Use of Pressure Fluctuations to Determine Online the Regime of Gas

Jun 9, 2009 - Use of Pressure Fluctuations to Determine Online the Regime of Gas−Solids Suspensions from Incipient Fluidization to Transport ... Fax...
0 downloads 5 Views 1MB Size
Download PDF
6830

Ind. Eng. Chem. Res. 2009, 48, 6830–6835

Use of Pressure Fluctuations to Determine Online the Regime of Gas-Solids Suspensions from Incipient Fluidization to Transport Miloslav Hartman,* Otakar Trnka, and Karel Svoboda Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague 6-Suchdol, Czech Republic

A novel quantity, based on the concept of symmetry of the sampled pressure fluctuating signal, is developed and incorporated into our extended fluctuation model of fluidized gas-solid suspensions. The new measure of the signal symmetry makes it possible to define the transition from the final bubbling regime to the onset of turbulence in the bed. Experimental measurements were performed in a transparent glass, 6-m-tall column with an inner diameter (i.d.) of 0.08 m. Three different kinds of solids were employed in the experiments: ceramsite (particle size 1.0-1.25 mm; group D particles; spoutable particles), glass beads (particle size 0.8-1.00 mm; group D particles), and high-calcium, coarse-grained limestone (particle size 0.50-0.65 mm; group B powder; sandlike particles). It was discovered that also the different bubbling regimes and the starting point of dilute (entrainment) regimes can be identified with the aid of the proposed method. The development of the diluted beds is considerably influenced by the architecture and configuration of the top of the fluidization column. Introduction A fluidized bed provides a practical method of contacting particulate solids with gases (or liquids). Commercial units with fluidized beds have been in use for decades and considerable progress has been achieved in their design and development. Difficulties and occasional failures of fluidized bed contactors/ reactors have usually been attributed to an unsufficient understanding of the physics of gas-solid fluidization.1,2 In particular, systems with widely polydispersed, irregularly shaped particles operated at higher gas velocities, elevated temperature and/or under elevated pressure are still relatively little understood. The existence and importance of different flow regimes (states of fluidization/contacting modes) in gas-solid suspensions have been recognized for a long time.3-8 The fluidization regimes are bounded by the onset of fluidization9,10 on the one side and by the commencement of elutriation of particles from the vessel (dilute transport flow) on the other side.10-13 There are more than five different fluidization regimes observed whose occurrence depends on the particle size, particle density, and particle geometry, gas density, and gas viscosity, and gas velocity and column geometry. With the increasing gas velocity and decreasing solid concentration, these are particulate (homogeneous) fluidization (group A particles of the Geldart classification14 only), bubbling (aggregative, heterogeneous) fluidization, slugging fluidization (laboratory/smaller columns only), turbulent fluidization, fast (entrainment) fluidization, and pneumatic transport. A practical classification of the flow regimes, including their simplified visual appearances, is presented in Figure 1. Different measurement techniques15-18 and interpretation methods can be employed to distinquish between the aforementioned flow patterns.7,18,19 Our experience demonstrates that transition between different modes of fluidization is not usually sharp, but rather gradual. Effects of factors such as the particlesize distribution and the size and column configuration also have to be taken into account. Visual observations indicate that transition among different flow regimes can occur locally (at different level) rather than throughout the entire bed. For * To whom correspondence should be addressed. Tel.: +420 220 390 254. Fax: +420 220 920 661. E-mail: [email protected].

example, a fast fluidized bed has a dense region at the bottom and a dilute region at the top of the vessel. Very useful information on the system behavior can be inferred from the study of pressure fluctuations within the bed.19-32 Spectral analysis is often employed to describe various modes of fluidization, but to the best knowledge of the authors,

Figure 1. Overview and numbering of fluidization regimes. Gas velocity and porosity of bed increase from top to bottom and from left to right.

10.1021/ie900055x CCC: $40.75  2009 American Chemical Society Published on Web 06/09/2009

Ind. Eng. Chem. Res., Vol. 48, No. 14, 2009

6831

Table 1. Physical Properties of Particulate Materials quantity

ballotini

limestone

ceramsite

particle size , d (mm) mean particle size, djp (mm) particle densityb, Fp (kg m-3) bulk density of poured bed, F (kg m-3) shape and surface of particles onset of fluidizationc, Umf (m s-1) onset of turbulent fluidizationd, Uturb (m s-1) onset of dilute bedd, Udil (m s-1) onset of elutriationd, Ume (m s-1)

0.8-1.0 0.9 2510 1570 spherical; smooth 0.50 0.97 2.06 3.50

0.50-0.65 0.575 2700 1390 irregular; smooth 0.25 0.70 1.22 2.53

1.0-1.25 1.125 1490 780 irregular; uneven 0.51 1.11 1.44 2.80

a

a Determined by sieving. b Determined by mercury displacement. c Determined by the standard procedure at 20 °C. fluctuation characteristics at 20 °C.

it is not reported in literature as being used for the online monitoring of the state of fluidized beds. This work is a sequel to previous studies of ours19-21,33-35 on pressure fluctuations in fluidized beds at ambient and elevated temperatures. The main aim of this work is to extend our fluctuation model with the use of a new function expressing the degree of symmetry of the fluctuating signal. Attempts are also made to determine numerical values of the pertinent fluidization quantities that objectively indicate the points of transition between different flow regimes. Model. The extended fluctuation model of a fluidized bed is based upon three governing quantities deduced from pressure fluctuations and which describe the state of fluidized bed: 1. The quantity E, defined as the square root of the spectral power of the pressure fluctuations in the chosen frequency band, or E ) (W)1/2

(1)

where W)

4 256

256

∑a

2 i

(2)

i-1

and ai is the amplitude pertaining to the i-line of the spectrum. The number 4 gives the length of time window (4 s) and the number 256 gives the number of spectral lines after FFT for the frequencies 0.25-64 Hz. 2. The divide ratio of the amplitude spectrum, M, given as M)1-

fM fmax

(3)

where the median of the assorted amplitude spectrum, fM, is introduced as fM ) fiM

(4)

and iM complies with iM

∑a i)1

256

i

)

∑

ai

(5)

i)iM+1

3. The newly introduced symmetry of the sampled fluctuating signal, S, defined as S)

Pmax - Pmean Pmax - Pmin

(6)

d

Determined on the basis of the

Further details, particularly about the original fluctuation model and the sampled data processing, can be found in recent articles of ours.21,35 Experimental Section Materials. The experimental materials employed in this work were ballotini (glass beads), limestone, and ceramsite. Ceramsite is an inert material manufactured by the calcination of claystone at 950 °C in an oxidizing environment. We have been using chemically and thermally stable ceramsite for several years in our studies on fluidized combustion and gasification.10,36 The employed glass beads were smooth, near-perfect spheres, whereas the mostly isotropic ceramsite particles had an uneven surface and were of irregular shapes. Pertinent physical properties of the three solids are given in Table 1. As all resulting characteric curves were very similar for the respective solids, only some results are presented. The ballotini spheres and the ceramsite particles belong to group D materials (spoutable particles) of the Geldart classification.14 The limestone particles belong to group B powders (sandlike solids). In contrast to smaller particles of group A (0.05-0.1 mm aeratable powders) interparticle forces between the B and D particles are negligible and bubbles commence forming at or only slightly above the minimum fluidization velocity, Umf. Very small bubbles (gas pockets) forming at the distributor grow larger by the process of coalescing as they move upward through the bed. Apparatus. The experimental setup, shown in Figure 2, consisted of several fundamental parts or sections: Transparent glass fluidization column, facility for recycling the elutriated particles, and facilities for measurement, processing, and storing pressure fluctuation signal within the bed. The fluidization vessel was constructed of a hard glass tube, 600 cm high and 8-cm diameter. Fluidization air was filtered and passed upward through the bed via a finely perforated plate distributor. The visual appearance of the bed was also observed and scanned, and images were stored. A detailed description of the experimental apparatus, measurement procedure, and signal processing can be found elsewhere.21,35 Three series of experimental runs were conducted for each material (glass beads, ceramsite, and limestone) for three volumes of poured, loosely packed (fixed) beds: 400, 700, and 1000 cm3 corresponding to fixed bed heights of 8, 14, and 20 cm, respectively. Every experimental series included 40-45 experimental data points for different air superficial velocities gradually increased from zero up to approximately 3.9 m s-1. Respective measurements started only after steady-state conditions of the whole experimental and measuring system were attained. The experiments took place at an ambient temperature of 20-21 °C. In the course of the measurement at one experimental point, digitized values of pressure, air velocity, and temperature were

6832

Ind. Eng. Chem. Res., Vol. 48, No. 14, 2009

Figure 2. Experimental setup: 1, fluidization column; 2, cyclone; 3, fluidized siphon; 4, inlet of air; 5, fluidized bed; 6, air valve; 7, flowmeter; 8, thermometer; 9, pressure probe; 10, analog/digital convertor; 11, computer; 12, digital videocamera; 13, image recording on digital media.

continuously recorded in the internal memory of the computer. The data were recorded for 64 s at a rate of 512 samples per second. Our transparent column also made it possible to visually observe and record the undistorted physical appearance of the explored bed with high imaging frequency. We believe that visual observation still plays an important role, particularly with laboratory scale equipment. Statistical analysis was carried out on the basis of 50 experiments with different materials. The sample variance indicates that 95% confidence limits on the quantities E and M, based upon the Student/Gosset/Fisher distribution, are (0.67 and (0.0048, respectively.

Figure 3. Segments of the fluctuation characteristic. Section F-B, fixed (static) bed; section B-T, bubbling (linear) regimes; section T-E, turbulent (concavely increasing) regimes; section E-D, oscillating, nonexpanding (dilute) beds. The dashed line depicts a linear trend. Bed material, ceramsite; particle size, 1.0 - 1.2 mm; bed volume, 700 mL; bed mass, 545 g; height of loosely poured bed, 14 cm; onset of fluidization, Umf ) 0.49 m s-1.

Results and Discussion General Properties of the Fluctuation (Operation) Characteristics. The measured fluctuation characteristic,21,35 given by eqs 1-5, can be divided into several typical sections. These segments correspond closely to the respective fluidization regimes summarized and numbered in Figure 1. Static Beds. Figures 3 and 4 depict the fluctuation characteristic of 1.1-mm ceramsite particles. Sections F-B (regimes 1, 2-) corresponds to fixed (static) beds. The quantity E does not change with the increasing gas velocity, U, and its value is very small. The packed bed itself does not generate any pressure fluctuations, a small value of E represents the random fluctuation signal of the background. In regime 1, the quantity M amounts to 0.66-0.67. The particles do not move; visual observations indicate that the bed is at a complete standstill. Regime 2- occurs at the close vicinity of Point B where sporadic small bubbles can be seen, but the particles remain at a standstill. The tiny bubbles cause very gentle fluctuations of pressure in the upward flowing gas. The function E(U) tends to increase slightly with the increasing gas velocity. The quantity M acquires values in the range between 0.68 and 0.70. In the area closely surrounding Point B is the point of minimum fluidization, Umf, that can also be determined by other, entirely independent experimental techniques.9 Bubbling Regimes. This class includes modes of fluidization such as bubbling beds (regime 2+ with frequent bubbles, and

Figure 4. Positions of the fluidization regimes on the fluctuation characteristic. The regimes are numbered in the same manner as in Figure 1. Bed and material specifications are given in the caption of Figure 3.

particles in movement), large bubbles (regime 3), exploding bubbles (regime 4), and slugging (regime 5). All the particles in the bed are moving in the bubbling regimes, but none of them are being entrained from the bed into the freeboard. The bubbling regimes are represented by the segment B-T on the fluctuation function E ) E(U) in Figure 3. It is characteristic of the aforementioned

Ind. Eng. Chem. Res., Vol. 48, No. 14, 2009 Table 2. Fluctuation Quantity M for the Static and Bubbling Beds regime numberb

state of bed

M

1; 2-

fixed bed, sporadic small bubbles, particles at standstill bubbles, particles in movement large bubbles exploding bubbles slugging

0.66-0.71

2+ 3 4 5

a Materials: ballotini, limestone, and ceramsite. numbered in the same manner as in Figures 1 and 5.

6833

a

0.69-0.91 0.90-0.96 0.95-0.97 0.96-0.99 b

Regimes are

Figure 6. Boundary line between dense and dilute fluidized beds. The position E marks the transition from the dense regime to the dilute (lean) regime. Bed and material specifications are given in the caption of Figure 3. The quantities E and Er are defined by eqs 1 and 7, respectively. Figure 5. Relative sizes and overlapping of the intervals of values of the quantity M for the static and bubbling regimes of fluidized beds. The regimes are numbered in the same manner as in Figure 1 and Table 2.

bubbling regimes that the quantity E increases linearly with the increasing excess gas velocity (U - Umf). The respective regimes of this bubbling class can be identified reliably by values acquired by the fluctuation quantity M under operation conditions of interest. Having compared the values of M determined by experiment, with the corresponding images of the bed behavior recorded during the experimental runs, Table 2 and Figure 5 were constructed. They present intervals of the M-values for the respective bubbling states of fluidization. As can be seen, these intervals of the quantity M overlap slightly for the bubbling regimes. This fact expresses a certain, hardly avoidable degree of indefinitess in the bed behavior and of the subjectivity in the visual observations. Our long-standing practical experience indicates that all sorts of transitions between different regimes, including the onset of fluidization (Umf) occur in a narrow interval of the gas velocity rather than at a single, rigorously defined point. The quantity M increases monotonously with the increasing gas velocity from 0.68 to Mmax at the end of the bubbling segment. The size of Mmax depends on the bed properties and can be viewed as a measure of the susceptibility of the bed to slugging. Our visual observations indicate that the beds are slugging for M equal to or larger than 0.96. Turbulent Regimes. The class of the turbulent regimes (regimes 6 and 7 in Figure 1) can be considered as the highest group of dense beds with respect to the increasing gas velocity. However, as visual observations show, geysers of particles shoot upward from the surface of the dense bed in this hydrodynamic state. The ejected particles remain above the bed for a short period of time comparable to the length of the time window for computing the FFT (fast Fourier transform) spectrum and return to the bed. Obviously, the rate of ejection is balanced by the rate of return. As a result, it appears from the standpoint of pressure fluctuations as if the mass of the dense bed were somewhat smaller than the mass of the whole particle inventory. On the basis of our experimental experience with different systems, it appears that the product of the quantities M and S can predict the transition between the bubbling beds and the turbulent beds quite reliably. While the bubbling regimes occur for MS e 0.5, the turbulent fluidization corresponds to MS > 0.5. The sample variance indicates that the confidence limits on the demarcation (MS ) 0.5) are (0.0075 (95% confidence interval).

As can be seen in Figures 3 and 4, the growth of the quantity E with the increasing gas velocity gradually slows. Since the particles ejected above the bed contribute very little to the measured pressure fluctuations, we believe that the concave shape of the curve E(U) in the segments 6 and 7 in Figure 4 is due to the above-mentioned “ejection-return” phenomena. Different to the quantity E(U), the values of the quantity M(U) decrease slightly with the increasing U and remain relatively high (above 0.9). These high values are supported by visual observations of the system. Both the direct observations of the turbulent bed and an analysis of the recorded images revealed considerable periodicities in the movement of particles within the bed. Unfortunately, it is hard to determine unequivocally the transition between the two turbulent regimes (regime 6 intermediate turbulence and regime 7 - full turbulence), whether by visual observations or through pressure fluctuations. Dilute (Entrainment) Regimes. As the starting point for these regimes, we consider point E shown in Figures 3 and 6 (regime 8 in Figure 4). This point at U ) Udil represents a situation where the curve E(U) commences to decrease (or stops rising) with the increasing U. The quantity E can be normalized with the use of eq 7 Er )

E ∆P

(7)

in which ∆P is the average pressure difference measured between the location of the pressure probe mouth and the gas outlet from the column. As illustrated in Figure 6, the onset of the regime 8 (Udil) can be determined quite reliably with the aid of Er(U) as this function exhibits the distinct global maximum. When U is gradually increased above Udil, a certain everincreasing mass fraction of solids (dilute fluid fraction) remains above the bed for a period of time that is longer than the length of the time window for FFT. The dilute fraction contributes very little to the generation of fluctuations. The measured fluctuations are generated by a “fluctuation core” of the bed, whose particles have a period of movement that is shorter than the time window for FFT. We can assume that the quantity E is given by the product E ) Esmc

(8)

where Es is generated by a mass unit of particles and mc is the mass of particles remaining in the core of the bed. While Es

6834

Ind. Eng. Chem. Res., Vol. 48, No. 14, 2009

increases with the increasing U, mc tends to decrease with the increasing U. As a result of these opposing tendencies, the (energy) function E(U) exhibits nonmonotonous (extreme) behavior. There is an uncertainty about smaller local extremes on the curve E(U) in Figures 3 and 4. It is likely that the local extremes are due to lack of uniformity in air flow and aerodynamic irregularities of the particles resulting in their classification. It is advantageous to divide the class of dilute beds into regimes 8-10, shown in Figure 1, which are recognizable by our instrumental means as well as by visual observations. The beginning of entrainment of U ) Udil is characteristic of the onset of the regime 8. As shown in Figure 6, the quantity Er decreases steadily for U > Udil. The point at which E starts its permanent decrease is considered as the end of the regime 8. The quantity M(E) decreases in this regime without fluctuations. The lower dense bed exhibits strong turbulence. Well-visible geysers penetrate deeply into the upper dilute bed that is also in perpetual motion. In region 9, both fluctuation functions E and M decrease steadily with the increasing gas velocity. Visual observations indicate that the fluctuation dense core is gaining turbulent dynamics, but simultaneously it is gradually losing its mass. The height of the geysers penetrating the dilute bed increases with U and approaches a certain maximum value. The fast moving geysers cause chaotic movements of the particle clusters in the lower section of the dilute bed. At the top of the dilute suspension, an ever-expanding section forms in which separate particles levitate freely in an upper section of the freeboard. The limiting situation, i.e., the transition to regime 10, arrives when the dilute part of the bed just reaches the gas outlet at the top of the column. At this moment U ) Ume and the first (the finest) particles tend to leave irreversibly (to be elutriated from) the bed and the fluidization column. The quantity Ume is considered as the onset of elutriation from the fluidized bed/ column. We should realize that except for regime 10, in which U g Ume, in all the other explored regimes, the total mass of particles in the fluidization vessel remained the same. Consequently, the fluctuation characteristic was accurately replicated, providing that the bed underwent the transitions from regime 1 to the regime 9. In other words, the fluidization characteristics of fluidized beds were invariant in time for U < Ume. It is apparent that the minimum elutriation velocity, Ume, defined and determined in this way, is the property of the entire bed of many different particles, rather than the free-fall velocity of an isolated particle.11-13 Our experimental experience indicates that the terminal velocities, Ut, predicted for the freefall of single spheres in an unrestricted medium under steadystate conditions, are somewhat larger than the corresponding measured values of Ume. This is probably caused by velocity profiles developed in the fluidization columns. At the moment, when the increasing gas velocity attains the value U > (Ume)1, bed 1 is losing some (finest) particles and occurs at an unsteady state. As we found, after 10-12 min of fluidization at U ) const., all relevant particles were removed (elutriated) from the bed and a new steady-state was established. This actual “equilibrium” state corresponds to a new transition point at (Ume)2 which is larger than (Ume)1. Compared to the original bed 1, the new bed 2 contains a smaller amount of solids, whose granularity is shifted toward larger particles. The effect of gradual elutriation of particles on the fluctuation characteristic is shown in graphical form in Figure 7. To keep a constant inventory of solids in the column operated in regime 10, fresh solids must be introduced continuously or

Figure 7. Fluctuation characteristics affected by the gradual elutriation of particles from the bed. Bed material, ceramsite; particle size, 1.0-1.2 mm; original bed volume, m1 ) 700 cm3, original bed mass, 545 g; height of loosely poured bed, 14 cm, (Umf)1 ) 0.49 m s-1. Values of m give the residual volumes of static beds after crossing the onset of elutriation in question and steadying up the process. Curve 2, m2 ) 542 cm3, (Ume)2 ) 2.6 m s-1; curve 3, m3 ) 420 cm3, (Ume)3 ) 2.8 m s-1; curve 4, m4 ) 320 cm3, (Ume)3 ) 3.1 m s-1; curve 5, m5 ) 250 cm3, (Ume)4 ) 3.4 m s-1.

the elutriated particles have to be separated from the outgoing gas and returned to the bottom of the bed. The latter system, known as a circulating fluidized bed, almost invariably includes a fluidized bed siphon operating in a bubbling bed regime. Evidently, the fluctuating pressure signals have to be withdrawn from several different points of such units and processed. Conclusions The fluctuation quantity M itself provides an objective and reliable means of identification particularly for bubbling beds. It acquires values from 0.68-0.70 at the point of incipient (minimum) fluidization, through 0.70-0.91 (a gently-to-lively bubbling bed), 0.91-0.96 (larger, fast moving bubbles), 0.95-0.97 (exploding bubbles), to 0.96-1 (slugging). The product of M and the newly introduced function S, expressing the degree of symmetry of the sampled fluctuating signal, defines the transition from the most developed bubbling regime (MS e 0.5) to the turbulent fluidization (MS > 0.5). The plateau formed by fluctuating points on the flat top of the curve E(U), corresponds to the state in which a significant amount of particles is repeatedly leaving the bed and returning back. The newly proposed energy function, Er, which is normalized with respect to the pressure conditions in the column, exhibits the significant global maximum. This maximum defines the onset of entrainment of particles into the freeboard above the bed. It should be emphasized that all the points of transition were very well reproducible providing that the total mass of particles in the fluidization vessel remained the same. In other words, all the proposed characteristics of fluidized beds are invariant in time when no particles are elutriated out of the system. The moment, when the first particles tend to leave the vessel, is also affected by the configuration and architecture of the top of the column. The developed procedure is not technically demanding and the computational analysis is rapid. We believe that it can be easily implemented online in real fluidized beds for the monitoring and control purposes. Acknowledgment The authors are grateful for the financial support provided by the Grant Agency of the Academy of Sciences of the Czech Republic through Grant IAA 400720701.

Ind. Eng. Chem. Res., Vol. 48, No. 14, 2009

Nomenclature ai ) amplitude pertaining to i-line of spectrum, Pa dp ) particle size (determined by sieving), mm, m djp ) mean particle size, mm, m E(U) ) characteristic quantity of pressure fluctuations defined by eq 1, Pa Er ) reduced quantity E, defined by eq 7 Es ) normalized quantity E, defined by eq 8, Pa g-1 fiM ) frequency pertaining to iM-line of amplitude spectrum, Hz fM ) median of assorted spectrum, Hz fmax ) maximum frequence of discrete Fourier spectrum, Hz FFT ) fast (discrete) Fourier transform i ) index of line in amplitude spectrum m ) volume of bed, cm3 mc ) mass of particles in the core of bed, g M(U) ) characteristic quantity of pressure fluctuations defined by eq 3 P ) pressure, Pa ∆P ) average pressure drop, Pa S ) characteristic quantity of pressure fluctuations defined by eq 6 U ) superficial gas velocity, m s-1 Udil ) onset of dilute bed, m s-1 Umax ) maximum superficial gas velocity, m s-1 Ume ) onset of elutriation (determined by visual observations), m s-1 Umf ) onset of fluidization, m s-1 Ut ) terminal (free fall) velocity of a single particle, m s-1 Uturb ) onset of turbulent fluidization, m s-1 W ) spectral power of fluctuations defined by eq 2, Pa2 Greek letters F ) bulk density of loosely packed (poured) bed of particles, g cm-3, kg m-3 Fp ) particle (apparent, mercury) density, g cm-3

Literature Cited (1) Yates J. G. Fundamentals of Fluidized-Bed Chemical Processes; Butterworths: London, 1983. (2) Gupta C. K., Sathiyamoorthy D. Fluid Bed Technology in Materials Processing; CRC Press: Boca Raton, FL, 1999. (3) Hartman, M.; Beran, Z.; Svoboda, K.; Vesely´, V. Operation regimes of fluidized beds. Collect. Czech. Chem. Commun. 1995, 60, 1–33. (4) Bi, H. T.; Grace, J. R. Flow regime diagrams for gas-solid fluidization and upward transport. In. J. Multiphase Flow. 1995, 21, 1229–1236. (5) Bai, D.; Shibuya, E.; Nakagawa, N.; Kato, K. Characterization of gas fluidization regimes using pressure fluctuations. Powder Technol. 1996, 87, 105–111. (6) Zijerveld, R. C.; Johnsson, F.; Marzocchella, A.; Schouten, J. C.; van den Bleek, C. M. Fluidization regimes and transitions from fixed bed to dilute transport flow. Powder Technol. 1998, 95, 185–204. (7) Bai, D.; Issangya, A. S.; Grace, J R. Characteristics of gas-fluidized beds in different flow regimes. Ind. Eng. Chem. Res. 1999, 38, 803–811. (8) Andreux, R.; Gauthier, T.; Chaouki, J.; Simonin, O. New description of fluidization regimes. AIChE J. 2005, 51, 1125–1130. (9) Hartman, M.; Coughlin, R. W. On the incipient fluidized state of solid particles. Collect. Czech. Chem. Commun. 1993, 58, 1213–1241. (10) Hartman, M.; Trnka, O.; Pohorˇely´, M. Minimum and terminal velocities in fluidization of particulate ceramsite at ambient and elevated temperature. Ind. Eng. Chem. Res. 2007, 46, 7260–7266. (11) Hartman, M.; Yates, J. G. Free-fall of solid particles through fluids. Collect. Czech. Chem. Commun. 1993, 58, 961–982. (12) Hartman, M.; Trnka, O.; Svoboda, K. Free-settling of nonspherical particles. Ind. Eng. Chem. Res. 1994, 33, 1979–1983.

6835

(13) Hartman, M.; Vesely´, V.; Svoboda, K. Havlı´n V. Explicit relationships for the terminal velocity of spherical particles. Collect. Czech. Chem. Commun. 1990, 55, 403–408. (14) Geldart, D. Types of fluidization. Powder Technol. 1973, 7, 285– 292. (15) Yates, J. G.; Simons, S. J. R. Experimental methods in fluidization research. Int. J. Multiphase Flow. 1994, 20, 297–330. (16) Werther, J. Measurement techniques in fluidized bed. Powder Technol. 1999, 102, 15–36. (17) Bi, H. T. Pressure and voidage fluctuations in slugging fluidized beds. Can. J. Chem. Eng. 1999, 77, 568–572. (18) Makkawi, Y. T.; Wright, P. C. Fluidization regimes in a conventional fluidized bed characterized by means of electrical capacitance tomography. Chem. Eng. Sci. 2002, 57, 2411–2437. (19) Svoboda, K.; Cˇerma´k, J.; Hartman, M.; Drahosˇ, J.; Selucky´, K. Pressure fluctuations in gas-fluidized beds at elevated temperatures. Ind. Eng. Chem. Process DeV. 1983, 22, 514–520. (20) Svoboda, K.; Cˇerma´k, J.; Hartman, M.; Drahosˇ, J.; Selucky´, K. Influence of particle size on the pressure fluctuations and slugging in a fluidized bed. AIChE J. 1984, 30, 513–517. (21) Trnka, O.; Vesely´, V.; Hartman, M.; Beran, Z. Identification of the state of a fluidized bed by pressure fluctuations. AIChE J. 2000, 46, 509–514. (22) Schouten, J. C.; van den Bleek, C. M. Monitoring the quality of fluidization using the short-term predictability of pressure fluctuations. AIChE J. 1998, 44, 48–60. (23) Van Ommen, J. R.; Coppens, M.-O.; van den Bleek, C. M.; Schouten, J. C. Early warning of agglomeration in fluidized beds by attractor comparison. AIChE J. 2000, 46, 2183–2197. (24) Quo, Q.; Yue, G.; Werther, J. Dynamics of pressure fluctuation in a bubbling fluidized bed at high temperature. Ind. Eng. Chem. Res. 2002, 41, 3482–3488. (25) Guo, Q.; Yue, G.; Suda, T.; Sato, J. Flow characteristics in a bubbling fluidized bed at elevated temperature. Chem. Eng. Process. 2003, 42, 439–447. (26) Van der Schaaf, J.; van Ommen, J. R.; Takens, F.; Schouten, J. C.; van den Bleek, C. M. Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds. Chem. Eng. Sci. 2004, 59, 1829–1840. (27) Chen, A.; Bi, H. T. Pressure fluctuations and transition from bubbling to turbulent fluidization. Powder Technol. 2003, 133, 237–246. (28) Hao, B.; Bi, H. T. Forced bed mass oscillations in gas-solid fluidized beds. Powder Technol. 2005, 149, 51–60. (29) Croxford, A. J.; Gilbertson, M. A. Control of the state of a bubbling fluidized bed. Chem. Eng. Sci. 2006, 61, 6302–6315. (30) Wu, B.; Kantzas, A.; Bellehumeur, C. T.; He, Z.; Kryuchkov, S. Multiresolution analysis of pressure fluctuations in a gas-solids fluidized bed: Application to glass beads and polyethylene powder systems. Chem. Eng. J. 2007, 131, 23–33. (31) Bi, H. T. A critical review of the complex pressure fluctuation phenomenon in gas-solids fluidized beds. Chem. Eng. Sci. 2007, 62, 3473– 3493. (32) Sasic, S.; Leckner, B.; Johnsson, F. Characterization of fluid dynamics of fluidized beds by analysis of pressure fluctuations. Prog. Energy Combust. Sci. 2007, 33, 453–496. (33) Trnka, O.; Hartman, M.; Vesely´, V. Characteristics of pressure fluctuations in different operation regimes of gas-solid suspensions. Chem Listy 2005, 99, 330–338. (34) Trnka, O.; Hartman, M. Influence of changes in physical parameters of fluidized beds on its characteristics of pressure fluctuations. Chem Listy 2007, 101, 515–523. (35) Hartman, M.; Trnka, O. Physical characteristics of fluidized beds via pressure fluctuation analysis. AIChE J. 2008, 54, 1761–1769. (36) Hartman, M.; Svoboda, K.; Pohorˇely´, M.; Trnka, O. Combustion of dried sewage sludge in a fluidized-bed reactor. Ind. Eng. Chem. Res. 2005, 44, 3432–3441.

ReceiVed for reView January 14, 2009 ReVised manuscript receiVed May 19, 2009 Accepted May 22, 2009 IE900055X