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Hydrodynamics of an i-CFB deNOx reactor
Powder Technology 251 (2014) 25–36
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Hydrodynamics of an i-CFB deNOx reactor Xingxing Cheng, Xiaotao T. Bi ⁎ Fluidization Research Centre, Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver V6T 2K9, Canada
a r t i c l e
i n f o
Article history: Received 10 May 2013 Received in revised form 12 September 2013 Accepted 11 October 2013 Available online 21 October 2013 Keywords: i-CFB Solid circulation rate Gas bypass Hydrodynamic model Optical fibre
a b s t r a c t Hydrodynamics of an i-CFB (internal circulating fluidized bed) deNOx reactor has been studied by both experiments and modeling. Gas bypass was investigated by CO2 tracer method, and solid circulation rate was measured using an optical fibre probe at bed solid loadings of 3.3 kg and 2.275 kg. Radial profiles of bed voidage and solid velocity were discussed in detail. A hydrodynamic model was developed based on mass and pressure balances. Discharging coefficient Cs was extracted from fitting the experimental data and an average value of 0.167 was taken for model simulation. The model could well capture the characteristics of the solid flow and gas flow distribution, and could serve as a useful tool for the design and simulation of the i-CFB deNOx reactor system. © 2013 Elsevier B.V. All rights reserved.
1. Introduction As a promising deNOx technology, hydrocarbon selective catalytic reduction (HC-SCR) has been widely studied since the mid 1980s. Due to the challenges in suppressing the catalytic oxidation of hydrocarbons by oxygen present in the combustion flue gases, research has been focused on how to improve the selectivity of the catalyst toward NOx reduction. To alleviate the negative impact of oxygen on the deNOx reactor performance, a dual adsorption and reduction system has been proposed [1] in which the NOx adsorption takes place in a separate column, decoupled from the catalytic reduction which takes place in another column. To facilitate the continuous adsorption–reduction operation and in-situ catalyst regeneration, a novel HC-deNOx internal circulating fluidized bed (i-CFB) reactor was recently proposed by Yang and Bi [1] in which NOx is adsorbed onto the catalyst surface in the adsorption zone, and the adsorbed NOx is reduced catalytically in the reduction zone, with the catalyst circulating between the adsorption and reduction zones. The performance of the i-CFB reactor is expected to be impacted significantly by the hydrodynamics in the i-CFB, including both the gas bypass between the core and the annulus regions and the internal solid circulation, which should be well studied in order to properly design the reactor and suitable operating conditions as well as to provide data for modeling such a reactor. Several studies have been reported on the hydrodynamics of i-CFB reactors, mainly focused on the measurement of solid circulation rates [2,3] and the development of correlations for predicting the solid circulation rate [4,5]. These ⁎ Corresponding author. Tel.: +1 604 822 4408; fax: +1 604 822 6003. E-mail address: [email protected] (X.T. Bi). 0032-5910/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2013.10.016
empirical or semi-empirical models could not be applied directly to i-CFBs with different configurations. In this study, the performance of the reactor was investigated both experimentally and analytically. Gas bypassing, bed expansion and solid circulation rate in a deNOx i-CFB reactor were tested in a cold model unit. The solid circulation rate was then predicted based on pressure and mass balance equations. 2. Experiment details 2.1. i-CFB configuration An i-CFB reactor was constructed with the configuration shown in Fig. 1. The dimensions of the model unit are listed in Table 1. There was a draft tube in the reactor. Gas was fed to both the draft tube and annulus at different velocities and the bed particles circulated between the draft tube and annulus. Building air was used as fluidizing gas. Zeolite particles were tested in this i-CFB with the properties given in Table 2. 2.2. Bed expansion Bed voidage is an important flow structure parameter that determines the pressure drop in i-CFB. Here, bed expansion was investigated in a fluidized bed with the same dimensions as the i-CFB reactor as shown in Fig. 1, but with a flat perforated plate as the distributor and without the draft tube. Building air was used as the fluidizing gas, and zeolite powders were used as the bed material. Pressure drop was measured between points D1 and D3 at different gas inlet velocities and the average voidage in the bed was calculated according to
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X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
Sampling, gas mixture
Sampling, outlet of draft tube
Vent
Cyclone
Building air
Bag house Sampling, outlet of annulus
D5
D4
CO2
Vent
D3
D2
D1
Gas Analyzer
Computer
Sampling, inlet of annulus Building air
Sampling, inlet of draft tube Fig. 1. Schematic of the i-CFB reactor.
Eq. (1). Losses due to acceleration and frictions between gas/particle mixture and wall surfaces were neglected because of the low superficial gas velocities (b0.5 m/s) used in this study. ΔP ¼ ρp gð1−εÞH:
ð1Þ
inlet of the draft tube and the annulus being monitored. Gas bypass ratios, which are defined in Eq. (2), were then calculated based on the mass balance of tracer CO2. RDA ¼
FDA F ; R ¼ AD : Fd0 AD Fa0
ð2Þ
2.3. Gas bypass 2.4. Solid circulation rate The gas bypass between the draft tube and annulus was studied by Yang [6] using CO2 tracer method with the bed loaded with 3.3 kg zeolite powders. At a given steady state operating condition, continuous CO2 tracer was injected into the inlet gas flow of the annulus, with CO2 concentrations at the outlet of the draft tube and the annulus, and the
Table 1 Dimensions of the cold model i-CFB unit. Item
Dimension
Draft tube diameter, mm Draft tube length, mm Column diameter, mm Column height, mm Freeboard diameter, mm Freeboard height, mm Annulus gas distributor opening ratio Holes on the distributor Gas nozzle diameter, mm
50.8 (I.D.), 63.5 (O.D.) 1016 101.6 (I.D.), 114.3 (O.D.) 1092 254.0 (I.D.), 266.7 (O.D.) 508 2.1% 52 holes of 1.6 mm diameter 34.9 (I.D.), 38.1 (O.D.)
Experimentally, solid circulation rate can be determined from the vertical flux of particles passing through one or more of the regions using a number of methods [7] such as multi-fiber optical probes, radioactive tracer particles, and hot solid tracer techniques. In the
Table 2 Particle properties. Bed material
Bulk density Average particle Umf (m/s)a (kg/m3) diameter (mm)
ZSM-5 powder 968
0.155
0.01
Uc (m/s)b
Ut (m/s)c
0.38
0.90
Note: a: measured; b: measured. c: calculated from correlation: 2
3−1
0:591 7 6 18 Ut ¼ 4 2 þ 0:5 5 dp dp
2 ;
dp ¼ dp 4
31=3 ρg ρp −ρg g 5 ; μ2
2 31=3 ρ2g 5 : Ut ¼ Ut 4 μ ρp −ρg g
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
0.9
0.8
Voidage, ε
current study, optical fiber probes were used to measure solid flux for fine catalyst particles. A particle velocity analyzer (PV-4A) manufactured by the Institute of Process Engineering, Chinese Academy of Sciences, was used for the measurement, which included an optical fibre probe, a light conversion box, a data acquisition board and a program for sampling and recording data into the computer for analysis. This technique has been widely applied to determine particle velocity and voidage in fluidized beds [8,9]. The optical fibre probe used in the current work is shown in Fig. 2. There are three bundles of fibres of 15 μm in diameter. Each bundle has a diameter of about 1 mm. The central bundle of fibres is for light projection, whereas the other two act as light receivers, corresponding to two sampling channels A and B. The intensity of the signals from both channels is in V. The basic mechanism to measure the velocity is to calculate the time lag, τ, between the moments when the particles pass the two light receivers by cross-correlation method. The particle velocity, Up, can then be calculated as: Up = Le / τ. The probe was calibrated employing the actual particles used in this study. A rotating plate with glued particles was driven by a motor. Particles rotated together with the rotating plate, at a preset particle velocity, Up, and the time lag, τ, between the two channels of the probe was measured by the cross-correlation of the signals from the two channels. The effective distance was then calculated by multiplying the particle rotating velocity and the time lag. In a typical measurement, two series of signals were recorded from the system, which represent the intensity of the reflected light through the two channels. These data series were divided into several groups, with cross-correlation being carried out on each group to find the time lag between the two channels. For the measurement of local bed voidage, the optical fibre probe was calibrated using the mixture of bed particles and coke particles at different volume fractions of coke, with the calibration curve shown in Fig. 3. The local voidage was then correlated with the probe reading (the average reading of both channels) by an exponential equation (see Fig. 3). Details on the optical fibre probe calibration by the mixture of two particle components can be found in [8,10]. The optical fibre probe captures the motions of very small amount of particles that pass by the probe tip. In the dense fluidized bed, no matter bubbling bed or turbulent bed, solids move both upward and downward as bubbles/voids pass the measurement region. When captured by the optical fibre probe, solid velocity values are scattered, ranging from positive (down-flowing solids) to negative values (up-flowing solids associated with bubbles). This will make the estimation of net solid flux or average particle velocity very challenging and lead to low accuracy of the net solid flux measurement. If the filled bed height in the annulus is lower than the draft tube, a particle raining-down region exists at the top of the annulus. It is located in the upper region of the fluidized bed in the annulus. It could be expected that most of the solids fall downward in this region. Therefore, the measurement of solid flux by the optical fibre probe could be more accurate because of the more uniform solid movements in this region. Point D4 in Fig. 1, which is 950 mm above the bottom, is the most possible location for the particle raining-down region and is therefore selected to
27
(-0.0157*V)
ε=0.775*e 2 R =0.99
+0.428
0.7
0.6
0.5
0.4 40
80
120 Voltage, (mV)
160
Fig. 3. Voidage calibration of the optical probe (symbols: experimental data, line: correlation).
insert the optical probe. Both local solid velocity and local voidage were measured along the radial direction at an interval of 2.5 mm. The average solid flux in the annulus could be calculated by the integration of local solid flux along the radial direction. Z Gs ¼ ρp
r2 r1
πð1−εÞ Up 2rdr:
ð3Þ
The particle backmixing in fluidized bed can affect the particle velocity measurement, and also its influence is difficult to be determined. In this work, the instantaneous particle velocity signals were obtained over a period of time, which then were averaged to give the average solid velocity, avoiding the effect of the particle backmixing on the particle velocity measurement [11]. 3. Hydrodynamics model of i-CFB 3.1. Mass and pressure balance equations In an i-CFB, the internal circulation of solids is created by the pressure difference between the draft tube and the annulus operating at different superficial gas velocities. The solid circulation rate dictates both the gas and solid residence time in each region and hence the extent of NOx adsorption and catalytic NOx reduction. There are several correlations in the literature, which link the bed hydrodynamics to the solid circulation rate [2,4,12]. Because the solid circulation rate is influenced by the bed geometry in addition to fluid and particle properties and gas velocity, those correlations from the literature could not be used directly when the geometry of the reactor is changed. In this research, the solid circulation rate is estimated based on the mass and momentum balances in the iCFB reactor. Solid mass balance equations include the conservation of total solid inventory in the system and solid circulation rate balance between the draft tube and the annulus: Mloading ¼ Ma þ Md ¼ ρp ð1−εa ÞAa Ha þ ρp ð1−εd ÞAd Hd Gs ¼ ρp Up;a ð1−εa Þ ¼ ρp Up;d ð1−εd Þ
Fig. 2. Details of the tip of the optical fibre probe for particle velocity measurement.
200
Aa : Ad
ð4Þ ð5Þ
The driving force of the solid circulation is the pressure difference between the annulus and the draft tube, subtracting the pressure drop
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X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
across the orifice connecting them. The pressure balance in the whole system is ΔPa ¼ ΔPd þ ΔPor :
ð6Þ
3.2. Pressure drop calculation In a fluidized state, the pressure drop could be expressed by Eqs. (7) and (8), which consist of the pressure drops due to gravity, solid acceleration, fluid–wall friction and particle–wall friction. 2
ΔPa ¼ Ha ð1−εa Þρp g−0:5ð1−εa Þρp Up;a þ Hdraft‐tube Fgw −Hdraft‐tube Fpw
ð7Þ
2
ΔPd ¼ Hd ð1−εd Þρp g þ 0:5ð1−εd Þρp Up;d þ Hdraft‐tube Fgw þ Hdraft‐tube Fpw
a
ð8Þ
b
c
d
Fig. 4. Schematic of four i-CFB flow modes and the effective bed height.
where Ha and Hd are the effective bed heights in the annulus and draft tube, respectively. Fgw and Fpw are the gas–wall and the particle–wall frictional force per unit volume of the column, respectively. In the case of gas velocities lower than 6 m/s, and column diameter in excess of 4 cm without bends, the contribution of gas–wall friction Fgw could be neglected [13]. Konno and Saito's equation [14], which was developed for relatively low concentration of solids in vertical column, was used to calculate the solid–wall friction. Fpw ¼ 0:057 Gs ðg=Dd Þ
0:5
ð9Þ
One should note that gas velocity in the annulus region is lower than in the draft tube. So solid concentration in the annulus is higher. The use of the Konno and Saito equation may lead to the inaccuracy of pressure drop calculated. However, wall friction could be neglected at very low gas velocities. So the uncertainty in the estimated pressure drop from the Konno and Saito equation could be negligible. The pressure drop across the orifice between the bottoms of annulus and draft tube could be correlated with solid circulation rate Gs. For mechanical valves like slide valves where the solid flow is controlled by changing the opening area, the pressure drop across the control valve and solid flux can be related by [15]: Gs ¼ Cs
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Aor u u2ρp ð1−εa ÞΔPor t 2 : Aa 1− Aor
ð10Þ
Aa
The discharge coefficient Cs in Eq. (10) has values typically between 0.2 and 0.6 with an average value of 0.4, although it depends on the geometrical configuration, orifice edge parameters and the Dor/dp ratio. So Cs needs to be fitted from the experimental data for specific configurations.
Hd0 ¼ Hdraft‐tube Ha0 ¼
Mloading −ρp ð1−εd ÞHd0 Ad ρp ð1−εa ÞAa
ð11Þ ð12Þ
ΔPa0 ¼ ρp ð1−εa ÞgHa0
ð13Þ
ΔPd0 ¼ ρp ð1−εd ÞgHd0 :
ð14Þ
If ΔPa0 b ΔPd0, there is no solid circulation. This regime is of little interest in the operation of i-CFB. However, this procedure could be used to identify whether there is solid circulation or not. It should be noted that if the gas velocity in the annulus is larger than that in draft tube, particles could be entrained to the annulus, forming a reverse solid circulation. However, this case is not considered for the i-CFB yet and will not be discussed here. • When the solid loading and/or the gas velocity in the draft tube are increased, particles fill up the draft tube and start to circulate to the annulus region. This corresponds to flow pattern (b) in Fig. 4. In this mode, the effective bed height in the draft tube is the same as the draft tube height, and the effective annulus bed height could be calculated by overall mass balance. • If the particle loading and/or gas velocity are further increased, the annulus bed height could exceed the height of the draft tube and flow pattern (c) in Fig. 4 is established. In this case, the effective annulus bed height can still be calculated by mass balance and the effective draft tube bed height is equal to the effective annulus bed height. An initial guessed value of effective draft tube height should be taken to start the mass balance calculation, and the mass balance equations are then iterated to obtain the final bed height values.
3.3. Effective bed height To obtain the effective bed height for Eqs. (7) and (8), the flow in the i-CFB was categorized into four different operating modes as shown in Fig. 4. It should be noted that the flow mode is classified here in such a way to facilitate the calculation of effective bed height and is different from the flow patterns reported in the literature [16]. • If there is no sufficient bed solid loading and the gas velocity inside the draft tube is lower than the particle transport velocity, the draft tube could not be fully filled with particles and a flow pattern in Fig. 4(a) will be created without internal solid circulation. The initial pressure drops in the two zones could be obtained by
Hd ¼ Ha0 Ha ¼
Mloading −ρp ð1−εd ÞHd Ad ρp ð1−εa ÞAa
ð15Þ ð16Þ
• When the bed loading or gas velocity is further increased, the annulus dense bed becomes too high and the gas jet on top of the draft tube becomes unstable or can no longer penetrate through. As a result, flow pattern (d) in Fig. 4 is formed. The vertical jet penetrate length
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
29
1.0
could be estimated in the same way as jet penetration depth in spoutfluid bed [17].
Experiment Cai's correlation
0.9 2
ð17Þ
The effective draft tube bed height, Ld, is the sum of draft tube length and jet height, and the effective annulus bed height La equals Ld. The detailed criteria and calculation procedures for each of the four flow patterns are given in Table 3.
R =0.953
Voidage, ε
Lj ρg U2d ¼ 11:52 Da ρp −ρg gDd
!0:1966 0.8
0.7
0.6
3.4. Modeling procedure 0.5
A correlation was first developed for the solids discharge coefficient Cs from measured solid circulation rates using the following procedure. For given feeding gas velocities in the annulus and draft tube (Ua0 and Ud0) and measured solid circulation rate Gs, the gas bypass ratios (RAD and RDA) were calculated by the correlations based on experimental data. Actual gas velocities in the annulus and the draft tube (Ua and Ud) were then obtained based on the gas feed rates and gas bypass ratios. The Cai equation was used to calculate voidages (εa and εd). Effective bed heights (Ha and Hd) were then obtained following the methods described in Section 3.3 and Table 3. Particle velocities (Up,a and Up,d) were calculated based on measured Gs by Eqs. (4) and (5). The pressure drop across the annulus and the draft tube (ΔPa and ΔPd) could now be obtained from Eqs. (8) and (9), and the pressure drop through the orifice was then obtained from Eq. (6). Using Eq. (12), solid discharge coefficient Cs was determined for a given operating condition. The correlation (an average value was taken) for solid discharge coefficient was subsequently developed which was then used for solid circulate rate (Gs) simulation by iteration. An initial value Gs0 is first assumed. The feeding velocities in the annulus and draft tube (Ua0 and Ud0) are known and are the only known operating parameters. Following the same procedure as used for developing the Cs correlation, we could calculate other parameters such as gas bypass ratios (RAD and RDA), actual gas velocities in the annulus and draft tube (Ua and Ud), particle velocities (Up,a and Up,d) and pressure drop in the annulus and the draft tube (ΔPa and ΔPd). Pressure drop through the orifice can be calculated from Eq. (6). Then by Eq. (12), a new solid circulation rate Gs is obtained. If the new Gs value is different from the previous value more than a tolerant value, the iteration will be repeated. A finally solid circulation rate could be obtained when Gs0–Gs b 0.1 kg/m2·s.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Inlet gas velocity, U (m/s) Fig. 5. Measured voidage data for ZSM-5 powders and comparison with the Cai [19] correlation (symbols: experimental data, line: correlation).
Cai [18] modified Babu's correlation [19] to fit their bed expansion data obtained in both bubbling and turbulent fluidization regimes. The bubble size and bubble rise velocity are estimated, respectively, as, 0:8 0:06
0:42
ð18Þ
:
ð19Þ
Db ¼ 0:21 H f P ðU−Umf Þ exp h i −4 2 2 −1:4 10 P −0:25ðU−Umf Þ −0:1 PðU−Umf Þ 0:5
Ub ¼ U−Umf þ 0:71ðgDb Þ
Gas flow rate in the bubble phase is calculated as Fb ¼ Ub δb A ¼ YðU−Umf ÞA
ð20Þ
with Y being correlated to 0:26
Y ¼ 0:108 Hs
ðU−Umf Þ
0:09 −0:48 −0:19 dp ρp
ð21Þ
where Hs = Hmf/(1 − εmf). By assuming no particles inside the bubble phase, the bubble phase fraction (δb) and the bed voidage in the fluidized bed could then be calculated as:
4. Results and discussion
δb ¼
YðU−Umf Þ Ub
ð22Þ
4.1. Bed expansion characteristics
ε ¼ δb þ ð1−δb Þεmf :
ð23Þ
The bed voidage at different inlet gas velocities was measured in a cylindrical fluidized bed and plotted in Fig. 5. The experimental data were fitted to obtain correlations for the modeling of bed voidage in the i-CFB reactor. Table 3 Calculation procedures for effective bed heights.
When the Cai correlation was compared with our experimental data, it was found that the correlation gave a good agreement with experimental data with an error within 3.24%. To further improve the bed expansion prediction, the correlation of Y in Cai's correlation is slightly modified to 0:26
Y ¼ 0:116 Hs
Flow pattern
ΔPa0 N ΔPd0 ?
Ha0 b Hd0 ?
Lj N Ha0 − Hd0 ?
Ha
Hd
(a)
N
–
–
(b)
Y
Y
–
Calculated from mass and pressure balance Hd = Hdraft ‐ tube
(c)
Y
N
Y
(d)
Y
N
N
Calculated from mass and pressure balance Calculated from mass balance Calculated from mass balance Ha = Hd
Hd = Ha Hd = Hdraft ‐ tube + Hj
ðU−Umf Þ
0:09 −0:48 −0:19 dp ρp :
ð24Þ
The calculated values from modified Cai correlation was plotted in Fig. 5, which has an error less than 2.44%. This correlation will be applied to both the annulus and draft tube zones of the i-CFB reactor. It should be noted that the Cai correlation can only be used for bubbling and turbulent regimes. If the gas velocity exceeds Ut, the draft tube is operated as a transport riser. The Pugsley correlation [20], which was developed for transport risers with diameters of 0.05 to
30
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
1 m and for particles with diameters of 50 to 350 μm, could be used for the estimation of voidage.
ε¼
Uρp Gs ψ þ Uρp
ð25Þ
where Gs is the solid circulation rate and U0 is the superficial gas velocity inside the draft tube. The slip factor was defined as the ratio of gas interstitial velocity to the average particle velocity and correlated to the Froude number.
It should be noted that the net gas exchange is mostly from draft tube to the annulus based on calculated gas flow rate both from the annulus to draft tube and from draft tube to annulus (results are not shown here), which is in opposite to the net solid flow from the annulus to the draft tube. The low gas bypass from annulus to draft tube can limit the oxygen concentration buildup in the NOx reduction zone in an i-CFB, leading to potential improvement of the overall deNOx efficiency. For modeling the hydrodynamics of the i-CFB, the gas bypass RDA data are correlated to Ua0 and Ud0 by RDA ¼ 1:039
ψ¼
U 5:6 0:41 þ 0:47 Frt ¼1þ εUp Fr
ð26Þ
where Fr and Frt are Froude number and particle Froude number, respectively. U Ut Fr ¼ ; Frt ¼ : ðgDd Þ0:5 ðgDd Þ0:5
ð27Þ
4.2. Gas bypass Gas bypass is very important for the design and operation of i-CFB, which determines both the gas velocities and actual reactant concentrations in the annulus and draft tube. The measured gas bypass data from Yang [6] were shown in Fig. 6, where RDA is the gas bypass ratio from draft tube to the annulus and RAD is from the annulus to draft tube. It can be seen from Fig. 6(a) that RDA increases with increasing Ud0, gas feed rate to the draft tube. It is seen that more gas leaks to the annulus as the gas velocity in the draft tube increases. However, when the gas velocity in the annulus is higher, less gas leaks from draft tube to the annulus, leading to a lower RDA. Also, the effect of feed gas velocity in the annulus is less significant at lower Ud0, as evidenced from the slopes of RDA at different Ud0. At Ud0 =0.45m/s, RDA is almost unaffected by Ud0. Compared to RDA, RAD data are much more scattered and show no obvious trend. The change in both Ua0 and Ud0 has almost no effect on RAD, which fluctuates in the range of 5–9%, as shown in Fig. 6(b). It is very likely that this small fraction of gas is carried by the particles flowing from the annulus to the draft tube through the orifice.
a
−0:616
Ud0 Umf
1:300 2 R ¼ 0:865 :
ð28Þ
Since RAD is much scattered across a narrow range, an average value of 7% was used. RAD ¼ 7%
ð29Þ
It should be noted that the equations are only valid within the experimental range, 0.45 m/s b Ud0 b 0.9 m/s and 0.2 m/s b Ua0 b 0.475 m/s. If Ud0 N 0.9 m/s, RDA is predicted to be more than 100% and is unrealistic. The same problem also happens when Ua0 is smaller than 0.2 m/s. It is observed that at a higher Ud0, the increase in RDA slows down with increasing Ud0. The difference between the values of RDA at Ud0 = 0.75 m/s and Ud0 = 0.9 m/s is very small. So, when Ud0 is higher than 0.9 m/s, the values of RDA at Ud0 = 0.9 m/s is taken in the modeling. Also, when Ua0 is smaller than 0.2 m/s, the RDA values at Ua0 = 0.2 m/s is used. It should be warned that this assumption could potentially lead to errors in the modeling, since these values have not been confirmed experimentally. The real gas velocities in the annulus and draft tube can now be calculated as: Ua ¼ Ua0 −RAD Ua0 þ RDA Ud0 ðAd =Aa Þ
ð30Þ
Ud ¼ Ud0 −RDA Ud0 þ RAD Ua0 ðAa =Ad Þ:
ð31Þ
4.3. Measured solid circulation rates The solid circulation rate in the i-CFB reactor was measured at two different particle loadings, 2.275 kg and 3.3 kg. The particle velocity and voidage in the annulus were measured at different radial positions by the optical fibre probe. Fig. 7(a) shows the particle velocity as a function of dimensionless radial positions at different annulus gas
b
65
Ud0=0.6 m/s
9
Ud0=0.6 m/s
55
Ud0=0.45 m/s
Bed loading=3.3 kg
Ud0=0.45 m/s
Bed loading=3.3 kg
60
Ud0=0.75 m/s
Ud0=0.75 m/s
50
Ud0=0.9 m/s
Ud0=0.9 m/s
8
RAD (%)
45
RDA (%)
Ua0 Umf
40 35
7
30 6
25 20
5
15 10 0.15
0.20
0.25
0.30
0.35
0.40
Annulus inlet velocity, Ua0 (m/s)
0.45
0.50
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Annulus inlet velocity Ua0 (m/s)
Fig. 6. Gas bypass ratios at different Ud0. (a), from draft tube to annulus, RDA; (b), from annulus to draft tube, RAD (symbols: experimental data, line: correlation).
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
a
b Mloading=2.275 kg
0.20 0.85
Ud0=1 m/s
0.15
Voidage, ε
Particle velocity, Up (m/s)
31
0.10
0.05
0.75
Ua0=0.1 m/s
0.00
Mloading =2.275 kg Ud0 =1 m/s
0.80
Ua0=0.1 m/s
Ua0=0.2 m/s
Ua0=0.2 m/s
Ua0=0.4 m/s
Ua0=0.4 m/s
Ua0=0.6 m/s
Ua0=0.6 m/s
0.70
-0.05 0.6
0.7
0.8
0.9
1.0
0.6
0.7
0.8
r/R0
0.9
1.0
r/R0
Fig. 7. Measured radial profiles of (a) particle velocity and (b) voidage at different Ua0 (Ud0 = 1 m/s, bed loading = 2.275 kg. Symbols: experimental data, lines: connection of symbols).
velocity Ua0 with a particle bed loading of 2.275 kg. The value of r is referred to the distance from the axis of the i-CFB to the measurement point and R0 is the column radius. The annulus zone is from r/R0 = 0.5 to r/R0 = 1. The positive values of the particle velocity indicate a downflow of particles while negative values indicate an upflow of particles. It can be seen that the particle velocity increases with decreasing Ua0. However, this does not necessarily mean that the solid circulation rate is higher, since the solid circulation is determined by both particle velocity and the local voidage. For most of the curves in Fig. 7(a), especially at lower Ua0, local particle velocity is higher at the outer side of the annulus than at the inner side. For a particle loading of 2.275 kg at a low annulus gas velocity, the flow pattern (b) in Fig. 4 is expected, in which solids fall down fast near the outer wall of the annulus. At a higher Ua0, particle velocities in the middle of the annulus are very low, and sometimes the solids can even move upward in the middle of the annulus due to uneven gas flow distribution. Most of the solids flow down the annulus along both the inner and outer walls of the annulus. The reactor may be operated with the flow pattern (c) in Fig. 4 at a higher annulus gas velocity, in which case some solids from the jet above the draft tube fall down along the outer side wall, and some solids penetrate through the jet to the dense annulus zone and then fall down along the inner wall. The measured radial voidage profile in the annulus is shown in Fig. 7(b). The voidage is seen to be very low near both inner and outer
a
b
0.25 Ua0=0.1 m/s Ua0=0.2 m/s
0.20
Ua0=0.4 m/s
Mloading =3.3 kg Ud0 =1 m/s
0.90
Ua0=0.6 m/s
0.15
Voidage, ε
Particle velocity, Up (m/s)
walls of the annulus, and reaches a peak around the middle of the annulus, indicating the presence of fewer particles in the middle region of the annulus. The voidage decreases with increasing annulus gas velocity, which is contradictory to that commonly observed in a fluidized bed where voidage increases with increasing inlet gas velocity. One likely explanation is that the optical probe at point D4 in Fig. 1 is located in the dilute region well above the upper surface of the dense fluidized bed. In the freeboard region of a fluidized bed or in the downcomer with countercurrent gas–solid flow, the voidage decreases with increasing inlet gas velocity. When particle loading is increased to 3.3kg, the radial distribution of axial particle velocity in the annulus varies only slightly in the middle section, as shown in Fig. 8(a). The particle velocity increases slowly from the inner wall toward the middle of the annulus. Close to the column wall, the velocity increases substantially. The particle velocity decreases first when Ua0 increases from 0 to 0.4 m/s and then increases a lot when Ua0 is further increased to 0.6 m/s. The radial voidage profile at a solid loading of 3.3 kg, as shown in Fig. 8(b), is also different from that at a solid loading of 2.275 kg. At a low Ua0, the voidage is almost flat along the radial direction, especially near the draft tube, indicating a uniform solid distribution in the annulus. At a high Ua0, voidage begins to decrease along the radial direction, leading to a denser region near the outer wall of the annulus. A valley appears on all profiles near the column wall. There is a sudden
0.10
0.85
Ua0=0.1 m/s
0.80
0.05
Ua0=0.2 m/s Ua0=0.4 m/s Mloading =3.3 kg
0.00
Ua0=0.6 m/s Ud0=1 m/s 0.75
0.5
0.6
0.7
0.8
r/R0
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
r/R0
Fig. 8. Measured radial profiles of (a) particle velocity and (b) voidage at different Ua0 (Ud0 = 1 m/s, bed loading = 3.3 kg. Symbols: experimental data, lines: connection of symbols).
32
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
increase in voidage close to the column wall. This could be caused by the gas flowing up near the wall because of the uneven gas distribution in the annulus. Combining with the radial particle velocity distribution, it can be concluded that more particles move downward near the column wall. Similar to Fig. 7(b) at the solid loading of 2.275 kg, the overall voidage decreases with increasing gas velocity. However, the voidage increases when Ua0 further increases to 0.6 m/s. This can be explained by the bed expansion at different Ua0. It is likely that the optical probe is already immersed in the dense region of the fluidized bed at Ua0 = 0.4 m/s. So if Ua0 further increases, the measured voidage increases in the same way as the overall bed voidage. Fig. 9 shows the measured radial profiles of particle velocity and voidage at different Ud0. The particle velocities show a similar trend at different Ud0, but the effect of Ud0 is not very clear. Compared to particle velocity, the voidage in Fig. 9(b) is greatly influenced by Ud0, decreasing with increasing Ud0. Combining the solid velocity and voidage in the annulus, it can be inferred that the solid circulation rate increases with increasing Ud0. The overall net solid flux in the annulus, Gs, is calculated from the integration of the local solid flux across the cross section of the annulus. Fig. 10(a) shows Gs as a function of Ua0 at different draft tube velocities with a solid loading of 2.275kg. As discussed above, the solid circulation rate mostly increases with increasing draft tube gas velocity Ud0, but decreases with increasing Ua0. This can be explained by the pressure balance over the i-CFB reactor. When the draft velocity increases at a constant annulus velocity, solid circulation is increased because of the increased pressure difference between the draft tube and the annulus. On the other hand, at a constant draft tube gas velocity, the increase of annulus gas velocity increases the bed expansion in the annulus, which lowers the pressure buildup in the annulus and the pressure difference between the draft tube and the annulus, leading to the reduced solid circulation rate. Gs at a high bed solid loading of 3.3 kg is not sensitive to the annulus gas velocity at high draft tube gas velocities. At a low draft tube velocity, Ud0 = 0.5 m/s, Gs increases from Ua0 = 0 to Ua0 = 0.1 m/s but decreases to less than 15 kg/m2·s when Ua0 is increased from 0.1 to 0.4 m/s. This is likely caused by the small gas velocity difference between the draft tube and annulus, which can lead to loss of pressure difference between these two zones. Also, Gs is less sensitive to Ud0 at 3.3 kg solid loading than at a bed solid loading of 2.275 kg. In previous literature, influences of gas velocity in the annulus and draft tube on solid circulation rate have been studied for various fluidized beds with draft tube. The results are different from the trends obtained in the current study due to different distributor configurations
a
4.4. Prediction of solid circulation rate The solid circulation rate at a bed solid loading of 3.3 kg is modeled by mass and pressure balance equations presented in Section 3. The real gas velocities in the annulus and draft tube are adjusted by the gas bypass ratios. Then voidage in both zones is calculated using Cai's correlation. Fig. 11(a) shows the estimated voidage, with the closed symbols corresponding to the voidage in the annulus and the open symbols for the voidage in the draft tube. It can be seen that the voidage in the draft tube is always higher than the voidage in the annulus, since the velocity in the draft tube is always higher than in the annulus. From the bed expansion characteristics shown in Fig. 5, voidage is expected to increase from 0.6 to 0.85 when the gas velocity increases from 0.1 m/s to 0.6 m/s. The curves of annulus voidage εa seem to be quite different from expected without gas bypass. The voidage in the annulus increases with increasing draft tube inlet gas velocity because more gas passes from the draft tube through the orifice to the annulus zone at higher Ud0. At the same Ud0, the slopes of most εa vs. Ua curves are lower than the slope in Fig. 5, due to smaller RDA values at higher Ua0. It can be concluded that the voidage in both zones of the i-CFB reactor is substantially changed by gas bypass.
b 1.0 0.25
Ud0=0.75 m/s
0.20
Ud0=1.25 m/s
Ud0=1.25 m/s
0.9
0.15
0.10 Mloading=2.275 kg
0.8
Mloading=2.275 kg
0.7
Ua0=0.1 m/s
Ua0=0.1 m/s
0.05
0.00 0.5
Ud0=0.75 m/s Ud0=1 m/s
Ud0=1 m/s
Voidage, ε
Particle velocity, Up (m/s)
and operating conditions. In most of these reactors [2–5,21,22], the annulus operates as a moving bed. For example, in the research of Kim's group [2–5], Ua0 was set to be 0.4–1.6 Umf and Ud0 was set to be 2.6–20.4 Umf. It was found that the solid circulation rate increased with increasing gas velocity in both the annulus and the draft tube. The same trends were also observed by other researchers [21,22]. However, in the current study, the annulus was operated in bubbling or turbulent fluidization. The characteristics of solid circulation rate are also different. It is seen from Fig. 10 that Gs is a strong function of bed solid loading and inlet gas velocities. At low bed solid loadings and low Ud0, Gs decreases as the annulus gas velocity increases. However, the trend changes and tends to be reversed at high bed solid loadings and high Ud0. Many factors may influence the solid circulation rate of the i-CFB at different solid loadings. The trends of these curves cannot be simply explained by the differences of the inlet gas velocities. Gas bypass at different bed solid loading and inlet gas velocities could directly influence the actual gas velocity in both the annulus and draft tube, which determines the voidage in each zone. Effective bed heights in both zones are also influenced by operating conditions. The reason for such a different trend is discussed in detail in the Appendix A.
0.6
0.7
0.8
r/R0
0.9
1.0
0.6 0.5
0.6
0.7
0.8
0.9
1.0
r/R0
Fig. 9. Measured radial profiles of (a) particle velocity and (b) voidage at Ua0 = 0.1 m/s (symbols: experimental data, lines: connection of symbols).
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
b Mloading=2.275 kg
Solid circulation rate, Gs (kg/m2.s)
Solid circulation rate, Gs (kg/m2.s)
a 60
33
Ud0=0.75 m/s Ud0=1 m/s
50
Ud0=1.25 m/s
40
30
20
35
30
25
Mloading =3.3 kg Ud0=0.5 m/s
20
Ud0=1 m/s Ud0=1.4 m/s
15
10
10 0.1
0.2
0.3
0.4
0.5
0.6
0.0
Annulus inlet velocity, Ua0, m/s
0.1
0.2
0.3
0.4
0.5
0.6
Annulus inlet velocity, Ua0, m/s
Fig. 10. Net solid circulation rate at different Ud0, with bed solid loadings of (a), 2.275 kg, and (b), 3.3 kg (symbols: experimental data, lines: connection of symbols).
Following the procedure given in Table 3, effective bed heights in the two zones are estimated through mass balance and plotted in Fig. 11(b). In the figures, ‘a’ is annulus and ‘d’ denotes draft tube. At low Ua0 and Ud0, type (b) flow pattern is expected with Hd = Hdraft-tube and Ha b Hd. But at higher Ua0 and Ud0, the flow patterns are expected to be either type (c) or type (d), with the effective heights of annulus and draft tube being the same and larger than the length of draft tube. It can be seen that the effective bed height increases with increasing both Ud0 and Ua0. At low Ud0, the slope of the curves is steep, because increasing inlet gas velocity can significantly increase the expansion of the fluidized bed. But at higher Ud0 and Ua0, the top of the annulus dense bed exceeds the height of the jet above the draft tube and flow patterns (c) or (d) in Fig. 4 are formed. Further increasing the inlet gas velocity has little effect on the effective bed height. Pressure drop across the annulus and draft tube is estimated based on the estimated voidage and effective bed height, and the pressure drop across the orifice ΔPor is obtained based on the pressure difference between the annulus and the draft tube. The values of ΔPor are further fitted into Eq. (10) to obtain the discharge coefficient Cs at each operating condition. The calculated Cs data are shown in Fig. 12 as a function of Reynolds number of the particles passing through the orifice, Rep, defined as: ρg dp Up;a : μ
ð32Þ
a 1.0
CO2 ;d ¼ CO2 ;a0
FAD U ¼ CO2 ;a0 RAD a0 Fd Ud
ð33Þ
Fig. 13(a) shows the predicted O2 concentration in the draft tube, CO2,d, at various inlet gas velocities. All the values of CO2,d are very low,
b Bed loading=3.3 kg
0.8
0.7
Annulus:Ud0 =0.5 m/s Draft tube:Ud0 =0.5 m/s Annulus:Ud0 =1 m/s
0.6
Draft tube:Ud0 =1 m/s
0.5 0.1
0.2
0.3
0.4
Effective bed height (m)
1.3
0.9
Voidage, ε
Rep ¼
The fitted Cs values are quite scattered and varied from 0.13 to 0.21, which falls reasonably into the range as reported in the literature [15]. Since no obvious trend with Rep was observed, an average Cs value of 0.167 is taken for further simulation. Using the current model, hydrodynamics at a bed solid loading of 3.3 kg is further investigated for the design of an i-CFB reactor. In an iCFB deNOx reactor, flue gas is fed into the annulus and NOx in the flue gas will be adsorbed onto the catalyst surface. The oxygen concentration in the flue gas is always high in lean combustion of fuels, and the presence of high level oxygen favors the NOx adsorption. In the draft tube, NOx adsorbed on the catalyst surface is reduced by hydrocarbons. The reduction reaction is inhibited by O2 because hydrocarbon reductant is consumed by oxygen. Therefore, careful control of the oxygen concentration inside the draft tube is of great importance to achieve the high deNOx efficiency of the deNOx reactor. Here, the actual O2 concentration in the draft tube is estimated based on the gas bypass ratios and the gas flow rate into the draft tube using Eq. (33). It is assumed that O2 only exists in the gas fed into the annulus with a concentration of 8%.
1.2 1.1 1.0 0.9
Draft tube:Ud0 =1.5 m/s
0.5
0.6
Draft tube, Ud0=0.5 m/s Annulus, Ud0=1 m/s
0.7 0.6
0.5
Annulus, Ud0=0.5 m/s
0.8
Annulus:Ud0 =1.5 m/s
Annulus inlet velocity, Ua0, m/s
Bed loading=3.3 kg
Draft tube, Ud0=1 m/s Annulus, Ud0=1.5 m/s Draft tube, Ud0=1.5 m/s
0.1
0.2
0.3
0.4
0.5
0.6
Annulus inlet velocity, Ua0, m/s
Fig. 11. Calculated (a) voidage and (b) effective bed height at a bed solid loading of 3.3 kg (symbols: experimental data, lines: connection of symbols).
34
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
0.35
circulation rate decreased as the annulus gas velocity increased. However, this trend could be reversed at high bed loading and high draft tube velocity. A hydrodynamic model was then developed based on mass and pressure balances. Discharging coefficient Cs was extracted from fitting the experimental data and an average value of 0.167 was taken for model simulation. The model could well capture the characteristics of the solid flow and gas flow distribution, and could serve as a useful tool for the design and simulation of the i-CFB deNOx reactor system. However, modeling at different bed solid loadings requires the gas bypass characteristics being measured. With data on both the gas bypass and solid circulation rate, the hydrodynamic behavior could be coupled with the reaction kinetics to simulate the iCFB performance for NOx reduction.
0.30 0.25
Cs
0.20 0.15 0.10 0.05 0.00 0.2
0.4
0.6
0.8
1.0
Rep Fig. 12. Fitted Cs values as a function of Rep.
ranging from 0.25% to 0.5%. This is due to the low gas bypass ratios from annulus to draft tube. The predicted low oxygen concentration in the draft tube can thus achieve a high NOx reduction efficiency. The overall NOx abatement efficiency is determined by both the adsorption in the annulus, which directly removes NOx from the flue gas, and the reduction in the draft tube. The NOx adsorption efficiency in the annulus is strongly affected by the solid circulation rate, which represents how the NOx can be efficiently transferred to the reduction zone and also determines the contact time between gas and catalyst. Fig. 13(b) shows the predicted solid circulation rate at different inlet gas velocities. It is seen that Gs is smaller at lower Ud0, e.g. 0.6 m/s. But further increasing Ud0 from 0.75 m/s to 0.9 m/s has little effect on Gs and even leads to lower values of Gs. The broad width of the peak also indicates that the i-CFB can be well operated over a wide range of Ua0, with the optimal annulus velocities between 0.25 and 0.45 m/s. 5. Conclusions Hydrodynamics of an i-CFB deNOx reactor has been studied by both experiment and modeling. Gas bypass was investigated by CO2 tracer method, and solid circulation rate was measured using an optical fibre probe at bed solid loadings of 3.3 kg and 2.275 kg. It was found that solid circulation rate was a strong function of bed loading and feeding gas velocities. At low bed loading and low draft tube velocity, solid
a
Nomenclature Aa cross area, m2 Ad cross sectional area of the draft tube, m2 Aor area of the orifice, m2 CO2,a0 O2 concentration in the gas fed into the annulus, mol/m3 CO2,d O2 concentration in the draft tube, mol/m3 Cs discharging coefficient of the orifice Da diameter of the annulus column, m Db diameter of the bubbles, m Dd diameter of the draft tube, m dp particle diameter, m dimensionless particle diameter dp⁎ Fa0 flow rate of gas fed to the annulus, m3/s FAD flow rate of gas bypassing from the annulus to the draft tube, m3/s Fb gas flow rate in the bubbles, m3/s Fd gas flow rate in the draft tube, m3/s Fd0 flow rate of gas fed to the draft tube, m3/s FDA flow rate of gas bypassing from the draft tube to the annulus, m3/s Fgw gas–wall friction force per unit volume of the column, N/m3 Fpw particle–wall friction force per unit volume of the column, N/m3 Fr Froude number Frt Froude number at terminal velocity g acceleration due to gravity, 9.8 m/s2 Gs solid circulation rate across the annulus, kg/m2·s H fluidized bed height, m Ha effective bed height in the annulus, m Ha0 initial effective bed height in the annulus, m Hd effective bed height in the draft tube, m
b 0.50
Ud0=0.75 m/s
30
Ud0=0.9 m/s
0.45
Gs, kg/m2.s
Bed loading = 3.3 kg
CO2,d, %
35
Ud0=0.6 m/s
0.40
0.35
25 20 Bed loading = 3.3 kg
15 Ud0=0.6 m/s Ud0=0.75 m/s Ud0=0.9 m/s
0.30 10 0.25 5 0.20
0.25
0.30
0.35
0.40
0.45
Annulus inlet velocity, Ua0, m/s
0.50
0.20
0.25
0.30
0.35
0.40
0.45
Annulus inlet velocity, Ua0,m/s
Fig. 13. Predicted (a) CO2,d and (b) Gs as a function of Ua0.
0.50
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
Greek symbols db bubble phase fraction ε voidage εa voidage in the annulus εd voidage in the draft tube μ dynamic viscosity, Pa·s ρg gas density, kg/m3 ρp density of particles, kg/m3 τ time lag, s ψ slip factor ∅s spherical coefficient
Acknowledgments The authors are grateful to the Natural Science and Engineering Research Council (NSERC) of Canada for the financial support in the form of a discovery grant. X. Cheng is also grateful to a scholarship from the China Scholarship Council (CSC). Appendix A Why Gs decreases when Ua0 increases at bed loading = 2.275 kg which contradicts the observation in the literature?
70
Exp-Ud0=0.75 m/s Exp-Ud0=1 m/s
60
50
Gs, kg/m2.s
Hd0 initial effective bed height in the draft tube, m Hdraft-tube height of draft tube, m Hf expanded bed height, m HG gap distance in the distributor, mm Hmf bed height at minimum fluidization, m Hs bed height, m Le effective distance of optical fibre, m Lj jet height of spout bed, m Ma mass of solids in the annulus, kg Md mass of solids in the draft tube, kg Mloading mass of solids loaded in the i-CFB reactor, kg P pressure, Pa r distance from the central of the bed, m R0 radius of fluidized bed, m RAD gas bypass ratio from the annulus to the draft tube, % RDA gas bypass ratio from the draft tube to the annulus, % Rec Reynolds number at transition velocity Rep Reynolds number around particles U gas velocity, m/s Ua real gas velocity in the annulus, m/s Ua0 feeding gas velocity in the annulus, m/s Ub bubble velocity, m/s Uc transition velocity at which standard deviation of pressure fluctuation reaches a maximum, m/s Ud real gas velocity in the draft tube, m/s Ud0 feeding gas velocity in the draft tube, m/s Umf gas velocity at minimum fluidization, m/s Up particle velocity, m/s Up,a particle velocity in the annulus, m/s Up,d particle velocity in the draft tube, m/s Ut terminal velocity, m/s dimensionless terminal velocity U⁎t Y dimensionless coefficient ΔP pressure drop, Pa ΔPa pressure drop in the annulus, Pa ΔPa0 initial pressure drop in the annulus, Pa ΔPd pressure drop in the draft tube, Pa ΔPd0 initial pressure drop in the draft tube, Pa ΔPor pressure drop through the orifice, Pa
35
Exp-Ud0=1.25 m/s
Ud0=1.25 m/s
Mloading=2.275 kg
Ud0=1 m/s
40
30
Ud0=0.75 m/s 20
10 0.1
0.2
0.3
0.4
0.5
0.6
Ua0, m/s Fig. A1. Experimental and modeled solid circulation rates at a bed solid loading of 2.275 kg (symbols: experimental data; lines: model prediction.).
Since the characteristics of gas bypass are unknown, detailed and accurate analysis could not be obtained. So here it is assumed that there is no gas bypass and the pressure drop could be analyzed quantitatively. Following the calculation procedure presented in Table 3, most of the tested conditions in Fig. 10(a) possess type (b) flow patterns. The effective bed height in the draft tube equals the height of draft tube height, and the annulus effective bed height changes with the voidage. Since the inlet gas velocity of the draft tube does not change, the pressure drop ΔPd remains a constant. For most of the data points, the annulus is operated as a fluidized bed. It can be assumed that the pressure drop in the annulus is determined by the weight of solid in the annulus. ΔPa ¼ gρp ð1−εa ÞHa ¼ gMa =Aa
ðA1Þ
If the draft tube gas velocity remains at a constant, voidage in the draft tube will not change, so does the amount of solids in the draft tube. Solid weight in the annulus does not change at various Ua0, which gives rise to a constant pressure drop across the annulus. Thus the pressure drop through the orifice, ΔPor, remains constant. According to Eq. (10), solid circulation rate is influenced by ΔPor and εa. At higher Ua0, εa becomes bigger, leading to a lower Gs. An attempt was made to model the solid circulation rate at bed solid loading of 2.275 kg, with the results plotted in Fig. A1 as lines. Gas bypass was not considered since there are no data available. Therefore, the modeling results are not reliable for reactor design purpose. But they could be used to check the trend of solid circulation rate at different conditions. It could be seen that all the modeling results fall into a reasonable range of the experimental data. All the solid circulation rates decrease with annulus gas velocity, confirming the consistency of the experiments and the proposed explanations. References [1] T.T. Yang, H.T. Bi, A novel fluidized bed reactor for integrated NOx adsorption– reduction with hydrocarbons, Environ. Sci. Technol. 43 (13) (2009) 5049–5053. [2] J.H. Jeon, S.D. Kim, S.J. Kim, Y. Kang, Solid circulation and gas bypassing characteristics in a square internally circulating fluidized bed with draft tube, Chem. Eng. Process. 47 (12) (2008) 2351–2360. [3] B.H. Song, Y.T. Kim, S.D. Kim, Circulation of solids and gas bypassing in an internally circulating fluidized bed with a draft tube, Chem. Eng. J. 68 (1997) 115–122. [4] H.S. Ahn, W.J. Lee, S.D. Kim, B.H. Song, Solid circulation and gas bypassing in an internally circulating fluidized bed with an orifice type draft tube, Korean J. Chem. Eng. 16 (1999) 618–623. [5] S.D. Kim, Y.H. Kim, S.A. Roh, D.H. Lee, Solid circulation characteristics in an internally circulating fluidized bed with orifice-type draft tube, Korean J. Chem. Eng. 19 (2002) 911–916.
36
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
[6] T.T. Yang, A Novel Fluidized Bed Reactor for Integrated NOx Adsorption–Reduction With Hydrocarbons, in Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, 2008. [7] T.D. Hadley, C. Doblin, J. Orellana, K.-S. Lim, Experimental quantification of the solids flux in an internally circulating fluidized bed, The 13th International Conference on Fluidization — New Paradigm in Fluidization Engineering, 2010. [8] Z. Chen, Hydrodynamics, Stability and Scale-up of Slot-rectangular Spouted Beds, in Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver, 2008. [9] J.Z. Liu, J.R. Grace, X.T. Bi, Novel multifunctional optical-fiber probe: I. Development and validation, AIChE J. 49 (6) (2003) 1405–1420. [10] X.Q. Song, H.T. Bi, C.J. Lim, J.R. Grace, E. Chan, B. Knapper, C. McKnight, Hydrodynamics of the reactor section in fluid cokers, Powder Technol. 147 (1–3) (2004) 126–136. [11] C.Y. Yan, C.X. Lu, Y.S. Liu, R. Cao, M.X. Shi, Hydrodynamics in airlift loop section of petroleum coke combustor, Powder Technol. 192 (2) (2009) 143–151. [12] W. Namkung, C. Guy, R. Legros, Prediction of solids circulation rate in the riser of an internally circulating fluidized bed (ICFB), Chem. Eng. Commun. 188 (1) (2001) 47–58. [13] K. Svoboda, S. Kalisz, F. Miccio, K. Wieczorek, M. Pohorely, Simplified modeling of circulating flow of solids between a fluidized bed and a vertical pneumatic transport tube reactor connected by orifices, Powder Technol. 192 (1) (2009) 65–73.
[14] H. Konno, S. Saito, Pneumatic conveying of solids through straight pipes, J. Chem. Eng. Jpn 2 (1969) 211–217. [15] M. Kuramoto, D. Kunii, T. Furusawa, Flow of dense fluidized particles through an opening in a circulation system, Powder Technol. 47 (2) (1986) 141–149. [16] W.Q. Zhong, M.Y. Zhang, B.S. Jin, X.P. Chen, Flow pattern and transition of rectangular spout-fluid bed, Chem. Eng. Process. 45 (9) (2006) 734–746. [17] Q.J. Guo, G.X. Yue, J.Y. Zhang, Z.Y. Liu, Hydrodynamic characteristics of a twodimensional jetting fluidized bed with binary mixtures, Chem. Eng. Sci. 56 (15) (2001) 4685–4694. [18] P. Cai, G.D. Michele, A.T. Gradassl, A generalized method for predicting gas flow distribution between the phases in FBC, Fluidized bed combustion 2 (1993) 991–1002. [19] S.P. Babu, B. Shah, A. Talwalkar, Fluidization correlations for coal gasification materials, minimum fluidization velocity and fluidized bed expansion ratio, AIChE Symp. Ser. 74 (1978) 176–186. [20] T.S. Pugsley, F. Berruti, A predictive hydrodynamic model for circulating fluidized bed risers, Powder Technol. 89 (1) (1996) 57–69. [21] H.Y. Zhang, R. Xiao, D.H. Wang, J.M. Cho, G.Y. He, S.S. Shao, J.B. Zhang, Hydrodynamics of a novel biomass autothermal fast pyrolysis reactor: solid circulation rate and gas bypassing, Chem. Eng. J. 181 (2012) 685–693. [22] R. Xiao, M.Y. Zhang, B.S. Jin, X.D. Liu, Solids circulation flux and gas bypassing in a pressurized spout-fluid bed with a draft tube, Can. J. Chem. Eng. 80 (5) (2002) 800–808.
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Hydrodynamics of an i-CFB deNOx reactor Xingxing Cheng, Xiaotao T. Bi ⁎ Fluidization Research Centre, Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver V6T 2K9, Canada
a r t i c l e
i n f o
Article history: Received 10 May 2013 Received in revised form 12 September 2013 Accepted 11 October 2013 Available online 21 October 2013 Keywords: i-CFB Solid circulation rate Gas bypass Hydrodynamic model Optical fibre
a b s t r a c t Hydrodynamics of an i-CFB (internal circulating fluidized bed) deNOx reactor has been studied by both experiments and modeling. Gas bypass was investigated by CO2 tracer method, and solid circulation rate was measured using an optical fibre probe at bed solid loadings of 3.3 kg and 2.275 kg. Radial profiles of bed voidage and solid velocity were discussed in detail. A hydrodynamic model was developed based on mass and pressure balances. Discharging coefficient Cs was extracted from fitting the experimental data and an average value of 0.167 was taken for model simulation. The model could well capture the characteristics of the solid flow and gas flow distribution, and could serve as a useful tool for the design and simulation of the i-CFB deNOx reactor system. © 2013 Elsevier B.V. All rights reserved.
1. Introduction As a promising deNOx technology, hydrocarbon selective catalytic reduction (HC-SCR) has been widely studied since the mid 1980s. Due to the challenges in suppressing the catalytic oxidation of hydrocarbons by oxygen present in the combustion flue gases, research has been focused on how to improve the selectivity of the catalyst toward NOx reduction. To alleviate the negative impact of oxygen on the deNOx reactor performance, a dual adsorption and reduction system has been proposed [1] in which the NOx adsorption takes place in a separate column, decoupled from the catalytic reduction which takes place in another column. To facilitate the continuous adsorption–reduction operation and in-situ catalyst regeneration, a novel HC-deNOx internal circulating fluidized bed (i-CFB) reactor was recently proposed by Yang and Bi [1] in which NOx is adsorbed onto the catalyst surface in the adsorption zone, and the adsorbed NOx is reduced catalytically in the reduction zone, with the catalyst circulating between the adsorption and reduction zones. The performance of the i-CFB reactor is expected to be impacted significantly by the hydrodynamics in the i-CFB, including both the gas bypass between the core and the annulus regions and the internal solid circulation, which should be well studied in order to properly design the reactor and suitable operating conditions as well as to provide data for modeling such a reactor. Several studies have been reported on the hydrodynamics of i-CFB reactors, mainly focused on the measurement of solid circulation rates [2,3] and the development of correlations for predicting the solid circulation rate [4,5]. These ⁎ Corresponding author. Tel.: +1 604 822 4408; fax: +1 604 822 6003. E-mail address: [email protected] (X.T. Bi). 0032-5910/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2013.10.016
empirical or semi-empirical models could not be applied directly to i-CFBs with different configurations. In this study, the performance of the reactor was investigated both experimentally and analytically. Gas bypassing, bed expansion and solid circulation rate in a deNOx i-CFB reactor were tested in a cold model unit. The solid circulation rate was then predicted based on pressure and mass balance equations. 2. Experiment details 2.1. i-CFB configuration An i-CFB reactor was constructed with the configuration shown in Fig. 1. The dimensions of the model unit are listed in Table 1. There was a draft tube in the reactor. Gas was fed to both the draft tube and annulus at different velocities and the bed particles circulated between the draft tube and annulus. Building air was used as fluidizing gas. Zeolite particles were tested in this i-CFB with the properties given in Table 2. 2.2. Bed expansion Bed voidage is an important flow structure parameter that determines the pressure drop in i-CFB. Here, bed expansion was investigated in a fluidized bed with the same dimensions as the i-CFB reactor as shown in Fig. 1, but with a flat perforated plate as the distributor and without the draft tube. Building air was used as the fluidizing gas, and zeolite powders were used as the bed material. Pressure drop was measured between points D1 and D3 at different gas inlet velocities and the average voidage in the bed was calculated according to
26
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
Sampling, gas mixture
Sampling, outlet of draft tube
Vent
Cyclone
Building air
Bag house Sampling, outlet of annulus
D5
D4
CO2
Vent
D3
D2
D1
Gas Analyzer
Computer
Sampling, inlet of annulus Building air
Sampling, inlet of draft tube Fig. 1. Schematic of the i-CFB reactor.
Eq. (1). Losses due to acceleration and frictions between gas/particle mixture and wall surfaces were neglected because of the low superficial gas velocities (b0.5 m/s) used in this study. ΔP ¼ ρp gð1−εÞH:
ð1Þ
inlet of the draft tube and the annulus being monitored. Gas bypass ratios, which are defined in Eq. (2), were then calculated based on the mass balance of tracer CO2. RDA ¼
FDA F ; R ¼ AD : Fd0 AD Fa0
ð2Þ
2.3. Gas bypass 2.4. Solid circulation rate The gas bypass between the draft tube and annulus was studied by Yang [6] using CO2 tracer method with the bed loaded with 3.3 kg zeolite powders. At a given steady state operating condition, continuous CO2 tracer was injected into the inlet gas flow of the annulus, with CO2 concentrations at the outlet of the draft tube and the annulus, and the
Table 1 Dimensions of the cold model i-CFB unit. Item
Dimension
Draft tube diameter, mm Draft tube length, mm Column diameter, mm Column height, mm Freeboard diameter, mm Freeboard height, mm Annulus gas distributor opening ratio Holes on the distributor Gas nozzle diameter, mm
50.8 (I.D.), 63.5 (O.D.) 1016 101.6 (I.D.), 114.3 (O.D.) 1092 254.0 (I.D.), 266.7 (O.D.) 508 2.1% 52 holes of 1.6 mm diameter 34.9 (I.D.), 38.1 (O.D.)
Experimentally, solid circulation rate can be determined from the vertical flux of particles passing through one or more of the regions using a number of methods [7] such as multi-fiber optical probes, radioactive tracer particles, and hot solid tracer techniques. In the
Table 2 Particle properties. Bed material
Bulk density Average particle Umf (m/s)a (kg/m3) diameter (mm)
ZSM-5 powder 968
0.155
0.01
Uc (m/s)b
Ut (m/s)c
0.38
0.90
Note: a: measured; b: measured. c: calculated from correlation: 2
3−1
0:591 7 6 18 Ut ¼ 4 2 þ 0:5 5 dp dp
2 ;
dp ¼ dp 4
31=3 ρg ρp −ρg g 5 ; μ2
2 31=3 ρ2g 5 : Ut ¼ Ut 4 μ ρp −ρg g
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
0.9
0.8
Voidage, ε
current study, optical fiber probes were used to measure solid flux for fine catalyst particles. A particle velocity analyzer (PV-4A) manufactured by the Institute of Process Engineering, Chinese Academy of Sciences, was used for the measurement, which included an optical fibre probe, a light conversion box, a data acquisition board and a program for sampling and recording data into the computer for analysis. This technique has been widely applied to determine particle velocity and voidage in fluidized beds [8,9]. The optical fibre probe used in the current work is shown in Fig. 2. There are three bundles of fibres of 15 μm in diameter. Each bundle has a diameter of about 1 mm. The central bundle of fibres is for light projection, whereas the other two act as light receivers, corresponding to two sampling channels A and B. The intensity of the signals from both channels is in V. The basic mechanism to measure the velocity is to calculate the time lag, τ, between the moments when the particles pass the two light receivers by cross-correlation method. The particle velocity, Up, can then be calculated as: Up = Le / τ. The probe was calibrated employing the actual particles used in this study. A rotating plate with glued particles was driven by a motor. Particles rotated together with the rotating plate, at a preset particle velocity, Up, and the time lag, τ, between the two channels of the probe was measured by the cross-correlation of the signals from the two channels. The effective distance was then calculated by multiplying the particle rotating velocity and the time lag. In a typical measurement, two series of signals were recorded from the system, which represent the intensity of the reflected light through the two channels. These data series were divided into several groups, with cross-correlation being carried out on each group to find the time lag between the two channels. For the measurement of local bed voidage, the optical fibre probe was calibrated using the mixture of bed particles and coke particles at different volume fractions of coke, with the calibration curve shown in Fig. 3. The local voidage was then correlated with the probe reading (the average reading of both channels) by an exponential equation (see Fig. 3). Details on the optical fibre probe calibration by the mixture of two particle components can be found in [8,10]. The optical fibre probe captures the motions of very small amount of particles that pass by the probe tip. In the dense fluidized bed, no matter bubbling bed or turbulent bed, solids move both upward and downward as bubbles/voids pass the measurement region. When captured by the optical fibre probe, solid velocity values are scattered, ranging from positive (down-flowing solids) to negative values (up-flowing solids associated with bubbles). This will make the estimation of net solid flux or average particle velocity very challenging and lead to low accuracy of the net solid flux measurement. If the filled bed height in the annulus is lower than the draft tube, a particle raining-down region exists at the top of the annulus. It is located in the upper region of the fluidized bed in the annulus. It could be expected that most of the solids fall downward in this region. Therefore, the measurement of solid flux by the optical fibre probe could be more accurate because of the more uniform solid movements in this region. Point D4 in Fig. 1, which is 950 mm above the bottom, is the most possible location for the particle raining-down region and is therefore selected to
27
(-0.0157*V)
ε=0.775*e 2 R =0.99
+0.428
0.7
0.6
0.5
0.4 40
80
120 Voltage, (mV)
160
Fig. 3. Voidage calibration of the optical probe (symbols: experimental data, line: correlation).
insert the optical probe. Both local solid velocity and local voidage were measured along the radial direction at an interval of 2.5 mm. The average solid flux in the annulus could be calculated by the integration of local solid flux along the radial direction. Z Gs ¼ ρp
r2 r1
πð1−εÞ Up 2rdr:
ð3Þ
The particle backmixing in fluidized bed can affect the particle velocity measurement, and also its influence is difficult to be determined. In this work, the instantaneous particle velocity signals were obtained over a period of time, which then were averaged to give the average solid velocity, avoiding the effect of the particle backmixing on the particle velocity measurement [11]. 3. Hydrodynamics model of i-CFB 3.1. Mass and pressure balance equations In an i-CFB, the internal circulation of solids is created by the pressure difference between the draft tube and the annulus operating at different superficial gas velocities. The solid circulation rate dictates both the gas and solid residence time in each region and hence the extent of NOx adsorption and catalytic NOx reduction. There are several correlations in the literature, which link the bed hydrodynamics to the solid circulation rate [2,4,12]. Because the solid circulation rate is influenced by the bed geometry in addition to fluid and particle properties and gas velocity, those correlations from the literature could not be used directly when the geometry of the reactor is changed. In this research, the solid circulation rate is estimated based on the mass and momentum balances in the iCFB reactor. Solid mass balance equations include the conservation of total solid inventory in the system and solid circulation rate balance between the draft tube and the annulus: Mloading ¼ Ma þ Md ¼ ρp ð1−εa ÞAa Ha þ ρp ð1−εd ÞAd Hd Gs ¼ ρp Up;a ð1−εa Þ ¼ ρp Up;d ð1−εd Þ
Fig. 2. Details of the tip of the optical fibre probe for particle velocity measurement.
200
Aa : Ad
ð4Þ ð5Þ
The driving force of the solid circulation is the pressure difference between the annulus and the draft tube, subtracting the pressure drop
28
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
across the orifice connecting them. The pressure balance in the whole system is ΔPa ¼ ΔPd þ ΔPor :
ð6Þ
3.2. Pressure drop calculation In a fluidized state, the pressure drop could be expressed by Eqs. (7) and (8), which consist of the pressure drops due to gravity, solid acceleration, fluid–wall friction and particle–wall friction. 2
ΔPa ¼ Ha ð1−εa Þρp g−0:5ð1−εa Þρp Up;a þ Hdraft‐tube Fgw −Hdraft‐tube Fpw
ð7Þ
2
ΔPd ¼ Hd ð1−εd Þρp g þ 0:5ð1−εd Þρp Up;d þ Hdraft‐tube Fgw þ Hdraft‐tube Fpw
a
ð8Þ
b
c
d
Fig. 4. Schematic of four i-CFB flow modes and the effective bed height.
where Ha and Hd are the effective bed heights in the annulus and draft tube, respectively. Fgw and Fpw are the gas–wall and the particle–wall frictional force per unit volume of the column, respectively. In the case of gas velocities lower than 6 m/s, and column diameter in excess of 4 cm without bends, the contribution of gas–wall friction Fgw could be neglected [13]. Konno and Saito's equation [14], which was developed for relatively low concentration of solids in vertical column, was used to calculate the solid–wall friction. Fpw ¼ 0:057 Gs ðg=Dd Þ
0:5
ð9Þ
One should note that gas velocity in the annulus region is lower than in the draft tube. So solid concentration in the annulus is higher. The use of the Konno and Saito equation may lead to the inaccuracy of pressure drop calculated. However, wall friction could be neglected at very low gas velocities. So the uncertainty in the estimated pressure drop from the Konno and Saito equation could be negligible. The pressure drop across the orifice between the bottoms of annulus and draft tube could be correlated with solid circulation rate Gs. For mechanical valves like slide valves where the solid flow is controlled by changing the opening area, the pressure drop across the control valve and solid flux can be related by [15]: Gs ¼ Cs
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Aor u u2ρp ð1−εa ÞΔPor t 2 : Aa 1− Aor
ð10Þ
Aa
The discharge coefficient Cs in Eq. (10) has values typically between 0.2 and 0.6 with an average value of 0.4, although it depends on the geometrical configuration, orifice edge parameters and the Dor/dp ratio. So Cs needs to be fitted from the experimental data for specific configurations.
Hd0 ¼ Hdraft‐tube Ha0 ¼
Mloading −ρp ð1−εd ÞHd0 Ad ρp ð1−εa ÞAa
ð11Þ ð12Þ
ΔPa0 ¼ ρp ð1−εa ÞgHa0
ð13Þ
ΔPd0 ¼ ρp ð1−εd ÞgHd0 :
ð14Þ
If ΔPa0 b ΔPd0, there is no solid circulation. This regime is of little interest in the operation of i-CFB. However, this procedure could be used to identify whether there is solid circulation or not. It should be noted that if the gas velocity in the annulus is larger than that in draft tube, particles could be entrained to the annulus, forming a reverse solid circulation. However, this case is not considered for the i-CFB yet and will not be discussed here. • When the solid loading and/or the gas velocity in the draft tube are increased, particles fill up the draft tube and start to circulate to the annulus region. This corresponds to flow pattern (b) in Fig. 4. In this mode, the effective bed height in the draft tube is the same as the draft tube height, and the effective annulus bed height could be calculated by overall mass balance. • If the particle loading and/or gas velocity are further increased, the annulus bed height could exceed the height of the draft tube and flow pattern (c) in Fig. 4 is established. In this case, the effective annulus bed height can still be calculated by mass balance and the effective draft tube bed height is equal to the effective annulus bed height. An initial guessed value of effective draft tube height should be taken to start the mass balance calculation, and the mass balance equations are then iterated to obtain the final bed height values.
3.3. Effective bed height To obtain the effective bed height for Eqs. (7) and (8), the flow in the i-CFB was categorized into four different operating modes as shown in Fig. 4. It should be noted that the flow mode is classified here in such a way to facilitate the calculation of effective bed height and is different from the flow patterns reported in the literature [16]. • If there is no sufficient bed solid loading and the gas velocity inside the draft tube is lower than the particle transport velocity, the draft tube could not be fully filled with particles and a flow pattern in Fig. 4(a) will be created without internal solid circulation. The initial pressure drops in the two zones could be obtained by
Hd ¼ Ha0 Ha ¼
Mloading −ρp ð1−εd ÞHd Ad ρp ð1−εa ÞAa
ð15Þ ð16Þ
• When the bed loading or gas velocity is further increased, the annulus dense bed becomes too high and the gas jet on top of the draft tube becomes unstable or can no longer penetrate through. As a result, flow pattern (d) in Fig. 4 is formed. The vertical jet penetrate length
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
29
1.0
could be estimated in the same way as jet penetration depth in spoutfluid bed [17].
Experiment Cai's correlation
0.9 2
ð17Þ
The effective draft tube bed height, Ld, is the sum of draft tube length and jet height, and the effective annulus bed height La equals Ld. The detailed criteria and calculation procedures for each of the four flow patterns are given in Table 3.
R =0.953
Voidage, ε
Lj ρg U2d ¼ 11:52 Da ρp −ρg gDd
!0:1966 0.8
0.7
0.6
3.4. Modeling procedure 0.5
A correlation was first developed for the solids discharge coefficient Cs from measured solid circulation rates using the following procedure. For given feeding gas velocities in the annulus and draft tube (Ua0 and Ud0) and measured solid circulation rate Gs, the gas bypass ratios (RAD and RDA) were calculated by the correlations based on experimental data. Actual gas velocities in the annulus and the draft tube (Ua and Ud) were then obtained based on the gas feed rates and gas bypass ratios. The Cai equation was used to calculate voidages (εa and εd). Effective bed heights (Ha and Hd) were then obtained following the methods described in Section 3.3 and Table 3. Particle velocities (Up,a and Up,d) were calculated based on measured Gs by Eqs. (4) and (5). The pressure drop across the annulus and the draft tube (ΔPa and ΔPd) could now be obtained from Eqs. (8) and (9), and the pressure drop through the orifice was then obtained from Eq. (6). Using Eq. (12), solid discharge coefficient Cs was determined for a given operating condition. The correlation (an average value was taken) for solid discharge coefficient was subsequently developed which was then used for solid circulate rate (Gs) simulation by iteration. An initial value Gs0 is first assumed. The feeding velocities in the annulus and draft tube (Ua0 and Ud0) are known and are the only known operating parameters. Following the same procedure as used for developing the Cs correlation, we could calculate other parameters such as gas bypass ratios (RAD and RDA), actual gas velocities in the annulus and draft tube (Ua and Ud), particle velocities (Up,a and Up,d) and pressure drop in the annulus and the draft tube (ΔPa and ΔPd). Pressure drop through the orifice can be calculated from Eq. (6). Then by Eq. (12), a new solid circulation rate Gs is obtained. If the new Gs value is different from the previous value more than a tolerant value, the iteration will be repeated. A finally solid circulation rate could be obtained when Gs0–Gs b 0.1 kg/m2·s.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Inlet gas velocity, U (m/s) Fig. 5. Measured voidage data for ZSM-5 powders and comparison with the Cai [19] correlation (symbols: experimental data, line: correlation).
Cai [18] modified Babu's correlation [19] to fit their bed expansion data obtained in both bubbling and turbulent fluidization regimes. The bubble size and bubble rise velocity are estimated, respectively, as, 0:8 0:06
0:42
ð18Þ
:
ð19Þ
Db ¼ 0:21 H f P ðU−Umf Þ exp h i −4 2 2 −1:4 10 P −0:25ðU−Umf Þ −0:1 PðU−Umf Þ 0:5
Ub ¼ U−Umf þ 0:71ðgDb Þ
Gas flow rate in the bubble phase is calculated as Fb ¼ Ub δb A ¼ YðU−Umf ÞA
ð20Þ
with Y being correlated to 0:26
Y ¼ 0:108 Hs
ðU−Umf Þ
0:09 −0:48 −0:19 dp ρp
ð21Þ
where Hs = Hmf/(1 − εmf). By assuming no particles inside the bubble phase, the bubble phase fraction (δb) and the bed voidage in the fluidized bed could then be calculated as:
4. Results and discussion
δb ¼
YðU−Umf Þ Ub
ð22Þ
4.1. Bed expansion characteristics
ε ¼ δb þ ð1−δb Þεmf :
ð23Þ
The bed voidage at different inlet gas velocities was measured in a cylindrical fluidized bed and plotted in Fig. 5. The experimental data were fitted to obtain correlations for the modeling of bed voidage in the i-CFB reactor. Table 3 Calculation procedures for effective bed heights.
When the Cai correlation was compared with our experimental data, it was found that the correlation gave a good agreement with experimental data with an error within 3.24%. To further improve the bed expansion prediction, the correlation of Y in Cai's correlation is slightly modified to 0:26
Y ¼ 0:116 Hs
Flow pattern
ΔPa0 N ΔPd0 ?
Ha0 b Hd0 ?
Lj N Ha0 − Hd0 ?
Ha
Hd
(a)
N
–
–
(b)
Y
Y
–
Calculated from mass and pressure balance Hd = Hdraft ‐ tube
(c)
Y
N
Y
(d)
Y
N
N
Calculated from mass and pressure balance Calculated from mass balance Calculated from mass balance Ha = Hd
Hd = Ha Hd = Hdraft ‐ tube + Hj
ðU−Umf Þ
0:09 −0:48 −0:19 dp ρp :
ð24Þ
The calculated values from modified Cai correlation was plotted in Fig. 5, which has an error less than 2.44%. This correlation will be applied to both the annulus and draft tube zones of the i-CFB reactor. It should be noted that the Cai correlation can only be used for bubbling and turbulent regimes. If the gas velocity exceeds Ut, the draft tube is operated as a transport riser. The Pugsley correlation [20], which was developed for transport risers with diameters of 0.05 to
30
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
1 m and for particles with diameters of 50 to 350 μm, could be used for the estimation of voidage.
ε¼
Uρp Gs ψ þ Uρp
ð25Þ
where Gs is the solid circulation rate and U0 is the superficial gas velocity inside the draft tube. The slip factor was defined as the ratio of gas interstitial velocity to the average particle velocity and correlated to the Froude number.
It should be noted that the net gas exchange is mostly from draft tube to the annulus based on calculated gas flow rate both from the annulus to draft tube and from draft tube to annulus (results are not shown here), which is in opposite to the net solid flow from the annulus to the draft tube. The low gas bypass from annulus to draft tube can limit the oxygen concentration buildup in the NOx reduction zone in an i-CFB, leading to potential improvement of the overall deNOx efficiency. For modeling the hydrodynamics of the i-CFB, the gas bypass RDA data are correlated to Ua0 and Ud0 by RDA ¼ 1:039
ψ¼
U 5:6 0:41 þ 0:47 Frt ¼1þ εUp Fr
ð26Þ
where Fr and Frt are Froude number and particle Froude number, respectively. U Ut Fr ¼ ; Frt ¼ : ðgDd Þ0:5 ðgDd Þ0:5
ð27Þ
4.2. Gas bypass Gas bypass is very important for the design and operation of i-CFB, which determines both the gas velocities and actual reactant concentrations in the annulus and draft tube. The measured gas bypass data from Yang [6] were shown in Fig. 6, where RDA is the gas bypass ratio from draft tube to the annulus and RAD is from the annulus to draft tube. It can be seen from Fig. 6(a) that RDA increases with increasing Ud0, gas feed rate to the draft tube. It is seen that more gas leaks to the annulus as the gas velocity in the draft tube increases. However, when the gas velocity in the annulus is higher, less gas leaks from draft tube to the annulus, leading to a lower RDA. Also, the effect of feed gas velocity in the annulus is less significant at lower Ud0, as evidenced from the slopes of RDA at different Ud0. At Ud0 =0.45m/s, RDA is almost unaffected by Ud0. Compared to RDA, RAD data are much more scattered and show no obvious trend. The change in both Ua0 and Ud0 has almost no effect on RAD, which fluctuates in the range of 5–9%, as shown in Fig. 6(b). It is very likely that this small fraction of gas is carried by the particles flowing from the annulus to the draft tube through the orifice.
a
−0:616
Ud0 Umf
1:300 2 R ¼ 0:865 :
ð28Þ
Since RAD is much scattered across a narrow range, an average value of 7% was used. RAD ¼ 7%
ð29Þ
It should be noted that the equations are only valid within the experimental range, 0.45 m/s b Ud0 b 0.9 m/s and 0.2 m/s b Ua0 b 0.475 m/s. If Ud0 N 0.9 m/s, RDA is predicted to be more than 100% and is unrealistic. The same problem also happens when Ua0 is smaller than 0.2 m/s. It is observed that at a higher Ud0, the increase in RDA slows down with increasing Ud0. The difference between the values of RDA at Ud0 = 0.75 m/s and Ud0 = 0.9 m/s is very small. So, when Ud0 is higher than 0.9 m/s, the values of RDA at Ud0 = 0.9 m/s is taken in the modeling. Also, when Ua0 is smaller than 0.2 m/s, the RDA values at Ua0 = 0.2 m/s is used. It should be warned that this assumption could potentially lead to errors in the modeling, since these values have not been confirmed experimentally. The real gas velocities in the annulus and draft tube can now be calculated as: Ua ¼ Ua0 −RAD Ua0 þ RDA Ud0 ðAd =Aa Þ
ð30Þ
Ud ¼ Ud0 −RDA Ud0 þ RAD Ua0 ðAa =Ad Þ:
ð31Þ
4.3. Measured solid circulation rates The solid circulation rate in the i-CFB reactor was measured at two different particle loadings, 2.275 kg and 3.3 kg. The particle velocity and voidage in the annulus were measured at different radial positions by the optical fibre probe. Fig. 7(a) shows the particle velocity as a function of dimensionless radial positions at different annulus gas
b
65
Ud0=0.6 m/s
9
Ud0=0.6 m/s
55
Ud0=0.45 m/s
Bed loading=3.3 kg
Ud0=0.45 m/s
Bed loading=3.3 kg
60
Ud0=0.75 m/s
Ud0=0.75 m/s
50
Ud0=0.9 m/s
Ud0=0.9 m/s
8
RAD (%)
45
RDA (%)
Ua0 Umf
40 35
7
30 6
25 20
5
15 10 0.15
0.20
0.25
0.30
0.35
0.40
Annulus inlet velocity, Ua0 (m/s)
0.45
0.50
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Annulus inlet velocity Ua0 (m/s)
Fig. 6. Gas bypass ratios at different Ud0. (a), from draft tube to annulus, RDA; (b), from annulus to draft tube, RAD (symbols: experimental data, line: correlation).
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
a
b Mloading=2.275 kg
0.20 0.85
Ud0=1 m/s
0.15
Voidage, ε
Particle velocity, Up (m/s)
31
0.10
0.05
0.75
Ua0=0.1 m/s
0.00
Mloading =2.275 kg Ud0 =1 m/s
0.80
Ua0=0.1 m/s
Ua0=0.2 m/s
Ua0=0.2 m/s
Ua0=0.4 m/s
Ua0=0.4 m/s
Ua0=0.6 m/s
Ua0=0.6 m/s
0.70
-0.05 0.6
0.7
0.8
0.9
1.0
0.6
0.7
0.8
r/R0
0.9
1.0
r/R0
Fig. 7. Measured radial profiles of (a) particle velocity and (b) voidage at different Ua0 (Ud0 = 1 m/s, bed loading = 2.275 kg. Symbols: experimental data, lines: connection of symbols).
velocity Ua0 with a particle bed loading of 2.275 kg. The value of r is referred to the distance from the axis of the i-CFB to the measurement point and R0 is the column radius. The annulus zone is from r/R0 = 0.5 to r/R0 = 1. The positive values of the particle velocity indicate a downflow of particles while negative values indicate an upflow of particles. It can be seen that the particle velocity increases with decreasing Ua0. However, this does not necessarily mean that the solid circulation rate is higher, since the solid circulation is determined by both particle velocity and the local voidage. For most of the curves in Fig. 7(a), especially at lower Ua0, local particle velocity is higher at the outer side of the annulus than at the inner side. For a particle loading of 2.275 kg at a low annulus gas velocity, the flow pattern (b) in Fig. 4 is expected, in which solids fall down fast near the outer wall of the annulus. At a higher Ua0, particle velocities in the middle of the annulus are very low, and sometimes the solids can even move upward in the middle of the annulus due to uneven gas flow distribution. Most of the solids flow down the annulus along both the inner and outer walls of the annulus. The reactor may be operated with the flow pattern (c) in Fig. 4 at a higher annulus gas velocity, in which case some solids from the jet above the draft tube fall down along the outer side wall, and some solids penetrate through the jet to the dense annulus zone and then fall down along the inner wall. The measured radial voidage profile in the annulus is shown in Fig. 7(b). The voidage is seen to be very low near both inner and outer
a
b
0.25 Ua0=0.1 m/s Ua0=0.2 m/s
0.20
Ua0=0.4 m/s
Mloading =3.3 kg Ud0 =1 m/s
0.90
Ua0=0.6 m/s
0.15
Voidage, ε
Particle velocity, Up (m/s)
walls of the annulus, and reaches a peak around the middle of the annulus, indicating the presence of fewer particles in the middle region of the annulus. The voidage decreases with increasing annulus gas velocity, which is contradictory to that commonly observed in a fluidized bed where voidage increases with increasing inlet gas velocity. One likely explanation is that the optical probe at point D4 in Fig. 1 is located in the dilute region well above the upper surface of the dense fluidized bed. In the freeboard region of a fluidized bed or in the downcomer with countercurrent gas–solid flow, the voidage decreases with increasing inlet gas velocity. When particle loading is increased to 3.3kg, the radial distribution of axial particle velocity in the annulus varies only slightly in the middle section, as shown in Fig. 8(a). The particle velocity increases slowly from the inner wall toward the middle of the annulus. Close to the column wall, the velocity increases substantially. The particle velocity decreases first when Ua0 increases from 0 to 0.4 m/s and then increases a lot when Ua0 is further increased to 0.6 m/s. The radial voidage profile at a solid loading of 3.3 kg, as shown in Fig. 8(b), is also different from that at a solid loading of 2.275 kg. At a low Ua0, the voidage is almost flat along the radial direction, especially near the draft tube, indicating a uniform solid distribution in the annulus. At a high Ua0, voidage begins to decrease along the radial direction, leading to a denser region near the outer wall of the annulus. A valley appears on all profiles near the column wall. There is a sudden
0.10
0.85
Ua0=0.1 m/s
0.80
0.05
Ua0=0.2 m/s Ua0=0.4 m/s Mloading =3.3 kg
0.00
Ua0=0.6 m/s Ud0=1 m/s 0.75
0.5
0.6
0.7
0.8
r/R0
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
r/R0
Fig. 8. Measured radial profiles of (a) particle velocity and (b) voidage at different Ua0 (Ud0 = 1 m/s, bed loading = 3.3 kg. Symbols: experimental data, lines: connection of symbols).
32
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
increase in voidage close to the column wall. This could be caused by the gas flowing up near the wall because of the uneven gas distribution in the annulus. Combining with the radial particle velocity distribution, it can be concluded that more particles move downward near the column wall. Similar to Fig. 7(b) at the solid loading of 2.275 kg, the overall voidage decreases with increasing gas velocity. However, the voidage increases when Ua0 further increases to 0.6 m/s. This can be explained by the bed expansion at different Ua0. It is likely that the optical probe is already immersed in the dense region of the fluidized bed at Ua0 = 0.4 m/s. So if Ua0 further increases, the measured voidage increases in the same way as the overall bed voidage. Fig. 9 shows the measured radial profiles of particle velocity and voidage at different Ud0. The particle velocities show a similar trend at different Ud0, but the effect of Ud0 is not very clear. Compared to particle velocity, the voidage in Fig. 9(b) is greatly influenced by Ud0, decreasing with increasing Ud0. Combining the solid velocity and voidage in the annulus, it can be inferred that the solid circulation rate increases with increasing Ud0. The overall net solid flux in the annulus, Gs, is calculated from the integration of the local solid flux across the cross section of the annulus. Fig. 10(a) shows Gs as a function of Ua0 at different draft tube velocities with a solid loading of 2.275kg. As discussed above, the solid circulation rate mostly increases with increasing draft tube gas velocity Ud0, but decreases with increasing Ua0. This can be explained by the pressure balance over the i-CFB reactor. When the draft velocity increases at a constant annulus velocity, solid circulation is increased because of the increased pressure difference between the draft tube and the annulus. On the other hand, at a constant draft tube gas velocity, the increase of annulus gas velocity increases the bed expansion in the annulus, which lowers the pressure buildup in the annulus and the pressure difference between the draft tube and the annulus, leading to the reduced solid circulation rate. Gs at a high bed solid loading of 3.3 kg is not sensitive to the annulus gas velocity at high draft tube gas velocities. At a low draft tube velocity, Ud0 = 0.5 m/s, Gs increases from Ua0 = 0 to Ua0 = 0.1 m/s but decreases to less than 15 kg/m2·s when Ua0 is increased from 0.1 to 0.4 m/s. This is likely caused by the small gas velocity difference between the draft tube and annulus, which can lead to loss of pressure difference between these two zones. Also, Gs is less sensitive to Ud0 at 3.3 kg solid loading than at a bed solid loading of 2.275 kg. In previous literature, influences of gas velocity in the annulus and draft tube on solid circulation rate have been studied for various fluidized beds with draft tube. The results are different from the trends obtained in the current study due to different distributor configurations
a
4.4. Prediction of solid circulation rate The solid circulation rate at a bed solid loading of 3.3 kg is modeled by mass and pressure balance equations presented in Section 3. The real gas velocities in the annulus and draft tube are adjusted by the gas bypass ratios. Then voidage in both zones is calculated using Cai's correlation. Fig. 11(a) shows the estimated voidage, with the closed symbols corresponding to the voidage in the annulus and the open symbols for the voidage in the draft tube. It can be seen that the voidage in the draft tube is always higher than the voidage in the annulus, since the velocity in the draft tube is always higher than in the annulus. From the bed expansion characteristics shown in Fig. 5, voidage is expected to increase from 0.6 to 0.85 when the gas velocity increases from 0.1 m/s to 0.6 m/s. The curves of annulus voidage εa seem to be quite different from expected without gas bypass. The voidage in the annulus increases with increasing draft tube inlet gas velocity because more gas passes from the draft tube through the orifice to the annulus zone at higher Ud0. At the same Ud0, the slopes of most εa vs. Ua curves are lower than the slope in Fig. 5, due to smaller RDA values at higher Ua0. It can be concluded that the voidage in both zones of the i-CFB reactor is substantially changed by gas bypass.
b 1.0 0.25
Ud0=0.75 m/s
0.20
Ud0=1.25 m/s
Ud0=1.25 m/s
0.9
0.15
0.10 Mloading=2.275 kg
0.8
Mloading=2.275 kg
0.7
Ua0=0.1 m/s
Ua0=0.1 m/s
0.05
0.00 0.5
Ud0=0.75 m/s Ud0=1 m/s
Ud0=1 m/s
Voidage, ε
Particle velocity, Up (m/s)
and operating conditions. In most of these reactors [2–5,21,22], the annulus operates as a moving bed. For example, in the research of Kim's group [2–5], Ua0 was set to be 0.4–1.6 Umf and Ud0 was set to be 2.6–20.4 Umf. It was found that the solid circulation rate increased with increasing gas velocity in both the annulus and the draft tube. The same trends were also observed by other researchers [21,22]. However, in the current study, the annulus was operated in bubbling or turbulent fluidization. The characteristics of solid circulation rate are also different. It is seen from Fig. 10 that Gs is a strong function of bed solid loading and inlet gas velocities. At low bed solid loadings and low Ud0, Gs decreases as the annulus gas velocity increases. However, the trend changes and tends to be reversed at high bed solid loadings and high Ud0. Many factors may influence the solid circulation rate of the i-CFB at different solid loadings. The trends of these curves cannot be simply explained by the differences of the inlet gas velocities. Gas bypass at different bed solid loading and inlet gas velocities could directly influence the actual gas velocity in both the annulus and draft tube, which determines the voidage in each zone. Effective bed heights in both zones are also influenced by operating conditions. The reason for such a different trend is discussed in detail in the Appendix A.
0.6
0.7
0.8
r/R0
0.9
1.0
0.6 0.5
0.6
0.7
0.8
0.9
1.0
r/R0
Fig. 9. Measured radial profiles of (a) particle velocity and (b) voidage at Ua0 = 0.1 m/s (symbols: experimental data, lines: connection of symbols).
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
b Mloading=2.275 kg
Solid circulation rate, Gs (kg/m2.s)
Solid circulation rate, Gs (kg/m2.s)
a 60
33
Ud0=0.75 m/s Ud0=1 m/s
50
Ud0=1.25 m/s
40
30
20
35
30
25
Mloading =3.3 kg Ud0=0.5 m/s
20
Ud0=1 m/s Ud0=1.4 m/s
15
10
10 0.1
0.2
0.3
0.4
0.5
0.6
0.0
Annulus inlet velocity, Ua0, m/s
0.1
0.2
0.3
0.4
0.5
0.6
Annulus inlet velocity, Ua0, m/s
Fig. 10. Net solid circulation rate at different Ud0, with bed solid loadings of (a), 2.275 kg, and (b), 3.3 kg (symbols: experimental data, lines: connection of symbols).
Following the procedure given in Table 3, effective bed heights in the two zones are estimated through mass balance and plotted in Fig. 11(b). In the figures, ‘a’ is annulus and ‘d’ denotes draft tube. At low Ua0 and Ud0, type (b) flow pattern is expected with Hd = Hdraft-tube and Ha b Hd. But at higher Ua0 and Ud0, the flow patterns are expected to be either type (c) or type (d), with the effective heights of annulus and draft tube being the same and larger than the length of draft tube. It can be seen that the effective bed height increases with increasing both Ud0 and Ua0. At low Ud0, the slope of the curves is steep, because increasing inlet gas velocity can significantly increase the expansion of the fluidized bed. But at higher Ud0 and Ua0, the top of the annulus dense bed exceeds the height of the jet above the draft tube and flow patterns (c) or (d) in Fig. 4 are formed. Further increasing the inlet gas velocity has little effect on the effective bed height. Pressure drop across the annulus and draft tube is estimated based on the estimated voidage and effective bed height, and the pressure drop across the orifice ΔPor is obtained based on the pressure difference between the annulus and the draft tube. The values of ΔPor are further fitted into Eq. (10) to obtain the discharge coefficient Cs at each operating condition. The calculated Cs data are shown in Fig. 12 as a function of Reynolds number of the particles passing through the orifice, Rep, defined as: ρg dp Up;a : μ
ð32Þ
a 1.0
CO2 ;d ¼ CO2 ;a0
FAD U ¼ CO2 ;a0 RAD a0 Fd Ud
ð33Þ
Fig. 13(a) shows the predicted O2 concentration in the draft tube, CO2,d, at various inlet gas velocities. All the values of CO2,d are very low,
b Bed loading=3.3 kg
0.8
0.7
Annulus:Ud0 =0.5 m/s Draft tube:Ud0 =0.5 m/s Annulus:Ud0 =1 m/s
0.6
Draft tube:Ud0 =1 m/s
0.5 0.1
0.2
0.3
0.4
Effective bed height (m)
1.3
0.9
Voidage, ε
Rep ¼
The fitted Cs values are quite scattered and varied from 0.13 to 0.21, which falls reasonably into the range as reported in the literature [15]. Since no obvious trend with Rep was observed, an average Cs value of 0.167 is taken for further simulation. Using the current model, hydrodynamics at a bed solid loading of 3.3 kg is further investigated for the design of an i-CFB reactor. In an iCFB deNOx reactor, flue gas is fed into the annulus and NOx in the flue gas will be adsorbed onto the catalyst surface. The oxygen concentration in the flue gas is always high in lean combustion of fuels, and the presence of high level oxygen favors the NOx adsorption. In the draft tube, NOx adsorbed on the catalyst surface is reduced by hydrocarbons. The reduction reaction is inhibited by O2 because hydrocarbon reductant is consumed by oxygen. Therefore, careful control of the oxygen concentration inside the draft tube is of great importance to achieve the high deNOx efficiency of the deNOx reactor. Here, the actual O2 concentration in the draft tube is estimated based on the gas bypass ratios and the gas flow rate into the draft tube using Eq. (33). It is assumed that O2 only exists in the gas fed into the annulus with a concentration of 8%.
1.2 1.1 1.0 0.9
Draft tube:Ud0 =1.5 m/s
0.5
0.6
Draft tube, Ud0=0.5 m/s Annulus, Ud0=1 m/s
0.7 0.6
0.5
Annulus, Ud0=0.5 m/s
0.8
Annulus:Ud0 =1.5 m/s
Annulus inlet velocity, Ua0, m/s
Bed loading=3.3 kg
Draft tube, Ud0=1 m/s Annulus, Ud0=1.5 m/s Draft tube, Ud0=1.5 m/s
0.1
0.2
0.3
0.4
0.5
0.6
Annulus inlet velocity, Ua0, m/s
Fig. 11. Calculated (a) voidage and (b) effective bed height at a bed solid loading of 3.3 kg (symbols: experimental data, lines: connection of symbols).
34
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
0.35
circulation rate decreased as the annulus gas velocity increased. However, this trend could be reversed at high bed loading and high draft tube velocity. A hydrodynamic model was then developed based on mass and pressure balances. Discharging coefficient Cs was extracted from fitting the experimental data and an average value of 0.167 was taken for model simulation. The model could well capture the characteristics of the solid flow and gas flow distribution, and could serve as a useful tool for the design and simulation of the i-CFB deNOx reactor system. However, modeling at different bed solid loadings requires the gas bypass characteristics being measured. With data on both the gas bypass and solid circulation rate, the hydrodynamic behavior could be coupled with the reaction kinetics to simulate the iCFB performance for NOx reduction.
0.30 0.25
Cs
0.20 0.15 0.10 0.05 0.00 0.2
0.4
0.6
0.8
1.0
Rep Fig. 12. Fitted Cs values as a function of Rep.
ranging from 0.25% to 0.5%. This is due to the low gas bypass ratios from annulus to draft tube. The predicted low oxygen concentration in the draft tube can thus achieve a high NOx reduction efficiency. The overall NOx abatement efficiency is determined by both the adsorption in the annulus, which directly removes NOx from the flue gas, and the reduction in the draft tube. The NOx adsorption efficiency in the annulus is strongly affected by the solid circulation rate, which represents how the NOx can be efficiently transferred to the reduction zone and also determines the contact time between gas and catalyst. Fig. 13(b) shows the predicted solid circulation rate at different inlet gas velocities. It is seen that Gs is smaller at lower Ud0, e.g. 0.6 m/s. But further increasing Ud0 from 0.75 m/s to 0.9 m/s has little effect on Gs and even leads to lower values of Gs. The broad width of the peak also indicates that the i-CFB can be well operated over a wide range of Ua0, with the optimal annulus velocities between 0.25 and 0.45 m/s. 5. Conclusions Hydrodynamics of an i-CFB deNOx reactor has been studied by both experiment and modeling. Gas bypass was investigated by CO2 tracer method, and solid circulation rate was measured using an optical fibre probe at bed solid loadings of 3.3 kg and 2.275 kg. It was found that solid circulation rate was a strong function of bed loading and feeding gas velocities. At low bed loading and low draft tube velocity, solid
a
Nomenclature Aa cross area, m2 Ad cross sectional area of the draft tube, m2 Aor area of the orifice, m2 CO2,a0 O2 concentration in the gas fed into the annulus, mol/m3 CO2,d O2 concentration in the draft tube, mol/m3 Cs discharging coefficient of the orifice Da diameter of the annulus column, m Db diameter of the bubbles, m Dd diameter of the draft tube, m dp particle diameter, m dimensionless particle diameter dp⁎ Fa0 flow rate of gas fed to the annulus, m3/s FAD flow rate of gas bypassing from the annulus to the draft tube, m3/s Fb gas flow rate in the bubbles, m3/s Fd gas flow rate in the draft tube, m3/s Fd0 flow rate of gas fed to the draft tube, m3/s FDA flow rate of gas bypassing from the draft tube to the annulus, m3/s Fgw gas–wall friction force per unit volume of the column, N/m3 Fpw particle–wall friction force per unit volume of the column, N/m3 Fr Froude number Frt Froude number at terminal velocity g acceleration due to gravity, 9.8 m/s2 Gs solid circulation rate across the annulus, kg/m2·s H fluidized bed height, m Ha effective bed height in the annulus, m Ha0 initial effective bed height in the annulus, m Hd effective bed height in the draft tube, m
b 0.50
Ud0=0.75 m/s
30
Ud0=0.9 m/s
0.45
Gs, kg/m2.s
Bed loading = 3.3 kg
CO2,d, %
35
Ud0=0.6 m/s
0.40
0.35
25 20 Bed loading = 3.3 kg
15 Ud0=0.6 m/s Ud0=0.75 m/s Ud0=0.9 m/s
0.30 10 0.25 5 0.20
0.25
0.30
0.35
0.40
0.45
Annulus inlet velocity, Ua0, m/s
0.50
0.20
0.25
0.30
0.35
0.40
0.45
Annulus inlet velocity, Ua0,m/s
Fig. 13. Predicted (a) CO2,d and (b) Gs as a function of Ua0.
0.50
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
Greek symbols db bubble phase fraction ε voidage εa voidage in the annulus εd voidage in the draft tube μ dynamic viscosity, Pa·s ρg gas density, kg/m3 ρp density of particles, kg/m3 τ time lag, s ψ slip factor ∅s spherical coefficient
Acknowledgments The authors are grateful to the Natural Science and Engineering Research Council (NSERC) of Canada for the financial support in the form of a discovery grant. X. Cheng is also grateful to a scholarship from the China Scholarship Council (CSC). Appendix A Why Gs decreases when Ua0 increases at bed loading = 2.275 kg which contradicts the observation in the literature?
70
Exp-Ud0=0.75 m/s Exp-Ud0=1 m/s
60
50
Gs, kg/m2.s
Hd0 initial effective bed height in the draft tube, m Hdraft-tube height of draft tube, m Hf expanded bed height, m HG gap distance in the distributor, mm Hmf bed height at minimum fluidization, m Hs bed height, m Le effective distance of optical fibre, m Lj jet height of spout bed, m Ma mass of solids in the annulus, kg Md mass of solids in the draft tube, kg Mloading mass of solids loaded in the i-CFB reactor, kg P pressure, Pa r distance from the central of the bed, m R0 radius of fluidized bed, m RAD gas bypass ratio from the annulus to the draft tube, % RDA gas bypass ratio from the draft tube to the annulus, % Rec Reynolds number at transition velocity Rep Reynolds number around particles U gas velocity, m/s Ua real gas velocity in the annulus, m/s Ua0 feeding gas velocity in the annulus, m/s Ub bubble velocity, m/s Uc transition velocity at which standard deviation of pressure fluctuation reaches a maximum, m/s Ud real gas velocity in the draft tube, m/s Ud0 feeding gas velocity in the draft tube, m/s Umf gas velocity at minimum fluidization, m/s Up particle velocity, m/s Up,a particle velocity in the annulus, m/s Up,d particle velocity in the draft tube, m/s Ut terminal velocity, m/s dimensionless terminal velocity U⁎t Y dimensionless coefficient ΔP pressure drop, Pa ΔPa pressure drop in the annulus, Pa ΔPa0 initial pressure drop in the annulus, Pa ΔPd pressure drop in the draft tube, Pa ΔPd0 initial pressure drop in the draft tube, Pa ΔPor pressure drop through the orifice, Pa
35
Exp-Ud0=1.25 m/s
Ud0=1.25 m/s
Mloading=2.275 kg
Ud0=1 m/s
40
30
Ud0=0.75 m/s 20
10 0.1
0.2
0.3
0.4
0.5
0.6
Ua0, m/s Fig. A1. Experimental and modeled solid circulation rates at a bed solid loading of 2.275 kg (symbols: experimental data; lines: model prediction.).
Since the characteristics of gas bypass are unknown, detailed and accurate analysis could not be obtained. So here it is assumed that there is no gas bypass and the pressure drop could be analyzed quantitatively. Following the calculation procedure presented in Table 3, most of the tested conditions in Fig. 10(a) possess type (b) flow patterns. The effective bed height in the draft tube equals the height of draft tube height, and the annulus effective bed height changes with the voidage. Since the inlet gas velocity of the draft tube does not change, the pressure drop ΔPd remains a constant. For most of the data points, the annulus is operated as a fluidized bed. It can be assumed that the pressure drop in the annulus is determined by the weight of solid in the annulus. ΔPa ¼ gρp ð1−εa ÞHa ¼ gMa =Aa
ðA1Þ
If the draft tube gas velocity remains at a constant, voidage in the draft tube will not change, so does the amount of solids in the draft tube. Solid weight in the annulus does not change at various Ua0, which gives rise to a constant pressure drop across the annulus. Thus the pressure drop through the orifice, ΔPor, remains constant. According to Eq. (10), solid circulation rate is influenced by ΔPor and εa. At higher Ua0, εa becomes bigger, leading to a lower Gs. An attempt was made to model the solid circulation rate at bed solid loading of 2.275 kg, with the results plotted in Fig. A1 as lines. Gas bypass was not considered since there are no data available. Therefore, the modeling results are not reliable for reactor design purpose. But they could be used to check the trend of solid circulation rate at different conditions. It could be seen that all the modeling results fall into a reasonable range of the experimental data. All the solid circulation rates decrease with annulus gas velocity, confirming the consistency of the experiments and the proposed explanations. References [1] T.T. Yang, H.T. Bi, A novel fluidized bed reactor for integrated NOx adsorption– reduction with hydrocarbons, Environ. Sci. Technol. 43 (13) (2009) 5049–5053. [2] J.H. Jeon, S.D. Kim, S.J. Kim, Y. Kang, Solid circulation and gas bypassing characteristics in a square internally circulating fluidized bed with draft tube, Chem. Eng. Process. 47 (12) (2008) 2351–2360. [3] B.H. Song, Y.T. Kim, S.D. Kim, Circulation of solids and gas bypassing in an internally circulating fluidized bed with a draft tube, Chem. Eng. J. 68 (1997) 115–122. [4] H.S. Ahn, W.J. Lee, S.D. Kim, B.H. Song, Solid circulation and gas bypassing in an internally circulating fluidized bed with an orifice type draft tube, Korean J. Chem. Eng. 16 (1999) 618–623. [5] S.D. Kim, Y.H. Kim, S.A. Roh, D.H. Lee, Solid circulation characteristics in an internally circulating fluidized bed with orifice-type draft tube, Korean J. Chem. Eng. 19 (2002) 911–916.
36
X. Cheng, X.T. Bi / Powder Technology 251 (2014) 25–36
[6] T.T. Yang, A Novel Fluidized Bed Reactor for Integrated NOx Adsorption–Reduction With Hydrocarbons, in Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, 2008. [7] T.D. Hadley, C. Doblin, J. Orellana, K.-S. Lim, Experimental quantification of the solids flux in an internally circulating fluidized bed, The 13th International Conference on Fluidization — New Paradigm in Fluidization Engineering, 2010. [8] Z. Chen, Hydrodynamics, Stability and Scale-up of Slot-rectangular Spouted Beds, in Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver, 2008. [9] J.Z. Liu, J.R. Grace, X.T. Bi, Novel multifunctional optical-fiber probe: I. Development and validation, AIChE J. 49 (6) (2003) 1405–1420. [10] X.Q. Song, H.T. Bi, C.J. Lim, J.R. Grace, E. Chan, B. Knapper, C. McKnight, Hydrodynamics of the reactor section in fluid cokers, Powder Technol. 147 (1–3) (2004) 126–136. [11] C.Y. Yan, C.X. Lu, Y.S. Liu, R. Cao, M.X. Shi, Hydrodynamics in airlift loop section of petroleum coke combustor, Powder Technol. 192 (2) (2009) 143–151. [12] W. Namkung, C. Guy, R. Legros, Prediction of solids circulation rate in the riser of an internally circulating fluidized bed (ICFB), Chem. Eng. Commun. 188 (1) (2001) 47–58. [13] K. Svoboda, S. Kalisz, F. Miccio, K. Wieczorek, M. Pohorely, Simplified modeling of circulating flow of solids between a fluidized bed and a vertical pneumatic transport tube reactor connected by orifices, Powder Technol. 192 (1) (2009) 65–73.
[14] H. Konno, S. Saito, Pneumatic conveying of solids through straight pipes, J. Chem. Eng. Jpn 2 (1969) 211–217. [15] M. Kuramoto, D. Kunii, T. Furusawa, Flow of dense fluidized particles through an opening in a circulation system, Powder Technol. 47 (2) (1986) 141–149. [16] W.Q. Zhong, M.Y. Zhang, B.S. Jin, X.P. Chen, Flow pattern and transition of rectangular spout-fluid bed, Chem. Eng. Process. 45 (9) (2006) 734–746. [17] Q.J. Guo, G.X. Yue, J.Y. Zhang, Z.Y. Liu, Hydrodynamic characteristics of a twodimensional jetting fluidized bed with binary mixtures, Chem. Eng. Sci. 56 (15) (2001) 4685–4694. [18] P. Cai, G.D. Michele, A.T. Gradassl, A generalized method for predicting gas flow distribution between the phases in FBC, Fluidized bed combustion 2 (1993) 991–1002. [19] S.P. Babu, B. Shah, A. Talwalkar, Fluidization correlations for coal gasification materials, minimum fluidization velocity and fluidized bed expansion ratio, AIChE Symp. Ser. 74 (1978) 176–186. [20] T.S. Pugsley, F. Berruti, A predictive hydrodynamic model for circulating fluidized bed risers, Powder Technol. 89 (1) (1996) 57–69. [21] H.Y. Zhang, R. Xiao, D.H. Wang, J.M. Cho, G.Y. He, S.S. Shao, J.B. Zhang, Hydrodynamics of a novel biomass autothermal fast pyrolysis reactor: solid circulation rate and gas bypassing, Chem. Eng. J. 181 (2012) 685–693. [22] R. Xiao, M.Y. Zhang, B.S. Jin, X.D. Liu, Solids circulation flux and gas bypassing in a pressurized spout-fluid bed with a draft tube, Can. J. Chem. Eng. 80 (5) (2002) 800–808.