Copyright, 1987, Scott P. Eisensmith) with an alpha value for T statistics of 0.9. The bubble rise velocity decreased with solids fraction for the specific gravity 1.02 solid phase (Fig. 3.11a). However, this trend was not observed for heavier particles (Fig. 3.11a - d). Bubble rise velocities were sometimes larger at higher solids fractions (representing lower bed expansions) than at lower solids fractions (higher bed expansions). 93 - -- UT = 1.86 crn/s 0.50- — UT = 12.8 cm/s - — UT = 18.8 cm/s - --- UT = 33.3 cm/s Alphal 0.00 ' ' ' 1.00 ' ' I200 Equivalent Bubble Diameter (cm) Fig. 3.8. Optimized fits for a,. Alph02 Fig. 3. 94 7.50~ . l l 6.50- 1 . ‘1 ‘ t 5.50- \,\ \ t ‘ t \ 4.50- \,\ . \ ’ ' \ 3.50- 2.50- 1.50- 0.50- “ --- 07 = 33.3 cm/s -.50~ —- Ufa-18.8cr1'I/s . -— UT = 12.8 cm/s -1.50 “'1‘"? "85”,” . , - , 0.00 0.50 1.00 1.50 2.00 Equivalent Bubble Diameter (cm) 9. Optimized fits for 012. 95 100 80: o Distilled Water J :1 ibleflcr 60- a EXperimenai Date a A " 0 m \ 40- °° E 0 £00 0 9?." 20- ° “3% t) a 2 O 0) > ‘0 .2 1°“. 1 a 8- ° 63 6- .0 - O .9 4- . O 0 O L d L C) (J 2- ° 1 U I U'I‘II' ‘ I "I‘I'l I D 0'00 0.01 0.1 0 1 .00 1 0.00 Equivalent Bubble Diameter (cm) Fig. 3.10. Comparison of solids-free bubble rise velocities with literature values (Haberman and Morton, 1953). 96 1.20 - 1 .00 0.80- 0.60- 0.40- 0.20- -— Quadratic lit x Experimental Corrected Bubble Velocity/Aver Vel No Solids 0.00 , , , 0.00 0.10 0.20 0.30 0.40 0.50 Solids Fraction Fig. 3.11. The normalized bubble rise velocity vs. solids fraction (d, = 0.07 cm). a.) U, = 1.86 cm/s. 97 1.20 ~ 1 .00 0.80- 0.60- Corrected Bubble Velocity/Aver Vel No Solids 0.40- 0.20- - Quadratic fit 0.00 x Expenmental 0.00 0.10 0.20 0.130 0.510 0.50 Solids Fraction b.) U, = 12.8 cm/s. 98 1.20 ’ l .00 0.80- 0.60- Ub/Ubsl‘ (L401 0.20- —- Quadratic Fit 0 Experimental Data 1 1 1 0.00 0.1 0 0.20 0.30 0.40 0.50 0.00 Solids F roction U, = 18.8 cm/s. 99 1.20 - 0.80d 0.40- 0.00-J — Quadratic fit 1: 1: Experimental Corrected Bubble Velocity/Aver Vei N0 Solids ”-40 I 1 1 I 0.00 0.10 0.20 . 0.30 0.40 0.50 Solids Fraction d.) U, 33.3 cm/s. 100 Fig. 3.12a - f compare the experimental data with eqn. 3.23 at equivalent bubble diameters ranging from 0.22 to 2.0 cm. The lines represent the proposed correlation (eqn. 3.21). The corrected Mendelson equation (eqn. 3.3) constant was found to be 1.04. Bubble rise velocities generally decreased with increasing particle density and solids fraction. The experimental data are shown versus the correlation predictions at constant particle specific gravity for three particles in Fig. 3.13a - c. Model Comparisons Comparisons of the proposed correlation (eqn. 3.23) as well as literature models to the experimental data are shown in Fig. 3.14a - c for three bubble sizes. The literature models include those of Darton (1985) and Tsuchiya et al. (1990). The pseudo-homogeneous model (Darton, 1985) was obtained by combining the apparent liquid densities and viscosities (eqns. 3.12 and 3.13) along with the bubble rise velocity given by Tsuchiya et al. (1990) with K, and K2 equal to one. The model of Jang (1989) (eqns. 3.14 and 3.15) was not analyzed because the parameter, n, in eqn. 3.14 was correlated in terms of the glass bead particle diameter. This model might have been adapted to other particle densities if the parameter, n, had been correlated in terms of the particle terminal velocity. The semi-empirical correlation (eqn. 3.23) provided a very reasonable fit to the experimental data as shown in 101 35.00 A 30.00- ”’ l \ g » v 25.00. .«i‘ t) 2 20 00 <11 - '- > .9. 3 .3 15.00- 00 '8 4,-3 10.00- Q) t. t. o. 0 5.001 — Correlation (Bqtn. 323) o S.G. - 1.46 A S.G. - 1.23 0.00 o S.G. - 1.02 1 0.00 0.10 0.20 0.30 0.40 0.50 Solids Fraction Fig. 3.12. Comparison of the experimental data with the developed correlation (eqn. 3.23). a.) 61c = 0.22 cm. 102 35.00 A 30.00- a: \ E 3, 25.00 _ 9?! 8 '5 20.00- > e a: :9 ‘ ' :1 15.00- 1 o (I) a i s . ° 0 . 48’ 10.00- i ‘ A s - O 5.00- -— Correlation (Bqtn. 3.23) a S.G. - 2.50 a S.G. -1.23 0.00 o S.G.-1.02 I 1 I T 0.00 0.1 0 0.20 0.30 0.40 0.50 Solids Fraction b.) d, = 0.44 cm. d 103 35.00 A 30.00- (I) \ E 3 25.00- >. +1 "13 o . 75 20.00- 0 8 ~— > 8 0 O g 15 00 ‘ I :1 ' ' e ' c0 ‘ 9 a s ‘ 2 '8 10.00- : 0) D t o 0 5.00- — Correlation (eqn. 323) o 5.0. - 1.46 A S.G. - 1.23 o S.G. - 1.02 0°00 1 1 1 . 1 0.00 0.1 0 0.20 0.30 0.40 Solids Fraction = 0.62 cm. 0 0.50 35.00 104 30.00~ 25.00- 20.00} 15.00-l Corrected Bubble Velocity (cm/s) Correlation (eqn. 3.23) S.G. - 1.46 8.0. - 1.23 S.G. - 1.02 10.00- 5.00- — D A 0.00 ° 0.00 d.) d, = 0.85 cm. 0.10 0320 0.30 0.40 Solids Fraction 0.50 105 O ODD .mqoe 20.00-J 1 5.00- 1 0.00- Corrected Bubble Velocity (cm/s) 5'00" -— Correlation (13.161. 3.23) A S.G. - 1.23 0.00 o S.G. - 1.02 0.00 0.10 0.20 0.30 0.40 0.50 Solids Fraction e.) d 1.1 cm. 1: 106 ’a t \ I 3 E o i 0 V .3." . 0 25000" .9. on > a) 20.00- 3 .0 :3 m 15.00- .0 0 "6 g 10.00- 0 0 5'00“ -- Correlation (eqn. 3.23) A S.G. - 1.23 o S.G. - 1.02 0‘00 I I I I 0.00 0.10 0.20 0.30 0.40 0.50 Solids Fraction f.) d, = 2.0 cm. 107 Corrected Bubble Velocity (cm/s) 10.00- B 5.0.}, — Correlation (Bqtn. 3.23) a abs-1L013n A db - 0.62 cm 0.00 a db -. 0.22 cm 0.00 0.110 0.20 0.30 0.40 0.50 Solids Fraction Fig. 3.13. Comparison of experimental data vs. the correlation (eqn. 3.23) predictions at constant particle specific gravity. a.) U,==1.86 cm/s. 108 35.00 A 30.001 01 \ E . 3 25.00 2 a 9?? ’ a 8 a O '35 20.004 ' ’ > 8 a .9. 3 f8 3 15.00- A m . 3 A '8 8 . *5 10.00- 6 : A A 0.) O o t ° 3 o 8 0 5,00- __ Correlation (Bqtn. 323) a db - 1.1 cm A db - 0.62 cm 0.00 O db '- 0.22 cm 0.00 0.10 0.20 0.30 0.110 0.50 Solids Fraction b.) U, = 18.8 cm/s. Corrected Bubble Velocity (cm/s) c.) 109 35.00 30.00- 20.00- 15.00- 10.00- a 5.00- 8 ° 2 O O °°°°" _ Correlation (eqn. 323) 8 A db - 0.44 cm 0 db - 0.22 cm “5.00 I . l I I 0.00 0.10 0.20 0.30 0.40 Ut_= 33.3 cm/s. Solids F roction 0.50 110 35.00 Ub (cm/s) 1 5.00- l 0.00 - 5.00- O ”t = 18.8 cm/s \ ..-- Darton (1985) \\ _.... Tsuchiya et al. (1990) _ Correlation (Elm. 3°23) 0.00 l 1 I 1 l 0.0 0.10 0.20 0.30 0.40 0.50 Solids Fraction . 3.14. Literature and correlation (eqn. 3.23) comparisons to experimental data (Tsuchiya et a1. 1990; Darton, 1985). a.) dc = 0.22 cm. 111 25.00 20.00 ‘\ 15.00- Ub(cm/s) 10.00- 5.00- . O Ut = 18.8 cm/s \ \ ---- Darton (1985) \ ‘ — — Tsuchiya et al. (1990) 0.00 —- Experlmental Correlation I I I I 0.00 0.10 0.20 0.30 0.40 Solids Fraction b.) dc = 0.62 cm. 0.50 c.) d C Ub (cm/s) 112 35.00 30.00- 25.00 “““““““ 4 ~~ _ g 8 a“ 8 ____________ _>_. \ \ \ 20.00" ‘- 15.00- 10.00- 5.00- O Ut = 1.86 cm/s ---- Darton (1985) -- Tsuchiya et' al. (1990) -— Correlation (Bqtn. 3.23) 0-00 a 1 1 I 0.00 0.10 0.20 0.30 0.40 Solids Fraction 1.]. C111. 0.50 113 Fig. 3.14a - c. The pseudo-homogeneous model generally fit the pattern of the experimental data though not always reasonably. Bubble rise velocities decreased with increasing solids fraction. Also, the effect was more apparent for smaller bubbles. The pseudohomogeneous concept, as given by Egtns. 3.12 and 3.13, was developed for small glass beads (dv'< 0.5 mm) and spherical cap bubbles. While the particle density is accounted for, the particle size is not. Thus, the model is not applicable to the range of experimental conditions studied. The model of Tsuchiya et al. (1990) provided a reasonable fit to experimental data at the larger bubble sizes (Fig. 3.14b - c.). However, the model severely over-predicted bubble rise velocities for the smaller bubble with light particles (Fig. 14a.). This result may have been expected since, for the experimental conditions used (dc>»1.2 cm), light particles (U,<.2 cm/s) had only a small effect on the bubble rise velocity. The empirical parameters K,‘and K2 (Egtns. 3.17 and 3.18) were obtained from these results. Because the proposed correlation is semi-empirical, the model would be expected to provide a reasonable fit to the experimental data used to determine the values of the coefficients. However, as illustrated in Fig. 3.15a - b., the correlation (Egtn. 3.23) fits literature values for solids fractions up to 0.43 for different particle sizes. The experimental parameters, a, and a2, were linearly interpolated with the particle terminal velocity in Fig. 3.8 114 40.00 ‘ 0 Darton and Harrison (1974) — Correlation (Egtn. 323) 35.00- 30.00- 25.00- 20.00- Ub (cm/s) l 5.00- 10.00- 5.00- 0.00 . , . , . , . , . 0.00 0.50 l .00 i .50 2.00 2.50 de (cm) Fig. 3.15. Correlation (Egtn. 3.23) comparisons to literature data. a.) Darton and Harrison, 1975. 115 40.00 0 dp = 0.163 mm I dp = 0.774 mm 3500.. A dp= 1.00 mm . — Correlation (Egtn. 3.23) I 30.00- A 25.00‘ a) \ g 20.00- J) I) 15.00- 10.00- 5.00- O'cc'l'l'l‘l‘ 0.00 0.50 1 .00 1 .50 2.00 2.50 de (cm) b.) Jang, 1989. 116 and 3.9. Thus, the particle terminal velocity provides a good criterion for the estimation of a1 and (12. The flow of a bubble through a liquid-solid suspension may be viewed as heterogeneous or pseudo-homogeneous depending upon the ratio of the bubble to solid particle diameters (Fan and Tsuchiya, 1989). If this ratio is small (dc==> dp) , the bubble rises as if the fluidized bed were a pseudo-homogeneous suspension. In this case, the bed can be assigned an apparent viscosity and density. Darton (1985) took this approach. However, he represented the apparent viscosity (Egtn. 3.12) as a function of the solids fraction only. The effects of particle density and size were not accounted for. Hydrodynamic interaction parameters (for example, k in eqn. 3.7) are dependent upon properties of the solid particle (Rutgers, 1962). Thus, a more appropriate representation of an apparent bed viscosity would include properties of the solid phase in addition to the solids fraction. An example of this analysis is given in Chapter 4. Virial expansions in the solids fractions have been used to describe an apparent suspension viscosity (Rutgers, 1962) as well as the hindered settling of a sphere 117 (Batchelor, 1972). Also, this expansion is similar to a virial expansion in volume or density to describe non-ideal gases (McQuarrie, 1976). However, Egtn. 3.23 does not define an apparent viscosity. An apparent viscosity would not be a function of the bubble diameter as represented in eqn. 3.23. At large bubble to particle diameter ratios, an apparent bed viscosity would be dependent upon the solid properties only. As this ratio is decreased, however, interactions between the bubble and particles would be dependent on both the particle and bubble properties. A large change in interactions would be expected at small bubble diameters. The virial expansion in solids fraction with analogy towards the hindered settling of a sphere accounts for the heterogeneous nature of the suspension at low bubble to particle diameter ratios and the pseudo-homogeneous nature at high ratios. The particle-bubble interactions at constant solids fractions represented by a, and 022 are strongly influenced by the bubble size and particle properties at small bubble diameters. As a result, these parameters change rapidly over the range of 0.201< 0.20 cm, solids fractions < 0.43, and a range of particle terminal velocities (1.8 < U,< 35 cm/s). These conditions cover the practical range of fluidized bed application. In addition, an analysis for small bubbles UL,< 0.20 cm) has been proposed for dispersion of the liquid phase (eqn. 3.24). Previously, correlations have generally been limited to glass particles hi,< 1mm) as the solid phase and spherical cap bubbles as the gas phase. Attempts to account for the bubble rise velocity of small bubbles (i.e., Fan, 1990) have not accounted for dispersion of the liquid phase. Chapter 4: RECOMMENDATIONS FOR FUTURE RESEARCH The results of Chapter 2 indicate that a large variation in gas hold-up occurs depending upon system parameters such as solid properties, liquid properties, and type of gas sparger used. This variance makes comparison with literature results and predictions of column operation difficult. For bioreactor operation, depending mainly upon the gas sparger configuration, hold-up values should be between those obtained for a non-coalescing and a coalescing medium (Van’t Riet, 1983). An empirical correlation taking into account these two extremes would be useful. A semi-empirical correlation to describe the bubble rise velocity in liquid-solid reactors was utilized in Chapter 3. The form of this correlation (eqn. 3.23) was developed with reference to the hindered settling of a sphere. This form fit the data quite well. The hindered settling of spheres derivation involves particles at low Reynold's numbers (Re << 1). As indicated in Fig. 3.4, the solid phase may remain approximately stationary during the bubble ascent. Thus, a low Reynold’s number approximation may be appropriate. The bubble, however, may rise at Reynold’s numbers up to 10000. It is recommended that the form of the proposed correlation (eqn. 3.23) be 123 124 theoretically justified if possible. Given the complicated nature of bubbles and bubble wake dynamics (a bubble rise velocity model taking into account the bubble wake has not been developed), this justification would be difficult. While the hindered settling analogy correlation presented in Chapter 3 (Egtn. 3.23) covers a large range of solids fractions, it could be extended to more concentrated suspensions. eqn. 3.24 could be modified to a cubic or higher order expansion in solids fraction. This modification would probably extend the correlation to the maximum solids fraction used in fluidized beds (approximately 0.55). As indicated in Chapter 3, correlations proposed by Fan (1990), Jang (1989), and Tsuchiya et al. (1990) may only be valid for small bubbles (dc<:0.20 cm) for plug flow of the liquid phase. To describe the bubble rise velocity of small bubbles, for example, in microbubble dispersions, knowledge of the liquid flow pattern would be essential. A method was proposed in Chapter 3 to account for deviations from ideal liquid flow (eqn. 3.24). It is recommended that this equation be tested for small bubbles (dc < 0.2 cm) . The hindered settling analogy presented in Chapter 3 was fairly successful at approximating bubble-particle interactions in three-phase reactors. This correlation (eqn. 3.23) is only valid for a single bubble rising in a liquid-solid suspension. The form of this equation may be useful in accounting for bubble-bubble interactions. 125 Namely, an expansion in the bubble fraction (similarly, the gas fraction) could be applied to a bubble rising in a multi-bubble system. Then, knowing the bubble formation characteristics of the gas sparger (bubble size and frequency), the gas hold-up in the reactor could be obtained. This analysis would be applicable to a non- coalescing medium, because bubble coalescence would not be accounted for. A liquid-solid suspension is often characterized in terms of an apparent viscosity and density. For three-phase fluidized beds, a pseudo-homogeneous view of the liquid- solid suspension would be valid for large bubble to particle diameter ratios. This approach was taken by Darton (1985). However, the apparent viscosity was only a function of the solids fraction and not the solids properties (for example, particle size and density). To cover the range of solids properties, it would be useful to define an apparent viscosity in terms of the solids characteristics. An expansion in the solids fractions (Rutgers, 1962) with the coefficients as functions of the solids properties is recommended. The effects of temperature on the proposed bubble rise velocity correlation should be examined. Namely, the particle terminal velocity is dependent upon the system temperature. While the particle terminal velocity is often a correlating parameter (Fan and Tsuchiya, 1990), a particle Reynold's number may be more appropriate in accounting for 126 ‘temperature effects. It may be useful to look at the complicated nature of three-phase fluidized bed reactors in terms of a statistical description of the particle and bubble locations. This type of analysis has been used by Batchelor (1972) in studying sedimentation in a dilute dispersion of spheres. BIBLIOGRAPHY Bailey, J.E., and D.F. Ollis, Biochemical Engineering Fundamentals, 2nd Ed., McGraw-Hill Book Co., New York, NY 1986. Batchelor, G.K., J. Fluid Mech. 52, 245, 1972. "Sedimentation in a Dilute Dispersion of Spheres." Batchelor, G.K., and J.T. Green, J. Fluidiflech.,§§, 401, 1972. "The determination of the bulk stress in a suspension of spherical particles to order cafl' Bly, M.J., and R.M. Worden, Applied Biochemistry and Biotechnology 24125, 553, 1990. "Gas Holdup in a Three-Phase Fluidized-Bed Bioreactor." Cussler, E.L., Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, New York, NY 1984. Dakshinamurty, P., V. Subrahmanyan, and J. Nageswara Rao, Ind. Eng. Chem. Process Des. Develop. 19, 322, 1971. "Bed Porosities in Gas-Liquid Fluidization." Darton, R.C., and D. Harrison, Trans. Inst. Chem. Engrs. 5;, 301, 1974."The Rise of Single Gas Bubbles in Liquid Fluidised Beds." Darton, R. C., Fluidization, 2nd ed. (J.F. Davidson, R. Clift, and D. Harrison, eds.), Chap. 15, pp. 495-528, Academic Press, London 1985. "The Physical Behaviour of Three-Phase Fluidized Beds." Darton, R.C., and D. Harrison, Chem. Eng! Sci. 39, 581, 1975. "Gas and Liquid Hold-up in Three-Phase Fluidisation." Davies, R.M. and 6.1. Taylor, Proc. Roy. Soc. A. 200, 375, 1950. Davison, B.H., Presented at 194th ACS National Meeting, 127 128 1987, "Hydrodynamics in a Three-Phase Fluidized—Bed Bioreactor: Nonintrusive Measurement of Gas Holdup and Liquid Dispersion by Conductivity." De Oliveira Mendes, C.L., and R.Y. Qassim, Chem. Eng. J. g§J 21, 1984. "Application of the Davies-Taylor Equation to a Large Bubble Rise in Liquid-fluidized Beds." Deckwer, W., R. Burckhart, and G. 2011, Chem. Eng. Sci. 22, 2177, 1974. "Mixing and Mass Transfer in Tall Bubble Columns." Dhanuka, V.R. and J.B. Stepanek, grog. Second Eng, Fpgpdation Qonf., J.F. Davidson and D.L. Keairns, Eds., Cambridge University Press p. 190, 1978. "Gas and Liquid Hold-up and Pressure Drop Measurements in a Three-Phase Fluidized Bed." Einstein, A., Ann. Phys. 12, 289, 1906. Epstein, N., Can. J. of Chem. Eng. 52, 649, 1981. "Three-Phase Fluidization: Some Knowledge Gaps." Fan, L. -S., Gas-Liguid-Solid Fluidization Engineering, Butterworth Publishing, Boston, MA 1989. Fan, L. -S., and K. Tsuchiya, Bubble Wake Dynamics in Liguids and Liguid-Solid Suspensions, Butterworth - Heineman, Stoneham, MA 1990. Frijlink, J.J., and J.M. Smith, International Conference on Bioreactor Fluid Dynamics, paper 23, 1986. "Coalescence in Three Phase Systems." Grover, G., C. Rode, and R. Chaudhari, Can. J. of Chem. Eng. pg, 501, 1986. "Effect of Temperature on Flow Regimes and Gas Hold-up in a Bubble Column." Haas, P., AIChE J. 2;, 383, 1975. "Formation of Liquid drop with Uniform and Controlled Diameters at Rates of 10 to 105 Drops per Minute." Haberman, W. L. and R. K. Morton, David W. Taylor Model Basin Report 802, Navy Dept., Washington, DC 1953. "An Experimental Investigation of the Drag and Shape of Air Bubbles Rising in Various Liquids," Hadamard, Comp. Rend. 1 4, 1735, 1911. Haque, M.W., and K. Nigan, Chem. Eng. J., 3;, 63, 1986. "Optimum Gas Sparger Design for Bubble Columns with a Low Height-to-Diameter Ratio." 129 Henricksen, H.K., and K. Ostergaard, Chem. Eng. J. 1, 141, 1974. "Characteristics of Large Two-Dimensional Air Bubbles in Liquids and in Three-Phase Fluidised Beds." Hikita, H., S. Asai, K. Tanigawa, K. Segawa, and M. Kitao, Chem. Eng. J. 29, 59, 1980. "Gas Hold-up in Bubble Columns." - Hill, C.G., An Introduction to Chemical Engineering Kinetics and Reactor Design, Ch. 11, John Wiley and Sons, New York, NY 1977. Jang, C.-S., "Hydrodynamics of Liquid-Solid Fluidization," M.S. Thesis, Ohio State Univ., Columbus, OH 1989. Jean, R.-H. and L.-S. Fan, Chem. Eng. Sci. 45, 1057, 1990."Rise Velocity and Gas-Liquid Mass Transfer of a Single Large Bubble in Liquids and Liquid-Solid Fluidized Beds." Jones, D.R.M., Ph.D Thesis, 1965, University of Cambridge. Joosten, G., J. Schilder, and J. Janssen, Chem. Eng. Sci. 22, 563, 1977. "The influence of suspended solid material on the gas-liquid mass transfer in stirred gas-liquid contactors." Joshi, J.B. and M.M. Sharma, Trans. Inst. Chem. Engrs. al. 244 1979. Kara, S., B.G. Kelkar, Y.T. Shah, and N. Carr, Ind. Eng. Chem. Process Des. Dev. 2;, 584, 1982. "Hydrodynamics and Axial Mixing in a Three-Phase Bubble Column." Kim, S., C. Baker, and M. Bergougnou, Can. J. Chem. Eng. pg, 695, 1972. "Hold-up and Axial Mixing Characteristics in Two and Three Phase Fluidized Beds." Kim, S.D., C. Baker, and M. Bergougnou, Can. J. of Chem. Eng. 52, 134, 1975. "Phase Holdup Characteristics of Three Phase Fluidized Beds." Kojima, E., T. Akehata, and T. Shirai, J. Chem. Eng. Japan 1. 45, 1968. Lee, J.C., and D.L. Meyrick, rans. Instn. Chem. En rs. p.T37, 1970. "Gas-Liquid Interfacial Areas in Salt Solutions in an Agitated Tank." Lessard, R., and S. Ziemeinski, Ind. Eng. Chem. Fund. 22, 260, 1971. "Bubble Coalescence and Gas Transfer in Aqueous Electrolytic Solutions." 130 Levich, V.G., Physicochemical Hydrodynamics, Prentice - Hall, Englewood Cliffs, NJ 1962. Loh,V.Y., S.R. Richards, and P. Richmond, International Conference on Bioreactor Fluid Dynamics, Paper 2, 1986. "Fluid Dynamics and Mass Transfer in a Three-Phase Circulating Bed Fermenter." Marrucci, G., and L. Nicodemo, Chem. Ena. Sci. 22, 1257, 1967. "Coalescence of gas bubbles in aqueous solutions of inorganic electrolytes." Massimilla, L., et al., Brit. Chem. Egg. 6, 232, 1961. McQuarrie, D.A., Stat'stical Mechan'cs, Harper and Row, New York, NY 1987. Mendelson, H. 0., AIChE J. 1;, 251, 1967. "The Prediction of Bubble Terminal Velocities from Wave Theory." Merzkirch, W., Flow Visualization, 2nd Edition, Academic Press Inc., New York, NY 1987. Michelsen, M.L., and K. Ostergaard, Chem. Eng. J. 2, 37, 1970. "Hold-up and Fluid Mixing in Gas-Liquid Fluidised Beds." Morooka, S., K. Uchida, and Y. Kato, J. Chem. Eng. Japan ;§, 29, 1982. Muroyama, K., and L.S. Fan, AICHE J. 2;, 1, 1985. "Fundamentals of Gas-Liquid-Solid Fluidization." Nguyen-Tien, K., A.N. Patwari, A. Schumpe, and W.D. Deckwer, AIChE J. 2;, 194, 1985. "Gas-Liquid Mass Transfer in Fluidized Particle Beds." Nigan, K., and A. Schumpe, AIChE J. 22, 328, 1987. "Gas-Liquid Mass Transfer in a Bubble Column with Suspended Solids." Ostergaard, K., Studies of Gas-Liguid Fluidization, Danish Technical Press, Copenhagen, Denmark, 1969. Ostergaard, K., Fluidization, J.F. Davidson and D. Harrison, Eds., Academic Press, London, p.751, 1971. "Three-phase Fluidization." Ostergaard, K., and P.I. Theisen, Chem. Eng. Sci. 21. 413, 1966. "The effect of particle size and bed height on the expansion of mixed phase (g-l) fluidized beds." Ozturk, S.S., and A. Schumpe, ghem. Eng. Sci. 22, 1781, 131 1987. "The influence of suspended solids on oxygen transfer to organic liquids in a bubble column." Patwari, A. K. Nguyen-Tien, A. Schumpe, and W. Deckwer, Chem. Eng. Commun. 22, p.49, 1986. "Three-Phase Fluidized Beds With Viscous Liquid: Hydrodynamics and Mass Transfer." Reed, C.C., and J.L. Anderson, AIChE J. 26, 816, 1980. "Hindered Settling of a Suspension at Low Reynold’s Number." Reith, T., S. Renken, and B. Israel, Chem. Eng. Sgi. 22, 619, 1968. "Gas hold-up and axial mixing in the fluid phase of bubble columns." Rice, R., J. Tupperainen, and R. Hedge, Can. J. of Chem. Eng. pg, 677, 1981. "Dispersion and Hold-up in Bubble Columns; Comparison of Rigid and Flexible Spargers." Rutgers, I.R., Rheol. Acta 2, 202, 1962. "Relative Viscosity and Concentration." Rybczynski, Bull. intern. acad. sci. Cracovie (A), 40, 1911. Shah, Y.T., B.G. Kelkar, and S.P. Godbole, AICHE J. 22, 63, 1982. "Design Parameters Estimations for Bubble Column Reactors." Smith, E.L., M. Jamialagmadi, J.T. Olajuyigbe, and J. Shayegan Salek, Int. Conf. on Bioreactor F2uid D namics, Paper 4, 1986. "The Effects of Phase Properties on Bubble Behaviors, Gas Hold-up, and Mixing in Bubble Columns." Stokes, G. G., Irans. Camb. Phil. Soc. 2, 8, 1851. "On the Effect of the Internal Friction of Fluids on the Motion of Pendulums." Tsuchiya, K., G.-H. Song, and L.S. Fan, Chem. Eng. Sci. 2;, 1429, 1990. "Effects of Particle Properties on Bubble Rise and Wake in a 2-D Liquid-Solid Fluidized Bed." Van't Riet, K., Ind. Eng. Chem. Process Des. Dev. 22, 337, 1979. "Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels." Van't Riet, K., Trends in Biotechnology 2, 113, 1983. "Mass transfer in fermentation." Verlaan, P., and J. Tramper, Int. Conf. on Bioreactors and Biot a sformations, Nov., 1987, Paper I4, p.363. "Hydrodynamics, Axial Dispersion, and Gas-Liquid Oxygen 132 Transfer in an Airlift-Loop Bioreactor with Three-Phase Flow." Wallis, G.B., One-Dimensionai Two Phase Flow, McGraw-Hill, New York, NY 1969. Worden, R.M., R. Subramanian, M.J. Bly, 8. Winter, and C.L. Aronson, Appiied Biochemistry and Biotechnology 28129, 267, 1991. "Growth Kinetics of Bacillus Stearothermophilus BR 219." "I1111111111“