Characterization of pressure fluctuations from a gas–solid fluidized bed by structure density function analysis

Author's Accepted Manuscript

Characterization of pressure fluctuations from a gas-solid fluidized BEd by structure density function analysis Yumin Chen, C. Jim Lim, John R. Grace, Junying Zhang, Yongchun Zhao, Chuguang Zheng

www.elsevier.com/locate/ces

PII: DOI: Reference:

S0009-2509(15)00112-8 http://dx.doi.org/10.1016/j.ces.2015.02.009 CES12167

To appear in:

Chemical Engineering Science

Received date: 10 August 2014 Revised date: 21 January 2015 Accepted date: 8 February 2015 Cite this article as: Yumin Chen, C. Jim Lim, John R. Grace, Junying Zhang, Yongchun Zhao, Chuguang Zheng, Characterization of pressure fluctuations from a gas-solid fluidized BEd by structure density function analysis, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2015.02.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Characterization of pressure fluctuations from a gas-solid fluidized bed by structure density function analysis Yumin Chena,b, C. Jim Limb, John R. Graceb, Junying Zhanga,*, Yongchun Zhaoa, Chuguang Zhenga a

State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, Hubei Province, China b

Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, Canada V6T 1Z3

Hydrodynamics in a gas-solid fluidized bed reactor were studied based on differential pressure signals measured over several height intervals at different temperatures. Structure density function analysis was utilized to study the dynamics of multi-scale structures. An amplitude division method based on the Gaussian distribution and the Kolmogorov-Smirnov test was developed to divide the structure density distribution of pressure signals into three characteristic regions linked to: I. fine-scale structures, II. small-scale structures, and III. large-scale structures. The frequency of large voids and the uniformity of multi-scale flow structures were quantitatively characterized by parameters SDFb,II and KSDF, respectively. KSDF reached a maximum when large bubbles or slugs dominated the flow, then decreased until it remained almost constant in the turbulent flow regime. Structure density function analysis showed that increasing the operating temperature enhanced the transition of flow regimes, while the transition direction was determined by the superficial gas velocity. Increased gas velocity and decreased minimum fluidization velocity at higher temperature were major factors promoting earlier flow regime transitions. The frequency of large-scale structures decreased at higher temperature for the same flow regime. Fluidized bed, Pressure fluctuations, High temperature, Structure density function, Multi-scale.

1

Introduction Fluidized bed reactors have been extensively used in industrial processes such as catalytic

cracking, reforming of hydrocarbons, biomass and coal gasification (Grace et al., 2005; Rakib, 2010). With hydrogen separated in-situ by selectively-permeating membrane panels, high-purity hydrogen can be produced in a fluidized bed reformer at moderate temperatures (Rakib, 2010). Since the performance of a fluidized bed reactor depends greatly on the flow dynamics in the bed, fluidized bed hydrodynamics have been studied by various methodologies. Pressure fluctuations are significant indicators of the hydrodynamics in gas-solid fluidized beds. Due to their ease of measurement and readily available analysis tools, pressure fluctuations can Corresponding author: Tel.: 86-27-87542417; Fax: 86-27-87545526 E-mail address: [email protected] (J.Y.Zhang)

provide useful data to investigate the performance of fluidized beds (Brue, 1996). Closely-spaced differential pressure probes can filter out pressure waves originating outside the interval so that their signals mainly reflect local void and particle behavior (Bi et al., 1995). Differential pressures have been studied intensively to investigate the hydrodynamics of fluidization (e.g. Bai et al., 1997; Bi et al. 2007; Croxford and Gilbertson, 2011). Standard deviation (Saxena et al., 1992; Bai et al., 1996; Schouten et al., 1998; de Martin et al., 2011; van Ommen et al., 2011; Bizhaem et al., 2013) and cycle frequency (Johnsson et al., 2000) from time domain analysis of pressure signals give macroscopic indications of the amplitude scale and time scale of pressure fluctuations. Although standard deviation and cycle frequency have been extensively utilized to characterize flow regimes, the information they provide on gas-solid fluidization systems is insufficient (Sasic et al., 2006). For gas-solid fluidization systems, pressure fluctuations originating from large bubbles, bed oscillations, small bubbles, particle clusters, particle motion and gas flow variations differ greatly in amplitude and time scales (Ren et al., 2001). Zhao et al. (2003) divided pressure signals measured from a gas-fluidized bed into micro-scale, meso-scale and macro-scale components. They found that micro and meso-scale dynamics were more complex than macro-scale dynamics. Wu et al. (2007) investigated the similarities and differences in bubbling behavior with different scales in a gas-solid fluidized bed. Multi-scale characteristics of pressure fluctuations in time were responsible for the multi-fractality of the data (Ghasemi et al., 2011a, 2011b).

Tahmasebpour et al. (2013) reported that the effects of smaller (micro- and meso-)

structures on the flow initially decreased with increasing gas velocity, and then increased after passing through a transition velocity. To improve understanding of the dynamics of gas-solid flow, it is important to study the multi-scale behavior of the flow. Multi-resolution analysis and frequency division analysis are powerful tools to treat the dynamics of multi-scale structures in gas-solid flow. Multi-resolution analysis decomposes the original signal discretely by lower resolutions, with each sub-signal corresponding to a scale level. Finer and coarse features of pressure signals are captured by the finer and coarse resolution components, respectively (Lu et al., 1999; Park et al., 2001; Wu et al., 2007). At the cost of computation capacity, multi-resolution analysis should be capable of providing information on frequency and amplitude properties of most disturbances, with different frequency-levels in pressure fluctuation series. van der Schaaf et al. (2002) decomposed power spectra of pressure fluctuations into coherent and incoherent components, related to bubble coalescence/formation and bubble passing, respectively. Another methodology based on frequency domain analysis to study the dynamics of multi-scale structures in gas-solid flow is frequency division, where three frequency regions are identified on power spectra of pressure signals, based on power-law fall-off or wide band energy distribution (Johnsson et al., 2000; Briongos et al., 2003; Gómez-Hernandez et al., 2012). The dynamics of macro-structure, finer structures and structures originating from fast fluidization phenomena are distinguished based on this frequency division method. Typically, divisions of frequency regions are 2

based on visual selection of power spectra cut-off frequencies. This observation division method has been employed in many studies, but it has the major drawback that the determination of boundaries between different frequency regions is affected by observer biases (van der Schaaf et al., 1999; Johnsson et al., 2000; Gómez-Hernandez et al., 2012). In this study, a computation-time-saving methodology based on amplitude division, named structure density function (SDF), is utilized to characterize the frequency and amplitude properties of multi-scale disturbances in pressure fluctuations series, so that the dynamics of multi-scale structures in gas-solid flow can be identified and studied. Amplitude divisions on SDF distributions are performed using a novel method which combines Gaussian fitting and the Kolmogorov-Smirnov test. The SDF distribution is divided into three regions, linked to the dynamics of fine-scale, small-scale and large-scale flow structures. This methodology is demonstrated by differential pressure fluctuations measurements from different positions of a fluidized bed reactor at temperatures from 25 to 514oC and superficial gas velocities from 0.03 to 0.37 m/s. The influences of superficial gas velocity and bed temperature on flow dynamics are also investigated based on SDF analysis. 2

Experimental apparatus and procedures Fig. 1 shows a schematic of the experimental system. The stainless steel column was rectangular

with cross-sectional dimensions of 81.3 × 34.9 mm, and the total reactor height was 2.36 m. Six vertical dummies of height 231.8 mm, width 73.0 mm and thickness 6.3 mm, representing membrane panels (Rakib, 2010) used for reforming tests, were installed in bed for every runs. The gap width between dummies was 22.2 mm, while the width of the gaps between the dummy membranes and the reactor wall was 14.3 mm on both sides. A cross-sectional area of 2.0 × 10-3 m2 was employed in calculating the superficial gas velocity for all heights at which dummy panels were present. The distributor was doughnut-shaped, with six equally-spaced holes drilled on the inner side. These holes pointed radially inward and downwards at an angle of 45o to the vertical, to reduce back-flow of particles into the plenum. A detailed description of this distributor was provided by Rakib (2010). The reactor was heated by four cable heaters inside and by ten band heaters and six strip heaters outside the column. Temperatures were measured at seven vertical positions inside the bed by K-type thermocouples. Signals from the thermocouples were sent to a control system to adjust and maintain the desired temperature during experiments. Compressed air at room temperature, monitored by a mass flow meter and controlled by a pressure regulator, was the fluidizing gas. In all experiments, the bed surface was at atmospheric pressure. Table 1 lists the properties of the particles used in the tests. Group d2 was used only in experiments conducted to investigate the effect of bed temperature. The minimum fluidization velocities are experimental values which are about 15% greater than predicted by the well-known Wen and Yu (1966) correlation. The initial bed height was 1.32 m for all cases. Superficial gas velocities of 0.03 to 0.37 m/s were investigated in this study. 3

Differential pressure signals at three vertical locations were recorded using rapid-response pressure transducers (Omega, 142PC01D5V). The arrangement of probes for pressure transducers is presented in Fig. 1. Each pressure probe port was located at the center of the column and covered by a porous screen welded onto the end of probe to prevent blockage by fine particles. The screens were purged by compressed air before starting experiments to minimize damping. Voltage signals were logged into a computer via an A/D converter with 12-bit resolution. For each measurement, 10,000 data points were acquired at a sampling frequency of 100 Hz. 3. Structure density analysis Variations of pressure signals reflect the instantaneous hydrodynamics within the bed. From origination to completed attenuation, a disturbance appears as a valley or peak in the differential pressure signals vs. time plot, as illustrated by Figs. 2 and 3. Large disturbances mainly relate to large bubbles. Small disturbances are linked to the motion of small bubbles or particle clusters, while particle motion, gas flow variations and bed oscillations may add fine disturbances to the flow (Johnsson et al., 2000; Zhao et al., 2003). Pressure waves transferring from the lower position have limit influence on the measurements, due to the small distance between pairs of probes. Since pressure signals from pressure transducers are usually complex and unsteady, they need to be characterized. Methodologies to describe the structure of fluctuations quantitatively or qualitatively have been proposed to study the hydrodynamics of fluidized beds (Zhao et al., 2003; van Ommen et al., 2011; Gómez-Hernandez et al., 2014). Here, we present a method, denoted “structure density function,” to characterize the dynamics of multi-scale structures in the flow. The intensity of the structure density function, SDF, is defined as the number of disturbances per second with a contained in the flow per second. I SDF = SDF (1) t Isdf is the number of disturbances, with amplitude scale >= R, recorded by time series X, and is calculated by N ¹ ¹ §§ ·§ ·· I sdf = ¦[1 − Θ ¨ ¨ xi − x − R ¸¨ xi +1 − x − R ¸ ¸] / 2 ¹© ¹¹ ©© i

(2)

R is the given fluctuation amplitude used in calculation, expressed as R = n ² ( max ( X ) − min ( X ) ) / 2 L ,

-L< n < L

(3)

θ is the Heaviside function, N is the length of pressure time series X, t is the sampling time, L is number of segments into which (max(X)-min(X))/2 is divided, and n ranges from - L to L. The limits of the fluctuation amplitude (max(X), min(X)) varied for different operating conditions. To compare the distribution patterns of SDF along the fluctuation amplitude for different operating conditions, SDF was plotted versus r, a dimensionless form of R normalized by (max(X)-min(X))/2. Therefore, 4

when “large”, “small” and “fine” are used to distinguish multi-scale structures in flow, they are relative measures. For any fluidization pattern, “large”, “small” and “fine” structures are identified, each with different effects on flow dynamics. Figs. 2 and 3 provide examples. Fig. 4 shows the distribution of SDF for pressure signals measured in the upper bed at U/Umf=17.1. Both U and Umf used in following discussions and figures are based on ambient temperature. A SDF distribution of pressure fluctuations can generally be divided into three different regions based on the evolution trends of SDF vs. r, as shown in Fig. 4(a). These three hydrodynamic regions are as follows: (a) Region I, where rb,I≤ r ≤ 0. Fine-scale structures corresponding to disturbances with small fluctuation amplitude in pressure time series were found in this region. Fewer fine disturbances contained in flow corresponded to slower increase of SDF with decreasing r in Region I. If the rate at which SDF increased with decreased r was much smaller than in Region II, a distinguishable leveling-off occurred in the evolution of SDF with r, as presented by the SDF distribution for slug flow in Fig. 4(a). The location of this leveling-off in region I is related closely to the extent that small disturbances are separate from the fine disturbances in amplitude and frequency. For example, the levelling-off appeared at larger r in region I of Fig. 4(a) for slug flow, where the two-phase structure was most distinguishable. For convenience in the following discussions, we used “mutation regime” to represent the part of Region I with r less than that corresponding to the leveling-off. (b) Region II, for which rb,II ≤ r < rb,I. The increasing rate of SDF with decreased r in Region II, denoted as KSDF, accounted for the uniformity of disturbances in amplitude scale. If there are more small-scale structures in the flow, SDF increased more quickly with decreasing r, resulting in smaller KSDF, signifying less uniform fluctuation amplitude. Non-uniformity of fluctuation amplitudes was mainly caused by small disturbances originating from the motion of small bubbles and particle clusters, or bubble breakage, coalescence and distortion. (c) Region III, where -1.0 ≤ r < rb,II. Large disturbances with low frequency which drive the long-time-scale dynamics of the flow are dominant in this Region. The intensity of structure density function at rb,II, SDFb,II, was employed as a criterion to compare the frequency of large “bubbles”. To perform the SDF analysis, different amplitude regions had to first be identified on the SDF distributions. Based on pressure signals measured in our experiments, the probability distribution of disturbances (SPDF) in pressure time series with fluctuation amplitude r can be approximated by a Gaussian distribution, as shown in Fig. 5, expressed as

§ ( r − ȝ )2 · 1 ¸ p ( r ȝ, ı ) = exp ¨ − ¨ 2ı 2 ¸ ı 2ʌ © ¹

(4)

There are two inflection points on the Gaussian distribution, at r = ı-ȝ and ı+ȝ, where the second 5

derivative of P(r) with r is zero. The region (ı-ȝ, ı+ȝ) exhibits different statistical characteristics compared to regions (-’, ı-ȝ) and (ı+ȝ, +’). An unbiased method with strict mathematical criteria is utilized to identify the boundaries that distinguish the three SDF distribution regions. This method assumed that the probability distribution of small structures with amplitude r can be described by region (ı-ȝ, ı+ȝ) on Gaussian distribution. However, not all parts of SPDF were approximated by Gaussian distribution with high accuracy, shown as cumulative energy distribution fitting in Fig. 6. Therefore, a feature region fitted by theoretical distribution with high accuracy on cumulative energy distribution was also identified. This process can be conducted using Kolmogorov-Smirnov test, which is a simple method to test whether a sample follows a specific distribution (Gómez-HernȐndez et al., 2014) or not. The test compared experimental cumulative energy distribution of SPDF, with the cumulative energy distribution of fitted Gaussian function (CDF), as follows: D n = max Ec ( r; n ) − CDF ( r )

(5)

Dn is distance between the cumulative energy distributions. Cumulative energy function of Gaussian distribution was expressed as

1§ § r − ȝ ·· CDF ( r ȝ,ı ) = ¨1 + erf ¨ ¸¸ 2© © ı 2 ¹¹

(6)

By this means, boundaries of Region II were identified from the overlap zone of region (ı-ȝ, ı+ȝ) and feature region derived from the K-S test. The procedure for region division on SDF distribution was generally as follows:

‹ Determination of the probability distribution of disturbances in pressure fluctuation series with fluctuation amplitude r and computation of cumulative energy distribution function.

‹ Fitting of the experimental cumulative energy distribution to the cumulative Gaussian distribution, assuming that the experimental cumulative energy distribution followed the non-standardized Gaussian distribution with all parameters unknown. With parameters of mean value ȝ and standard deviation ı, a characteristic region (ı-ȝ, ı+ȝ) was then distinguished on cumulative energy distribution.

‹ Determination of the feature region on the experimental cumulative energy distribution where the cumulative Gaussian distribution ceased to satisfy the Kolmogorov-Smirnov test with a significance level exceeding 5%.

‹ Comparison of regions (ı-ȝ, ı+ȝ) and the feature region on experimental cumulative energy distribution and localization of boundaries at the edges of the overlap region. Typically, the energy contained by macro-structures related to dynamics of “bubble flow” contain about 70-85% of the total energy of pressure signals for gas-solid fluidized beds (Johnsson, et al., 2000; Gómez-Hernandez et al., 2014), while that contributed by Region I is generally less than 25% 6

of the total energy (Gómez-Hernandez et al., 2014). In our case, disturbances related to large bubbles and small bubbles/particle clusters contained about 74% - 85% of energy of all disturbances in pressure fluctuations, as shown in Fig. 6. Small-scale structures, represented by Region II on the amplitude division and corresponding to the domain frequency region on power spectra (Johnsson, et al., 2000), represented over half of the total cumulative energy. This observation is consistent with results reported derived from frequency division (Gómez- Hernandez et al., 2014).

4

Applications of SDF analysis

4.1 Comparison between SDF analysis and frequency division Frequency division was also used to study multi-scale characteristics of gas-solid flow, as shown in Fig. 7. Several features of the SDF analysis differed from the frequency division analysis. (i) Region division was conducted in the amplitude domain for SDF analysis, whereas it was in the frequency domain for the frequency division method; (ii) Boundaries between amplitude regions were recognized based on Gaussian fitting/K-S test, instead of visual selection, which has usually been utilized when carrying out frequency division; (iii) Physical phenomena linked with regions are interpreted differently. Fine structures related to measurements or environment disturbances rather than fluidization regimes (Johnsson, et al., 2000) are exhibited in Region I of the frequency division, while this scale-level structure cannot be distinguished by the amplitude division. On the other hand, amplitude division treats dynamics of structures originating from large “bubbles” and small “bubbles”/particles clusters (Zhao et al., 2003) separately in Region III and II, but these two scale-level structures cannot be distinguished by frequency division, where they were identified as “bubble flow” entirely, with links to Region III (Johnsson, et al., 2000). Disturbances from large/super “bubbles” drove the long-time-scale dynamics of gas-solid flow localized on the low frequency part of Region III, while disturbances from small “bubbles”/particles clusters were concentrated in the domain frequency region of Region III in the frequency domain, but without boundaries between them, as shown in Fig. 7. Dynamics of large/super “bubbles” can also be identified by coarse resolution components in multi-resolution analysis (Zhao et al., 2003; Wu et al. 2007), but more computation work is required by multi-resolution analysis than for amplitude division and frequency division, especially when finer resolution decomposition is conducted. Discrepancies between amplitude division and frequency division are summarized in Table 2. 4.2 Effect of superficial gas velocity The change of standard deviation with superficial gas velocity at ambient temperature is presented in Fig. 8. For a time series of pressure signals, xi ( i = 1, 2, 3, " , N ) , standard deviation is calculated from:

7

ı=

¹ 1 N § · ¨ xi − x ¸ ¦ N − 1 i =1 © ¹

¹

x is the average

2

(7)

1 N ¦xi . For different measuring positions, the standard deviation increased with N i =1

increasing superficial gas velocity until a maximum value was reached, and then decreased gradually. This suggested that bubble growth ceased beyond a critical velocity. The turning-point can be interpreted as the onset of turbulent fluidization (Grace, 1990; Bi et al., 2000). So, bubbling, slugging and turbulent flow occurred in succession as the superficial gas velocity increased from 0.05 to 0.37 m/s according to the standard deviation analysis. The standard deviation gives some indication of the length-scale of voids in the bed at different superficial gas velocities, but more information can be provided by SDF analysis. Figure 9 shows the influence of superficial gas velocity on SDF distributions of pressure fluctuations measured across three height intervals in the bed. The SDF distributions corresponding to different flow regimes show different patterns. A mutation regime in Region I (leveling-off occurred at larger r) can be easily identified on the SDF distribution for slug flow, but almost merged with Region II or decreased greatly in width for bubbling and turbulent flow. More fine structures were contained in these two flow regimes (Bai et al., 1996), and the amplitudes of pressure fluctuations originating from small structures were less than for slug flow (Johnsson et al., 2000). Similar results were obtained when differential pressure fluctuations measured without dummies installed in the column were subjected to SDF analysis, as shown in Fig. 10. Therefore, the proposed analysis method can also be applied in characterization of differential pressure fluctuations from a normal fluidized bed reactor without internal baffles. Studies on the influence of dummy membrane panels on hydrodynamics in bed are important, but outside the scope of this work, which is focused on the SDF analysis method. SDFb,II derived from SDF analysis enables quantitative estimation of the frequency of large-scale structures governing the long-time-scale flow dynamics. Frequencies of <0.5 Hz and ~1.1 Hz corresponded to large slugs in slug flow and to large voids in turbulent flow, respectively. For the specific operating conditions identified in Fig. 11, SDFb,II for slug flow was lower than for bubbling or turbulent flow because most of the bed cross-section was occupied by slugs. Turbulent flow had higher SDFb,II due to the vigorous and continuous coalescence and breakage of voids. Fig. 12 shows that the slope, KSDF, reached a maximum in slug flow and then decreased until it remained relatively stable in the turbulent flow regime. Slug flow was dominated by large slugs, with the amplitudes of fluctuations then being more uniform. Smaller KSDF was achieved in the turbulent flow regime where many small transitory voids of varying size were undergoing continuous breakage and coalescence. Bubbles dominated the bubbling flow regime, but the variation of bubble sizes led to KSDF being smaller than for slug flow. KSDF based on the SDF distribution of pressure fluctuations was lowest in the bottom region of the bed, indicating that flow structures were most irregular there. 8

Kage et al. (2000) also reported that flow dynamics in the region near the distributor were more complex than for other regions of a gas-solid fluidized bed. Comparison of Figs. 12 and 8 suggests that KSDF can be employed as a parameter to identify flow regimes. Visual observations and SDF distribution patterns for specific flow regimes are compared in Table 3. Slug-like structures were observed at the beginning of turbulent fluidization in the experiments, as also reported by Grace (1990). Slug flow should normally be avoided in catalytic fluidized bed reactors because big bubbles lead to gas by-passing, reducing the reactor efficiency. 4.3 Effect of bed temperature Industrial fluidized bed reactors generally operate at high temperature, so investigations are needed on the effects of temperature on hydrodynamics. There have been previous studies on the effects of temperature on the domain frequency of power spectra, minimum fluidization velocity, amplitude of pressure fluctuations and dense phase properties (e.g. Svoboda et al., 1983; Lettieri et al., 2001; Formisani et al., 2002; Guo et al., 2002, 2003; Falkowski and Brown, 2004), but work concerning influences of bed temperature on multi-scale flow behavior are few in number. To investigate the influence of bed temperature on hydrodynamics, experiments were conducted at temperatures from 25 to 514°C and at different superficial gas velocities (0.05 - 0.18 m/s). Temperature gradients were observed close to the distributor, so only results from the 0.93 - 0.68 m and 1.43 - 1.18 m intervals were analyzed. The dependence of fluctuation amplitude on bed temperature at different gas velocities is presented in Fig. 13. Increasing the temperature led to decreased mean amplitude of pressure fluctuations for inlet gas velocities above a critical value, with the opposite trend at lower velocities. For (d2, U = 0.05 m/s) and (d1, U = 0.14 m/s), the standard deviation increased with temperature and then decreased (upper section) or remained stable (middle section) with increasing temperature. Svoboda et al. (1983) and Guo et al. (2002; 2003) reported a reduction of bubble/void size with increasing temperature in a bubbling-turbulent fluidized bed The variation of mean bubble size with increasing temperature was insufficient to describe the detailed changes of flow dynamics, so pressure signals were subjected to structure density function analysis, with results shown in Fig. 14 and 15. For d1 particles at U = 0.14 m/s, as bed temperature increased, the SDF distribution had a narrower mutation regime (leveling-off occurred at smaller r in Region I) and higher peak intensity, these being features of the turbulent flow regime. On the other hand, SDF distributions of d2 particles at U = 0.05 m/s showed a more distinct mutation regime in Region I, but decreased peak intensity as temperature increased, indicating that the flow dynamics were more and more governed by large voids. Fig. 16 shows that increasing temperature led to increased KSDF at low inlet gas velocity (U = 0.05 m/s, d2), but decreased KSDF at a high inlet gas velocity (U = 0.14 m/s, d1). This meant that increasing the bed temperature decreased the uniformity of the flow at high superficial gas velocity, but enhanced the flow dynamics to become more regular at lower velocity. The changes of flow dynamics as temperature increased can be summarized as 9

follows. At high inlet gas velocities, more fine and small structures were contained in the flow at higher temperature. At low inlet gas velocities, large voids became more predominant and the uniformity of flow increased with increasing temperature. Comparison of Figs. 14 and 15 with Fig. 9 reveals a shift in fluidization flow regimes from bubbling towards slug flow, and slug flow towards turbulent flow, respectively, for low and high gas velocities at higher temperature. In this study, there were no gas volumetric flowrate variations caused by reactions or gas addition/extraction. Hence flow regime transitions were mainly driven by changes in the properties of the gas-solid system caused by increasing temperature, such as changes in gas viscosity, gas density and possibly particle properties (such as coefficient of restitution). Agglomeration of FCC particles at 25 to 514°C in a fluidized bed was not expected according to experiments conducted by Formisani et al. (2002) using materials and operating conditions similar to this study. With the specific particle diameter, density and inlet gas velocities, the Reynolds number was only 0.04 - 1.82. According to Appendix A, the minimum fluidization velocity decreased with increasing temperature, confirmed by experiments of Guo et al. (2002; 2003). The flowrate of air entering bed was measured and controlled at ambient temperature. Hence, as the bed temperature increased, the superficial gas velocity increased. Therefore, decreased minimum fluidization velocity and increased superficial gas velocity mainly contributed to the change of flow dynamics as the temperature increased. As the temperature increased from 100 to 514°C, the boundary intensity SDFb,II increased slightly from 0.6 (middle bed) and 0.5 (upper bed) to ~0.8 for d1 particles, as shown in Fig. 17. From a comparison with Fig. 11, the frequencies of larger voids in turbulent flow at 400-514°C were lower than at room temperature. The frequency of these larger voids mainly depends on the flow regime and particle properties (Svoboda et al., 1983). Decreased minimum fluidization velocity at increased temperature promoted transition to the turbulent flow regime at lower superficial gas velocities, so the frequency of large slugs normally found at room temperature was achieved by voids in the turbulent flow regime at higher temperatures. A slight decrease of SDFb,II with increasing temperature was observed at low gas velocity. This observation is consistent with the conclusion that the flow regime underwent transition from bubbling to slug flow as temperature increased at lower superficial gas velocity. The frequency of large voids also seemed to be smaller with larger particles as bed materials, but more experiments are required to confirm this observation.

5

Conclusions Differential pressure fluctuations were measured in a gas-solid fluidized bed reactor containing

dummy-membrane baffles, operated at different temperatures, with FCC as the bed material and air as the fluidizing gas. Data were subjected to structure density function analysis. By combining Gaussian distribution fitting and the Kolmogorov-Smirnov test, the SDF distribution of pressure fluctuations was divided into three regions in the amplitude domain, so that 10

the dynamics of large-scale, small-scale and fine-scale structures could be analyzed. As superficial gas velocity increased from 0.03 to 0.37 m/s, bubbling, slugging and turbulent fluidization were identified from the change of mean fluctuation amplitude, SDF distribution and KSDF with increasing superficial gas velocity. Variation of KSDF showed that the amplitude of pressure fluctuations became more uniform when slugs dominated the flow. Due to the violent and continuous breakage and coalescence of transient voids, the frequency of voids was higher (~1.1 Hz) in the turbulent flow regime, and the flow dynamics were more governed by fine/small structures compared with the bubbling and slug flow regimes. Structure density function analysis was helpful in characterizing flow dynamics. As temperature increased, the SDF distribution of pressure fluctuations indicated that more fine-scale structures were contained in the flow at high superficial gas velocity, while large-scale structures were more predominant at low gas velocity. In addition, multi-scale structures were less uniform at high inlet gas velocity with increasing temperature, but the opposite trend was observed at low gas velocity. SDF analysis indicated that the flow regime transitions were affected by increased superficial gas velocity and decreased minimum fluidization velocity as temperature increased.

Appendix A Bubble size was estimated by equation (a1), with the minimum fluidization velocity given by correlation of Wen and Yu (1966). 0.8

d b = 0.54 ( U − U mf )

0.4

§ A · −0.2 ¨¨ h + 4 ¸¸ g N or ¹ ©

(a2)

Remf µ g

U mf =

(a1)

d p ρg

(

Remf = 27.22 + 0.0408Ar

)

0.5

− 27.2

(a3)

To show dependence between Remf and Ar, equation (a1) can be transformed as 2 Remf + 54.4 Remf = 0.0408Ar

(a4)

Ar is the Archimedes number. Ar =

d 3p g ρ g ( ρ p − ρ g )

µ g2

(a5)

Based on the ideal gas law, the density of air at ambient pressure depends on temperature as 358.2 ρg = (a6) T The effect of temperature on the viscosity of air can be approximated by equation given by Allamagny (1976). 11

µg =

( 4.261×10 ) T −7

0.66

(a7)

As a result, Ar ∝ T-2.33. For small Reynolds numbers (Re < 1), Re ∝ Ar, and the minimum fluidization velocity decreases with increasing bed temperature, with Umf ∝ T-0.66. For large Reynolds numbers (Re>1000), Re ∝ Ar0.5, and Umf increases with bed temperature as Umf ∝ T0.5.

Acknowledgement This work was supported by the National Science Foundation of China (41172140, 50906031) and the Doctorate Foundation of Huazhong University of Science and Technology. The China Scholarship Council (CSC) is thanked for its financial support of Yumin Chen during his visiting study at the University of British Columbia.

Notation References Allamagny, P., 1976. Gas Encyclopedia. Elsevier, Amsterdam. Abba, I. A., Grace, J. R., Bi, H. T., 2003. Spanning the flow regimes: generic fluidized bed reactor model. AIChE Journal 49, 1838-1848. Bai, D., Bi, H. T., Grace, J. R., 1997. Chaotic behavior of fluidized beds based on pressure and voidage fluctuations. AIChE Journal 43, 1357-1361. Bai, D., Shibuya, E., Nakagawa, N., Kato, K., 1996. Characterization of gas fluidization regions using pressure fluctuations. Powder Technology 87, 105-111. Bi, H. T., 2007. A critical review of complex pressure fluctuations phenomenon in gas-solids fluidized beds. Chemical Engineering Science 62, 3473-3493. Bi, H. T., Ellis, N., Abba, I. A., Grace, J.R., 2000. A state-of-the art review of gas-solid turbulent fluidization. Chemical Engineering Science 55, 4789-4825. Bi, H. T., Grace, J. R., Lim, K. S., 1995. Transition from bubbling to turbulent fluidization. Industrial and Engineering Chemistry Research 11, 4003-4008. Bi, H. T., Grace, J. R., Zhu, J., 1995. Propagation of pressure waves and forced oscillations in gas-solid fluidized beds and their influence on diagnostics of local hydrodynamics, Powder Technol. 82, 239-253. Bizhaem, H. K., Tabrizi, H. B., 2013. Experimental study on hydrodynamic characteristics of gas-solid pulsed fluidized bed. Powder Technology 237, 14-23. Briongos, J. V., Soler, G. J., 2003. Free top fluidized bed surface fluctuations as source of hydrodynamic data. Powder Technology 134: 133-144. Brue, E., 1996. Pressure fluctuations as a diagnostic tool for fluidized beds. Ph. D. thesis, Iowa State University, USA. Constantineau, J. P., Grace, J. R., Lim, C. J., Richards, G. G., 2007. Generalized bubbling - slugging fluidized bed reactor. Chemical Engineering Science 62, 70-81. Croxford, A. J., Gilbertson, M. A., 2011. Pressure fluctuations in bubbling gas-fluidized beds. 12

Chemical Engineering Science 66, 3569-3578. de Martin, L., van den Dries, K., van Ommen, J., 2011. Comparison of three different methodologies of pressure signal processing to monitor fluidized-bed dryers/granulators. Chemical Engineering Journal 172, 487-499. Falkowski, D., Brown, R. C., 2004. Analysis of pressure fluctuations in fluidized beds. Industrial and Engineering Chemistry Research 43, 5721-5729. Fan, L. T., Ho, T. C., Hiraoka, S., Walawender, W. P., 1981. Pressure fluctuations in a fluidized bed. AIChE Journal 27, 388-396. Formisani, B., Girimonte, R., Pataro, G., 2002. The influence of bed temperature on the dense properties of bubbling fluidized beds of solids. Powder Technology 125, 28-38. Ghasemi, F., van Ommen, J. R., Sahimi, M., 2011a. Analysis of pressure fluctuations in fluidized beds. I. Similarities with turbulent flow. Chemical Engineering Science 66: 2627-2636. Ghasemi, F., Sahimi, M., 2011b. Analysis of pressure fluctuations in fluidized beds. II. Reconstruction of the data by the Fokker-Planck and Langevin equations. Chemical Engineering Science 66: 2637-2645. Ghasemi, F., van Ommen, J. R., Sahimi, M., 2011a. Analysis of pressure fluctuations in fluidized beds. I. Similarities with turbulent flow. Chemical Engineering Science 66: 2627-2636. Gómez-Hernandez, J., SȐnchgez-Proeto, J., Briongos, J. V., Sabtana, D., 2012. Fluidized bed with a rotating distributor operated under defluidization conditions. Chemical Engineering Journal 195-196: 198-207. Gómez-Hernandez, J., Sanchgez-Proeto, J., Briongos, J. V., Sabtana, D., 2014. Wide band energy analysis of fluidized bed pressure fluctuation signals using a frequency division method. Chemical Engineering Science 105: 92-103. Grace, J. R., 1982. Fluidized-Bed Hydrodynamics. In Handbook of Multiphase Systems; Hetsroni, G., Ed.; Hemisphere, Washington, D.C.; Chapter 8, pp. 5-64. Grace, J. R., 1990. High-velocity fluidized bed reactors. Chemical Engineering Science 45, 1953-1966. Grace, J. R., Elnashaie, S. S. E. H., Lim, C. J., 2005. Hydrogen production in fluidized beds with in-situ membranes. International Journal of Chemical Reactor Engineering 3, A41. Guo, Q., Yue, G., Werther, J., 2002. Dynamics of pressure fluctuation in a bubbling fluidized bed at high temperature. Industrial and Engineering Chemistry Research 41, 3482-3488. Guo, Q., Yue, G., Suda, T., Sato, J., 2003. Flow characteristics in a bubbling fluidized bed at elevated temperature. Chemical Engineering and Processing 42, 439-447. Johnsson, F., Zijierveld, R. C., Schouten, J. C., van den Bleek, C. M., Leckner, B., 2000. Characterization of fluidization regions by time-series analysis of pressure fluctuations. International Journal of Multiphase Flow 26, 663-715. Kage, H., Agari, M., Ogura, H., Matsuno, Y., 2000. Frequency analysis of pressure fluctuations in 13

fluidized bed plenum and its confidence limit for detection of various modes of fluidization. Advanced Powder Technology 11, 459-475. Lettieri, P., Newton, D., Yates, J. G., 2001. High temperature effects on the dense phase properties of gas fluidized beds. Powder Technology 120, 34-40. Lu, X. S., Li, H. Z., 1999. Wavelet analysis of pressure fluctuation signals in a bubbling fluidized bed. Chemical Engineering Science 75: 113-119. Rakib, M. A., 2010. Fluidized bed membrane reactor for steaming reforming of higher hydrocarbons. Ph. D. Thesis, University of British Columbia, Vancouver, Canada. Ren, J., Mao, Q., Li, J., Lin, W., 2001. Wavelet analysis of dynamic behavior in fluidized beds. Chemical Engineering Science 56: 981-988. Sasic, S., Leckner, B., Johnsson, F., 2006. Time-frequency investigation of different modes of bubble flow in a gas-solid fluidized bed. Chemical Engineering Journal 121: 27-35. Saxena, S. C., Tanjore, V. N., Rao, N. S., 1992. Basic hydrodynamic characteristics of a fluidized-bed incinerator. Energy Fuels 6, 502-511. Schouten, J.C., van den Bleek, C.M., 1998. Monitoring the quality of fluidization using the short-term predictability of pressure fluctuations. AIChE Journal 44, 48-59. Svoboda, K., Cermak, J., Hartman, M., Drahos, J., Seluchy, K., 1983. Pressure fluctuations in gas-fluidized beds at elevated temperatures. Industrial and Engineering Chemistry Process Design and Development 122, 514-520. Tahmasebpour, M., Zarghami, R., Sotudeh-Gharebagh R., Mostoufi, N., 2013. Characterization of various structures in gas-solid fluidized beds by recurrence quantification analysis. Particuology, 2013, 11: 647-656. van der Schaaf, J., Johnsson, F., Schouten, J. C., van den Bleek C. M., 1999. Fourier analysis of nonlinear pressure fluctuations in gas-solids flow in CFB risers – Observing solids structures and gas/particles turbulence. Chemical Engineering Science 54: 5541-5546. van der Schaaf, J., Schouten, J. C., Johnsson, F., van den Bleek, C. M., 2002. Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of power spectral density of pressure time series. International Journal of Multiphase Flow 28: 865-880. van Ommen, J.R., Sasic, S., van der Schaaf, J., Gheorghiu, S., Johnsson, F., Copper, M. O., 2011. Time-series analysis of pressure fluctuations in gas-solid fluidized beds - A review. International Journal of Multiphase Flow 37, 403-428. Wen, C. Y., Yu, Y. H. A., 1966. A generalized method for predicting minimum fluidization velocity. AIChE Journal 3, 610-612. Wu, B., Kantzas, A., Bellehumeur, C. T., He, Z., Kryuchkov, S., 2007. Multiresolution analysis of pressure fluctuations in a gas-solids fluidized bed: Application to glass beads and polyethylene powder systems. Chemical Engineering Journal 131: 23-33. Zhao, G. B., Yang, Y. R., 2003. Multi-scale resolution of fluidized-bed pressure fluctuations. AIChE 14

Journal 49: 869-882.

15

Table 1 Properties of particulate materials Designation

Material

Diameter range (mm)

Particle density, ȡp (kg/m3)

Umf (cm/s)

d1

FCC

0.06 - 0.12

1450

0.94

d2

FCC

0.15 - 0.20

1450

2.56

Table 2 Comparison of amplitude division and frequency division methods 16

Comparison

Amplitude division (this work)

Boundary determination

Gaussian fitting combined with K-S test Fine structures originating from particles,

Region I

bed surface oscillations and gas flow variations

Links with flow dynamics

Region II

Region III

Derived parameters

Frequency division Visual selection of cut-off frequencies on power spectra No clear dependence on fluidization regime (Johnsson et al., 2000)

Small structures originating from small

Finer structures related to bulk

“bubbles” and particle clusters

dynamics (Johnsson et al., 2000)

Large structures originating from large

Macro structures related to bubbles

“bubbles” (including slugs)

(Johnsson et al., 2000)

Characteristics slope, KSDF; boundary intensity, SDFb,II

Fall-off, Į; cut-off frequencies

Table 3 Comparison of specific flow regimes. Flow regime

Visual observation

SDF distribution 17

Bubbling regime

Slugging regime

Turbulent regime

Small bubbles evenly distributed over

Symmetrical peak with low intensity; small slope;

bed cross-section;

higher SDFb,II

Large bubbles; high periodicity; bed

Levelling-off occurred at larger r in regime I

surface rises and falls periodically.

(wide mutation regime); larger slope; low SDFb,II

Transient darting voids; particle clusters; diffuse bed surface

Steep peak with high intensity; small slope; levelling-off may exist in regime I, but at smaller r (narrow mutation regime); higher SDFb,II

Highlights (revised) z z z

Structure density function was proposed to characterize differential pressure signals measured in gas-solid fluidized bed. An amplitude division method based on Gaussian distribution and the Kolmogorov-Smirnov test was developed. Increasing the operating temperature enhanced the transition of flow regimes.

Fig. 1 Schematic of experimental system. Fig. 2 Illustration of methodology used in structure density analysis. Fig. 3 Variation of differential pressure with time showing fluctuations. Operating conditions: U/Umf=14.8, d1 particles, Ho=1.32 m, P=0.1 MPa, T=25oC; measurement interval: 1.43 - 1.18 m.

Fig. 4 Distribution of pressure fluctuations: (a) structure density distribution; (b) cumulative energy. Operating conditions: U/Umf=14.8, d1 particles, Ho=1.32 m, P=0.1 MPa, T=25oC; measurement interval: 1.43 - 1.18 m.

Fig. 5 Effect of superficial gas velocity on structure probability distribution of pressure series with fluctuation amplitude r at different levels. Operating conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC. Fig. 6 Effect of superficial gas velocity on cumulative energy distribution structure probability function for different height intervals in fluidized beds. Other operating conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC. Fig. 7 Illustration of frequency division analysis. Operating conditions: U/Umf=14.8, d1 particles, Ho=1.32 m, P=0.1 MPa, T=25oC; measurement interval: 1.43-1.18 m. Fig. 8 Effect of superficial gas velocity on mean amplitude of pressure fluctuations at different height intervals in fluidized bed. Other operation conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC.

Fig. 9 Effect of superficial gas velocity on structure density distribution at different vertical positions in fluidized bed. Other operation conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC. 18

Fig. 10 Illustration of the application of SDF analysis in characterizing differential pressure fluctuations measured from normal bed without dummy membranes. Operation conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC. Fig. 11 Effect of superficial gas velocity on SDFb,II of structure density distribution at different vertical positions in fluidized bed. Operation conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC. Fig. 12 Effect of superficial gas velocity on KSDF of structure density distribution at different vertical positions in fluidized bed. Other operation conditions: Ho=1.32 m, d1 particles, P=0.1 MPa, T=25oC. Fig. 13 Effect of temperature on mean amplitude of pressure fluctuations in two height intervals of fluidized bed at different superficial gas velocities. Solid symbols: 0.93 - 0.68 m; open symbols: 1.43 - 1.18 m. Other operating conditions: Ho=1.32 m, P=0.1 MPa. Fig. 14 Effect of bed temperature on structure density distribution of pressure fluctuations. Other operating conditions: U/Umf=14.8, d1 particles, Ho=1.32 m, P=0.1 MPa. Fig. 15 Effect of bed temperature on structure density distribution of pressure fluctuations. Other operating conditions: U/Umf=2.2, d2 particles, Ho=1.32 m, P=0.1 MPa. Fig. 16 Effect of bed temperature on slope KSDF of structure density distribution at different superficial gas velocities and height intervals. Other operating conditions: Ho=1.32 m, P=0.1 MPa.

Fig. 17 Effect of bed temperature on boundary intensity SDFb,II of structure density distribution at specific superficial gas velocities and measuring locations. Other operating conditions: Ho=1.32 m, P=0.1 MPa.

19

Figure-1

Figure-2

Figure-3

Figure-4

Figure-5

Figure-6

Figure-7

Figure-8

Figure-9

Figure-10

Figure-11

Figure-12

Figure-13

Figure-14

Figure-15

Figure-16

Figure-17