A comparative study on hydrodynamics of circulating fluidized bed riser and downer

Powder Technology 247 (2013) 235–259

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A comparative study on hydrodynamics of circulating fluidized bed riser and downer Dongbing Li, Madhumita B. Ray, Ajay K. Ray, Jingxu Zhu ⁎ Department of Chemical & Biochemical Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9

a r t i c l e

i n f o

Available online 7 January 2013 Keywords: Circulating fluidized beds Hydrodynamics Solid fraction Velocity distribution

a b s t r a c t Hydrodynamics in a 76 mm i.d., 10.2 m high circulating fluidized bed (CFB) riser and a 76 mm i.d., 5.8 m high CFB downer were studied for superficial gas velocities ranging from 2 to 5 m/s and solid circulation rates up to 100 kg/(m2 s). Solid holdup, particle velocity and solid flux profiles in the radial and axial positions were presented. Under these operating conditions, axial solid holdup profiles in the riser and the downer could be approximated by an exponential decay function. The radial gradients of the solid holdup profiles in the riser were much higher than those in the downer, showing that the downer had much more uniform solid distribution. The average solid holdup for the entire riser was about 1.5 times higher than the predicted value from Gs/(ρpUg). However, for the downer reactor this ratio dropped to 0.45–0.98 which increased with increasing superficial gas velocity and decreasing solid circulation rate. Solid flow developed much slower in the riser than in the downer. Negative particle velocity was observed in the near-wall region for nearly the entire height of the riser. The average particle velocity for the entire riser was 0.8–0.96 times higher than the superficial gas velocity, and increased with increasing superficial gas velocity and decreasing solid circulation rate. However, in the downer the average particle velocity was 1.13–2.13 times higher than the superficial gas velocity, and increased with both superficial gas velocity and solid circulation rate. High local solid fluxes were observed in the near wall region of the CFB riser and downer reactor. Over-estimation of the calculated cross-sectional average solid flux over the solid circulation rate in the CFB riser was attributed to the fluctuations of the solid holdup and particle velocity. © 2013 Published by Elsevier B.V.

1. Introduction The commercial interest in circulating fluidized bed (CFB) technology can be dated back to the 1940s when the fluid catalytic cracking (FCC) process was first developed [1,2]. But due to low catalyst activity and other technical difficulties, it was not until in the 1970s when high velocity CFB technology was “re-invented” [3]. CFB reactor has been providing many advantages over bubbling fluidized bed reactors such as higher gas–solid contact efficiency, reduced axial dispersion for both gas and solid phases and higher gas/solid throughput [4,5]. The CFB riser reactor has been widely used in various industries [4,6] such as combustion of low-grade fuels, mineral processing, FCC and as a catalytic reactor for the production of a number of specialty chemicals [7]. On the other hand, the CFB riser suffers from solid backmixing, macro segregations of gas and solid phases due to the non-uniform flow structure in radial and axial directions, and micro segregations caused by particle clustering. These drawbacks are results of both gas and solids flowing against gravity [5], which reduce gas-solid

⁎ Corresponding author. Tel.: +1 519 661 3807; fax: +1 519 850 2441. E-mail address: [email protected] (J. Zhu). 0032-5910/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.powtec.2012.12.050

contact efficiency and lead to undesired distribution of products due to reduced selectivity. The disadvantages of the riser reactor may be overcome in a new type of chemical reactor – a CFB downer reactor [5,8,9], where gas and solid phases flow co-currently downward, in the same direction as gravity force. In a CFB downer, particles accelerate much more quickly since they gain momentum from both the gas and the force of gravity. Hydrodynamic studies show that the radial distribution of flow parameters such as solid holdup and particle velocity in the CFB downers is more uniform than that in the CFB risers [10–12]. This radial uniformity further reduces gas and solid dispersion and leads to nearly plug flow for both phases in the downer [12,13]. With reduced axial dispersion and more uniform gas and solid residence times, CFB downer reactors become more advantageous than CFB risers for reactions requiring short residence times [9], especially where intermediates are the desired products, such as the FCC and residual fluidized catalytic cracking processes [5,12]. Hydrodynamic studies are very important in understanding the CFB riser and downer reactors. In spite of numerous earlier studies on hydrodynamics in CFB reactors, this study provides a complete mapping of the local volumetric solid holdup, particle velocity, and solid flux at variable radial and axial positions in the 76 mm i.d. riser and downer reactors with superficial gas velocity ranging from 2 to 5 m/s and solid circulation rates at 50 and 100 kg/(m2 · s).

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2. Experimental 2.1. CFB experimental setup Experiments were carried out in a circulating fluidized bed system illustrated in Fig. 1. Major components included a 76 mm i.d., 10.2 m high CFB riser, a 203 mm i.d. downcomer, a 457 mm i.d. storage tank, a 76 mm i.d., 5.8 m high CFB downer and another 51 mm i.d., 4.9 m high CFB downer, sampling ports, gas distributors, and cyclones and bagfilter for gas solid separation. The entire fluidized bed system used aluminum as the main construction material and was electrically grounded to remove electrostatic charges formed in the columns. A measuring device for solid circulation rate was installed in the top section of the downcomer. By regulating the ball valve located in the solid feeding line connecting the storage tank and the riser column, the solid circulation rate was adjusted and maintained at a desired value during each experiment. For CFB riser operations, solid particles fluidized by auxiliary air entered into the bottom of the riser and obtained momentum from the air passing through the gas distributor made of perforated plates (9.5 mm × 30 holes, 47 % voids). The solid particles flowed upward together with the air, and were separated by the cyclones and returned to the downcomer. Fine particles leaving the cyclones were trapped by the bagfilter and returned periodically to the downcomer. This was, however, a very small amount of solids compared to the flow in CFB columns due to high efficiency of the cyclones. For CFB downer operations, solid particles were lifted through the riser, separated by the cyclones and fed into the downer. Gas and solid phases passed through the distributor (with its detail design also shown in Fig. 1), and then together flowed downward along the column. After fast separation at the exit of the downer column, most particles were retained in the storage tank, with the remaining particles captured by the primary and secondary cyclones and the bagfilter. The operating conditions were superficial velocities of 2, 3, 4, and 5 m/s, with solid circulation rates being 50 and 100 kg/(m 2 s). The axial sampling positions were 0.11, 0.57, 1.02, 1.48, 1.94, 2.39, 2.85,

4.78, 7.32, 9.61 m above the gas distributor for the riser, and 0.22, 0.61, 1.12, 1.63, 2.13, 2.64, 3.26, 4.02, and 4.99 m below the gas distributor plate for the downer. The dimensionless radial sampling positions (r/R) for both the CFB riser and the downer were 0 (center), 0.316, 0.548, 0.707, 0.837 and 0.949 (close to wall). 2.2. Solid particles Fresh FCC catalyst particles impregnated with ferric oxide (Fe2O3) were used in this hydrodynamic study and other catalytic ozone decomposition studies by the authors [14,15]. Since particle size is an important factor affecting the hydrodynamics in the fluidized beds [4,6], to achieve a stable particle size distribution (PSD) for the CFB experiments the particles after the impregnation process were subjected to run through the riser for 7 days to remove the fines. More details on the catalyst impregnation process, and how the particle size distribution changed during catalyst preparation can be found in the research paper by Li et al. [14]. When stable PSD was achieved, the Sauter mean particle size was 60 μm, and the apparent particle density (ρp) and bulk density (ρb) were determined to be 1370 kg/m3 and 795 kg/m3, respectively. 2.3. Measurement and calculation of solid holdups Reflective-type optical fiber probes offer a simple and more affordable way to measure local solid holdup in fluidized bed systems, providing many advantages such as minimum disturbance to the gas–solid flow and negligible interference by temperature, humidity, electrostatics and electromagnetic fields [16]. In this study PV-5 optical fiber probes (manufactured by the Institute of Process Engineering, Chinese Academy of Sciences) were used to measure the local volumetric solid holdup. An illustration of the optical fiber probe and the measurement principle is provided in Fig. 2. The diameter of the probe is 4 mm, with 2 vertically aligned sub-probes in a square shape of 1 × 1 mm2. The maximum distance the probe can be inserted into the column is 400 mm. The optical fiber probe has both light emitting and receiving

Fig. 1. The CFB experimental setup.

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237

Fig. 2. Schematic of the optical fiber probe and its working principle.

quartz fibers of diameter 25 μm arranged in an alternating array, corresponding to emitting and receiving fiber layers. In order to prevent particles from occupying the blind zone, a Plexiglas cover of 0.2 mm thickness was placed over the probe tip (the underlying theory was elaborated by Liu et al. [17,18]). Through the light-emitting fibers, light from the source illuminated a measuring volume of particles. Light reflected by the particles was partially captured by the lightreceiving fibers and through a photo-multiplier the light intensity was converted into voltage signal. The voltage signals were further amplified and fed into a PC. Since the relationship between the output signals of the optical fiber probe and the solid holdup was non-linear, a calibration curve relating the voltage output and the solid holdup in a defined range was required. Calibration tests for the optical fiber probes were performed in a CFB downer system as shown in Fig. 3(a). It mainly consists of two storage tanks, an upflow pipe for lifting solids from the bottom to the upper storage tank, a vibrating pipe with the function of adjusting the amount of solids flowing into the downer column, a 13 mm i.d., 5 m long downer column, and two pinch valves together with two small sections of latex tubes for the purpose of locking the solids in a measuring column section. The measuring column section between the two pinch valves are 0.94 m in height, and is located in the fully developed region of the gas-solid downer flow so that a stabilized solid holdup can be achieved. The optical fiber probe is inserted into the center of the column at the mid-point of the measuring column section. The diameter of the CFB downer is small enough to assume uniform radial solid holdup distribution so that a local solid holdup measurement will yield a cross-sectionally averaged value. By changing the amount of gas flowing through the vibrator, different vibration intensities of the vibrating pipe will produce different solid holdup in the downer column. A more detailed description of the calibration apparatus can be found in [16]. Before the calibration experiments, the lower and upper limits of the voltage output (V) from the optical fiber probe were set to 0 and 4.5 volts. The lower voltage limit corresponds to the condition where the solid holdup is zero; and the upper voltage limit corresponds to the solid fraction in a loosely packed bed. For the catalyst particles used in this study, a solid holdup of 0.58 was set for the upper voltage limit of 4.5 volts. For this purpose, an empty black box (εs =0) and a black box filled with loosely-packed test particles (εs = 0.58) were used to adjust the signal drift and amplifier parameters in the PV-5 service unit so that the voltage signals were 0 and 4.5 volts, respectively.

When measuring solid holdup profiles in the CFB units, the same pre-test adjustment procedure was followed. During the calibration tests, when a steady solid flow was achieved inside the downer, a 2048-milisecond sampling of the voltage signals was acquired at a frequency of 2 kHz, immediately followed by the closure of the pinch valves. By collecting and weighing the particles trapped in the column section between the two pinch valves, the volumetric solid holdup corresponding to each voltage signal series was calculated: εs ¼

m=ρp Vc

ð1Þ

where Vc is the volume of the measuring column section, m is the mass of the particles, and ρp is the particle density. The mass flow rate of the particles was varied in a range to generate enough data points for plotting an accurate calibration curve. Specifically, the calibration results on optical fiber probe #5 are presented in Fig. 3(b, c and d). Fig. 3(b) shows two typical voltage time series with average values being 0.593 and 3.099 volts, respectively. Normal fluctuations around the average value were observed, showing steady solid flow in the measuring column section. The average voltage output and its corresponding average solid holdup calculated from Eq. (1) are shown as discrete data points in Fig. 3(c). Three functions passing through the origin were tested to fit the experimental data: εs = aVb, εs = aV+ bV2, and εs = a(bV − 1), where V is the voltage output from the optical fiber probe, εs is the local solid holdup, a and b are fitting parameters. The regression results are also shown in Fig. 3(c). The exponential function εs = a(b V − 1) gives the smallest summed square of residuals (S), which shows that it is the best function to fit the calibration data. Fig. 3(d) presents the calibration curve for two channels of the same optical fiber probe, with minor discrepancy observed. For the CFB riser and downer experiments in this study, voltage signals from the optical fiber probes were sampled at a high frequency of 100 kHz in order to capture the dynamic nature of the solid flow and for a time interval of 16.384 s, giving voltage time series V(t) of 1,638,400 data points for both channels. From the voltage time series and the calibration equation, local instantaneous solid holdup, εs(t), can be calculated: ε s ðt Þ ¼ f ½V ðt Þ

ð2Þ

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b

a To bagfilter Cyclones

Upper storage tank Fluidized feeder Vibrating pipe

c

Feeding funnel

ε Downer test column (13 mm i.d., 5 m high)

ε ε

Latex tubing Pinch valves

Optical fiber probe

Latex tubing

PV-5 service unit

Lower storage tank

d

To PC

Solids inlet

ε ε

Air

Fig. 3. Calibration of the optical fiber probes: (a) apparatus, (b) typical voltage signals, (c) comparison of three fitting functions, and (d) calibration curves for channel 1 and 2.

where f is the calibration function. Integrating εs(t) over the time span, T, will give the average solid holdup at a certain position in the column: T

εs ¼

1 ∫ ε ðt Þdt T0 s

ð3Þ


 The cross-sectional average solid holdup ε s;r can be calculated as ε s;r ¼

1 R 2 R ∫0 2πrεs dr ¼ 2 ∫0 εs rdr πR2 R

ð4Þ

Accordingly, the average solid holdup at a certain
radial  position over the entire height of the riser or downer column ε s;z can be calculated as ε s;z ¼

1 H ∫ ε dz H 0 s

ð5Þ

where H is the height of the riser or downer column. An overall average solid holdup over the entire riser or downer column can be determined by εs ¼

2 H R ∫0 ∫0 εs rdrdz HR2

ð6Þ

2.4. Calculation of particle velocities Assuming that particles are moving at a constant speed in the vertical direction for the short distance (less than 2 mm) between the two light-receiving fibers, particle velocity, vp, can be determined from vp ¼

Le τ

ð7Þ

where Le is the effective distance between light-receiving fiber 1 and 2, and τ is the transit time. Note that Le is, in general, not equal to the

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distance between the axes of the two fibers [18]. The effective distances for probes 4 and 5 used in this study were given by the manufacturer, 1.61 and 1.71 mm, respectively. Transit time (τ) is evaluated from the time lag by cross-correlation. In signal processing, cross-correlation is a measure of similarity between two waveforms where one of them has a time-lag as compared to the other. Cross-correlation involves shifting one signal and multiplying another signal. The cross-correlation function ϕ12(τ) of the two voltage time series V1(t) and V2(t) obtained from the optical fiber probe can be expressed as ϕ12 ðτ Þ ¼

1 T ∫ V ðt ÞV 2 ðt þ τ Þdt T 0 1

239

→

←

ð8Þ

or in normalized form, 

ϕ12 ðτ Þ ¼

1 T V 1 ðt Þ−V 1 ∫ T 0 σ1

!

! V 2 ðt þ τÞ−V 2 dt σ2

ð9Þ

where T is the time interval of signal acquisition, V 1 and V 2 , σ1 and σ2 are the mean and the standard deviation of the two signals. When ϕ12 reaches maximum, the corresponding τ value is used to determine the particle velocity by Eq. (7). Given the complex and dynamic nature of the flow structure in the CFBs, particles traveling non-vertically past one fiber may not be detected by the second fiber, resulting in low or indeterminate crosscorrelation coefficients [18], so that only data with good crosscorrelation coefficients can be used. Militzer et al. [19] deleted data with correlation coefficients less than 0.5 and with calculated velocities differing by more than two standard deviations from the average. Werther et al. [20] only accepted data with cross-correlation coefficients greater than 0.6, causing 20–30 % of their data to be discarded. The latter criterion was followed in this study. For each radial and axial position under certain superficial gas velocity and solid circulation rate, the 1,638,400 voltage data points for each channel of the optical fiber probe were used to calculate the particle velocity. These data were divided into some subgroups so that for each subgroup the time lag or the particle velocity was calculated. The obtained time lags were selected based on the criterion that the shift index could not be zero and that the cross-correlation coefficient should be greater than 0.6. In this selection process, some data with poorer correlation was discarded. The average particle velocity and its standard deviation were then calculated. Fig. 4 shows an example of how the number of subgroups affects the calculated particle velocity. The voltage time series data used in this example were obtained from the column center (r/R= 0) of the riser, with the axial position at z = 0.11 m above the gas distributor plate. The superficial gas velocity and solid circulation rate used were 3 m/s and 100 kg/(m 2 s), respectively. Subgroup numbers ranged from 1 to 400. For each number of subgroups, an average particle velocity was obtained, shown in the left y-axis. Percentage of voltage data that remain valid after screening by the correlation coefficients is also presented. Only a very small amount of voltage data were discarded, showing that most of the cross-correlation coefficients were higher than 0.6. As can be seen from Fig. 4, the number of subgroups used to divide voltage data for cross-correlation leads to different values for the average particle velocity. To have a consistent value, the average particle velocities obtained under each sub-grouping method were further subject to a screening process by counting the occurrences at different velocity ranges with a bin width of 0.5 m/s. Those velocities that fell in the bin with maximum occurrences were averaged to give the final particle velocity (vp). In Fig. 4, the particle velocities shown in closed circles showed very good consistency and thus were taken to estimate the final particle velocity. Given the local particle velocities (vp) at different radial and axial positions, the cross-sectional average particle velocity, axial average

Fig. 4. Calculated particle velocity versus number of subgroups for the voltage time series data.


 particle velocity and entire-bed mean particle velocity v p;r ; v p;z ; and v p can be calculated: v p;r ¼

2 R 1 H 2 H R ∫0 rvp dr; v p;z ¼ ∫0 vp dz; v p ¼ ∫0 ∫0 rvp drdz H R2 HR2

ð10Þ

The average particle velocities defined by Eq. (10) disregard non-uniform solid holdup distribution in the riser or downer, which can only be seen as average “particle” velocities. The average solid ve
 locities v s;r ; v s;z ; and v s taking into account the radial and axial solid holdup profiles can be defined as v s;r ¼

2 1 H 2 H R R ∫0 vp εs rdr; v s;z ¼ ∫ v ε dz; v s ¼ ∫0 ∫0 vp εs rdrdz Hε s;z 0 p s R2 ε s;r HR2 ε s

ð11Þ Based on the experimental data at different radial and axial positions, trapezoidal rule was applied to obtain numerically the integrations shown in these equations. 2.5. Calculation of solid fluxes Local solid flux, Fs, can be determined by F s ¼ ρp vp εs

ð12Þ

where ρp is the particle density, εs and vp are local solid holdup and particle velocity, respectively. Similarly,cross-sectional, axial, or entire-bed  average solid fluxes F s;r; F s;z and F s can be calculated by F s;r ¼

2 R 1 H 2 H R ∫0 F s rdr; F s;z ¼ ∫0 F s dz; and F s ¼ ∫0 ∫0 F s rdrdz H R2 HR2

ð13Þ

3. Results and discussion Solid holdup (εs), particle velocity (vp) and local solid flux (Fs) profiles were taken at variable superficial gas velocities (Ug = 2–5 m/s) and solid circulation rates (Gs = 50 and 100 kg/(m 2 s)) for both the riser and the downer. Measurements were taken at quite a few axial positions (10 positions from 0.11 to 9.63 m above the gas distributor for the riser, 9 positions from 0.22 m to 4.99 m below the gas distributor for the downer) and 6 radial positions ranging from r/R = 0 to 0.949. When presenting the experimental results, each subsection starts with a 3-dimensional plot, providing an overview of the solid holdup, particle velocity, or local solid flux profiles under six operating

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conditions. To better observe profiles, a second plot of di
the radial  mensionless solid holdup εs =ε s;r , dimensionless particle velocity

 vp =v p;r , or dimensionless local solid flux F s =F s;r profile follows, where ε s;r ; v p;r ; and F s;r are the cross-sectional average solid holdup, particle velocity, and solid flux at a specific axial distance, with numerically integrated values based on trapezoidal rule. For these dimensionless parameters, deviation from 1 indicates how much local solid holdup, particle velocity, or solid flux differs from their crosssectional mean. Overall mean values for the entire column are also given in these plots. A third plot shows the cross-sectional average values
 for the solid holdup, particle velocity, and solid flux ε s;r ; v p;r ; and F s;r at


 different elevations and the axial average values ε s;z ; v p;z ; and F s;z at different radial positions. Negative values shown in Figs. 9–14 represent particle velocities or solid fluxes against the gas flow direction, i.e., particles are flowing downward in the CFB riser.

3.1. CFB riser — solid holdup Fig. 5 provides an overview of the solid holdup profiles in the CFB riser. It becomes obvious that for each elevation level, solid holdup in the wall region is higher than that in the column center, and

⋅

ε

ε

⋅

⋅

ε

ε

⋅

⋅

ε

ε

⋅

Fig. 5. Solid holdup profiles in the riser.

D. Li et al. / Powder Technology 247 (2013) 235–259

decreases with height. Solid holdup increases with reduced superficial gas velocity and increased solid circulation rate. Fig. 6 plots the dimensionless solid holdup (εs =ε s;r where ε s;r is the cross-sectional mean) versus r/R for different axial positions at six operating conditions. From Fig. 6, it is observed that in most cases local solid holdup reaches its cross-sectional average at r/R = 0.7–0.8. The fact that solid holdup in the wall region is higher than that in the column center is further illustrated by Fig. 7(a) which plots the average solid holdup over the entire height of the riser for different radial positions. The axially averaged solid holdup has a more uniform

distribution in the center region up to r/R = 0.5–0.6. For r/R > 0.5–0.6, solid holdup increases significantly. Cross-sectional average solid holdup profiles at different axial positions are presented in Fig. 7(b). With the increase of riser height, cross-sectional average solid holdup decreases rapidly in the flow developing zone or bottom section of the riser, and then levels off in the fully developed region or top section of the riser. The length of the flow developing zone is observed to be approximately 23 m, and it decreases with increased superficial gas velocity and reduced solid circulation rate.

ε ε¯ s, r = 0 .0234 ε¯ s, r = 0 .0157 ε¯ s, r = 0 .0102 ε¯ s, r = 0 .0359 ε¯ s, r = 0 .0221 ε¯ s, r = 0 .0209

ε¯ s, r = 0 .0255 ε¯ s, r = 0 .0164 ε¯ s, r = 0 .0105 ε¯ s, r = 0 .0377 ε¯ s, r = 0 .0225 ε¯ s, r = 0 .0201

ε¯ s, r = 0 .0268 ε¯ s, r = 0 .0164 ε¯ s, r = 0 .0109 ε¯ s, r = 0 .0353 ε¯ s, r = 0 .0253 ε¯ s, r = 0 .0202

ε¯ s, r = 0 .0304 ε¯ s, r = 0 .0161 ε¯ s, r = 0 .0111 ε¯ s, r = 0 .0371 ε¯ s, r = 0 .0241 ε¯ s, r = 0 .0198

ε¯ s, r = 0 .0329 ε¯ s, r = 0 .0170 ε¯ s, r = 0 .0114 ε¯ s, r = 0 .0367 ε¯ s, r = 0 .0243 ε¯ s, r = 0 .0220

ε ε

241

ε¯ s, r = 0 .0347 ε¯ s, r = 0 .0198 ε¯ s, r = 0 .0125 ε¯ s, r = 0 .0364 ε¯ s, r = 0 .0265 ε¯ s, r = 0 .0227

ε¯ s, r = 0 .0340 ε¯ s, r = 0 .0202 ε¯ s, r = 0 .0146 ε¯ s, r = 0 .0378 ε¯ s, r = 0 .0292 ε¯ s, r = 0 .0249

ε¯ s, r = 0 .0366 ε¯ s, r = 0 .0224 ε¯ s, r = 0 .0169 ε¯ s, r = 0 .0481 ε¯ s, r = 0 .0340 ε¯ s, r = 0 .0306

ε¯ s, r = 0 .0400 ε¯ s, r = 0 .0270 ε¯ s, r = 0 .0183 ε¯ s, r = 0 .0487 ε¯ s, r = 0 .0437 ε¯ s, r = 0 .0394

ε¯ s, r = 0 .0435 ε¯ s, r = 0 .0288 ε¯ s, r = 0 .0258 ε¯ s, r = 0 .0564 ε¯ s, r = 0 .0576 ε¯ s, r = 0 .0581

Fig. 6. Radial solid holdup profiles in the riser.

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ε

a

ε

b

Fig. 7. Axial and cross-sectional average solid holdup profiles in the riser.

From Fig. 6, mixed results on radial solid holdup gradients are observed. At Ug = 2 m/s and Gs = 50 kg/(m 2 s), radial distribution of the solid holdup is fairly uniform in the solid entrance region. With the increase of axial distance, radial gradient intensifies and then levels off. When superficial gas velocity is increased to Ug = 3 or 5 m/s while keeping the same Gs = 50 kg/(m 2 s), radial gradient of ε s =ε s;r has its maximum in the very bottom of the riser and then decreases with height. For the same superficial gas velocity of Ug = 3 m/s, when Gs increases to 100 kg/(m 2 s), the radial gradient profile exhibits very similar characteristics to that at Ug = 2 m/s and Gs = 50 kg/(m 2 s). To quantify how radial solid holdup gradient changes with axial position, cross-sectional average radial gradients for three operating conditions, with Ug [m/s] − Gs [kg/(m2 · s)]=2–50, 3–50 and 3–100, were calculated and plotted versus riser height as shown in Fig. 8. At low superficial gas velocities and high solid circulation rates, the radial gradient of εs =ε s;r increases to a maximum and then levels off, while at a higher superficial gas velocity, maximum radial gradient occurs at the solid inlet and then levels off. This suggests that when solid holdup is high (at a lower Ug and higher Gs), peak radial gradient occurs at some distance above the distributor (in this case, it is at z = 1.5–3 m), while for more dilute solid suspension, peak radial gradient appears at the very bottom of the riser. Table 1 provides a comparison between the measured average solid holdups ( ε s ; defined by Eq. (6)), and the predicted values based on the superficial gas velocity (Ug), average particle velocity (v p , defined by Eq. (10)), and average solid velocity (v s , defined by Eq. (11)). For all the six operating conditions, the measured solid

holdups are approximately 1.5 times of the predicted values from the superficial gas velocity, or 1.3–1.4 times of the predicted values from the average particle velocity, whereas the predictions based on the average solid velocity are only slightly less than the experimental values. The reasons and implications are dealt with later in this paper.

Fig. 8. Radial solid holdup gradients at different axial positions in the riser.

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3.2. CFB riser — particle velocity

Table 1 Comparison between measured and predicted solid holdups in the riser. Ug–Gs

ε s ½−

ε s =ε s1 ½−⁎

ε s =ε s2 ½−⁎

ε s =ε s3 ½−⁎

2–50 3–50 5–50 3–100 4–100 5–100

0.0290 0.0178 0.0120 0.0382 0.0263 0.0230

1.59 1.46 1.57 1.44 1.65 1.57

1.29 1.35 1.41 1.38 1.43 1.31

1.10 1.09 1.04 1.13 1.11 1.12

      ⁎ Definitions: ε s1 ¼ Gs = ρp U g ; ε s2 ¼ Gs = ρp v p ; ε s3 ¼ Gs = ρp v s .

243

Fig. 9 provides an overview of the particle velocity profiles under the six operating conditions in the CFB riser. Please note that, for better illustration, the view angle in Fig. 9 is different from that in Fig. 5. Parabolic radial particle velocity profiles are observed, with high velocities in the center and negative values in the wall region, where particles are flowing downward against the gas flow direction. In the center region of r/R b 0.6–0.8, particle velocity can be greater than the

⋅

⋅

⋅

⋅

⋅

⋅

Fig. 9. Particle velocity profiles in the riser.

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superficial gas velocity, whereas in the wall region of r/R >0.9, negative velocities are observed.
 Fig. 10 depicts the dimensionless radial particle velocity vp =v p;r profiles at different riser heights. For all the six operating conditions, radial particle velocity distribution is fairly uniform in the solid entrance region, showing the effect of gas distributor. However, only

in a short distance from the gas distributor plate the radial gradients become steep and this increased radial gradient persists over the entire height of the CFB riser. Fig. 11(a) shows axial average particle velocities at six radial positions. Parabolic particle velocity profile persists over the entire column, with average particle velocity decreasing from the column

Fig. 10. Radial particle velocity profiles in the riser.

D. Li et al. / Powder Technology 247 (2013) 235–259

245

a

b

Fig. 11. Axial and cross-sectional average particle velocity profiles in the riser.

center to the wall region. Fig. 11(b) presents the cross-sectional average particle velocities at different heights. With very low velocities in the solid entrance region, particles quickly accelerate. After contacting with fluidization gas passing through the gas distributor, the particles typically take 1–2 m to complete the acceleration process. When compared to around 2–3 m for full development of the solid holdup profiles, particle velocity completes the flow development process faster. In the top section of the column, particle velocity does not increase significantly.
 A comparison between overall average particle velocity v p , average solid velocity ðv s Þ, and the superficial gas velocity (Ug) is provided in Table 2. For operating conditions of Ug and Gs up to 5 m/s and 100 kg/(m 2 · s), average particle velocity is slightly smaller than the superficial gas velocity, with the ratio of v p =U g falling in the range of 0.81 to 0.96. Taking non-uniform solid holdup distributions into account, the average solid velocity is much smaller than the superficial gas velocity, with the ratio of v s =U g falling in the range of 0.66 to 0.78. This partly explains why using Gs and Ug to predict the solid holdup will give lower values than the actual experimental data as seen in Table 1.

Table 2 Comparison between particle velocity and superficial gas velocity in the riser. Ug–Gs

2–50

3–50

5–50

3–100

4–100

5–100

v p [m/s] v s [m/s] v p =U g ½− v s =U g ½−

1.62 1.38 0.81 0.69

2.78 2.23 0.93 0.74

4.32 3.36 0.86 0.67

2.69 1.98 0.90 0.66

3.83 3.14 0.96 0.78

4.15 3.56 0.83 0.71

3.3. CFB riser — solid flux Fig. 12 provides an overview of the local solid flux profiles in the riser under six operating conditions. With particles flowing downward in the wall region (vp b 0), local solid fluxes at near-wall region are negative, whereas maximum local solid fluxes occur at r/R= 0.8–0.9. In the bottom region of the riser, local solid flux can be significantly higher than Gs. Fig. 13 gives a more detailed description on radial solid flux profiles. From Figs. 12 and 13, it is observed that in the centre region of r/R= 0–0.8, radial solid flux distribution is pretty flat. It is also interesting to note that the local solid flux in the column center seems to be closer to the solid circulation rate. Axial average solid fluxes at different radial positions shown in Fig. 14(a) suggest that local solid fluxes at an extended radial region (r/R = 0–0.8) are uniform. With maximum local solid fluxes occur at r/R = 0.8–0.9 and negative values in the wall region, radial gradient of local solid flux is very high in this near-wall region. As shown in Fig. 14(b) the cross-sectional average solid fluxes at different axial positions significantly deviate from the solid circulation rate in the bottom region of the riser reactor. The authors examined the possible reason(s) for this overestimation phenomenon. Apart from the experimental errors, it can be partly explained by the calculation method itself. In this study, time-averaged solid holdup (εs) and particle velocity (vp) are used to calculate the local solid flux (Fs),

T

T

1 1 F s ¼ ρp εs vp ¼ ρp ⋅ ∫ ε s ðt Þdt ⋅ ∫ vp ðt Þdt T0 T0

ð14Þ

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⋅

⋅

⋅

⋅

⋅

⋅

⋅

⋅

⋅

⋅

⋅

⋅

Fig. 12. Local solid flux profiles in the riser.

However, in theory true local solid flux is given by instantaneous solid holdup and instantaneous particle velocity,

or T

F s;true ¼ ρp vp εs þ ρp ∫0 Δvp ðt ÞΔε s ðt Þdt  1 T 1 T F s;true ¼ ρp ⋅ ∫0 vp ðt Þεs ðt Þdt ¼ ρp ⋅ ∫0 vp þ Δvp ðt Þ ðεs þ Δεs ðt ÞÞdt T T ð15Þ

ð16Þ

where Δεs(t) and Δvp(t) are the fluctuation terms for the solid holdup and the particle velocity, respectively. Considering that particle velocity tends to decrease with increasing solid holdup due to the particle

D. Li et al. / Powder Technology 247 (2013) 235–259

G s = 50 kg/(m2 ·s)

⋅

⋅

|

⋅

247

Gs = 100 kg/(m2·s )

⋅

⋅

⋅

F¯ s, r = 49.2

F¯ s, r = 48.3

F¯ s, r = 49.1

F¯ s, r = 107.6

F¯ s, r = 109.3

F¯ s, r = 101.7

F¯ s, r = 50.2

F¯ s, r = 49.8

F¯ s, r = 52.0

F¯ s, r = 99.4

F¯ s, r = 104.6

F¯ s, r = 99.7

F¯ s, r = 49.8

F¯ s, r = 52.7

F¯ s, r = 51.4

F¯ s, r = 97.9

F¯ s, r = 113.6

F¯ s, r = 102.3

F¯ s, r = 56.0

F¯ s, r = 54.3

F¯ s, r = 51.4

F¯ s, r = 97.5

F¯ s, r = 102.5

F¯ s, r = 103.8

F¯ s, r = 59.7

F¯ s, r = 53.7

F¯ s, r = 50.7

F¯ s, r = 102.1

F¯ s, r = 103.3

F¯ s, r = 112.9

F¯ s, r = 54.9

F¯ s, r = 59.2

F¯ s, r = 53.7

F¯ s, r = 100.6

F¯ s, r = 115.2

F¯ s, r = 116.5

F¯ s, r = 55.3

F¯ s, r = 54.6

F¯ s, r = 65.1

F¯ s, r = 101.6

F¯ s, r = 111.3

F¯ s, r = 121.6

F¯ s, r = 63.2

F¯ s, r = 59.5

F¯ s, r = 69.4

F¯ s, r = 121.9

F¯ s, r = 107.5

F¯ s, r = 138.4

F¯ s, r = 83.9

F¯ s, r = 78.3

F¯ s, r = 69.2

F¯ s, r = 139.3

F¯ s, r = 124.0

F¯ s, r = 143.7

F¯ s, r = 84.3

F¯ s, r = 54.6

F¯ s, r = 72.0

F¯ s, r = 101.3

F¯ s, r = 107.2

F¯ s, r = 130.3

Fig. 13. Radial local solid flux profiles in the riser.

clustering phenomenon, the second term in the right-hand side of Eq. (16) becomes negative. Therefore, F s;true b ρp vp εs ¼ F s

ð17Þ

Since the local solid fluxes at the measured radial and axial positions are over-estimated, naturally the calculated cross-sectional average solid flux will be higher than the solid circulation rate. In an attempt to verify this explanation that the fluctuations contribute to the difference between the apparent cross-sectional solid

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⋅

a

⋅

b

Fig. 14. Axial and cross-sectional average solid flux profiles in the riser.

flux and the solid circulation rate, and also to show the magnitude of the fluctuations, for the case of Ug = 3 m/s and Gs = 100 kg/(m 2 · s), the voltage time series V(t) of 1,638,400 data points for each measuring point were divided into N subgroups, yielding N pairs of local solid holdup and particle velocity data. Now it is possible to take account of the fluctuations of the local solid holdups and particle velocities. Derived from Eqs. (14) and (16), the following equation was used to calculate the ratio of the apparent solid flux to the true local solid flux, or the fluctuation factor (α): α¼

Fs ¼ F s;true

1 1þ

N  X

vp;i =vp −1

  εs;i =εs −1

different radial positions, average values ðα z Þ were taken along the same radial positions and are also shown in Fig. 15. It is interesting that in the near-wall region the fluctuation factor is actually smaller than the column center (r/R =0), whereas the local solid flux in the near wall region is significantly higher than that in the column center.

ð18Þ

←

→

α

rR

where N is the total number (N = 10 or 20 in this case) of local solid holdup and particle velocity data pairs (εs,i and vp,i, i = 1 ~ N). For each measurement grid point in the riser reactor, an α was obtained. Further, the cross-sectional average values ðα r Þ at different riser heights were calculated and shown in Fig. 15, which verifies that the fluctuations contribute to an over-estimation of the apparent cross-sectional average solid flux than the solid circulation rate because α > 1. Increasing the number of N from 10 to 20 or less fluctuations dampened by the averaging technique gives a higher level of the fluctuation factor (α). In the meantime, the values of the fluctuation factor become more inconsistent, making it impossible to further extend N to an even higher number so that the calculated apparent solid flux further approaches its true value. To compare the magnitude of the fluctuation factor at

z

i¼1

α

Fig. 15. Cross-sectional and axial average values of the ratio (α) between apparent solid fluxes and the solid circulation rate in the riser (Ug =3 m/s and Gs =100 kg/(m2 ·s)), where z is the riser height, r/R is dimensionless radial position.

D. Li et al. / Powder Technology 247 (2013) 235–259

3.4. CFB downer — solid holdup Figs. 16 and 17 plot the solid holdup profiles at different radial and axial positions in the CFB downer. Six operating conditions are Ug = 2, 3, 5 m/s and Gs = 50, 100 kg/(m 2 · s). For each axial position, solid holdup in the wall region is higher than that in the center region, and decreases with height (Set z = 0 at the top gas distributor of the CFB downer). A lower superficial gas velocity and a higher solid circulation rate give higher solid holdup.

From Fig. 18(a) which plots the axial average solid holdups at different radial positions, a more uniform radial solid holdup distribution is observed in the center region of the downer with r/R up to 0.5–0.6 than the near-wall region. Cross-sectional average solid holdup profiles at different axial positions are presented in Fig. 18(b). With the increase of downer height, cross-sectional average solid holdup decreases rapidly in the flow developing zone or top section of the downer, and then levels off in the fully developed region or lower section of the downer. The length of the flow developing

⋅

ε

ε

⋅

⋅

ε

ε

⋅

⋅

ε

⋅

ε

249

Fig. 16. Solid holdup profiles in the downer.

250

D. Li et al. / Powder Technology 247 (2013) 235–259

G s = 50 kg/(m2 ·s)

|

Gs = 100 kg/(m2·s )

ε ε¯ s, r = 0 .0071 ε¯ s, r = 0 .0074 ε¯ s, r = 0 .0064 ε¯ s, r = 0 .0131 ε¯ s, r = 0 .0111 ε¯ s, r = 0 .0094

ε¯ s, r = 0 .0074 ε¯ s, r = 0 .0072 ε¯ s, r = 0 .0066 ε¯ s, r = 0 .0148 ε¯ s, r = 0 .0114 ε¯ s, r = 0 .0096

ε¯ s, r = 0 .0079 ε¯ s, r = 0 .0082 ε¯ s, r = 0 .0062 ε¯ s, r = 0 .0150 ε¯ s, r = 0 .0115 ε¯ s, r = 0 .0107

ε ε

ε¯ s, r = 0 .0085 ε¯ s, r = 0 .0088 ε¯ s, r = 0 .0068 ε¯ s, r = 0 .0149 ε¯ s, r = 0 .0121 ε¯ s, r = 0 .0114

ε¯ s, r = 0 .0088 ε¯ s, r = 0 .0085 ε¯ s, r = 0 .0071 ε¯ s, r = 0 .0158 ε¯ s, r = 0 .0129 ε¯ s, r = 0 .0122

ε¯ s, r = 0 .0093 ε¯ s, r = 0 .0094 ε¯ s, r = 0 .0071 ε¯ s, r = 0 .0167 ε¯ s, r = 0 .0142 ε¯ s, r = 0 .0147

ε¯ s, r = 0 .0096 ε¯ s, r = 0 .0096 ε¯ s, r = 0 .0072 ε¯ s, r = 0 .0179 ε¯ s, r = 0 .0160 ε¯ s, r = 0 .0156

ε¯ s, r = 0 .0138 ε¯ s, r = 0 .0113 ε¯ s, r = 0 .0093 ε¯ s, r = 0 .0196 ε¯ s, r = 0 .0210 ε¯ s, r = 0 .0174

ε¯ s, r = 0 .0250 ε¯ s, r = 0 .0180 ε¯ s, r = 0 .0115 ε¯ s, r = 0 .0278 ε¯ s, r = 0 .0230 ε¯ s, r = 0 .0218

Fig. 17. Radial solid holdup profiles in the downer.

zone is approximately 1–2 m, and this length decreases with increased superficial gas velocity and reduced solid circulation rate. Radial gradients of the cross-sectional average solid holdup for 3 operating conditions, Ug [m/s] − Gs [kg/(m 2 · s)] = 2–50, 3–50 and 3–100, were calculated and plotted versus downer elevations as shown in Fig. 19. The same trend as in CFB riser is observed: At low

superficial gas velocities and high solid circulation rates, the radial gradient of εs =ε s;r increases to a maximum and then levels off, while at a higher superficial gas velocity, maximum radial gradient occurs at the solid inlet, then decreases and levels off. However, when comparing Fig. 19 with Fig. 8, radial solid holdup gradients in the CFB downer (with typical values of 1 to 1.5) are significantly smaller

D. Li et al. / Powder Technology 247 (2013) 235–259

251

ε

a

ε

b

Fig. 18. Axial and cross-sectional average solid holdup profiles in the downer.

than those in the riser (with typical values of 1.5 to 3.5). In addition, the radial gradients are more uniform along the downer column. Operating conditions have much less effect on radial gradients in the downer, where three operating conditions have very close radial gradient profiles, while in the riser the changes are significant. Table 3 provides a comparison between the measured average solid holdups (ε s , defined by Eq. (6)), and the predicted values based on the superficial gas velocity (Ug), average particle velocity (v p , defined by Eq. (10)), and average solid velocity ( v s , defined by Eq. (11)). The

measured solid holdups are significantly smaller than those predicted values, especially under low superficial gas velocities and solid circulation rates. This is contrary to the trend in the riser, where the measured solid holdups are approximately 1.5 times of the predicted values. In addition, the solid holdup values predicted from the average particle velocity and the average solid velocity are very close, showing that the solid holdups are more uniformly distributed over the entire downer column. Predictions based on average solid velocities are only slightly less than the experimental values. 3.5. CFB downer — particle velocity Fig. 20 provides an overview of the particle velocity profiles at the six operating conditions in the downer. Fig. 21 depicts the radial par
 ticle velocity vp =v p;r profiles at different elevations. From Figs. 20 and 21, it is observed that in the solid entrance region, maximum particle velocity occurs in the column center. With the development of solid flow, particles have lower velocities in the column center and Table 3 Comparison between measured and predicted solid holdups in the downer.

Fig. 19. Radial solid holdup gradients at different axial positions in the downer.

Ug–Gs

ε s ½−

ε s =ε s1 ½−⁎

ε s =ε s2 ½−⁎

ε s =ε s3 ½−⁎

2–50 3–50 5–50 2–100 3–100 5–100

0.0182 0.0122 0.0073 0.0365 0.0243 0.0146

0.52 0.74 0.98 0.45 0.57 0.87

1.11 1.11 1.11 1.03 1.06 1.08

1.11 1.11 1.10 1.04 1.07 1.08

      ⁎ Definitions: ε s1 ¼ Gs = ρp U g ; ε s2 ¼ Gs = ρp v p ; ε s3 ¼ Gs = ρp v s .

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⋅

⋅

⋅

⋅

⋅

⋅

Fig. 20. Particle velocity profiles in the downer.

the near-wall regions, with maximum particle velocity taking place at r/R = 0.8–0.9. With maximum particle velocity occurs in the center of the solid entrance region, and later in the wall region for the fully developed flow zone, a combined result is to exhibit a very uniform profile for the axial average particle velocity at different radial positions, as shown in Fig. 22(a). Fig. 22(b) presents the cross-sectional average particle velocity at different elevations. With initial velocities close to the superficial gas velocity in the solid entrance region, particles further accelerate until the solid flow is fully developed. The particles

typically take 1–2 m to complete the acceleration process in the riser, whereas in the downer the acceleration process is greatly extended. This length is longer than the height of the flow development of the solid holdup. After full flow development, particle velocity does not increase significantly.
 A comparison between entire-bed average particle velocity v p , average solid velocity ðv s Þ, and superficial gas velocity (Ug) is provided in Table 4. For the operating conditions of Ug and Gs up to 5 m/s and 100 kg/(m 2 · s), v p and v s are very close, showing a more uniform solid holdup distribution in the downer. Average particle velocities

D. Li et al. / Powder Technology 247 (2013) 235–259

253

Fig. 21. Radial particle velocity profiles in the downer.

are much higher than the superficial gas velocities, with the ratio of v p =U g falling in the range of 1.1 to 2.1 due to extra particle acceleration momentum from the gravity force, whereas for the riser this ratio is only at 0.81–0.96 where the gravity force acts against the particle upflow. Increasing superficial gas velocities and solid circulation rates decrease the ratio of v p =U g .

3.6. CFB downer — solid flux Fig. 23 provides an overview of the local solid flux profiles in the downer, while Fig. 24 gives detailed radial solid flux profiles. Since the solid holdups and the particle velocities in the near wall region are higher, the solid fluxes in this region are higher than those in

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a

b

Fig. 22. Axial and radial average particle velocity profiles in the downer.

the column center, especially at a low superficial gas velocity and a high solid circulation rate. The radial gradients are noticeably higher than those observed in the riser which are shown in Fig. 12. It is also observed that with the increase of distance from the gas distributor, the radial gradient of the local solid fluxes intensifies. Axial average solid fluxes profiles at different radial positions shown in Fig. 25(a) suggest that the local solid fluxes are less uniform than those in the riser where for an extended radial region (r/R= 0–0.8) the radial solid flux is uniform. At Ug = 2 m/s and Gs = 100 kg/(m 2 · s), solid fluxes in the downer are only uniform for a very limited center region of r/R= 0–0.4. However, uniform cross-sectional solid fluxes at different axial positions are observed in Fig. 25(b). In the bottom region, solid flux is only slightly higher than the solid circulation rate, whereas in the riser, this deviation is significant. When applying the same theory formulated in Section 3.3 to explain the deviation from the measured cross-sectional average solid flux and the solid circulation rate, it is important to note that the second term in the right hand side of Eq. (16) will be positive (or Fs b Fs,true) if particle cluster formation is a severe problem: A denser (heavier) particle

Table 4 Comparison between particle velocity and superficial gas velocity in the downer. Ug–Gs

2–50

3–50

5–50

2–100

3–100

5–100

v p [m/s] v s [m/s] v p /Ug [−] v s /Ug [−]

4.26 4.28 2.13 2.14

4.50 4.51 1.50 1.50

5.64 5.62 1.13 1.12

4.60 4.68 1.53 1.56

5.63 5.62 1.41 1.42

6.24 6.25 1.25 1.25

cluster tends to flow faster in the downward direction in the CFB downer so that a higher particle velocity comes with an increased solid holdup. However, the solid concentrations in the CFB downer reactor in this study are pretty dilute so that the effect of the fluctuations is minimal. Calculation results showed that the fluctuation factor (α) is only slightly deviated from 1, 0.98 b α b 1.02. Therefore, the differences between the very close values of the cross-sectional average solid flux and the circulation rate are mainly due to experimental error and the dynamic nature of the solid flow in the CFB downer reactor.

3.7. Comparison between flow structures in CFB riser and downer A comparison of the average solid holdup, particle velocity, solid velocity, and solid flux over the entire CFB riser and downer is provided in Fig. 26. Under the same operating conditions, the CFB riser has a much higher solid holdup than the downer. The ratio of these two quantities has its maximum at a low superficial gas velocity and solid circulation rate, i.e., at Ug = 2 m/s and Gs = 50 kg/(m 2 · s), where the average solid holdup in the riser can be three times higher than that in the downer. Average particle velocity in the downer is much higher than the superficial gas velocity (at Ug = 2 m/s and Gs = 100 kg/(m 2 s), it is 2.3 times higher), whereas in the riser the average particle velocity is lower than superficial gas velocity. The main reason is that the gravity force acts against particle acceleration in the riser while for it in the downer. For the CFB riser, the ratio of vp/Ug increases with increasing superficial gas velocity and reduced solid circulation rate,

D. Li et al. / Powder Technology 247 (2013) 235–259

255

Fig. 23. Local solid flux profiles in the downer.

whereas for the downer this ratio increases with reduced superficial gas velocity and increasing solid circulation rate. The average solid velocities in the riser and downer showed a similar trend with that of the average particle velocity. The main difference lies in that, in the riser the average solid velocity is much lower than the particle velocity, whereas in the downer they are about the same. A comparison of the ratio between the average solid flux to solid circulation rate shows that, the riser has a slightly higher ratio than that in the downer, where the ratio approaches to unity.

The cross-sectional average profiles for solid holdup, particle velocity, and local solid flux at different elevations in the riser and the downer are presented in Fig. 27. From the solid holdup profiles, it is observed that the length of flow developing zone is longer in the riser (2–3 m) than that in the downer (1–2 m). The length decreases with increasing superficial gas velocity and reduced solid circulation rate. Considering from the particle velocities, the acceleration process completes in 1–2 m in the riser, whereas in the downer, the acceleration process is greatly extended. In the entrance region of

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D. Li et al. / Powder Technology 247 (2013) 235–259

G s = 50 kg/(m2 ·s)

⋅

|

Gs = 100 kg/(m2·s )

⋅

⋅

⋅

⋅

⋅

F¯ s, r = 50.1

F¯ s, r = 51.9

F¯ s, r = 53.2

F¯ s, r = 99.4

F¯ s, r = 100.2

F¯ s, r = 101.5

F¯ s, r = 50.7

F¯ s, r = 50.1

F¯ s, r = 54.2

F¯ s, r = 103.5

F¯ s, r = 100.5

F¯ s, r = 101.2

F¯ s, r = 50.8

F¯ s, r = 53.9

F¯ s, r = 49.6

F¯ s, r = 103.9

F¯ s, r = 102.0

F¯ s, r = 100.1

F¯ s, r = 53.7

F¯ s, r = 57.8

F¯ s, r = 52.7

F¯ s, r = 101.5

F¯ s, r = 103.1

F¯ s, r = 105.1

F¯ s, r = 51.2

F¯ s, r = 53.4

F¯ s, r = 55.9

F¯ s, r = 98.9

F¯ s, r = 100.6

F¯ s, r = 102.8

F¯ s, r = 51.9

F¯ s, r = 55.9

F¯ s, r = 56.7

F¯ s, r = 102.8

F¯ s, r = 105.6

F¯ s, r = 107.0

F¯ s, r = 50.0

F¯ s, r = 51.1

F¯ s, r = 52.1

F¯ s, r = 101.0

F¯ s, r = 108.9

F¯ s, r = 104.5

F¯ s, r = 56.3

F¯ s, r = 56.2

F¯ s, r = 59.9

F¯ s, r = 103.7

F¯ s, r = 98.4

F¯ s, r = 97.4

F¯ s, r = 54.3

F¯ s, r = 57.0

F¯ s, r = 63.6

F¯ s, r = 99.9

F¯ s, r = 100.4

F¯ s, r = 115.3

Fig. 24. Radial local solid flux profiles in the downer.

the riser and the downer, the cross-sectional net solid flux deviates heavily from the solid circulation rate. When gas solid flow is fully developed, they become very close. Determination of the length of flow development from solid flux produces very similar results to that from the axial solid holdup profiles.

4. Conclusions Using optical fiber probes, hydrodynamic studies on solid holdup, particle velocity, and solid flux were performed in a 76 mm i.d. CFB riser and downer. A complete mapping of the solid holdup, particle

D. Li et al. / Powder Technology 247 (2013) 235–259

⋅

a

⋅

b

Fig. 25. Axial and radial average solid flux profiles in the downer.

Fig. 26. Comparison of overall mean solid holdup, particle velocity, solid velocity, and solid flux in the riser and downer.

257

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D. Li et al. / Powder Technology 247 (2013) 235–259

a)

ε

⋅

ε

⋅

b)

Fig. 27. Determination of length of flow developing zone in the riser and downer from cross-sectional average solid holdup, particle velocity, and solid flux profiles.

velocity and solid flux profiles at different radial and axial positions were provided. Under the operating conditions of superficial gas velocities ranging from 2 to 5 m/s and solid circulation rates up to 100 kg/(m 2 · s), axial solid holdup profiles in the riser and the downer could be approximated by an exponential decay function: the solid holdup was high in the flow developing region and gradually decreased downstream in the fully developed region. The radial gradients of the solid holdup profiles in the riser were much higher than those in the downer, showing that the downer had much more uniform solid distribution. The average solid holdup for the entire riser reactor was about 1.5 times higher than the

predicted value from Gs/(ρpUg). However, for the downer reactor this ratio dropped to 0.45–0.98 which increased with increasing superficial gas velocity and decreasing solid circulation rate. Solid flow developed much slower in the riser than in the downer. Negative particle velocity was observed in the near-wall region for nearly the entire height of the riser. The average particle velocity for the entire riser was 0.8–0.96 times higher than the superficial gas velocity, and increased with increasing superficial gas velocity and decreasing solid circulation rate. However, in the downer the average particle velocity was 1.13–2.13 times higher the superficial gas velocity, and increased with both superficial gas velocity and solid circulation rate.

D. Li et al. / Powder Technology 247 (2013) 235–259

High local solid fluxes were observed in the near wall region of the CFB riser and downer reactor, whereas in the column center region the local solid flux profiles are pretty flat. Over-estimation of the calculated cross-sectional average solid flux over the solid circulation rate in the CFB riser was attributed to the fluctuations of the solid holdup and particle velocity. Nomenclature a,b fitting coefficient [−] f calibration function for optical fiber probe Fs solid flux [kg/(m 2 s)] Fs average solid flux in the entire column [kg/(m 2 s)] F s;r cross-sectional average solid flux [kg/(m 2 s)] F s;z axial average solid flux [kg/(m 2 s)] Gs solid circulation rate [kg/(m 2 s)] H height [m] Le effective distance between light-receiving fiber A and B [m] m mass of the solid particles [kg] N number of subgroups for voltage time series data [−] r/R dimensionless radial sampling positions S summed square of residuals [−] t time [s] T time interval [s] Ug superficial gas velocity [m/s] vp particle velocity [m/s] vp average particle velocity in the entire column [m/s] v p;r cross-sectional average particle velocity [m/s] v p;z axial average particle velocity [m/s] vs average solid velocity in the entire column in Eq. (11) [m/s] v s;r cross-sectional average solid velocity in Eq. (11) [m/s] v s;z axial average solid velocity in Eq. (11) [m/s] V voltage [volt] V average voltage [volt] V(t) voltage time series [volt] Vc volume of the measuring column section [m 3] z axial coordinate, or distance from gas distributor [m]

Greek letters α fluctuation factor or the ratio between the apparent and true solid fluxes [−] εs solid holdup [−] εs(t) local instantaneous solid holdup [−] εs average solid holdup in the entire column [−] ε s;r cross-sectional average solid holdup [−] ε s;z axial average solid holdup [−] ρb, ρp bulk density, apparent particle density [kg/m 3] σ standard deviation τ lag time [s] ϕ12 cross-correlation function Δvp(t) fluctuation term for particle velocity [m/s] Δεs(t) fluctuation term for solid holdup [−]

259

Subscripts 1, 2 channel 1 and 2 of optical fiber probe g gas p particle r radial s solid

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