Fluidization regimes in a conventional fluidized bed characterized by means of electrical capacitance tomography

Chemical Engineering Science 57 (2002) 2411 – 2437

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Fluidization regimes in a conventional #uidized bed characterized by means of electrical capacitance tomography Y. T. Makkawi, P. C. Wright ∗ Department of Mechanical and Chemical Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK Received 5 October 2001; received in revised form 20 February 2002; accepted 6 March 2002

Abstract The purpose of the present study is to verify di3erent analysis approaches and provide a quantitative and qualitative classi5cation of #uidization regimes. The experimental study has been carried out in a cold conventional #uidized bed using electrical capacitance tomography (ECT). The system compromises a twin-plane ECT in a 15 cm diameter acrylic column. The experiments were carried out at ambient conditions and under di3erent #uidization velocities, ranging from 0.2 to 2:0 m=s using air as the #uidizing gas. A mixture of spherical glass ballotini ranging from 150 to 1000
m diameter and average density of 2600 kg=m3 were used as the #uidizing particles. Measurement of solid volume fraction was recorded over a 20 s interval at a 100 Hz sample rate. Four di3erent #uidization regimes were identi5ed based on a distinct transition velocity: single bubble, slugging bed, turbulent #ow and fast #uidization regime. Di3erent analysis methods employed with the solid fraction #uctuations have shown good agreement. The transition velocities determined by standard deviation, amplitude and solid fraction distribution analysis almost coincide, while results obtained with the peak and cycle frequencies analysis only shows the transition to slugging bed and fast #uidization regime. Bubble rise velocity analysis shows a maximum at the onset of turbulent #uidization, but no further conclusions could be made. Analyses based on power spectra and probability distribution of amplitude are also discussed. The regime classi5cation shows no variation with respect to height within the bottom level of the bed, however, regime transitions are strong functions of the radial measuring position. Conclusions are drawn about the adequacy of each analysis method applied in this study, and a brief description on the characteristics of each #ow regime is presented. Several available correlations from the literature for Umf ; Uc and Uk are tested and compared with the experimental 5ndings. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Process tomography; Fluidization regimes; Multiphase #ow; Hydrodynamics; Solid fraction measurement; Imaging

1. Introduction Previous experimental studies on conventional #uidized beds have con5rmed the existence of at least six di3erent #uidization regimes: (i) single bubble regime (ii) multiple bubble regime (iii) exploding bubble regime (iv) turbulent regime (v) slugging bed regime (vi) fast #uidization regime (Zijerveld et al., 1998; Johnsson et al., 2000; Svensson, Johnsson, & Leckner, 1996a). Di3erent terminology appears in the literature for the same #uidization behaviour, while di3erent regimes have been identi5ed, even if the reported operating conditions were the same. These diverse 5ndings are probably due to the ∗ Corresponding author. Tel.: +44-131-4518165; fax.: +44-131-4513129. E-mail address: [email protected] (P. C. Wright).

di3erences in the column diameter, solid type, distributor design, measurement technique and data analysis method. The e3ect of the last two factors on the validity of the results has not been extensively studied, while numerous studies have appeared in the literature in analysing the e3ect of the bed diameter, solid type and distributor design (Wiman & Almstedt, 1998; Bai et al., 1996; Svensson, Johnsson, & Leckner, 1996b). For instance, Svensson et al. (1996b) reported that the multiple bubble regime was observed during operation with low gas velocity and high pressure drop across the distributor (GPdis ), while the single bubble regime was observed at low gas velocity and low pressure drop across the distributor. Therefore, care should be taken when comparing di3erent results obtained with di3erent distributor designs. Conventionally, #uidization regimes are identi5ed by use of the standard deviation and amplitude of a measured variable such as pressure #uctuations (Bai et al., 1996;

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 2 ) 0 0 1 3 8 - 0

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Table 1 Summary of previous studies on regime classi5cation in #uidized beds

Operating conditions

Parameters studied

Pressure taps

System: circulating FB

DP #uctuations

•

System: circulating FB

DP #uctuations

•

System: di3erent sizes of rectangular AP #uctuations & circular x-sections of circulating FB Visual observation Column: di3erent riser’s height

•

Optical probes

Pressure taps

Remarks

Three di3erent #uidization regimes were identi5ed: single bubble regime, mul- Svensson et al. (1996a) tiple bubble regime and exploding bubble regime Column: 8:5 m & 13:5 m height 0:12 × Porosity variations • The existence of single or multiple bubble regimes is directly related to the 0:7 & 1:47 × 1:42 X-section distributor pressure drop • The maximum in amplitude of pressure #uctuation is nothing more than an Particles: 150 –500
m, 2600 kg=m3 , spherical silica sand indication of redistribution of bed materials ◦ ◦ Fluidization gas: air at 40 & 850 C • The bubble frequency at the exploding regime is independent of gas velocity, estimated at 0:5 Hz. Single bubble regime frequency was about 1–2 Hz

Column: 3 m height, 0:97 cm dia., acrylic riser Particles: 166 & 51:9
m, FCC & spherical silica sand Fluidization gas: ambient air Pressure taps

Four #uidization regimes were identi5ed: bubbling #uidization, turbulent #u- Bai et al. (1996) idization, fast #uidization and pneumatic transport • The standard deviations of pressure #uctuations were successfully applied in de5ning transition between di3erent regimes • Distinct variation in solid hold up identi5ed the transition regimes. However, the provided solid hold up values are roughly estimated based on a simple assumption

•

Particles: 300
m, silica sand

•

Fluidization gas: ambient air

• •

Pressure taps

Source

System: circulating FB riser

DP #uctuations

Visual observation Column: rectangular, 0:12 × 0:7 m, 8:5 m height Video recording Particles: 310
m, silica sand Fluidization gas: ambient air

• • • • • •

FB, 5uidized bed; DP, di7erential pressure; AP, absolute pressure

Ten di3erent #uidization regimes were identi5ed ranging from bubbling bed to Zijerveld et al. (1998) dilute transport regime Three di3erent analysis methods were employed: amplitude analysis, power spectra analysis and Kolmogorov entropy analysis Kolmogorov analysis discriminates between the dynamics in large and small facilities, while the amplitude analysis does not The maximum in amplitude was considered as the end of slugging bed due to break down of bubbles There exists a minimum column diameter below which the hydrodynamic behaviour is di3erent from those observed in a large column diameter The study was mainly focused on comparison between di3erent analysis methods Johnsson et al. (2000) in characterizing the #uidized bed hydrodynamics Four #uidization regimes were identi5ed: multiple bubble, single bubble, exploding bubbles and transport condition The multiple bubble regime occurs at low gas velocity and high distributor pressure drop, while the single bubble regime occur at low gas velocity and low distributor pressure drop The maximum in standard deviation of pressure #uctuation when plotted against gas velocity is considered as the transition point from single or multiple bubble regime to exploding bubble regime The study showed that analysis of the bottom bed voidage could give a clear indication on regimes transition when plotted against gas super5cial gas velocity Amplitude of pressure #uctuation alone does not give direct information on the regimes transitions

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

Experimental technique

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

Johnsson et al., 2000). The frequency spectrum, dominant frequency, signal amplitude and standard deviations have also been found to be strongly dependent on the bed hydrodynamics. In a recent comprehensive study by Johnsson et al. (2000), four di3erent #uidization regimes were identi5ed: multiple bubble, single bubble, exploding bubble and transport regime. The study concluded that #uidization regimes characterized by time domain analysis (amplitude of pressure #uctuations) could be misleading, while both frequency and state space analysis are found to be in good agreement and can be used complementary to each other. However, it was also noted that caution must be taken when comparing regime classi5cation identi5ed by bubble frequency analysis, since what is regarded as bubble peak may not be considered as one by others. Little attention has been paid in the literature to analysing #ow regimes by measuring bubble rise velocity or solid fraction distribution. Bubble characteristics in 3-D beds have been mostly studied by capacitance imaging and capacitance probes. Werther (1972) made one of the early attempts by applying an electrical capacitance probe with two needles, the probe records an electric impulse when the rising bubbles strike the needles. Later, Halow, Fasching, Nicoletti, and Spenik (1993) provided quantitative information on bubble characteristics by using capacitance-imaging techniques but no information was given on relating the bubble characteristic to the #ow regimes. Fan, Ho, Hiraoka, and Walawender (1993) characterized the #uidization regimes in a bubbling bed by measuring the bubble velocity with increasing gas #ow. It was shown that the bubble velocity increases with increasing gas velocity up to a point where the bubble velocity becomes independent of the gas super5cial velocity, this velocity was de5ned as the onset to turbulent #uidization. One of the early works on studying the #uidization regimes by measuring the solid distribution was carried out by Yerushalmi and Avidan (1985, Chapter 7). The study was mainly concerned with proving the existence of these regimes and exploring the di3erences between them. Fibre optics probes were used to quantify the axial and radial solid distribution. The transition regimes were identi5ed based on time-averaged solid fraction distribution with respect to changing gas velocity. In a recent study by Mudde, Harteveld, van den Akker, van der Hagen, and van Dam (1999), the radial solid distribution within the turbulent regime and at di3erent levels above the distributor were measured using non-invasive densitometry. The measurements at low heights have shown a wide range of void fraction distribution at the centre of the bed ranging from a packed bed to fully transporting regimes. Close to the walls the packed bed condition prevails at low heights and decreases till reaching the full void condition at high levels. In this paper, we present a case study based on a single particle type and size to de5ne the #uidization regimes by making use of non-intrusive and powerful imaging

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technique. The need for a reliable non-intrusive technique encouraged much research on the application of electrical capacitance tomography (ECT), which has proved to be a very successful tool over the past few years (Malcus, Chaplin, & Pugsley, 2000; Lehner & Wirth, 1999; Dyakowski et al., 1997). Very few experiments on #uidized bed behaviour have been conducted with ECT systems (Wange et al., 1995; Srivastava et al., 1998), even fewer with twin plane ECT (Malcus et al., 2000). As far as the authors are aware, so far nothing has been published on applying twin-plane ECT systems on de5ning the #uidization regimes in #uidized beds. A summary on recent studies on regime classi5cation in #uidized beds is given in Table 1, as shown the pressure #uctuation is the main measured parameter but the experimental conditions are quite di3erent. 2. Aim of the study This paper aims to shed light on some of the methods applied in de5ning the #uidization regimes, in addition to providing a pictorial description of di3erent regime characteristics. Measurement of the solid fraction distribution at the bottom of the bed and at two di3erent elevations will be used to analyse the characteristic behaviour of #uidization regimes over a wide range of gas velocities. Different statistical approaches including standard deviation, frequency, and amplitude will be tested. Bubble rise velocity and local solid fraction analysis will be compared with the statistical 5ndings. Comparison between the experimentally determined transition velocities and some of the available correlations in the literature will also be discussed. From a practical point of view, we are quite convinced that the #ow regimes existing in an industrial scale #uidized bed are far from easy to compare with laboratory scale 5ndings, so it is of interest to explore di3erent analysis techniques besides providing a pictorial description on each regime separately. 3. Electrical capacitance tomography (ECT) The basic theory behind the ECT technique is to measure the permittivity distribution of two non-conducting materials, in a containing vessel, by measuring the capacitance between electrode pairs placed around the column circumference. The ECT system applied here is compromised of twin adjacent planes each of 3:8 cm in axial length, containing eight electrodes and driven axial electrode guards each of 7:6 cm long. This makes a total sensor length of 22:9 cm, with the total sensor length being 52% greater than the sensor diameter. The sensors and the driven guard electrode arrangement is shown in Fig. 1. All sensors were connected to a data acquisition module (DAM 2000) and a computer (Pentium 500 MHz). Pixel resolution of 32 × 32 was used to represent the sensor cross-sectional

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Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 190 mm 150 mm

Electrodes Pipe bore 76 mm, Guards 38 mm, Plane-1 38 mm, Plane-2

Insulation

76 mm, Guards

Fig. 1. Schematic of the sensors arrangement.

~1.0

13.8 ~1.0 60

o

O-ring grove

1.0 Plan

Elevation

Fig. 2. Schematic diagram for the distributor design used in this study. Total number of holes = 155, hole diameter = 0:2 cm. All dimensions are in cm.

area, which makes a total of 1024 permittivity values per image (pixel area: 0:18 cm2 ). For online data capturing and control, special software based on the linear back projection algorithm (LBP) was used, namely the ECT32 software. For data image improvement another piece of o3-line software, based on an iterative method was used, namely PTL IU2000. Both, commercially available software and hardware were acquired from Process Tomography Ltd (Manchester, UK). 4. Experimental set-up and procedure Experiments were carried out in a cold conventional #uidized bed. The apparatus consists of 15 cm diameter cast acrylic tube of 1:5 m high, equipped with a 0:8 cm thick PVC gas distributor located 24 cm above the bottom of the column. This was designed to allow the ECT sensor ring to capture images right at the distributor level. The air distributor was a perforated plate with 155 holes each of 2 mm

diameter (3.3% free area), this is shown schematically in Fig. 2, the pressure drop through the distributor as function of gas super5cial velocity is shown in Fig. 11. Pressure gauge for monitoring inlet line pressure and an oil=moisture trap were 5tted online before the inlet to the #uidization column. Air at ambient temperature was introduced to the bottom of the column from a main air compressor through a rotameter. A pressure tap placed at the bottom of the column and connected to a U-tube manometer was used for measuring the overall bed pressure drop. A mixture of 150 –1000
m spherical glass ballotini particles was used as the #uidizing solid (mixture of Group B particles), according to Geldart classi5cation (Geldart, 1973), particle density is 2600 kg=m3 . Following a sieving process, the mean particle diameter was calculated according to surface to volume ratio as follows: dR p =


m  i=1

−1 (xi =dpi )

:

(1)

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

4.1. ECT measurements

100 90

d p =0.53 micron

Cumulative mass fraction (-)

80 70 60 50 40 30 20 10 0

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2

3

10

10 Particle size (micron)

Fig. 3. Cumulative particle size distribution used in this study.

Outlet Air

The ECT sensors were placed exactly above the distributor level. Before commencing data recording, the system was calibrated for two extreme points; when the column is empty (5lled with low-permittivity material, air) and when the column was tightly packed with the high-permittivity material (glass ballotini). The calibration data was stored and loaded for each running test. Each run was recorded for 20 s time at 100 Hz. A Pentium II, 500 MHz computer was used for data recording and image processing as discussed in the previous section. Data were recorded at two di3erent axial positions; at 1.9 and 5:7 cm above the distributor level (actually the data recorded is the average over a 3:8 cm height). Throughout this study we shall refer to these as the lower and upper levels, respectively. The experimental conditions are summarized in Table 2. To con5rm reproducibility, experiments were carried out in at least duplicate with each set of experiments containing 50 recorded 5les. MATLAB software, version 5.3, was used for data analysis and calculation of time-averaged solid fraction. 5. Results and discussion

∅13.8

150.0

Acrylic column

Guard electrode Upper & lower level sensor’s 24.0

Guard electrode Air distributor Pressure tap

Inlet Air Fig. 4. Experimental set-up.

The cumulative particle size distribution is shown in Fig. 3. The static bed height was 13:8 cm (shallow bed, Hst = Dt ). The experimental set-up is shown in Fig. 4.

Fluidized beds exhibit a very chaotic and non-linear dynamic behaviour with respect to variable operating conditions. Over the last few years, it has been proven that the use of a statistical analysis approach along with imaging systems is a very successful mean for better describing the gas–solid interaction (Malcus et al., 2000; Mudde et al., 1999; Lehner & Wirth, 1999). Therefore, in this study, part of the analysis was done using statistical techniques applied to time series measurement. A computer program was speci5cally developed in the MATLAB environment to carry the statistical analysis. Other conventional means such as, visual observation, image analysis are also discussed. The ECT measurement of solid fraction distribution presented here covers four di3erent #ow regimes: single bubble regime (Umf ¡ U ¡ Us ), slugging bed regime (Us ¡ U ¡ Uc ), turbulent #uidization regime (Uc ¡ U ¡ Uk ) and fast #uidization regime (U ¿ Uk ). Within the range of operating conditions considered in this study, the approximate experimentally de5ned transition velocities are Umf ∼ 0:37 m=s; Us ∼ 0:63 m=s; Uc ∼ 0:87 m=s and Uk ∼ ¿ 1:4 m=s. The reproducibility of each transition point was con5rmed with an average accuracy of 5%. Table 3 shows a summary of the #ow regimes, including an illustrative diagram showing the response of the measured parameter to gas velocity variation. 5.1. Frame-by-frame analysis The possibility of 3-D high imaging frequency, and at di3erent levels, makes the ECT a very powerful tool in a

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Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

Table 2 Summary of the experimental operating conditions

Experimental unit

Operating conditions

Column Distributor Particle Fluidizing gas Fluidization velocity, U Static bed height, Hs Min. #uidization velocity, Umf ECT system

Dia: = 0:138 m; height = 1:5 m, material: cast acrylic Perforated PVC; 155 holes of 2 mm dia. Mean dia: = 530
m, density p = 2600 kg=m3 , material: glass ballotini Air at ambient conditions 0.2 to 2 m=s 13:8 cm 0:37 m=s Twin plane, eight electrodes per plane

frame-by-frame analysis technique. Here we present an approximate quantitative, as well as qualitative, classi5cation of #uidization regimes based on the bubble diameter, shape and frequency. This approach is somewhat tedious, but it is worth comparing such approach with usual methods. On the other hand, it is very diScult to compare our observations with previous studies due to the di3erences in experimental set-up and the lack of similar imaging techniques in the #uidization literature. The recorded image for a bubble passing through the bed at U = 0:5 m=s is shown in Fig. 5. At the lower level (x = 1:9 cm above the distributor) a single bubble starts to form at the centre of the bed, the maximum bubble diameter is db; max ∼ 0:37Dt , the bubble peak frequency is ∼ 3:5 Hz. The bubble peak is considered between two successive maximum bubble sizes. An average pause of 0:14 s has been noticed between each successive bubble cycle. The bubble cycle is estimated from the recorded images as the time taken from the 5rst formation of a tiny bubble until it disappears. At the upper level, the images almost show the same trend in terms of peak and cycle frequency, except that the bubble size increases to an approximate diameter, db; max ∼ 0:55Dt . In the following sections we shall refer to this as the single bubble regime. According to Svensson et al. (1996a), the single bubble regime usually occurs when operating at low gas velocity and low pressure drop through the distributor. This is in good agreement with our observation, since the applied distributor here has a medium pressure drop with maximum GPdis = 3:1 kPa at U = 1:8 m=s (see Fig. 11). An interesting observation can be seen at U = 0:67 m=s (Fig. 6). The bubble size in the upper level increases suddenly to an approximate diameter db; max ∼ 0:75Dt . At the lower level, the bubble size is approximately db; max ∼ 0:38Dt . The bubble frequency in both levels is ∼ 3:0 Hz. Earlier Canada, McLaughlin, and Staub (1978) referred to this regime as an apparent slug #ow regime for shallow beds (Hst =Dt ¡ 1). Here, we shall refer to it as the slugging bed regime. In general, the distinction between the single bubble and slugging bed is not easy to identify, as will be discussed in the next sections. Fig. 7 shows a bubble passing through the bed at U = 1:0 m=s. This is the regime in which large bubbles disappeared, instead, small bubbles started to form. At the upper level, the approximate bubble frequency is 4:0 Hz, and the

maximum roughly estimated bubble diameter is db; max ∼ 0:38Dt (usually two or three bubbles at a time). At the lower level, only single bubbles can be observed at a time, the bubbling frequency is roughly the same as in the upper level, the maximum bubble diameter is db; max ∼ 0:4Dt . In both levels, the bubble #ow is semi-continuous, very short periods of pause between bubble cycles can be seen (¡ 0:05 s). Violent bubble eruptions can also be seen visually at the bed surface. Our experimental observation supports the previous study by Bai et al. (1996) where it was reported that the large bubbles start to break up into smaller ones if the velocity reaches the transition to turbulent #uidization regime. Zijerveld et al. (1998) refereed to this regime as the exploding bubble regime. In the following sections we shall refer to it as the turbulent regime. A lean core and a dense annulus at the wall usually characterizes the fast #uidization regime, also the S-shaped axial pressure or solid fraction pro5les are another features of fast #uidization (Rhodes, Sollaart, & Wang, 1998). Fig. 8 demonstrates the lean and dense core case for a typical image taken at U = 1:6 m=s. At the upper level, a large bubble or void with uniform shape occupies the whole centre of the bed. The bubble diameter is db; max ∼ 0:9Dt . At the lower level, the maximum bubble size is db; max ∼ 0:45Dt . It was diScult to extract the bubble frequency from the images for this situation, due to the apparent continuity of the bubbles with no clear pause between image frames. Di3erent names appear in the literature when de5ning this type of #ow. In the following sections we shall refer to it as fast #uidization regime. 5.2. Visual observation Much of the earlier academic research in #uidization systems was carried out in 2-D transparent containers to allow for visual observations. Although, in recent years, huge improvements in measuring techniques have been achieved, visual observation can still play a role in #uidization studies, especially with laboratory scale equipment. The observations given here are meant to support the experimental measurements. Single bubble and slugging bed regimes (Umf ¡U ¡Uc ): At low gas velocity, the gas #ows upward through the bed

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

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Table 3 Comparison between experimental transition velocities and reported correlations in the literature

centre in the form of single bubbles, and the particles #ow down to the distributor through the wall region. The bottom half of the bed remains in a semi-packed bed state. Clear particle segregation can be noticed, the large particles remain stagnant above the distributor. Increasing the air velocity further (U ¿ 0:6 m=s) causes an increase in the bubble size, in-

dicated by the upward solid movement at the wall. Slugging #ow patterns can then be noticed. The bottom-particle segregation starts to decrease and the upward solid #ow along the wall increases considerably with increasing gas velocity. Turbulent 5uidization regime (U ¿ Uc ): In this regime, the upward solid movement at the wall increases. The bub-

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Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

Red: packed solid

Blue: Air Ai

(a)

(b)

Fig. 5. Image taken at U = 0:53 m=s (single bubble regime): (a) lower level, (b) upper level.

(a)

(b)

Fig. 6. Image taken at U = 0:67 m=s (slugging bed regime): (a) lower level, (b) upper level.

(a)

(b)

Fig. 7. Image taken at U = 0:1 m=s (turbulent #uidization regime): (a) lower level, (b) upper level.

(a)

(b)

Fig. 8. Image taken at U = 0:1:8 m=s (fast #uidization regime): (a) lower level, (b) upper level.

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

ble frequency, as well as the mixing e3ects, increases with increasing gas velocity. The particles are well distributed over the upper level. At the bed surface, it was clear that the solids are pushed violently upward into the free board as a result of bubble explosions. The solids then fall down through a dilute region at the bed centre. Fast 5uidization regime (U ¿ Uk ): At high velocities, a clear transition to fast #uidization can be noticed with a sharp decrease in back-pressure as indicated by the sudden increase in the gas #ow rate, this is mainly due to the bed expansion. Clear circulating solids with turbulent movement can be noticed at the bottom region. At higher levels the bed expands with over through of solids at the walls. 5.3. Solid fraction distribution analysis 5.3.1. Solid fraction pro:les Applying a direct measurement of solid fraction in characterizing the #ow regime in a #uidized bed has a great advantage compared to the usual pressure #uctuation measurement, as the later is always assumed as an indirect indication of solid fraction distribution inside the bed. The measured solid fraction distribution presented here is taken over the mean of a 20 s sample recording time. The results represent the whole bed diameter (32 grids in the radial direction). Comparing the solid fraction pro5le for di3erent gas velocities reveals an accurate description of the #uidization regimes. Here, we assume that a shift in the trend of the solid distribution pro5le with velocity variation indicates a regime transition, although this is usually gradual in nature but we demonstrate here that it can be detected via the ECT system. Fig. 9a and b shows the solid fraction pro5le at the upper and lower levels, measured over a wide range of gas velocity. Generally, we can see a considerable decrease in the solid fraction at the core region with increasing gas velocity, while at the wall, the solid fraction changes are relatively low. As shown in Fig. 9b, at the low-range velocity between U ∼ 0:4 m=s and 0:8 m=s (single bubble and slugging bed regime) the solid fraction is decreased by ∼22% at the centre and ∼1.2% at the wall. This is expected, as the bubble moves through the centre and the drag force is not strong enough to move the highly concentrated solids at the walls. This wide range in solid fraction variation distinguishes the bed behaviour within the single bubble and slugging bed regimes. No clear transition between the two regimes can be seen. As the gas velocity increases beyond U = 0:8 m=s, a great change in solid pro5le marks the transition to the turbulent regime. It is clear that for the velocity between Uc = 0:9 and Uk = 1:4 m=s (turbulent regime) the solid fraction pro5le varies within a medium range, decreasing by ∼ 14% in the centre, while at the wall it decreases by only ∼ 0:5%, again this is expected since the bubble e3ects on the wall region are reduced due to the break down of large bubbles.

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The pro5le shape shows a #attering in the centre (between r=R = 0 and r=R = ±0:6) and steep variations in the region close to the walls (between r=R = ±0:6 and r=R = ±0:97). This is a typical observation seen in turbulent #uidized beds, i.e. the solid–gas mixing increases as a result of disappearance of large bubbles. At Uk ¿ 1:4 m=s, another change in solid fraction pro5le marks the transition to the fast #uidization regime. Within this regime, the overall solid fraction variation is relatively low, decreasing by ∼ 11% at the centre and ∼ 2:5% at the wall. This is due to the fact that the wall e3ect becomes dominant at high velocities and the bubble diameter becomes limited by the bed diameter. In this regime, the solid fraction becomes almost independent of gas velocity. Under the operating conditions covered in Fig. 9b, the solid fraction variations at the centre region appear to decrease with increasing gas velocity. In the turbulent regime, the wall variations are almost negligible. At the lower level (Fig. 9a), the same transition velocities can be identi5ed, but with less obvious changes in pro5les when compared to the more developed #ow pattern at the upper level. 5.3.2. Average solid fraction The variation in average solid fraction with gas velocity is shown in Fig. 10 for two di3erent levels. A clear regime transition can be noticed, marked with a distinct linear solid fraction variation for each di3erent regime. Three regimes can be identi5ed: bubbling regime for a velocity range between Umf ∼ 0:37 m=s and Uc ∼ 0:84 m=s, turbulent regime for the velocity range between Uc ∼ 0:84 m=s and Uk ∼ 1:43 m=s and fast #uidization regime for Uk ¿ 1:43 m=s. No distinct transition between single and slugging beds can be identi5ed. There exists an intermediate transition regime between the turbulent and fast #uidization marked with a sudden drop in solid fraction. 5.4. Standard deviation analysis 5.4.1. Estimation of minimum 5uidization velocity The classical experimental method for de5ning the minimum #uidization velocity is by measuring the bed pressure drop (GP) with respect to decreasing gas super5cial velocity to zero. The intersection point of the extrapolated constant pressure drop with the extrapolated 5xed pressure drop is de5ned as the minimum #uidization velocity (Davidson & Harrison, 1963; Gauthier, Zerguerras, & Flamant, 1999). Our experimental experience with this technique has shown that a maximum and #attening in the pressure drop curve with respect to decreasing gas velocity cannot be achieved under the operating conditions considered in this study as shown in Fig. 11. Another problem with this technique is that its not accurate due to the pressure #uctuations and overshoot at the stage close to the full de#uidization point (transition from bubbling to 5xed bed). However, the method can still be used to de5ne the minimum #uidization velocity

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Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 U=0.4 m/s 0.59

U=0.5 U=0.6 U=0.7

0.54

U=0.8

solid fraction (-)

U=0.9 U=1 0.49

U=1.1 U=1.2 U=1.3

0.44

U=1.4 U=1.5 U=1.6

0.39

U=1.7 U=1.8 U=1.9

0.34 -1.0

-0.9

-0.8

-0.6

-0.5

(a)

-0.4

-0.3

-0.1

0.0

0.1

0.3

0.4

0.5

0.6

0.8

0.9

1.0

dimensionless coordinate, r/R (-)

U=0.4 m/s

0.59

U=0.5 U=0.6 0.54

U=0.7 U=0.8 U=0.9

solid fraction (-)

0.49

U=1 U=1.1 0.44

U=1.2 U=1.3 U=1.4

0.39

U=1.5 U=1.6 U=1.7

0.34

U=1.8 U=1.9 0.29 -1.0

(b)

-0.9

-0.8

-0.6

-0.5

-0.4

-0.3

-0.1

0.0

0.1

0.3

0.4

0.5

0.6

0.8

0.9

1.0

dimensionless coordinate, r/R (-) Fig. 9. Solid fraction pro5les: (a) lower level, (b) upper level.

if we consider the sudden sharp decrease of pressure drop when decreasing the gas velocity as indication of the transition from bubbling to 5xed bed. Another change in the GP curve at Uk ∼ 1:4 m=s also indicates the transition to the fast #uidization regime.

Standard deviation analysis applied to pressure #uctuation measurement is one of the most common methods in de5ning the transition to the turbulent #uidization regime, whereby the maximum in the standard deviation curve against gas velocity is widely accepted as the transition to

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

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0.6

0.57

0.51

fast fluidization

transitional

0.54

fixed bed

average solid fraction (-)

turbulent fluidization (multi bubbles)

0.48 single bubble & slugging bed 0.45

0.42

Umf 0.39 0.2

0.4

Uc 0.6

0.8

Uk 1

1.2

1.4

1.6

1.8

2

U (m/s)

Fig. 10. Average solid fraction of gas super5cial velocity, + lower level, ∗ upper level. 3.3

5.5 overall pressure drop 5

3

distributor pressure drop 2.7

4.5

Single bubble, slugging bed & turbulent fluidization

4

2.4

∆P (KPa)

Fixed bed

3

1.8

Fast fluidization

2.5

1.5

2

1.2

1.5

0.9

1

0.6

Umf

0.5

∆Pdis (KPa)

2.1

3.5

0.3

Uk 0

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

U (m/s)

Fig. 11. Bed and distributor pressure drop as function of gas super5cial velocity.

turbulent regime. Despite its simplicity and applicability to industrial application, little work has been published in using this approach in de5ning the minimum #uidiza-

tion velocity. Previously Wilkinson (1995) and Puncohar, Drahos, Cermak, and Selucky (1985) reported one of the rare studies on determining the minimum #uidiza-

2422

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 0.10

upper level lower level

standard deviation (-)

0.08

0.06

0.04

Umf ~0.37 m/s 0.02

0.00 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

U (m/s)

Fig. 12. Standard deviation of average solid fraction measured at the bubbling regime. Linear regression used to de5ne the minimum #uidization velocity.

tion velocity using standard deviation of pressure #uctuation measured in the plenum (below the gas distributor). The technique is simple and reliable, especially for industrial applications where it is more practical to de5ne Umf without the need to de#uidize the bed. Here, we used the same approach using the standard deviation of the solid fraction measured by the ECT at the lower portion of the bed. Apart from being accurate with a measuring frequency of 100 Hz, the ECT is a very useful tool for industrial application, due to its non-invasive nature and suitability for high operating temperature and pressure. The measured standard deviation is de5ned mathematically as follows:    s = +

N

1  (s − s )2 : N −1

(2)

i=1

Fig. 12 shows the standard deviation of solid fraction measured at two di3erent levels for a few measurements within the bubbling regime. The gas #ow was kept low to ensure that the bed is running within the bubbling regime (Umf ¡ U ¡ Uc ). Here, we de5ne the velocity at which the bed starts to change from a 5xed bed to a bubbling bed when increasing gas velocity as the minimum #uidization velocity (Umf ) or in other words the velocity at which the standard deviation equals zero. This is in line with the fact that the

standard deviation of solid fraction in the bed is linearly related to the gas velocity as long as the bed is operated within the bubbling regime. The linear regression for two elevations (upper and lower levels) coincidence at Umf ∼ 0:37 m=s. Here it is demonstrated that with the ECT system we can de5ne the minimum #uidization velocity in a very simple process without the need to de-#uidize the bed. 5.4.2. Estimation of Us , Uc and Uk Fig. 13 shows the standard deviation of average solid fraction plotted against gas velocity for a wide range of #ow between 0.2 and 2:0 m=s. The measurements were taken at two di3erent levels and represent the entire bed at the measuring level. Four di3erent #uidization regimes can be identi5ed from this diagram ranging from the single bubble regime to the fast #uidization regime. At low gas velocity, just above Umf , the standard deviation increases till reaching a maximum at a gas velocity of 0:87 m=s. This peak is the well known Uc , which is de5ned by many researchers as the mark for the transition from bubbling to turbulent #uidization regime (Bai et al., 1996; Geldart & Rhodes, 1986). A closer look at the curve between Umf and Uc reveals another interesting observation indicated by the sudden decrease in the standard deviation at a super5cial gas velocity Us ∼ 0:63 m=s. This is mainly due to the formation of single large bubble (slug) or in other words due the #uctuations between dense and dilute phases.

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

2423

0.08

upper level lower level

0.07

0.05

0.04

slugging bed regime

single bubble regime

standard deviation (-)

0.06

fast fluidization regime

turbulent fluidization

0.02

fixed bed

0.03

0.01

Umf 0.00 0.2

Us

0.4

0.6

Uc

0.8

Uk

1

1.2

1.4

1.6

1.8

2

U (m/s)

Fig. 13. Standard deviation of average solid fraction against wide range of super5cial gas velocities at two di3erent levels.

Here we de5ne Us as the point for the transition from the single bubble to the slugging bed regime. For gas velocities higher than Uc , the standard deviation diagrams show a levelling o3 until reaching the transition to the fast #uidization regime at Uk ∼ 1:4 m=s. This gradual level o3 is mainly due to the disappearance of bubbles at high gas velocity. It should be noted that some researchers de5ned Uk as the onset of turbulent #uidization (Yerushalmi & Crankurt, 1979), others suggested that it is more or less the same as the transport velocity, i.e. particle carry over (Bi & Fan, 1992). According to our results, no particle carry over occurred, and the standard deviation shows little variation beyond Uk that con5rms the existence of fast #uidization regime as shown in Fig. 13. Uk could also be considered as an indication to the end of the turbulent regime. 5.4.3. Standard deviation of local solid fraction 5uctuation One single recorded image using the ECT system covers a total of 1024 points inside the bed for each horizontal level. This high accuracy makes it possible to characterize the #uidization regimes locally as well as for the entire bed. Previous studies by Bai et al. (1996) noted that there might exist di3erent local #uidization regimes within the bed under the same operating condition. This is also con5rmed later by some researchers when comparing the bottom zone to the dilute region on the top (Rhodes et al., 1998), but very

little attention was given on characterizing the #uidization regime with respect to radial variations. Recently Bai, Issangya, and Grace (1999) investigated the radial variation of standard deviation and found that it is high at the wall regions (r=R ¿ 0:85), and decreases sharply when moving towards the centre. In order to investigate the local #uidization regimes, measurements taken at di3erent radial positions have been studied using the standard deviation analysis. Comparison between the standard deviation of solid fraction #uctuation measured at the same level, but at di3erent radial positions, is shown in Fig. 14a. It is clear that no regime transition can be noticed at the wall region (r=R = ±0:97), instead there is a continuous increase in the standard deviation curve, which means that at this position the bed remains in a bubbling state without reaching the turbulent behaviour. This observation is seen up to r=R = 0:78, then moving gradually towards the centre, it was possible to de5ne Uc indicated by the decrease in standard deviation beyond Uc ∼ 0:8 m=s, but the curve show another increase at U ¿ 1:2 m=s. At the centre (r=R = 0), a clear transition to turbulent regime can be identi5ed. When comparing the regime transition identi5ed by local and average bed solid fraction, we can conclude that standard deviation obtained with the average bed solid fraction (Fig. 13) gives clear and pronounced transition velocities, which represent the overall bed behaviour. While the local solid measurement (Fig. 14) strongly

2424

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 0.12

0.10

standard deviation (-)

0.08

0.06

0.04

r/R=0.03 (centre) r/R=0.97 (wall) r/R=0.78

0.02

Uc 0.00 0.2

0.4

0.6

0.8

1.0

(a)

1.2 U (m/s)

1.4

1.6

1.8

2.0

0.08

0.07

standard deviation (-)

0.06

0.05

0.04

0.03

0.02

r/R=0.03 (centre) r/R=0.97 (wall) r/R=0.78

0.01

Uc 0.00 0.2

0.4

0.6

0.8

(b)

1.0

1.2 U (m/s)

1.4

1.6

1.8

2.0

Fig. 14. Local standard deviation over a wide range of super5cial gas velocities: (a) upper level, (b) lower level.

depends on the radial position, neither Us nor Uk can be clearly identi5ed and the results obtained are too far away to represent the entire bed behaviour. Previous studies on

local voidage #uctuations measured by capacitance and optical 5bre probes have also led to the same conclusion (Abed, 1984; Chehbouni et al., 1994). The transition to

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

2425

0.6 peak 0.58

signal amplitude

solid fraction (-)

0.56

0.54

0.52

0.5 peak 0.48 0.5

0.7

0.9

1.1

1.3

1.5

time (sec)

Fig. 15. A typical peak to peak amplitude illustrating the calculation method on time series measurements.

turbulent #uidization Uc is diScult to identify from local measurement, and if it exists, then it only represents the speci5c measured point. This might explain some of the contradictory results reported in the literature when applying the standard deviation approach. Measurements taken at the lower level (Fig. 14b) show the same trend, but with less pronounced transition between regimes, which suggests that, at the denser lower portion of the bed, the variation in bed dynamics depends strongly on the radial positions, rather than on the axial position. Therefore, caution should be exercised when comparing di3erent experimental 5ndings with di3erent bed diameters, even if all the operating conditions remain the same. 5.5. Amplitude analysis Analysis based on the amplitude measurement has been the subject of discussion over the last few years, casting doubts on its reliability when applying di3erent measuring methods. Johnsson, Svensson, and Leckner (1992) carried out an experimental study using di3erential measurements of pressure #uctuations, and found that no maximum could be seen on the amplitude versus velocity curve when the applied amplitude is normalized with the bed pressure drop. Hence, it was not possible to de5ne either Uc or Uk . Furthermore Svensson et al. (1996b) reported that the maximum in the pressure #uctuation amplitude, when plotted against gas velocity, could be as a result of a redistribution of the bed material and only seen as a relative indication of the bubble size. Recently Johnsson

et al. (2000) pointed out that caution must be exercised when applying the amplitude measurement in studying #ow characteristics, and it was also mentioned that the amplitude alone is not suScient for such studies. Although, the measurement method applied here is di3erent, it was of interest to investigate the validity of this approach when using solid fraction #uctuations measured with the ECT system. Five di3erent amplitude results are presented here: mean amplitude, normalized mean amplitude, standard deviation of amplitude, maximum amplitude and normalized maximum amplitude. Normalization of amplitude was done with respect to the average solid fraction. The calculated peak to peak amplitude is taken from the solid fraction measurement signal as illustrated in Fig. 15 for a typical recorded sample. In all the 5ve di3erent methods, a clear on-set to turbulent #uidization can be identi5ed ranging between Uc = 0:8 and 0:87 m=s, as shown in Figs. 16 and 17. A clear peak at Uc ∼ 0:87 and levels o3 at Uk ∼ 1:4 m=s can be observed. The end of curve level o3 at Uk is mainly due to the considerable decrease in solid fraction #uctuations (continuous dilute phase at the core region) as mentioned earlier. The transition from the single bubble regime to the slugging bed regime (Us ) is always diScult to identify, but here we can observe this behaviour marked with the sudden decrease in amplitude at Us ∼ 0:63 m=s. Apart from being simple, the amplitude analysis applied with solid fraction measurement can be used successfully to identify both the low-velocity regimes: single bubble and slugging bed, as well as the high-velocity regimes: turbulent and fast #uidization.

2426

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 0.18 mean amp. STD of amp.

mean, STD, normalized mean amplitude (-)

0.16

normalized mean amp. 0.14 0.12 0.10 Single bubble regime

0.08

Turbulent fluidization regime

Slugging bed regime

Fast fluidization regime

0.06 0.04 0.02 Us

Uk

Uc

0.00 0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

U (m/s)

Fig. 16. Mean amplitude, normalized mean amplitude and STD of amplitude as function of super5cial velocity, measurement taken at the upper level.

0.8

maximum, normalized maximum amplitude (-)

0.7

0.6

0.5

Single bubble regime

Turbulent fluidization regime

Slugging bed regime

0.4

Fast fluidization regime

0.3

0.2

0.1

max. amplitude

Us 0.0 0.3

0.5

Uc 0.7

Uk 0.9

1.1

1.3

norm. maximum amplitude

1.5

1.7

1.9

U (m/s)

Fig. 17. Maximum amplitude and normalized maximum amplitude as function of gas super5cial velocity, measurements taken at the upper level.

To investigate the possibility of additional information being obtained from amplitude measurements we considered the normal probability density function. The variable amp, which is the signal amplitude, has the probability density

function: p(amp) =

1 √

amp



1 exp − 2 2



amp − amp amp

2

;

(3)

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

2427

0.40 U=0.4 m/s U=0.43 U=0.5 U=0.6 U=0.84 U=1.2 U=1.67 U=1.87

0.35

pdf (-)

0.30 0.25 0.20 0.15 0.10 0.05 0.00 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

amplitude distribution (-)

Fig. 18. Probability density of signal amplitude for various gas velocities.

where amp is the standard deviation and amp is the mean of signal amplitude. From Fig. 18 it appears that the amplitude distribution is directly proportional to the increase in gas velocity until reaching the onset to turbulent #uidization, after which, the distribution inversely changes with increasing gas velocity. This distinguishable change in the amplitude distribution signi5es the transition to turbulent #uidization. As we expected, the signal amplitude reaches its wider distribution as the velocity increases towards the end of the slugging regime (U ∼ 0:84 m=s). In this regime the bed moves like a piston due to the increase in bubble diameter, and the recorded signal of solid fraction ideally should cover a wide range from full-packed bed signal (∼ 0:6) to complete void signal (∼ 0). In the turbulent regime, the amplitude distribution curve shifts towards the left, but still remains in a wide distribution, indicating less probability of high solid concentration due to the break down of slugs. 5.6. Frequency analysis A simple algorithm was developed in MATLAB software to account for the number of bubble peaks or cycles in a 20 s measurement sample. The bubble peaks frequency in a signal is de5ned in the computer algorithm as the point when the solid fraction reaches minimum and the slope of the line connecting two successive signals changes sign from (−) to (+). The bubble cycles frequency is de5ned as the total number of times the signal passes over its mean divided by two. Fig. 19 shows an illustrative diagram for a typical bubble peak and bubble cycle. This is de5ned mathematically

as follows: fp =

Np ; T

(4)

fc =

Nc ; 2T

(5)

where, T represents the total sampling period in seconds. In most of the reported studies, analysis based on frequency measurement has shown di3erent results. In general, the frequency domain analysis depends strongly on the sampling frequency, number of samples, and the method employed in de5ning the dominant frequency. In a bubbling #uidized bed, a measuring frequency of 20 Hz is quite suScient (Johnsson et al., 2000; Svensson et al., 1996a, b), this is also con5rmed by the measurement obtained with our system (maximum measured cycle and peak frequency is 4.2 and 6:5 Hz, respectively). As mentioned earlier, the imaging frequency in this study was quite high (5 times the minimum requirement). Most studies dealing with frequency analysis in #uidized beds focused on the dominant peak frequency, and not enough information is yet available on comparison between the peak and cycle frequency. Johnsson et al. (2000) reported that the peak frequency alone is not enough to characterize the bed hydrodynamics, but no comparison between the two frequencies was given. The results presented here are an attempt to compare between these two di3erent approaches. Fig. 20 shows the cycle frequency measured over a wide range of gas velocity. It can be seen that at low gas velocity, just above Umf , the bed starts with high cycle frequency (3:5 Hz) and then decreases,

2428

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 0.6

cycle frequency

solid fraction (-)

0.55

mean

0.5

0.45

peak frequency

peak frequency

cycle frequency 0.4 3.1

3.3

3.5

3.7

3.9

4.1

4.3

4.5

time (sec)

Fig. 19. Calculation method for the cycle and peak frequency taken from a typical time series measurement of solid fraction #uctuation.

4.3

Slugging bed & turbulent fluidization regimes

cycle frequency (Hz)

4.0

3.8

Single bubble regime Fast fluidization regime

3.5

3.3

3.0

2.8

Us 2.5 0.3

0.5

Uk 0.7

0.9

1.1

1.3

1.5

1.7

1.9

U (m/s) Fig. 20. Average cycle frequency against gas super5cial velocity measured at di3erent #ow regimes, measurements taken at the upper level.

reaching a minimum at Us ∼ 0:6 m=s. This marks the end of single bubble regime as identi5ed earlier. Beyond Us , the cycle frequency increases considerably until a transition to fast #uidization can be seen, marked with #attering in the

curve at Uk ∼ 1:43 m=s. No transition between the slugging bed and turbulent regime can be identi5ed. The cycle frequency at the single bubble regime is within a range of 3:5 ⇒ 2:6 Hz and at the fast #uidization regime at a range of

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

2429

6.7

Slugging bed and turbulent fluidization regimes

6.2

peak frequency (Hz)

Single bubble regime 5.7

Fast fluidization regime

5.2

4.7

4.2

Uk

Us 3.7 0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

U (m/s) Fig. 21. Average peak frequency against gas super5cial velocity measured at di3erent #ow regimes, measurements taken at the upper level.

3:7 ⇔ 4:2 Hz. The in-between regime has a wide frequency range of 2:6 ⇒ 4:0 Hz. Analysis with the peak frequency shows more or less the same trend as shown in Fig. 21, but the transition to the fast #uidization regime here is over estimated at Uk ∼ 1:6 m=s in comparison to the other techniques described earlier. The bed starts with a very high peak frequency (6:5 Hz) and then decreases until reaching a minimum at approximately Us ∼ 0:6 m=s. This marks the end of the single bubble regime. The high peak frequency obtained at the single bubble is in agreement with previous results reported by Svensson et al. (1996b). However, numerical comparison is diScult due to the di3erences in experimental set-up and operating conditions. The peak frequency at the single bubble regime is within a wide range of 6:5 ⇒ 4:0 Hz. Beyond Us , the peak frequency increase considerably within the range of 4:0 ⇒ 6:5 Hz until reaching a maximum at Uk ∼ 1:6 m=s to mark the transition to fast #uidization regime. Comparison between the prediction obtained with the cycle and peak frequency techniques reveals that both methods give almost the same transition velocity Us , but the peak frequency may give slightly overestimated value for Uk . Measurements taken at the lower level (x = 1:9 cm) show more or less the same trend, and lead to the same transition points. So there is no much e3ect of axial measuring position, as long as the measurements are taken within the bottom of the bed (i.e. x ¡ Hst ). The conclusion is that the cycle and peak frequency is a successful method to identify both transition velocities Us and Uk , no clear transition from slugging bed to turbulent #uidization regime can be identi5ed.

5.7. Power spectra analysis Several researchers have employed power spectra analysis in analysing #uidized bed hydrodynamics (Johnsson et al., 2000; Svensson, Johnsson, & Leckner, 1996a; Malcus, Chaplin, & Pugsley, 2000). The method has also been widely used to estimate the dominant frequency. Usually a wide band spectra is considered to signify an increase in the number of bubbles, while a narrow band with sharp peaks either signi5es a single bubble or slugging bed behaviour (Svensson et al., 1996a). The power spectra presented here were calculated using the Fast Fourier Transform algorithm built into the MATLAB signal-analysis toolbox. The spectra were based on a 20 s sample and a power spectra resolution frequency of 0:05 Hz. Fig. 22 shows the power spectra for a wide range of gas velocities covering di3erent #uidization regimes. It is clear that the spectra band and magnitude varies considerably with the gas velocity. Within the bubbling regime, a broad-banded spectra is observed (see Figs. 22a–c), this indicates a distinguishable bubbling behaviour with low amplitude, as seen in the power spectra scale. The dominant frequency is approximately 3 Hz. Fig. 22d–f shows the power spectra for a selected range of gas velocity within the slugging regime, a relatively narrow-banded spectrum with high power spectra magnitude signi5es this regime. The dominant frequency is relatively low (∼ 2:5 Hz). This is in good agreement with our previous observation when analysing the bubble cycle frequency. The power spectra for a higher gas velocity covering the turbulent regime is shown in Fig.

2430

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 15

70

9 6

120

U=0.53 m/s

50

power spectra

power spectra

power spectra

60

U=0.46 m/s

12

40 30 20

U=0.6 m/s

90

60

30

3 10 0

0

1

2

3

(a)

4 5 6 7 frequency (Hz)

8

9

0

10

0

1

2

3

(b)

4 5 6 7 frequency (Hz)

8

9

0

10

0

1

2

3

(c)

4 5 6 7 frequency (Hz)

8

9

10

8

9

10

8

9

10

9

10

600

500

500

U=0.66 m/s

400 300 200 100 0

500 400

U=0.73 m/s

400

power spectra

600

power spectra

power spectra

Single bubble regime

300 200

0

1

2

3

4 5 6 7 frequency (Hz)

8

9

0

10

200 100

100

(d)

U=0.8 m/s 300

0

1

2

3

(e)

4 5 6 7 frequency (Hz)

8

9

0

10

0

1

2

3

(f)

4 5 6 7 frequency (Hz)

350

250

250

300

200

200

U=1.0 m/s

150 100 50 0

power spectra

300

power spectra

power spectra

Slugging bed regime 300

U=1.2 m/s

150 100 50

0

1

2

3

(g)

4

5

6

7

8

9

0

10

200

U=1.33 m/s

150 100 50

0

1

2

3

(h)

frequency (Hz)

250

4

5

6

7

8

9

0

10

0

1

2

3

(i)

frequency (Hz)

4

5

6

7

frequency (Hz)

Turbulent regime 250

200

200

150 100

U=1.5 m/s

(j)

100

U=1.77 m/s

0

1

2

3

4 5 6 7 frequency (Hz)

8

9

0

10

100

U=1.9 m/s 50

50

50 0

150

150

power spectra

power spectra

power spectra

200

0

1

2

3

(k)

4 5 6 7 frequency (Hz)

8

9

0

10

(l)

0

1

2

3

4 5 6 7 frequency (Hz)

8

Fast fluidization regime Fig. 22. Power spectra density for various gas velocities.

22g–i. This regime is signi5ed by a relatively clear dominant frequency (∼ 3:0 Hz) with a moderate spectra magnitude. At a higher gas velocity range covering the fast #uidization regime (U ¿ 1:4 m=s), the power spectra is broad and several peaks can be noticed, as shown in Fig. 22j–l. The domi-

nant peak frequency shows no much change when compared to the turbulent regime, but the power spectra magnitude is considerably lower. Accordingly, we conclude that the power spectra analysis is generally in agreement with the observations shown

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

2431

0.6 x=5.7 cm x=1.9 cm 0.58

0.56

solid fraction (-)

0.54 ∆Τ 0.52 lower level bubble peak 0.5

0.48 upper level bubble peak 0.46

0.44 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

time (sec)

Fig. 23. Calculation method for the bubble rise velocity illustrated on a typical time series measurement of average solid fraction at the upper and lower levels.

by the other analysis methods discussed in this study. However, it must be noted that a precise estimate of a transition velocity cannot be extracted from the power spectra analysis, this is mainly due to the similarity in the spectra shape and the diSculties in obtaining an accurate estimate of the dominant frequency. Nevertheless, this method can still provide valuable information on the general hydrodynamic behaviour of the bed, and also could be used as a con5rmation approach to verify the transition velocities determined by other methods. 5.8. Bubble rise velocity If we consider the minimum solid fraction in a speci5c time interval as the bubble peak, then by time series measurement of solid fraction at two di3erent levels it is possible to de5ne the bubble velocity. Fig. 23 is an illustration of the concept applied here in calculating the bubble rise velocity between the lower level at 1:9 cm and the upper level at 5:7 cm. The time di3erence between reaching a peak at the upper and lower levels is calculated based on the mean value obtained over 20 s sample. Accordingly, the bubble velocity is de5ned in the following equation: N 1  Gx Ub = ; (6) N −1 Gti i=1

where Gti = tb2 − tb1 :

(7)

tb1 and tb2 represent the time when the bubble peak passes through the lower and upper level sensors, respectively. Gx represents the distance between the centre of the two sensors. It must be noted that this is an approximate approach, since the actual sensor measuring space is an average over a 3:8 cm length. Since we are presenting in this paper different analysis techniques it was of interest to compare and con5rm the reliability of this approach with the widely used cross correlation function method (CCF). The cross correlation of the signals produced by the two sensors was used to estimate the lag-time between the bubble peaks at the lower and upper sensors. CCF is the average product of the signal f1 (t) and a time-shifted signal produced by the upper sensor f2 (t + ). This is de5ned in integral form as  1 T R R() = lim f1 (t)f2 (t + ) dt: (8) T →∞ T 0 Applying Eq. (5) in a discrete form leads to n

 R =1 f1 (i!)f2 (i! + j!) R() n

j = 1; 2; 3; : : : ; m;

(9)

i=1

where ! represents the sampling interval, n is the selected number of sample intervals and m is a selected number (¡ n). The experimental results are compared with the widely used theoretical model (Davidson & Harrison, 1963): Ub = U − Umf + 0:711(gdb; max )0:5 :

(10)

2432

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437 0.80 detailed signal analysis cross-correlation Eq. 10 2 per. average

0.75

0.70

Ub

0.65

0.60

0.55 single bubble & slugging bed regimes

0.50

turbulent & fast fluidization regimes

Uc

0.45 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

U (m/s)

Fig. 24. Experimental and predicted bubble rise velocity against super5cial gas velocity.

0.29144

Ub=0.7 m/s

0.29141

cross-correlation (-)

0.29138 0.29135 0.29132 0.29129 0.29126 0.29123 0.29120 0.00

lag time=0.054 s

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

lag time (s)

Fig. 25. A typical cross-correlation function estimate of bubble rise velocity.

The bubble size is a very sensitive parameter with respect to the column diameter and the measuring position, so applying any of the available correlations may give misleading results. Therefore, the applied db; max in Eq. (10) was estimated from the ECT images as the maximum bubble diameter at the upper level (developed #ow). Fig. 24 shows the experimental results for two di3erent analysis methods, and the prediction from Eq. (10). It is clear that the model is in relatively good agreement with the experimental results up to the point of on set to turbulent #uidization, Uc ∼ 0:82 m=s (at maximum bubble velocity). The three approaches typically show a general increase in the bubble velocity with increasing gas velocity up to Uc ∼ 0:82 m=s. Beyond this, each method shows a di3erent result, either decreasing or constant bubble velocity. This is justi5ed with

the fact that the theoretical model of Eq. (10) and the CCF method both do not represent the average bubble velocity. The approximate value of db substituted in Eq. (10) represents the maximum bubble size, which lead to an overestimated bubble velocity. On the other hand, the lag-time estimated by the CCF is in fact represent the highest occurring lag-time not the average, and so the values estimated might not be accurate. A typical cross-correlation estimate of lag-time is shown in Fig. 25. Similar notes on the accuracy of the CCF method in estimating the bubble rise velocity was reported earlier by Van Lare et al., 1997. Another interesting observation seen in Fig. 22 is the low bubble velocity at the onset to slugging behaviour (∼ 0:6 m=s). This is clearly seen when we look at the points representing the detailed signal analysis method for the range of gas

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

velocities between U ∼ 0:58 and 0:63 m=s. The same observation cannot be seen with the CCF method or the prediction from Eq. (10). A peak in the bubble rise velocity at the onset of turbulent #uidization supports the previous 5ndings reported earlier by Yamazaki et al., 1991. At U Uc , the bubble velocity is apparently independent of super5cial gas velocity. According to our visual observations and experimental results, the scenario for the bubble rise velocity can be summarized as follows: at low gas velocity (U ¡ Uc ), the bubble rise up faster due to the limited available bubble passage in the dense bottom, and the bubble velocity is more or less equal to the gas super5cial velocity. At Uc ∼ 0:8 m=s the bubble velocity reaches its maximum and then decreases with increasing gas super5cial velocity. This decrease is probably due to the bed expansion and the increase in the drag force that tends to decrease the concentrated solid layer at the walls. At U Uc the bubble rise velocity becomes almost independent of the gas super5cial velocity, as a result of the transition to the fast #uidization regime (lean core and dense annulus) or in other words as a result of change from bubbling behaviour to a continuous void #ow. The conclusion here is that the bubble rise velocity diagram is a successful approach for de5ning the transition from the bubbling regime (single bubble and sluggish bed) to the turbulent #uidization regime marked with a maximum

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bubble velocity at Uc . A decrease in bubble velocity at high gas super5cial velocity could also be a feature of the transition to fast #uidization, however, this is not easy to identify at this stage. It should be noted that the literature is full of scattered results in regard to the bubble rise velocity. Al-Zahrani and Daous (1996) reported that rise velocity of a single bubble injected into a gas–solid #uidized bed is independent of the overall gas #ow rate and the state of the bed. Farag et al., 1997 also reported a negative bubble velocity at the bed centre. Fan et al. (1993) reported a constant bubble velocity beyond the onset of turbulent #ow. In a recent study by Kantzas et al., 2001, it was concluded that measurement of bubble or void characteristics may give a better understanding on regime transitions. Since the results presented here are limited with the bed geometry and the particle size used, further investigations on using bubble rise velocity as a tool for regimes characterization is recommended. 6. Comparison of experimental results with available correlations Table 4 compares our experimental values for Umf ; Uc and Uk with some of the reported correlations in the literature selected according to their applicability to our operating

Table 4 Summary of #uidization regimes Source

Eq. no.

Equations

Predictions Umf

Wen and Yu (1966)

A1

Grace (1982, Chapter 8)

A2 A3 B1 C1 B2

Umf =



$ dp g



33:72 +

0:0408d3p g s g $g2

0:5

Uc

Uk

−33:7

Lee and Kim (1988) Nakajima, Harada, Asai, Yamazaki, and Jimbo (1991)

B3 B4 C2 B5 B6

Cai, Jin, Yu, and Wang (1989)

B7

0.22 — — Remf = (27:72 + 0:0408)0:5 − 27:2 0.25 — — 0.30 — — Umf = 0:00075d2p s g=$

Uc = 3:0(p dp; max )0:5 − 0:77a — 2.75 — — — 7.45 Uk = 7:0(p dp; max )0:5 − 0:77a — 2.46 — Rec = 1:243 Ar 0:447a Rec = 0:565 Ar 0:461b — 1.28 — 2.16 — Uc =(gDt )0:5 = 0:463 Ar 0:145 Rec = 0:936 Ar 0:475 — 2.42 — Rek = 1:46 Ar 0:472 — — 3.67 Rec = 0:7 Ar 0:485c — 1.99 — — 1.52 — Rec = 0:633 Ar 0:467

0:2 







0:27 1=0:2  $g20 s −g Uc Dt g20 2:42×10−3 0:211 b = + 0:27 1:27 d $   (gd )0:5

Perales et al. (1991) Bi and Fan (1992) Tsukada, Nakanishi, and Horio (1994) Fan (1992)

C3 C4 C5 C6

Rek Rek Rek Rek

Yerushalmi and Crankurt (1979) Bi and Grace (1995) Chehbouni et al. (1994) Horioi (1991)

a From

di3erential pressure #uctuation data. absolute pressure #uctuation data. c From bed expansion data. b From

p

g

Dt

= 1:95 Ar 0:453b = 2:28 Ar 0:419 = 1:31 Ar 0:45b = 0:3(gDt )0:5 + Umf

Dt

% |Error|

g

— — — — —

g

0.99 — — — —

42 36 19 216 365 182 47 149 178 129 129 74

p

— 4.26 3.59 2.67 0.72

14 166 124 67 55

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Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

conditions. Eq. (A3) by Grace (1982) appears to give the best prediction for Umf . Eq. (B7) by Cai, Jin, Yu, and Wang (1989) and Eq. (C6) by Fan (1992) gave the closest prediction for Uc and Uk , respectively. It should be noted that both of these Eqs. (B7) and (C6) incorporated the e3ect of bed size represented by Dt . This strongly suggests that the bed diameter have a signi5cant in#uence on the correlation prediction. In general, very poor agreement with the experimental results can be seen. This is mainly due to the fact that most of these correlations do not take into consideration the e3ect of static bed height (Uc increases with increasing Hst ), bed diameter, the particle size distribution and the distributor design. In fact, such variation, especially in Uc and Uk could also be due to the di3erences in the measuring method, for instance, Uc from di3erential pressure measurements is systematically higher than from absolute pressure #uctuations, also transition velocities based on void #uctuation always appear to be lower than from the pressure #uctuation method (Bi et al., 2000). More work is required to obtain a better correlation equation for transition velocities, these equations must be classi5ed according to the analysis method, and their applicability to the operating conditions. As indicated by the wide variation in prediction shown in Table 4, simple equations based on Reynolds number (Re) and Archimedes number (Ar) numbers are de5nitely misleading. 7. Conclusion The ECT system can be successfully used to identify the transition regimes in a conventional #uidized bed. In a related study carried out by Johnsson et al. (2000) it was pointed out that in order to have a reliable approach in #ow characterization, the applied technique should be simple and suitable for industrial application. Here, with con5dence we can say that both requirements are ful5lled. Few measurements within the bubbling regimes can give an accurate estimate for the minimum #uidization velocity (Umf ). Five di3erent #uidization regimes have been identi5ed using di3erent analysis approaches, these regimes are summarized as follows according to their occurrence when increasing the gas velocity: Single bubble regime: at low gas velocity, just above Umf , the bed starts bubbling with a single bubble at a time. The bubble cycle is followed by a short pause (∼ 0:14 s). Substantial decrease in average solid fraction is noticed as the gas velocity increases. The bubble rise velocity is more or less equal to the super5cial gas velocity. The bubble frequency is rather high (fc : 3:5 ⇒ 2:6 Hz; fp : 6:5 ⇒ 4:0 Hz) but decreases with increasing gas velocity. The standard deviation and amplitude of solid fraction #uctuation is linearly related to the gas super5cial velocity. Slugging bed regime: This regime follows the single bubble regime but is not always easy to identify. The on set of slugging behaviour occurs at the minimum bubbling fre-

quency. The regime can be characterized by the sudden decrease in the amplitude or the standard deviation of solid fraction #uctuation when increasing the super5cial gas velocity (deviation from linearity). The regime is also characterized by the formation of uniform large bubbles (db ∼ 0:75Dt ), and the increase in bubble frequency with increasing gas velocity. In this regime, the bubble rise velocity is almost equal to the air super5cial velocity. The probability distribution of amplitude is proportional to increasing gas velocity within the bubbling and slugging bed. Analysis based on the power spectra indicates a high spectra magnitude in this regime. Turbulent 5uidization regimes: This is easy to identify, characterized by a maximum in the standard deviation and amplitude of solid fraction #uctuations. Multiple bubbles exist simultaneously, and the bubble rise velocity reaches its maximum at the transition velocity Uc . At the upper level (x=5:7 cm) the solid fraction pro5le shows a clear #attening in the core region, and steep variation in the region close to the walls. Slight variations in the average solid fraction can be noticed when increasing the gas velocity. Both cycle and peak frequencies (fc and fp ) increase with increasing gas velocity. Analysis based on the probability density of amplitude shows the widest distribution at the transition velocity Uc . After the onset of turbulent #uidization, the distribution is inversely proportional with increasing gas velocity, but still remains within a broad distribution. Fast 5uidization regimes: Experimentally, the transition to fast #uidization can be identi5ed by the considerable bed expansion and the sudden increase in gas velocity due to the sudden drop in back pressure. The solid fraction takes a typical plug #ow pro5le with a clear dense annulus and dilute core. The level o3 in the standard deviation and amplitude marks the transition to this regime. The bubble rise velocity (Ub ), as well as the cycle and peak frequency (fc and fp ) values remain almost constant within this regime (variations within a very limited range). The power spectra analysis shows a broad band spectra with high dominant frequency and relatively low magnitude. Comparison between the di3erent analysis approaches presented in this study reveals the following: Frame-by frame analysis: This method is not highly recommended to draw a conclusion on regime transitions, it is time consuming to analyse each frame separately (20 s sample produces a total of 2000 image frames), it should only be used to con5rm the experimental 5ndings obtained by other usual methods. The method is useful in providing better understanding of solid distribution, especially at the region above the distributor level where usual measuring techniques could fail. Visual observation analysis: The #uidization regimes are highly dependent on the characteristics of the #ow pattern in the centre of the bed. It is usually very diScult to visually observe this region (especially in industrial applications, where the containing vessel is usually constructed of a non-transparent material), therefore this method alone

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

is not suitable to draw concrete conclusions in #uidization regimes. However, according to our experiments, the transition to fast #uidization was easy to identify indicated by the sudden increase in the gas velocity and considerable bed expansion. Pressure drop analysis: Pressure drop variation measured at a position below the distributor level could be applied in de5ning both the Umf and Uk . It was not possible to de5ne Us and Uc . Another, problem is that in order to de5ne Umf the bed should be de-#uidized, which is not highly recommended in industrial applications. Average solid fraction analysis: This is a very successful means of de5ning Uc and Uk . The time-averaged solid fraction shows a linear relationship with the gas velocity, with a clear transition regime. Transitions within the bubbling regimes cannot be identi5ed. Local solid fraction analysis: The radial pro5le of solid fraction measured with the ECT system can provide a clear understanding of the #ow pattern, which makes it easy to characterize the #ow regime. The local measurement also has a strong potential to provide a reliable local regime transition when applied with the standard deviation method. Standard deviation analysis: This is a very successful means to characterize the #uidization regimes over a wide range of operating conditions. All four #uidization regimes observed in this study were clearly identi5ed with pronounced transitions. These results were also con5rmed by the frame-by-frame analysis approach. This method could also be used to distinguish between the local transition regimes in di3erent radial positions. Amplitude analysis: All the 5ve di3erent methods tested with amplitude analysis provided a clear transition to turbulent #uidization and fast #uidization, marked with the curve peak at Uc ∼ 0:87 and level o3 at Uk ∼ 1:4. The probability distribution of signal amplitude is another helpful statistical method in analysing the #uidization regimes, but can only be used to identify the transition to turbulent #uidization. Frequency analysis: Due to the high data capturing rate obtained with the ECT, the frequency results presented here are very accurate and reliable. The peak and cycle frequencies (fp and fc ) are a very successful means to de5ne Us and Uk . The peak frequency gives slightly higher values for Uk when compared to other methods. It is not possible to identify the transition to slugging beds or turbulent #uidization regimes. Power spectra analysis: The power spectra analysis alone is not a recommended approach in identifying the transition velocities for the reasons discussed above. Several peaks may appear in the same spectra, which makes it diScult to identify the average frequency. However, the method provides a general description of the bed dynamics. It also has a role as a con5rmation approach for results obtained with other more precise methods. Bubble rise velocity analysis: This is a suitable approach to de5ne the transition to turbulent #uidization. The cross-correlation function (CCF) method has its limitations,

2435

and it was found that the calculated bubble velocity is overestimated due to the reasons discussed above. However, the transition velocity Uc determined from both methods of CCF and the detailed signal analysis agree well. No additional conclusions could be made at this stage. Further investigations shall be considered in the future. Comparison between the available correlation’s for transition velocity, and our experimental 5ndings, has shown poor agreement, even a great controversy exists when comparing between each correlation prediction. Therefore, further work on classifying the correlation equations according to the operating conditions and the analysis method is highly recommended.

Notation Ar amp db; max di dp dR p Dt f1 ; f2 fp fc g Hst N Nc Np GP r RR R Remf Rec Rek T t tb1 tb2 U Umf Us Uc

Archimedes number signal amplitude maximum bubble diameter, m ith particle diameter of sieved particles, m particle diameter, m mean particle diameter, m column, bed diameter, m Average-bed solid fraction signal measured at the lower and upper sensors, respectively mean bubble peak frequency, Hz mean bubble cycle frequency, Hz gravity acceleration, m=s2 static bed height, m total number of sample images (signals) total number of bubble cycles total number of bubble peaks pressure drop, kPa radial co-ordinate, m cross-correlation function de5ned in Eqs. (8) and (9) column, bed radius, m Reynolds number at minimum #uidization velocity (=g Umf dp =$g ) Reynolds number at the transition to turbulent #uidization (=g Uc dp =$g ) Reynolds number at the transition to fast #uidization (=g Uk dp =$g ) total sampling time, s time, s time at which bubble pass the lower level sensor, s time at which bubble pass the upper level sensor, s super5cial gas velocity, m=s super5cial gas velocity at minimum #uidization, m=s super5cial gas velocity at the transition to slugging bed regime, m=s super5cial gas velocity at the transition to turbulent #uidization regimes, m=s

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Uk Ub x xi

Y. T. Makkawi, P. C. Wright / Chemical Engineering Science 57 (2002) 2411–2437

super5cial gas velocity at the transition to fast #uidization regime, m=s bubble rise velocity, m=s axial co-ordinate, cm mass fraction of the ith particle with diameter, di

Greek letters s Rs mf $ g g20 s s 

solid fraction time-averaged solid fraction void fraction at minimum #uidization gas viscosity, kg=m s gas density, kg=m3 ◦ gas density at 20 c, kg=m3 , solid density, kg=m3 standard deviation of solid fraction #uctuation lag-time between bubble peaks at the upper and lower sensors (s)

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