Article pubs.acs.org/IECR
Assessment of Stability of Spouted Bed Using Pressure Fluctuation Analysis Palash Kumar Mollick* and Dakshinamoorthy Sathiyamoorthy Powder Metallurgy Division, Bhabha Atomic Research Centre, Trombay, Mumbai-400085, India ABSTRACT: Spouted beds are widely used in many industrial applications for achieving good gas−solid contact/mixing especially for a bed of coarse/nonspherical particles. The stability of the spouted bed is important and critical for certain sensitive applications like coating, blending, catalytic conversion, etc. This paper presents the results of experimental investigations carried out using both two-dimensional and three-dimensional spouted beds to identify various transition velocities and condition to arrive at a stable spouted bed. Standard deviation and power spectral density (PSD) of pressure fluctuation were used to determine the stable operating fluidization/spouting velocity. Zirconia microspheres were used as the spouted bed material and argon, nitrogen, and methane were used as spouting gases. Standard deviation of pressure fluctuation was calculated at minimum spouting velocity and at a velocity corresponding to transition from stable spouting to unstable spouting condition. It is shown that standard deviation of pressure fluctuation and PSD varies with various spouting gases and seen to follow a trend with Archemedes number of a given gas−solid system.
1. INTRODUCTION Ever since the discovery of the spouted bed by Mathur and Epstein,1 numerous attempts have been made to identify various spouting regimes which dictate regions of different heterogeneous contact patterns.2−6 Investigations on identification of the stable spouting regime using pressure fluctuation technique have been the subject of interest especially for particle coating by chemical vapor deposition (CVD).7 CVD is extensively and efficiently used for selective deposition of thin films of a large variety of materials mainly as protective coatings. In particle coating, the CVD process is efficient with respect to uniform deposition of the coating material provided uniform mass and heat transfer environment is present. The CVD process is essentially a chemical reaction associated with the cracking of a precursor molecule at suitable process conditions followed by deposition of cracked species on target surface. This requires a good heat and mass transfer environment for achieving high efficiency of the process. Generally, CVD at moderate/high temperature on large/heavy particulate solids is accomplished using a spouted bed for good heat and mass transfer.8 For such a process, it is essential to identify the hydrodynamic regimes/ spouting stability to achieve desired coated products. A recent paper9 on TRISO coating of nuclear fuel using a spouted bed confirms the importance of the bed stability to arrive at a uniform coating by CVD on uranium microspheres. Many methods to use pressure fluctuation as a diagnostic tool to identify various regimes have been reported in the literature. Some of the well-known methods are conventional statistical analysis,2,3,7,10 power spectrum analysis,2,3,7,11 chaotic analysis,12−14 Shannon entropy analysis,15 mutual information functions analysis,4 auto regressive model power spectrum analysis,16 and rescaled range analysis (Hurst exponent).17 However, there is a need to use a simple technique to identify the transitions in terms of Archimedes number and statistical moments of pressure fluctuation. It is found from various available techniques that a simple statistical analysis lies within the time and phase space domain.18,19 © 2012 American Chemical Society
Analysis in the time domain is often the simplest approach whereas, most common frequency domain method is power spectrum analysis.18 This paper attempts to unveil the necessity of pressure fluctuation data to identify the stable spouting regime in terms of average pressure drop across the bed and standard deviation of pressure fluctuation with Archimedes number. 1.1. Origin of Pressure Fluctuation. Typical stable spouting regime lies in between (i) transitions from fixed bed to spouting condition (or reverse) and (ii) transition from stable condition toward turbulent spouting (or reverse).2−7,10,11,20 A purely stable spouting regime has low amplitude of pressure fluctuation and hence low standard deviation of the fluctuating signal.2 Hence low amplitude of fluctuation in a spouted bed is free from bubble motion and slugging.15 It can be assumed that, at the stable spouting condition, interparticle and gas-particle interactions are mainly within the extended spout zone (up to the tip of the fountain) of the bed and the pressure fluctuation originates from the residual forces acting over single or multiple particles simultaneously. It is expected that the interparticle and gas−particle interactions in principle should increase with increase in the number of particles within that spout volume occupied mainly by a gas jet within the bed. The spout diameter can be increased by increasing the flow rate of gas and the size of gas inlet orifice1,21−23 whereas, the length of the spout depends on the bed height. As the spout volume increases, the number of particles that come from annular zone would increase thereby increasing pressure fluctuation. On the other hand, the drag force acting on a particle changes with the combined effect of the fluid−solid property and velocity. Received: Revised: Accepted: Published: 12117
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wall and (ii) 3D typea conical base cylindrical type apparatus made up of transparent acrylic material, named as the transparent 3D bed. Dimensions of 2D and 3D beds are given in the Table 1. A pressure sensor (Euro Sensor, EPT
The stability of a spouted bed is dependent on the size of the gas inlet pipe/slot. A recent literature24 on the choice of slot dimension for a rectangular type inlet confirms this result. It is further interesting to note that when the square root of the slot area to particle size ratio is less ( UM, ΔP decreased drastically to a point b indicating the tendency of spout approaching the bed surface as shown in Figure 3b. When U is further increased slightly, a spout with continuous fountain of solid at the bed surface is established corresponding to a velocity Uos (i.e., onset of spouting) which occurs at relatively low ΔP as indicated at c in Figure 2 and shown in snapshot Figure 3c. Beyond U > Uos, and up to a transition velocity Utr, stable spouting is observed as seen in Figure 3d 12119
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Figure 3. Snapshots of 2D spouted bed at various spouting gas velocities (during increasing gas velocity).
between Ums and Utr is therefore marked as the stable spouting regime. Beyond Utr, the bed is always unstable, and instability increased with further increase of superficial gas velocity. The plot in Figure 7 shows the variation of σ for three different spouting gases (i.e., for three Ar numbers) over the range of 0.8Ums < U < 1.8Ums. It is clear from this plot that there exists three distinct zones, first at U/Ums < 1 (i.e., packed bed), the second for 1 < U/Ums < 1.3 (i.e., stable spouting zone), and at the third U/Ums > 1.3 (i.e., unstable spouting zone). It may be noted from this plot that Ums and Utr can precisely be evaluated by evaluating σ values also. This can be accomplished by data acquisition of pressure fluctuation using high speed computers, thereby making the system controllable online especially at high temperature operations. Figure 7 also gives useful information on the nature of variation of σ with U/Ums. σ in the packed bed condition increases almost linearly until a maxima is reached followed by a sudden fall at Ums. From Ums until Utr, σ increases to a second maxima and then tends to increase monotonically. 4.3. Influence of Spout and Particle Size on Pressure Fluctuation. Standard deviation of pressure fluctuation is found to be influenced significantly by the aspect ratio Hms/di in addition to the gas−solid properties (i.e., Ar number). Where, Hms is bed height at minimum spouting velocity and di is inlet orifice diameter. Figure 8 shows variation of standard deviation of pressure fluctuation at minimum spouting velocity
It is interesting to note that Ums obtained in 3D bed is far less than UM whereas it is opposite in the case of the 2D bed. This shows that 2D bed experiments cannot properly evaluate fundamental parameters like Ums. Figure 5 also shows that the σ values are much lower for decreasing gas flow than increasing gas flow rates. This trend is same as observed in 2D bed but with large differences in σ values for U < Uos. The above studies were extended for the estimation of Ums in 3D bed at ambient condition using nitrogen and methane as spouting gases. The Ums values for all spouting gases were identified from the pressure drop data and also were checked by visual observations. The Ums for methane, nitrogen, and argon were found to be 33.2, 26.0, and 20.6 m/s, respectively, at the static bed height 0.06 m for zirconia particles (ρp = 6300 kg/m3, dp = 500 μm). Figure 7 depicts the variation of standard deviation of pressure fluctuation (σ) with operating gas velocity ratio (U/Ums) for each of the three spouting gases depicted as Archimedes number, Ar. This figure shows three distinct regimes very similar to earlier witnessed observation by several authors.2,3,7,11,12,15 The maximum pressure fluctuation is seen to occur during the sudden transition from the packed bed to spouting regime. At Ums, minimum pressure fluctuation is obtained, and this gradually increased up to transition velocity (Utr) at which onset of unstable spouting regime occurred. Visual observations revealed stable operation of the bed at a velocity within a region bounded by Ums and Utr which is close to 1.3Ums. The region 12120
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Figure 4. Snapshots of 2D spouted bed at various spouting gas velocities (during decreasing gas velocity).
number for a given ρs, the volume of particles occupying the spout is large enough to bring down ultimately the number of particles in the spout. This implies that a lower number of particles in the spout can improve the stability due to the fact that the pressure fluctuation is less when the spout is free from solids. 4.4. Power Spectral Density (PSD) Analysis. Power spectral density is the measure of the power of repeatability of a set of random data, at a particular time interval, and this can be used to identify intensity of fluctuations at any major transitions.2,3,7,11 In principle, if any set of fluctuation data is random, the power of a particular frequency will be distributed randomly for a given time interval. It is seen that high pressure fluctuation values which are periodic in nature can be observed during transition of the spouting regime. For example, transitions from stable to unstable spouting regime can be identified by sharp and peak values at a particular frequency. In the present study, PSD analysis was carried out in order to find out the relative time scale of various particle−particle and gas−particle interactions inside a spouted bed. The PSD results are interpreted here with the observed spouting phenomena at various spouting regimes and transitions from one to other regimes. PSD obtained using Fast Fourier Transform (FFT) are plotted against the frequencies of the pressure fluctuations as shown in Figure 9a−e for superficial gas velocities ranging from U/Ums = 0.94−1.45 using argon as the spouting gas in a 2D bed. Pressure fluctuation data was collected from the 2D bed and PSD plots were drawn and compared with spouting
Figure 5. Pressure drop and standard deviation profile with operating gas velocity of argon, (3D bed, Ho = 0.06 m, dp= 500 μm, di = 0.006 m).
(σms) with bed height at minimum spouting velocity to inlet orifice diameter ratio (Hms/di) for various Ar numbers. It is seen that σms increases as Hms/di increases and decreases as Ar number increases. In other words, stable spouting seems to be possible at low aspect ratio and at high Ar number. Figure 8 also shows that if di/dp is brought down, σms is decreased indicating a stable spouting. This low di/dp is usually achieved at high Ar number even if ρs is less. In case of high Ar 12121
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Figure 6. Snapshots of 3D spouted bed at various spouting gas velocities.
Figure 8. Variation of standard deviation of pressure fluctuation with spout geometry and particle population inside spout zone. (3D bed).
Figure 7. Stable spouting regime and various transitions in spouting regime occurring in a spouted bed. (3D bed, do = 0.006 m, Ho = 0.06 m, di = 0.006 m). 12122
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Figure 9. PSD curve for argon (as spouting gas) at U = (a) 0.94, (b) 1.1, (c) 1.16, (d) 1.29, and (e) 1.45Ums (2D bed, di = 0.006 m, dp = 500 μm, ZrO2 particle, data sampling rate = 200 Hz).
spouting, U os (i.e., 0.94Ums ) indicating the power of repeatability of a particular pressure fluctuation values at this
phenomena which are shown in snapshots. Figure 9a shows a specific dominant frequency near 22 Hz at the onset of 12123
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frequency. A sharp peak near 22 Hz is due to periodic and high energy particle− particle interaction inside a submerged spout as seen in Figure 3b. These high energy particles are responsible to overcome the resistance of static head above the tip of the submerged spout and to initiate a spout with a fountain at the bed surface. During stable spouting conditions, particles are circulated through the spout-fountain-annulus and again to the spout. Therefore, limited highly energized particles can be present in the continuous spout. This situation results in peaks with less intensity in PSD as shown in Figure 9b for the case of U > Ums. However, with increasing gas velocity, particles are enriched with kinetic energy and hence PSD has multiple peak values as seen in Figure 9c (corresponding snapshot in Figure 3d). When U ≥ 1.3Ums, the fountain as seen in Figure 3e tends to disappear indicating a transition in spouting regime. PSD at this transition velocity, i.e., U ≈ Utr has again a very sharp peak and distinct high magnitude near 20 Hz as shown in Figure 9d. This sharp peak may be due to the commencement of periodic pulsation inside the spout. When U ≫ Utr, the presence of low magnitude PSD disappears and highly unstable spouting with several sharp clusters of high value PSD appear as shown in Figure 9e. This indicates a predominant unstable/ undesirable spouting regime. From the forgoing PSD data, it is possible to access precisely the stable spouting regime just from the PSD vs frequency plot.
NOMENCLATURE
Abbreviation
CVD = chemical vapor deposition PSD = power spectral density TRISO = tri-isotropic material Notations
Ar = Archimedes number, gdp3ρ(ρs − ρ)/μ2 (−) dp = diameter of particle (m) di = diameter of gas inlet nozzle (m) Dc = column diameter (m) E[.] = expectation operator (−) f b = buoyancy force (N) fc = collision force (N) fd = drag force (N) H = height of the cylindrical section (m) Ho = static bed height (m) Hms = bed height at minimum spouting velocity (m) Hc = height of the conical (kg·m2) section (m) I = inertia coefficient (kg·m2) M = moment (kg·m2/s2) N = number of occurrence (−) Re = Reynolds number, ρdpU/μ (−) Sx = power spectral density (Pa/s2) T = temperature (°C) t = time (s) U = superficial gas velocity (m/s) Ums = minimum spouting velocity (m/s) UM = superficial gas velocity at maximum bed pressure drop (m/s) Uos = velocity corresponding onset of spouting (m/s) Us = velocity corresponding stable spouting condition, Ums < Us < Utr (m/s) Utr = superficial gas velocity at transition between stable and unstable spouting regime (m/s) u = relative velocity of single particle (m/s) xi = ith value of “x” (−) x̅ = average value of “x” (−)
5. CONCLUSIONS Hydrodynamic characteristics of a conventional spouted bed (conical base cylindrical) have been studied both in 2D and 3D beds using three spouting gases namely argon, nitrogen, and methane. Flow visualizations on the growth of submerged spout for the case of 2D bed as well as 3D bed were used to find out the basic hydrodynamic parameters like Ums. Visual observations in 2D bed revel that spouting behavior is significantly different for various spouting gases used. An attempt has been made to show the changes in stable spouting behavior with dimensionless Archimedes number where in gas properties (viz., density and viscosity) were incorporated. It is also seen that with change in spouting gases, the pressure drop behavior across a particulate bed is different. It is also seen that various spouting regimes in a spouted bed can be identified by pressure fluctuation analysis. Three distinct regimes namely, packed, stable spouting, and unstable spouting have been identified from the standard deviation of the pressure fluctuations. It is also found that the standard deviations of pressure fluctuations at transitions is a strong function of fluid−particle properties (incorporated in Ar) and bed geometries (i.e., Ho and di). The knowledge of operating a spouted bed in a stable regime will greatly assist in controlling the particle coating in the spouted bed CVD process.8,9
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Greek Letters
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μ = gas viscosity (Pa·s) ρ = gas density (kg/m3) ρs = solid particle density (kg/m3) σ = standard deviation (−) ψ = arbitrary variable ω = angular velocity (rad/s)
REFERENCES
(1) Mathur, K. B.; Epstein, N. Spouted Bed; Academic Press: New York, 1974. (2) Piskova, E.; Morl, L. Fluidization regimes in different spouted bed apparatus construction. Chem. Eng. Process. 2007, 42, 695. (3) Xu, J.; Bao, X.; Wei, W.; Shi, G.; Shen, S.; Bi, H. T.; Grace, L. R.; Lim, C. J. Statistical and frequency analysis of pressure fluctuations in spouted beds. Powder Technol. 2004, 140, 141. (4) Xu, J.; Bao, X.; Wei, W.; Shi, G.; Shen, S.; Bi, H. T.; Grace, L. R.; Lim, C. J. Mutual Information functions of differential pressure fluctuations in spouted beds. Ind. Eng. Chem. Res. 2004, 43, 5754. (5) Bacelos, M. S.; Freire, J. T. Stability of spouting regimes in conical spouted beds with inert particle mixture. Ind. Eng. Chem. Res. 2006, 45, 808−817. (6) Freitas, L. A. P.; Dogan, O. M.; Lim, C. J.; Grace, J. R.; Bai, D. Identification of flowregimes in slot-rectangular spouted beds using pressure fluctuations. Can. J. Chem. Eng. 2004, 82, 60−73.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]. Tel.: +91 22 2559 3937. Fax: +91 22 2784 0032. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We sincerely acknowledge Mr. P. T. Rao, PMD, BARC, for his help during carrying out experiments. 12124
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(7) Lopes, N. E. C.; Moris, V. A. S.; Taranto, O. P. Analysis of spouted bed pressure fluctuations during particle coating. Chem. Eng. Process 2009, 48, 1129−1134. (8) Mollick, P. K.; Sathiyamoorthy, D.; Rao, P. T.; Rao, V. G. Modeling of chemical vapor deposition of pyrolytic carbon in a gas spouted bed reactor. Ind. Eng. Chem. Res. 2011, 50, 13313−13321. (9) Liu, M.; Shao, Y.; Liu, B. Pressure analysis in the fabrication process of TRISO UO2-coated fuel particle. Nucl. Eng. Des. 2012, 250, 277−283. (10) Leu, L.-P.; Pan, R.-S. Pressure fluctuation in jet spouted bed. Can. J. Chem. Eng. 2004, 82, 1044−1047. (11) Alberto, C.; Felipe, S.; Rocha, S. C. S. Time series analysis of pressure fluctuation in gas-solid spouted beds. Braz. J. Chem. Eng. 2004, 21, 497−507. (12) Vaccaro, S.; Musmarra, D.; Petrecca, M. A technique for measurement of the jet penetration height in fluidized bed by pressure signal analysis. Powder Tech. 1997, 92, 223−231. (13) Van den Bleek, M.; Schouten, J. C. Deterministic chaos: a new tool in fluidized bed design and operation. Chem. Eng. J. 1993, 53, 75− 87. (14) Ellis, N.; Briens, L. A.; Grace, J. R.; Bi, H. T.; Lim, C. J. Characteristics of dynamic behavior in gas− solid turbulent fluidized bed using chaos and wavelet analyses. Chem. Eng. J. 2003, 96, 105− 116. (15) Zhong, W.; Zhang, M. Characterization of dynamic behavior of a spout-fluid bed with Shannon entropy analysis. Powder Technol. 2005, 159, 121−126. (16) Zhong, W.; Zhang, M. Pressure fluctuation frequency characteristics in a spout-fluid bed by modern ARM power spectrum analysis. Powder Technol. 2005, 152, 52−61. (17) Xu, J.; Bao, X.; Wei, W.; Shen, S.; Bi, H. T.; Grace, L. R.; Lim, C. J. Characterization of gas spouted beds using the rescaled range analysis. Can. J. Chem. Eng. 2004, 82, 37−46. (18) Van Ommen, J. R.; Sasic, S.; Van der Schaaf, J.; Gheorghiu, S.; Johnsson, F.; Coppens, M.-O. Time-series analysis of pressure fluctuations in gas-solid fluidized beds - A review. Int. J. Multiphase Flow 2011, 37 (5), 403−428. (19) Wu, B.; Orta, A.; Kantzas, A. Experimental flow measurements of a spouted bed using pressure transducer and X-ray CT scanner. Int. J. Chem. React. Eng. 2011, 9, A32. (20) Bi, H. T.; Fan, L. Existence of turbulent regime in gas− solid fluidization. AIChE J. 1992, 38, 297. (21) Lefroy, G. A.; Davidson, J. F. The mechanics of spouted bed. Trans. Inst. Chem. Eng. 1969, 47, T120. (22) Malek, M. A.; Madonna, L. A.; Benjamin, C. Estimation of spout diameter in a spouted bed. Ind. Eng. Chem. Process Des. Dev. 1963, 2 (1), 30−34. (23) San Jose, M. J.; Olazar, M.; Alvarez, S.; Morales, A.; Bilbao, J. Spout and fountain geometry in conical spouted beds consisting of solids of varying density. Ind. Eng. Chem. Res. 2005, 44, 193−200. (24) Chen, Z.; Lim, C. J.; Grace, J. R. Stability of slot-rectangular spouted beds: Effect of slot configuration. Can. J. Chem. Eng. 2011, 89 (6), 1401−1407.
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