Characteristics of Gas-Fluidized Beds in Different Flow Regimes

Jan 20, 1999 - the Hurst exponent, correlation dimension, and Kol- mogorov entropysare also calculated and compared for the same conditions. Statistic...
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Ind. Eng. Chem. Res. 1999, 38, 803-811

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Characteristics of Gas-Fluidized Beds in Different Flow Regimes D. Bai, A. S. Issangya, and J. R. Grace* Department of Chemical and Bio-Resource Engineering, University of British Columbia, 2216 Main Mall, Vancouver, British Columbia, Canada V6T 1Z4

Hydrodynamic characteristics among different flow regimes of gas fluidized beds are compared on the basis of experiments with fluidized catalytic cracking particles in a 76.2 mm diameter riser. Pressure and local voidage fluctuations were analyzed using both statistical and chaotic tools. The standard deviations of local voidage fluctuations are much lower in a high-density circulating fluidized-bed riser than in the bubbling and turbulent flow regimes, even for identical local time-mean voidages. A chaotic time series analysis can distinguish flow structures of the various flow regimes. Bifractal structures, characterized by two Hurst exponents, two correlation dimensions, and two Kolmogorov entropies, characterize the motions of the dilute and emulsion phases in the bubbling and turbulent flow regimes. The two-phase structure becomes less distinguishable with increasing gas velocity, eventually disappearing on reaching dilute phase transport. However, for high solids concentrations, the bifractal character persists, suggesting that particles may travel in two different forms. Radial profiles of chaotic parameters are relatively flat in the bubbling and turbulent flow regimes, but significantly nonuniform in dense suspension upflow. Flow behavior in the high-density riser and in the dense bottom region of a low-density riser operated in the fast fluidization regime differ from the bubbling and turbulent flow regimes, even when compared where there are equal local voidages. Introduction Gas fluidized beds have been widely classified into several flow regimes including bubbling fluidization, turbulent fluidization, fast fluidization, and dilute pneumatic conveying. We have recently suggested1 a further flow regime, dense suspension upflow, to cover the observed flow in high-density risers operated with approximately 20% solids by volume and no downflow of particles at the outer wall. Despite the extensive literature devoted to gas-solid fluidized beds over the past 4 decades, flow structures in the various hydrodynamic regimes are still not well-understood. Some of the difficulties that stand in the way of achieving a full understanding include the following: (1) There are many different experimental techniques available for studying gas-solid systems,2-4 each subject to limitations in terms of such factors as interference with local flow behavior, indistinct delineation of the measuring volume, time response, drift, and so forth. (2) The signals obtained from measurements, whether taken at the wall or in the interior of flowing gas-solids suspensions, can be analyzed using a wide variety of techniques, statistical5 or those based on chaos analysis.5 There is no standardization and limited agreement on the relative merits of the various alternative measurement analysis tools. (3) While considerable progress has been made in applying scaling laws to fluidized beds7 and in solving fundamental governing equations of motion for fluidized systems,8,9 the complexity of the systems and the number of variables has so far limited the utility of these approaches. (4) There has been very little work for conditions which are difficult to explore experimentally, even when * To whom correspondence should be addressed. Tel.: 604822-3121. Fax: 604-822-6003. E-mail: [email protected].

they are important industrially, such as flow in highdensity risers. The study reported in this paper seeks to improve our understanding of the complex hydrodynamic behavior in dense suspension upflow in comparison to more conventional flow regimes of gas fluidized beds. Dynamic pressure and local voidage signals were measured for fluidized catalytic cracking (FCC) particles in different flow regimes in a 76.2 mm diameter riser. Statistical properties of the signals such as averages, standard deviations, intermittency indices, probability distributions, and amplitude spectra, as well as cycle frequencies, are compared with those for bubbling, turbulent, and fast fluidization. Three chaotic measuress the Hurst exponent, correlation dimension, and Kolmogorov entropysare also calculated and compared for the same conditions. Statistical and chaotic methods lead to similar conclusions. Experimental Section 1. Apparatus. The experimental high-density circulating fluidized bed (HDCFB) equipment is shown schematically in Figure 1. Measurements were carried out in the main riser (riser A): i.d. (internal diameter) 0.0762 m and height 6.1 m. Riser B had an internal diameter of 0.102 m and a height of 8.32 m. Air from a blower and a compressor was fed to the two risers, allowing independent control of their flows. Compressed air was also introduced into the two downcomers (both 0.305 m i.d.) where the solids were maintained at minimum fluidization. The particle flows from downcomer 2 to riser A and from downcomer 1 to riser B are both controlled by gate valves. Steady state was reached by adjusting these valves until the levels of solids in the two downcomers remained constant. At the exit of riser A, solids were separated from the air by an inertial gas-solids separator and cyclone and returned to down-

10.1021/ie9803873 CCC: $18.00 © 1999 American Chemical Society Published on Web 01/20/1999

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Figure 1. Schematic of the dual-loop high-density circulating fluidized-bed system: (1) riser A; (2) inertial gas-solid separator; (3) downcomer 1; (4) riser B; (5) downcomer 2; (6) baghouse; (7) gate valve; (8) cyclone; (9) butterfly valve; (10) orifice meter; (11) rotameter; (12) gate valve.

comer 1. Particles entrained from riser B were separated by a cyclone and returned to downcomer 2 where the solids level was high enough to provide the pressure head required to push solids into riser A at sufficient circulation fluxes that high solids concentrations were achieved in riser A. In the bubbling flow regime, no significant solids were carried out of riser A. In this case, the solids flow valve from downcomer 2 was closed. With increasing gas velocity, the bed operated in the turbulent flow regime and solids were continuously fed into riser A from downcomer 2 in a carefully controlled manner to maintain a constant solids inventory (corresponding to a static bed height of 0.46 m) in riser A. The optical fiber probe was inserted into the bed 0.38 m above the distributor. It was confirmed visually and from the pressure fluctuations that there was no slug flow regime for the system studied, even though the static bed height to bed diameter ratio was >6. This is probably because the maximum stable bubble size, estimated to be 0.027 m, is much less than the column diameter.10 FCC particles of mean diameter 70 µm and density 1600 kg/m3 were used in the experiments. Measurements of pressure fluctuations as a function of superficial gas velocity indicated that the transition velocity, Uc, from bubbling to the turbulent flow regime was 0.44 m/s, consistent with predictions from a previous paper.11 The significant entrainment velocity, Use, the lower limit of the fast fluidization regime, is estimated11 to be 1.23 m/s. 2. Measurement Techniques. A reflection-type optical fiber probe12 with a tip diameter of 1.5 mm was used to measure local instantaneous voidages. The

probe is composed of two bundles of 0.015 mm diameter fibers, with alternating layers for light projection and reception. The receiving optical fibers transmit visible light reflected by particles to a photomultiplier, and the signals are then logged into a personal computer via an A/D converter. For our experiments, the probe was inserted into the riser at different levels. At each level, data were recorded at 10 radial positions from the axis to the wall. A separate apparatus13 was used to calibrate the optical probe, with particles being dropped from a hopper through a tube. A small section containing the probe was then isolated by simultaneously closing two identical solenoid valves, one above and the other below the probe, and the solids concentration was determined from the fraction of volume occupied by solids in that section. For the experiments in the bubbling and turbulent flow regimes, absolute pressure signals were recorded at z ) 0.03 m, while differential pressure signals were measured between z ) 0.03 m and z ) 0.38 m above the distributor. For the experiments under fast fluidization and dense suspension upflow conditions, 10 rapidresponse (response time: 1 ms) differential pressure transducers (Omega, PX162) were connected to equally spaced pressure taps, while absolute pressure fluctuations near the riser bottom (z ) 0.22 m) were also measured. All pressure ports were flush with the wall, with suitable precautions taken to ensure accurate readings.6 To prevent blockage by fine particles, each port was covered by a porous screen and purged frequently with air. Pressure signals were logged into a computer via an A/D converter (DAS08-EXP16) with 12-bit resolution and accuracy better than 99.99%. A digital data acquisition system, Labtech Notebook Software, was used to record the pressure and local voidage signals. The data sampling frequency was 100 Hz, with 10 000 individual points recorded for each data point given below. This combination of the sampling rate and sampling length ensured that the full spectra of hydrodynamic signals of interest were captured from the gas fluidized bed.14 We have demonstrated that the number of data points used in the chaos analysis is sufficient by showing that there was negligible change in the estimated correlation dimension for N > 3000 with a sufficiently large vector. A low-pass filter and numerical smoothing were employed to reduce lowamplitude, high-frequency noise. Results and Discussion 1. Statistical Properties. Typical local voidage fluctuation signals for two radial positions, one at the axis and the other near the wall of the column, are presented in Figure 2 for the bubbling (U ) 0.24 m/s), turbulent (U ) 0.67 m/s), and dense suspension upflow (Gs ) 425 kg/m2s, U ) 8 m/s) regimes. Voidage peaks near 1 and the voidage at minimum fluidization, mf ()0.45 here), show the coexistence of voids and dense emulsion in the bubbling and turbulent flow regimes, with some decreases in void frequency and volume fraction toward the wall of the experimental column. For the dense suspension upflow case, there is a less concentrated suspension carried upward in the core and a suspension of intermediate density rising near the wall with an absence of voids at all radial positions. The periodicity and regularity of the signal are also seen to decrease with increasing gas velocity. This observation is examined quantitatively in terms of probability

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Figure 2. Typical local voidage fluctuation signals for three superficial gas velocities at two radial positions. Data were measured at z ) 0.38 m for the bubbling and turbulent fluidization cases and at z ) 1.57 m for the dense suspension upflow conditions.

Figure 3. Probability density distributions of the time series corresponding to Figure 2.

density distributions in Figure 3. It is seen that all three flow regimes (B ) bubbling, T ) turbulent, and DSU ) dense suspension upflow) show an evolution to increased low-voidage content with increasing radial distance, with greater evolution in the bubbling regime and the least shift for the DSU case. Amplitude spectra for three gas velocities corresponding to the bubbling (U ) 0.24 m/s), turbulent (U ) 0.67 m/s), and dense suspension upflow (Gs ) 425 kg/m2s, U ) 8 m/s) regimes are plotted in Figure 4. In the bubbling regime, there is a dominant frequency of about 1.5-2

Hz at the bed center and 0.5-1 Hz near the wall. In the turbulent regime, the dominant frequency appears to decrease to 0.4-1.5 Hz, depending on the radial position. A very broad spectrum with no clear dominant frequency is usually obtained for the high-density riser signals, suggesting a lesser degree of periodic motion in dense suspension upflow than in the bubbling and turbulent flow regimes. The measured dominant frequencies and their variation are in good agreement with those reported by Chehbouni et al.15 who analyzed local voidage fluctuations from a capacitance probe in the bubbling and turbulent flow regimes, and by Lee and Kim16 who analyzed pressure fluctuations in a turbulent bed. Xia et al.17 and Bouillard and Miller18 also observed very low dominant frequencies in the fast fluidization regime. Figure 5 shows radial profiles of the local time-mean voidage, standard deviation, and intermittency index19 for the three flow regimes investigated. The local timemean voidage is lowest and has a relatively flat radial distribution in the bubbling regime. With increasing gas velocity to the turbulent regime, the local voidage in the center region increases, and the radial distribution of time-mean voidage becomes steeper. In the dense suspension upflow case, the central region becomes more dilute, but the local time-mean voidages at the riser wall are almost the same as those in the bubbling and turbulent regimes. This suggests that a dilute core surrounded by a dense-annular zone still exists in the HDCFB riser. Note the marked difference among the three flow regimes. Because of the presence of voids, the standard deviation of voidage and intermittency index in the bubbling and turbulent flow regimes are much higher than those in dense suspension upflow. The standard deviation and intermittency index are higher at the center of the column and decrease monotonically toward the wall in the bubbling regime. In the turbulent regime, a transitional regime, the radial profiles of the standard deviation and intermittency index change to a mode rather like the dense suspension upflow profiles where both parameters are lower at the

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Figure 4. Amplitude spectra of the local voidage fluctuation signals for three gas velocities and three radial positions.

Figure 6. Standard deviation and intermittency index as functions of local time-mean voidage for three flow regimes at 10 radial positions and various heights. Figure 5. Radial distributions of time-mean voidage, standard deviation, and intermittency index for different flow regimes.

center, increase with increasing dimensionless radial position (φ ) radial coordinate/column radius) to a maximum at φ ≈ 0.8 and decrease thereafter toward the wall. This suggests that the radial position where the highest degree of phase segregation occurs is at the axis of the column for the bubbling regime, moving to near the wall for dense suspension upflow. Note the similarity in the intermittency index profiles in the latter case for net circulation fluxes, Gs, of 249 and 425 kg/m2‚s. Figure 6 further demonstrates the difference between dense suspension upflow and the bubbling and turbulent flow regimes by plotting the standard deviation and intermittency index against the corresponding local time-mean voidage. At equal values of local time-mean voidage, there is little or no difference between the bubbling and turbulent flow regimes, suggesting that the bubbling and turbulent flow regimes may have similar two-phase structures involving voids in a dense

suspension. A similar conclusion was reached by Werther and Wein.20 However, Figure 6 shows that the standard deviation and intermittency index for dense suspension upflow conditions are significantly smaller than those for the bubbling and turbulent regimes, suggesting that the local structures are quite different, even when the local solids concentration is as high as in the bubbling and turbulent regimes. Another parameter which has been used to characterize fluctuating signals is the cycle frequency, defined as the number of times per second that a signal crosses its time-average value. Results presented by van der Stappen et al.21 suggest that higher cycle frequencies correspond to higher Kolmogorov entropies for fluidized beds, and thus to more complex dynamic systems. Cycle frequencies from local voidage signals corresponding to the bubbling, turbulent, and fast fluidization conditions are shown in Figure 7. Except for one point at the wall, the cycle frequency for the bubbling regime is of the order 5-10 Hz, depending on superficial gas velocity, and changes little with the radial position (see Figure

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Figure 7. Radial profiles of cycle frequency for different flow regimes. Data were obtained at z ) 0.38 m for the bubbling and turbulent fluidization cases and at z ) 1.57 m for the fast fluidization and dense suspension upflow conditions.

7a). As shown in Figure 7b, in the turbulent regime, the cycle frequency decreases with an increasing radial distance from the axis. Figure 7c shows quite different behavior in the fast fluidization (Gs < 270 kg/m2‚s for U ) 8.0 m/s) and dense suspension upflow regimes (Gs g 270 kg/m2‚s), where the cycle frequency is seen to be a strong function of the radial position, with a maximum value of about 25 Hz at the center of the column, decreasing to about 5 Hz at the wall. 2. Chaotic Properties. The hydrodynamics of fluidized beds exhibit many features of chaotic dynamic systems.18,21-25 Given the different fluid dynamics and mechanism for the different regimes established above, chaos analysis may provide useful tools for distinguishing and characterizing the dynamics of fluidized beds operating in the various flow regimes. (a) Hurst Exponents. The Hurst exponent is estimated from the measured time series as a means of describing the degree of self-similarity and the complexity of the system. The analytical approach leading to the exponent, called rescaled range analysis, was originated by Hurst26 and used by later investigators (e.g., Fan et al.;14,27 Drahos et al.28). It has been shown to be useful for gas-solid systems.29 A detail description has

been given by Feder.30 In our computer algorithm, a sufficiently large number of starting points (e.g., 1000) have been chosen at random in order to increase the statistical accuracy. Figure 8 shows the calculation results for measured absolute pressure (aP), differential pressure (dP), and local voidage fluctuations obtained by means of an optical probe (OP) in various flow regimes. For the bubbling regime (U ) 0.09 and 0.24 m/s), the three types of signals all give two clear linear sections. Hence, two distinct Hurst exponents can be derived, H1 being the slope at smaller τ (or higher frequency) and H2 the slope at larger τ (or lower frequency). This suggests a bifractal structure of gassolids flow in the bubbling flow regime, with H1 and H2 resulting respectively from the emulsion phase and voids in the bed. Bifractal flow behavior has also been observed for gas-liquid two-phase flows31-33 and gassolids fluidized beds,25 and appears to be characteristic of a number of heterogeneous multiphase flows. Bifractal behavior is also consistent with estimations of the correlation dimension and Kolmogorov entropy presented below. The two-phase character in gas-fluidized beds becomes less distinguishable as the gas velocity is increased. As a result, although two linear regions are still observable in the Pox diagram for the turbulent flow regime (U ) 0.58 and 0.67 m/s), they are less distinct. When the CFB riser is in the fast fluidization regime (U ) 6 m/s, Gs ) 82 kg/m2‚s), only one Hurst exponent can be determined from the R/S versus τ curve for both differential pressure and local voidage fluctuation signals, suggesting dilutely dispersed particles. On the other hand, when the CFB riser is operated under highdensity (dense suspension upflow) conditions (U ) 8 m/s, Gs ) 425 kg/m2‚s), two linear regions again appear in the Pox diagram. Since gas voids do not exist under these conditions, the two Hurst exponents may suggest that the particles under such conditions take two forms, for example, dispersed individual particles and ag-

Figure 8. Pox diagrams for pressure and local voidage fluctuation signals from different flow regimes. In (a) and (b), aP and OP were measured at z ) 0.03 and 0.38 m, respectively, while dP was measured between z ) 0.03 and 0.38 m.

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Figure 10. Variation of the Hurst exponents from differential pressure signals with superficial gas velocity. Data were measured at z ) 0.38 m for U < Use and at z ) 1.57 m for U > Use. Figure 9. Radial distributions of Hurst exponents from local voidage signals for (a) bubbling; (b) turbulent fluidization; (c) fast fluidization (squares) and dense suspension upflow (circles). Data were taken at z ) 0.38 m for (a) and (b), at z ) 1.57 m for U ) 8 m/s, Gs ) 425 kg/m2‚s, and z ) 2.18 m/s for U ) 7.1 m/s, Gs ) 249 kg/m2‚s.

gregated clusters. This is consistent with correlation dimensions calculated from differential pressure signals25 and local voidage signals (see below). The reciprocal of the break point, τ, between the two linear regions is similar to the dominant frequency of the signal, discussed above. Fan et al.14 pointed out that a break (or overlapping) in the rescaled range at time lag τ can be caused by a dominant periodic component of the signal. Our results appear to be consistent with this finding, as demonstrated in Figure 8 where there is a dominant frequency of 1-2 Hz corresponding to log(τ) ) 1.7-2.0 for the bubbling regime, 0.5-1 Hz corresponding to log(τ) ) 2.0-2.3 for the turbulent regime, and 0.3-0.5 Hz corresponding to log(τ) ) 2.32.5 for the dense suspension upflow regime. The Hurst exponents from local voidage fluctuations in the four flow regimes are given in Figure 9. Reflecting the particle flow, H1 is always greater than 0.5, indicating a persistent or divergent system behavior; that is, the trend will likely propagate itself. With an increasing dimensionless radial coordinate, φ, H1 decreases slightly in the bubbling regime, and increases considerably in high-density fast fluidization and dense suspension upflow, with the turbulent regime showing intermediate behavior. There is no clear dependence of H1 on either the radial position or on the operating conditions within each flow regime. Values of H2 in the bubbling flow regime are less than 0.5, indicating that the bubbles constitute an antipersistent or convergent system; that is, the trend will likely reverse itself. This may be due to bubble interactions leading to coalescence and splitting. At low U, bubble coalescence predominates over splitting. When a disturbance occurs to split the bubbles into smaller ones, they grow again because of coalescence. On the other hand, when splitting of voids becomes dominant, as for the turbulent flow regime, this represents a divergent system with H2 > 0.5. Under fast fluidization and dense suspension upflow conditions, H2, which probably reflects the motion of particle clusters, is always greater than 0.5 and changes little with the radial position. Figure 9c also suggests that the difference between H1 and H2 is smaller toward the center of the column and increases toward the wall, suggesting more phase segregation near the wall than in the interior of the column. The exponents near the wall differ significantly for the different flow regimes, even

though the time-mean voidages are almost equal near the wall, as indicated in Figure 5 above. The Hurst exponents from differential pressure fluctuations are plotted as a function of the superficial gas velocity in Figure 10. The data for the HDCFB are all from the lower part of the riser (z ) 1.57 m). The Hurst exponents are insensitive to the solids circulation rate. Similar to the Hurst exponents from local voidage fluctuations, H1 ≈ 0.9-0.95 and is almost independent of gas velocity, while H2 changes from below 0.5 (convergent system) in the bubbling regime to a maximum of about 0.6 (divergent system) as the gas-solids flow changes to the turbulent fluidization flow regime, and then decreases slightly and stays almost constant (at approximately 0.55) for fast fluidization and dense suspension upflow conditions. Although probably not sensitive enough to allow determination of the flow regime transitions which, in any case, is beyond the scope of this work, the Hurst exponent appears to be different in the various flow regimes as demonstrated in this figure. (b) Correlation Dimension and Kolmogorov Entropy. A chaotic system is usually characterized by its fractal structure and by its sensitivity to initial conditions. These properties can be quantitatively described (e.g., van den Bleek and Schouten34) by the correlation dimension, Dc, and the Kolmogorov entropy, K. Both have been shown to be useful for the characterization of gas-solid systems (e.g., Marzocchella et al.35). K is determined from the relation36,37

C(r) ∝ rDc exp(-(d - 1)τ∆tK)

(1)

where d is the embedding dimension, r the radius of a hypersphere, ∆t the sampling time interval, and τ the delay time in the integer number of sampling intervals. The correlation integral, C(r), is defined as

2 [number of pairs with δij ) C(r) ) lim M(M - 1) Mf∞ |Xi - Xj| < r] (2) where Xi is the d-dimensional reconstructive vector randomly drawn from the time series of measured values of an experimental signal, x, that is

Xi ) {xi, xi+τ, ‚‚‚, xi+(d-1)τ}

(i ) 1, 2, ‚‚‚, M) (3)

In practical calculations, the appropriate embedding dimension and time delay are chosen on the basis of the effects of these parameters on the calculation results.

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Figure 11. Typical correlation integrals of local voidage signals for three gas velocities at two radial positions: d ) 16; τ ) 15; M ) 1000. Figure 13. Radial distributions of the Kolmogorov entropies from local voidage signals for different flow regimes. Data were measured at z ) 0.38 m for (a) and (b) and at z ) 1.57 m for (c).

Figure 12. Radial distributions of correlation dimensions from local voidage signals for different flow regimes. Data were measured at z ) 0.38 m for (a) and (b) and at z ) 1.57 m for (c).

To increase the statistical accuracy, a vector of M ) 1000, created at random 10 times, was employed in the present calculations. The choice of these parameters and the calculation procedures are discussed elsewhere.25 Figure 11 presents the correlation integrals calculated from local voidage fluctuations for three superficial gas velocities. For the bubbling regime (U ) 0.24 m/s), two linear regions with a transition region between them can be observed in the correlation integral curves, both at the axis and near the wall. This division into two regions suggests distinguishable two-phase behavior in this flow regime. For the turbulent regime (U ) 0.67 m/s), the core of the column is rich in voids and it is hard to define the two linear regions in the correlation integral curve. However, the two-phase structure becomes clear near the wall, reflected in the existence of a two-linear-region integral curve. While a two-linearregion integral curve is still obtainable near the wall in dense suspension upflow, only a single linear region with one correlation dimension is generally identifiable at the center of the riser because of the absence of voids and a relatively homogeneous gas-solids flow structure. The correlation dimensions for different operating conditions appear in Figure 12. There are significant differences among the flow regimes. Because of relatively regular bubble behavior (e.g., size and shape) and a high degree of turbulence, the correlation dimension Dc1, which reflects the motion of emulsion particles, is highest, while Dc2, which portrays the bubbles, is lowest at the center of the column for the bubbling regime (Figure 12a). The larger difference between Dc1 and Dc2

Figure 14. Variation of correlation dimension and Kolmogorov entropy from differential pressure signals with superficial gas velocity. z ) 0.38 m for U < Use, while z ) 1.57 m otherwise: d ) 16, τ ) 15, M ) 1000.

near the axis suggests two-phase structure. In the wall region, the bubble behavior becomes more irregular and the turbulence intensity decreases. Consequently, Dc1 decreases while Dc2 increases so that the difference between Dc1 and Dc2 is diminished and the two-phase structure becomes less clear, consistent with the results based on local voidage fluctuations discussed above. In the turbulent regime (Figure 12b), a transition region between the bubbling and the higher velocity flow regimes, the two-phase structure is most distinguishable at φ ≈ 0.8. The central region of the column contains more voids, while the wall region retains more particles; this structure is reflected by the radial distribution shown in Figure 12b. For fast fluidization (Figure 12c, Gs ) 181 kg/m2‚s) and dense suspension upflow (Figure 12c, Gs ) 425 kg/m2‚s), Dc1 and Dc2 depend strongly on the radial position, reaching their highest values in the interior of the column and their lowest values at the wall. This is consistent with the data reported by Yang et al.38 The Kolmogorov entropies, K1 and K2, are plotted in Figure 13 on the basis of the same data as those used to plot Figure 12. In the bubbling regime the bubble phase and the emulsion phase have Kolmogorov entropies of the same order (Figure 13a). K1 and K2 differ for the turbulent regime (Figure 13b), indicating different information loss rates for the lean phase and the emulsion phase. Except near the wall, the Kolmogorov entropy is almost independent of the radial position for both the bubbling and turbulent regimes, but changes significantly with the radius for fast fluidization (circles in Figure 13c), and even more so for dense suspension

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upflow (squares in Figure 13c). The central region of the riser appears to be more complicated and unpredictable than the region near the wall. Note that there are again significant differences among K values at the wall for the various flow regimes, even when (see Figure 5) the time-mean local voidages are similar. Figure 14 shows the correlation dimension and Kolmogorov entropy from differential pressure signals as a function of the superficial gas velocity. The correlation dimension and Kolmogorov entropy are high in the bubbling regime (U < Uc) and decrease as the superficial gas velocity is increased to reach the turbulent fluidization flow regime (Uc e U e Use). Beyond Use, the correlation dimension and Kolmogorov entropy increase again, suggesting more complicated and unpredictable behavior. Conclusions A comprehensive experimental investigation of the statistical and chaotic properties of pressure and local voidage fluctuations has been carried out, allowing a comparison of four flow regimes. Statistical and chaotic methods lead to almost identical conclusions. Gassolids flow in dense suspension upflow differs hydrodynamically from that in the bubbling, turbulent, and fast fluidization flow regimes, even when compared for equal values of local time-mean voidages. The flow structures differ quite clearly both in terms of their statistical and their chaotic hydrodynamic characteristics, and with respect to the radial distributions of the various parameters which are compared. Acknowledgment The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for supporting this work. Notation aP, dP ) absolute, differential pressure C(r) ) correlation integral defined by eq 2 Dc ) correlation dimension d ) embedding dimension f ) frequency fcy ) cycle frequency Gs ) solids circulation flux H ) Hurst exponent K ) Kolmogorov entropy M ) length of vector Xi OP ) optical fiber probe R ) rescaled range r ) radial distance of hypersphere S ) standard deviation of a subrecording U ) superficial gas velocity Uc ) onset velocity of turbulent flow regime Use ) significant entrainment velocity introduced and defined by Bi and Grace11 X ) reconstructed vector defined by eq 3 x ) amplitude of signal z ) axial coordinate Greek Symbols γ ) intermittency index introduced and defined by Brereton and Grace19 δij ) distance between Xi and Xj ∆t ) sampling time interval  ) voidage

φ ) dimensionless radial position from center (i.e., radial coordinate/column radius) σ ) standard deviation of time series τ ) delay time in integer number of sampling time intervals

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Received for review June 12, 1998 Revised manuscript received October 7, 1998 Accepted October 8, 1998 IE9803873