The Gaussian spectral pressure distribution applied to a fluidized bed

The Gaussian spectral pressure distribution applied to a fluidized bed

Chemical Engineering and Processing 48 (2009) 120–125 Contents lists available at ScienceDirect Chemical Engineering and Processing: Process Intensi...

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Chemical Engineering and Processing 48 (2009) 120–125

Contents lists available at ScienceDirect

Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep

The Gaussian spectral pressure distribution applied to a fluidized bed M.R. Parise a,∗ , P.R.G. Kurka b,1 , O.P. Taranto a a b

School of Chemical Engineering, University of Campinas (UNICAMP), P.O. Box 6066, 13083-970 Campinas, SP, Brazil Faculty of Mechanical Engineering, University of Campinas (UNICAMP), P.O. Box 6122, 13083-970 Campinas, SP, Brazil

a r t i c l e

i n f o

Article history: Received 31 August 2007 Received in revised form 21 February 2008 Accepted 22 February 2008 Available online 29 February 2008 Keywords: Gas–solid fluidized bed Defluidization Pressure fluctuations Fourier transform Gaussian distribution curve

a b s t r a c t The present work applies the methodology proposed by Parise et al. [M.R. Parise, O.P. Taranto, P.R.G. Kurka, L.B. Benetti, detection of the minimum gas velocity region using Gaussian spectral pressure distribution in a gas–solid fluidized bed, Powder Technol. 182 (2008) 453–458], as an alternative to the spectral analysis of pressure fluctuation measurements to find the region where the minimum velocity gas takes place in a gas–solid fluidized bed, that is, the zone where the bed is tending to defluidization. The technique is applied to analyze the effect of fixed bed height and particle density in defluidization conditions for particles of microcrystalline cellulose and sand. Tests are carried out for three fixed bed heights (0.15, 0.20 and 0.25 m) and two particle densities (980 and 2650 kg/m3 ). Experiments show that the best conditions for identifying the defluidization zone are obtained with lower bed aspect ratios (H/D) and lower particle density. The results indicate the high potential of the proposed method for industrial applications, especially for on-line control of gas–solid fluidized bed processes where the defluidization phenomenon needs to be detected and avoided. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Fluidization is an important technology employed in industrial processes, such as coal and biomass combustion, drying of solids, particles coating, material processing and biotechnology [1]. An adequate mixture of gas and particles is essential in fluidized bed processes. In practical terms, however, the mixing of particles may become inefficient during operation. The process of drying of solids or particles coating, for example, may suffer the undesired effect of agglomeration of particles due to the presence of moisture, subsequently followed by defluidization of the bed, which may cause critical situation leading to an inevitable process shut down. The superficial gas velocity is responsible for the formation and maintenance of the fluidized bed condition. If the velocity is not kept to a sufficiently high value, the defluidization of the bed may occur affecting the process. Such a phenomenon may happen so abruptly, that its detection by simple visualization is just not possible. A more appropriate way to perform the identification of the minimum gas flow to avoid the defluidization is through the analysis of pressure fluctuations, which are usually originated by the formation, rise and eruption of bubbles, gas turbulence, bed mass oscillation and bubble coalescence [2,3].

∗ Corresponding author. Tel.: +55 19 3521 3895; fax: +55 19 3521 3910. E-mail address: [email protected] (M.R. Parise). 1 Tel.: +55 19 3521 3175; fax: +55 19 3289 3722. 0255-2701/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2008.02.010

Pressure fluctuations have been used to describe the fluidized beds characteristics, such as the quality of fluidization [3], bubble frequency [4], transition from bubbling to turbulent fluidization [5], differentiation of states of typical fluidization [6], the minimum fluidization gas velocity [7–10], and the minimum fluidization gas velocity region [11]. Normally, time series data originated from pressure fluctuations are treated by statistical analysis, by spectral analysis, and by chaos analysis [3]. Parise et al. [11] developed a methodology to identify the region where the bed is tending to defluidization, in order to be applied in gas–solid fluidized bed processes. This technique is based on Fourier transform and Gaussian distribution, using pressure fluctuation measurements. The objective of this work is to verify the influence of the fixed bed height and the solid density on the methodology proposed by Parise et al. [11], specifically for microcrystalline cellulose and sand particles. 2. Normal spectral distribution in the fluidization process The stages of fluidization carry different dynamic characteristics that can be observed in the spectral distribution of the plenum pressure. The dynamics of a fixed bed tends to be that of a bulk or “heavy” body, displaying lower frequencies in the pressure spectral range. The transition bed has a combination of the dynamics of bulk and light bodies, displaying a few frequencies that are higher in the spectral range, together with the characteristic low frequencies of the fixed bed behavior.

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The pressure spectrum in a fluidization process, except at the slugging regime, does not present predominant frequencies. Spectral amplitudes obtained in a fluidized behavior are randomly spread out through most frequencies, suggesting that the dynamic analysis of the pressure signal must take into account the statistical distribution of its spectrum. In the fluidized bed condition, the dynamics of light bodies is predominant, inducing faster oscillations of the pressure and a higher range of spectral frequencies. The statistical distribution of the spectral lines is a better indicator of the fluidization state of the process. A Gaussian curve fitted to the pressure amplitude spectrum illustrates the stage of the fluidization process. Low mean frequency values of the normal distribution indicate fixed bed behavior and higher mean frequency values indicate a fluidized bed. The normal distribution curve has the following expression:

G(fk ) =

2 1 2 e−(fk −fm ) /2 √  2

(1)

where fm is the mean frequency value,  is the standard deviation of the spectral distribution and k = 0, 1, . . ., M − 1. Amplitudes of the frequency spectrum are the data for fitting the Gaussian curve. The range of frequencies used in the Gaussian curve fit may be limited to the low-pass filter cut off frequency. The cost function  is minimized through a mean square procedure shown below

=

M−1 

A(fk ) −

k=0

2 1 2 e−(fk −fm ) /2 √  2

2 (2)

where A(f) is the measured amplitude of the pressure spectrum.

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3. Materials and methods The experimental set-up used in this work is shown in Fig. 1. The Plexiglas column is 0.143 m in inner diameter and 0.71 m in height. The gas distributor is made of a 1.62-mm thick stainless steel perforated plate with 1 mm holes on a triangular pitch. The size of the pitch of holes in the distributor is 8.5 mm. A fine screen is installed above the distributor to avoid particles from falling into the plenum. The rotation of a 3-kW air blower is regulated by a frequency inverter (Danfoss VLT, 2800). The air flow rate is obtained through an orifice plate. A pressure transmitter (Cole Parmer, 07356-01, range: 0–210.8 kPa) and a differential pressure transmitter (Smar, LD301, range: 0.125–5 kPa) are used in order to measure the up-wind pressure of the orifice plate and the pressure drop across the bed, respectively. The bed pressure is measured in the plenum employing a differential pressure transmitter (Cole Parmer, 68014-18, range: 0–6.2 kPa, response time of 250 ms). The pressure data is acquired through a PCI 6024 E dataacquisition system (National Instrument). LabView 7.1 software is used for all data acquisition and signal processing. The pressure in the plenum, the up-wind pressure of the orifice plate and the pressure drop across the bed are sampled at a frequency of 400 Hz, with 8192 data points. The data acquisition rate of 400 Hz is chosen in accordance to other previous works that study fluidized bed [12]. The number of 8192 data points yields a frequency resolution of 0.048 Hz, which is convenient for analysis in the low-frequency range of the spectrum. The relevant pressure amplitudes observed in fluidized bed applications occur in the approximate range 0–10 Hz [12]. A practical range 0–20 Hz is hence adopted in the present paper for the frequency analysis. The low-pass filter cut-off frequency is set accordingly to 20 Hz. Two types of the solid particles are tested: microcrystalline cellulose (MCC) and sand. The properties of such particles are given in

Fig. 1. Experimental set-up. Table 1 Characteristics of solid materials s (kg/m3 )

Solid particles

dp (␮m)

H (m)

Microcrystalline cellulose

325 (300–350)

0.15, 0.20 and 0.25

980

umf (m/s) 0.06

Sand

325 (300–350)

0.15, 0.20 and 0.25

2650

0.12

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Fig. 2. Segment of pressure fluctuation signal of (a) fixed bed regime for MCC; (e) fixed bed regime for sand; (c) fluidized bed for MCC; (g) fluidized bed for sand. Fourier transform of the signal of (b) fixed bed regime for MCC; (f) fixed bed regime for sand; (d) fluidized bed for MCC; (h) fluidized bed for sand.

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Fig. 2. (Continued ).

Table 1. The particle size distribution is determined by sieve analysis and the mean diameter is obtained by Sauter definition. Water picnometry is used to measure the apparent particle density. 4. Results and discussion Fig. 2 illustrates a time segment of the bed pressure signals measured in the plenum and the respective Fourier transform of pressure fluctuation for the two materials used. The fixed bed regime is shown in Fig. 2(a) and (b) for MCC, and 2(e) and (f) for sand. On the other hand, the fluidized bed condition is illustrated in Fig. 2(c), (d), (g) and (h) for the same solid particles. Comparative results with the fluidized bed condition show that all fixed bed regimes have lower pressure fluctuation amplitudes, which is a consequence of the absence of bubbles. It is believed that the small pressure fluctuations observed in fixed bed regimes (Fig. 2(a) and (e)) are caused by vibration of some particles during the gas flowing through the bed. On the other hand, in fluidized bed, the amplitude of the pressure fluctuations increases with the particle diameter and the superficial gas velocity [13,14]. Additionally, the pressure spectrum obtained in fluidized bed shows peaks at higher amplitudes and frequencies than those observed in the fixed bed. Figs. 3–8 show the progress of the Gaussian distribution parameters of the Fourier transforms of the pressure signals for the two particles used. The parameters are the standard deviation of the spectral distribution and Gaussian mean frequency value of the pressure spectrum, together with the fluid dynamic curve for decreasing superficial gas velocity. Figs. 3–5 and 6–8 illustrate the evolution of such parameters to MCC and sand for bed height of 0.15, 0.20 and 0.25, respectively. Fixed bed regime is characterized by pressure signals at low frequencies, so in this regime low values of Gaussian mean frequency are expected when the Gaussian curve is fitted to the pressure spectrum. Such a behavior, however, was not obtained in tests with MCC (Figs. 3–5) for fixed bed condition. Here, the gas velocities that were insufficient to maintain fluidization led to a Gaussian mean frequency of about 5 Hz, which is a high value for the fixed bed regime. In the fixed bed regime, the components of high frequency (amplitude around 0.3 Pa, Fig. 2(b)) are responsible for the displacement of the mean value of the Gaussian curve. On the other hand, in the fluidized bed regime (Fig. 2(d)), the amplitude values of the Fourier transform (responsible for the increase of the mean value of the Gaussian curve) are about 10–18 times higher than those related to

Fig. 3. Fourier transform with Gaussian distribution of MCC, decreasing superficial gas velocity, fixed bed height of 0.15 m.

Fig. 4. Fourier transform with Gaussian distribution of MCC, decreasing superficial gas velocity, fixed bed height of 0.20 m.

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Fig. 5. Fourier transform with Gaussian distribution of MCC, decreasing superficial gas velocity, fixed bed height of 0.25 m.

Fig. 6. Fourier transform with Gaussian distribution of sand, decreasing superficial gas velocity, fixed bed height of 0.15 m.

Fig. 8. Fourier transform with Gaussian distribution of sand, decreasing superficial gas velocity, fixed bed height of 0.25 m.

frequencies between 4 and 8 Hz, obtained in the fixed bed regime. In the case of sand, in fixed bed regime, the mean Gaussian frequency value is lower than that obtained with MCC under the same condition. Such results are attributed to the higher density of the sand in comparison with MCC. Figs. 3–5 also show that the value of the Gaussian mean frequency increases with the superficial gas velocity after reaching the region where the bed is tending to defluidization. Such an increase is more intensely observed for a fixed bed height of 0.15 m (H/D = 1.05). Nevertheless, the minimum fluidization region can be still detected for a fixed bed height of 0.25 m (Fig. 5). This behavior probably occurs due to the combination of the particle size used and the fixed bed height of 0.25 m, which promotes a slugging fluidization regime. In the case of sand, the region where the bed is tending to defluidization can be clearly identified in Figs. 6 and 7. However, in the case of Fig. 8 (H/D = 1.75), the defluidization zone is not easily detected. This behavior is probably due to the fact that the bed tends to have a considerable amount of large bubbles close to the minimum fluidization velocity, and the bubbles grow when the superficial gas velocity is increased. Additionally, during the experimental test related to Fig. 8, the fluidization regime approached slugging and a conventional bubbling bed was not obtained. Results show that the above methodology is appropriate to detect the region where the bed is tending to defluidize in a conventional bubbling fluidization. Under other fluidization regimes, such as the one obtained in Fig. 8, this region cannot be clearly identified. Additionally, it was observed that it is not possible to establish a value of proportionality between fixed bed height and Gaussian mean frequency. The Gaussian mean frequency diminishes whenever the fixed bed height increases, when the fluidized bed regime is considered. The standard deviation parameter increases slightly near the region where the bed is tending to defluidization, as seen in Figs. 3–8. Such a behavior however is not as effective in identifying the defluidization region as is the Gaussian mean frequency. 5. Conclusions

Fig. 7. Fourier transform with Gaussian distribution of sand, decreasing superficial gas velocity, fixed bed height of 0.20 m.

The methodology based on the spectral distribution of pressure measurements is consistent with the results obtained through the fluid dynamic curve. Therefore, it identifies the region where the bed is tending to defluidization in conventional bubbling fluidization regime.

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The defluidization condition is clearly identified for all tests carried out with MCC particles. The phenomenon however is detected only at bed aspect ratio (H/D) less than 1.75 in a bed configuration which uses high-density particles (sand), suggesting that the methodology is more appropriated for use with shallow beds and low-density particles. In the case of deep beds and high-density particles, the technique can be successfully applied to determine the transition of a bubbling fluidization regime to the slugging condition. Acknowledgment The authors would like to thank National Council of Technological and Scientific Development (CNPq) for the financial support of the present work. Appendix A. Nomenclature

A(f) dp f fm H H/D M umf

measured amplitude of the pressure spectrum (Pa) Sauter mean diameter (␮m) frequency (Hz) Gaussian mean frequency (Hz) Fixed bed height (m) bed aspect ratio 8192 data points minimum fluidization velocity (m/s)

Greek letters  cost function s apparent density (kg/m3 )  the standard deviation of the spectral distribution (Hz)

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