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Separation performance in a novel coupled cyclone with built-in circulating granular bed filter (C-CGBF) Sihong Gao, Dandan Zhang, Yiping Fan, and Chunxi Lu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b02278 • Publication Date (Web): 21 Aug 2018 Downloaded from http://pubs.acs.org on August 28, 2018
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Separation performance in a novel coupled cyclone with built-in circulating granular bed filter (CCGBF) Sihong Gao, Dandan Zhang, Yiping Fan*, Chunxi Lu* State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum, Beijing, 102249, China *Corresponding author. E-mail address:
[email protected] (Y. Fan);
[email protected] (C. Lu)
ABSTRACT: A compact dedust scheme coupling a cyclone with a built-in circulating granular bed filter (C-CGBF) for continuous hot gas cleanup is introduced. The effects of the operation parameters including the inlet dust concentrations, the inlet gas flowrates and the granules circulation fluxes on the separation performance of the C-CGBF are experimentally investigated using the FCC catalyst particles in a cold model setup. Experimental results reveal that stable/high collection efficiency, generally higher than 98%, is achieved. A real-time monitoring method is developed for timely reflecting the instantaneous variation of the granules circulation flux, in which way a notable critical flux is observed as the transition from the fixed bed into the moving bed regime. The individual separation contributions of the cyclone and the built-in
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granular bed are both estimated. The particles collected by them are also analyzed respectively for comparing their size distributions.
KEYWORDS: Gas-solids separation; Coupled separator; Cyclone separator; Granular bed filter 1. Introduction With increasing consumption of fossil fuel, especially the coal and petroleum, the problems of air pollution as a result of industrial waste gases emission have been long recognized and become the subject of a substantial amount of current researches. A high efficiency, economical and long-period stable operation equipment for gas purification gradually become the most important unit for many current industrial processes including the advanced electricity generation, the gasification and combustion, as well as the fluidized catalytic cracking (FCC)1-5. A great number of efforts has been made in utilizing the traditional equipment such as the electrostatic precipitators, the wet scrubbers, the ceramic filters, the cyclone separators and the granular bed filters1,
6, 7
. However, single-stage gas cleanup device often fails to meet the
requirements for the commercial application and the increasingly stringent effluent standards, especially under the high temperature high pressure (HTHP) situations. Consider the extensive energy-consumption and the limitation in operating temperature, electrostatic precipitators8,
9
and wet scrubbers10,
11
are not widely applied in the practical
industrial processes, especially under the HTHP situations, although they are very efficient in collecting the fine particles12. Ceramic filters have an excellent performance in filtering particles with sevral micrometers under the HTHP situations. Therefore, they have the most common industrial practice compared with other dust removal equipment, particularly in the conditions of HTHP13-18. However, frequent blowback is required because of the micropore congestion during
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filtration and then a continuous operation cannot be accomplished. Although many work has been carried out for improving the perfomance of cyclones by experimental study and/or numerical simulations19-22, the low separation efficiency for the fine particles less than 10 µm is still determined by the strong swirling turbulence and the procession vortex core (PVC) in cyclones. In order to remove the particles with sevral micrometers for meeting the requirements of the downstream units such as the gas turbines, arranging multiple cyclones in series or/and improving the gas velocity are the common methods. However, it is not suitable for a large handling capacity; while the covering area is also an important restricting factor for economic considerations23, 24. Cyclone separators are commonly adopted as a preliminary treatment for the dust-laden gas in a multiple-stage gas purification process, on account of their simple structure and the efficient separating ability for particles large than 10 µm. Granular bed filters, on the other hand, generally utilize cheap and refractory granules media with great technical/economic superiorities in hot gas cleanup25, 26. It also has the potential of simutaneously adsorbing gasous impurities27, 28. “Particle”, in this paper, generally refers to the fine dust particles contained in gas streams; while “granule” means the larger particles utilized as the filter media filled in the granular bed. The granular bed filters can be roughly devided into two operating regimes, according to the movement of the filter media. Compared to the fixed bed (FB) regime, the moving bed (MB) regime is more attractive as its no need for periodic blowback; the dust deposits inside the filter bed are continuously transported out by the downward granular flow. If combined with a regenerating system for the reuse of the filter media, the moving bed granular filters offer an option for a long-period stable operation. However, granular bed filtration is generally adopted to clean a small number of fine particles contained in the gas streams29. The performance of granular bed filters is essentially influenced by the operation regime30, 31, the
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filtration superfacial velocity32, the granules circulation flux32-35, the inlet dust concentation36, the filter cake formation30, 37-39, the properties of the dust particles and the collector granules34, 35, 40, 41
, as well as the distribution and flow patterns of the inlet gas and the collector granules36, 42, 43. For the purpose of improving the separation efficiency and operation stability, multiple
separation mechanisms combined/coupled into one scheme are also seen. A counter-current moving bed granular filter was proposed by Brown et al.29; it has two distinct sections for filtering, an interfacial and a downcomer section. The interfacial section captures nearly 86% particles wherein a prominent filter cake forms. A circulating granular filter system (CGBFCLPs), using a dust/collector particles separator to regenerate the collector granules, was designed and investigated by Bai et al.44. It was found that the fine particles partially returning to the granular bed filter reduced the bed voidage, as well as increased the dust collection efficiency. On the other hand, external field, such as electrostatic, acoustic and magnetic field, are also employed for enhancing the particle removal efficiency considering the fact that the field force increases the collision chance of particles1, 45, 46. A research on the use of a continuously counter-current moving bed filter with the electrostatic enhancement was carried out at 850℃ and 10 bar by Delft University of Technology47. A compact dedust scheme coupling a cyclone with a built-in circulating granular bed filter (C-CGBF)48 for continuous hot gas cleanup is introduced in this paper. The centrifugal separation (the cyclone) and the filtration (the built-in granular bed filter) are then reasonably combined in one device. The main purpose of this paper is to experimentally explore the influences of the inlet dust concentrations, the inlet gas flowrates and the granules circulation fluxes on the separation performance of this coupled separator by using the FCC catalysts as the dust particles. The separation efficiency and the pressure drop of this separator are measured in a
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cold model setup. A real-time monitoring method is developed for easily and timely reflecting the instantaneous variation of the granules circulation flux in the circulating granular bed during operation. In order to estimate the individual separation contributions of the cyclone and the granular bed, the FCC catalyst particles separated by them are collected and weighed respectively. Those particles are also analyzed respectively for comparing their size distributions. 2. Experimental setup and methodology 2.1 Experimental setup The experimental setup used in this study is illustrated in Figure 1. Air is sucked off by the draught fan to enter the C-CGBF inlet. The dashed arrows in Figure 1 indicate the gas flow direction of the introduced-air. The air flowrate is controlled by a set of rotameters in the CCGBF outlet pipe. Dust particles are introduced into the inlet pipe at the Venturi section using a screw feeder, so as to efficiently disperse the introduced particles by a comparatively high gas velocity. The dust concentration in the inlet of the C-CGBF is determined by the inlet gas flowrate and the rotational speed of the screw feeder.
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Figure 1. Experimental setup.
Figure 2 shows the structure details of the C-CGBF used in this paper; it mainly consists of three sections: the cyclone, the granular bed filter and the riser-spouted bed regenerator. Except for the granular bed filter, the other sections of the C-CGBF system are constructed by transparent perspex for the convenience of observation. The inner diameter of the cyclone shell is 380 mm while the wrapping angle of the volute inlet is 180°. The inlet of the cyclone shell has a rectangular cross section of 227×108 mm2. The total height of the cyclone shell is 2480 mm, including a cylinder (1600 mm) and a cone (880 mm).
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As illustrated in Figure 2(a), the granular bed filled with the filter media is located between the two coaxial sleeves. The diameter of the inner sleeve is 127 mm; while the radial deepness of the granular bed is 50 mm. The walls in the cross-flow section of the inner and outer walls are both constructed by the stainless Johnson screen. The slot opening of the screen wall is chose as 0.75 mm for supporting the collector granules and reducing the dust congestion; its detailed structure is shown in Figure 2(c). Three walls including the cyclone shell and two coaxial sleeves are radially located with a common axis, so as to three relatively independent vertical spaces are determined, including two annular space and a core tube.
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Figure 2. The experimental rigs of the C-CGBF.
The first space is interlaid between the cyclone and the granular bed, wherein a swirl flow is formed by the volute inlet. Thereby the swirling gas stream crossing through the granular bed. In the cyclone shell, large particles contained in the gas stream are directly separated by the centrifugation and collected in the dust tank Ⅰ underneath. Those fine particles contained in the
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tangential-radial airflow are further filtered by the granular bed; thereby, the purified gas streams are acquired from the core tube. Under the circulating condition, the filter media in the granular bed moves downward under the force of gravity. The spent collector granules inclined pipe connects the dipleg and the prelift section of the riser. Setting a butterfly valve on the inclined pipe is originally intended to adjust the granules circulation flux. However, it is found that only two valid and discernible granular circulation fluxes (0.04 and 0.22 kg/s) are achieved by varying the opening of the valve because of its insufficient flexibility48. Although mechanical valves including the rotary valve are commonly used in cold-model experimental setup, they are normally perceived as not suitable for industrial application, especially in the HTHP situations. Therefore, a V type pneumatic valve is proposed in this paper. As illustrated in Figure 1, a transporting air jet along the centerline of the right-side pipe of the V type valve is directed into the pre-lift section of the riser, supplied by an air compressor. The granules circulation flux is adjusted more flexibly by changing the gas flowrate of the transporting air, as described in section 2.4. The total gas flowrate of the pneumatic air (also called by the regenerating gas) in the riser is maintained at 98 m3/h, which is determined by the transport velocity of the collector granules. The collector granules and the filtered fine particles are pneumatically conveyed by the riser into a regenerating vessel (the spouted bed regenerator); and then they are separated due to the difference of their transport velocities. The gas flow in the riser-spouted bed regeneration system is marked by the solid arrows in Figure 1, supplied by the air compressor. Figure 2(b) shows the detailed connecting structure between the riser and the spouted bed vessel. The refreshed collector granules travel through the regeneration pipe which connects the bottom of the spouted bed vessel and the top of the
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granular bed; therefore, the circulation loop of the collector granules in the C-CGBF system is realized. The regenerating gas containing the filtered dust particles is directed into a small cyclone and a filter-bag before expanding to the atmospheric pressure, so as to collect the fine particles. In order to estimate the individual separation contributions of the cyclone and the granular bed, the FCC catalyst particles separated by them are collected and weighed respectively. Those particles are also analyzed respectively for comparing their size distributions. 2.2 Materials For assessing the C-CGBF system, the FCC catalysts are used as the dust particles. The size distribution of the inlet FCC catalyst particles is plotted in Figure 3, measured by a LS-909 laser size analyzer. The median diameter D50 of the inlet FCC catalyst particles is 45.1 µm.
Figure 3. Size distribution of the inlet FCC catalyst particles.
UOP 13X-APG zeolite adsorbents with an average diameter 2.07 mm are filled in the granular bed as the collector granules. The particle density ρp and the bulk density ρb of the 13XAPG zeolite adsorbents are 1049 kg/m3 and 666 kg/m3, respectively. 2.3 Pressure drop and collection efficiency
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The energy consumption of cyclones in industrial process is generally evaluated by its static pressure drop; while the sequence of the pressure drop is usually employed to judge the filtering condition of granular bed filters. The C-CGBF is virtually a coupled separator covering a cyclone and a granular bed filter, therefore the static pressure drop ∆P of the C-CGBF is expressed as: ∆P = ∆Pc + ∆Pg (1)
∆Pc is caused by the gas vortex motion in the first annular space while ∆Pg represents the friction loss by the gas stream tangentially-radially crossing through the built-in granular bed. An electrical conversion software and an AZ82062 digital manometer are applied to transform and save the pressure drop signals to a computer. The signals are recorded continuously at 1 Hz. For the purpose of eliminating the stochastic fluctuation, the sequences of the average pressure drop (average value of the original signals at 100 s intervals) are plotted and analyzed. The separation efficiency η is expressed as Equation (2). It is usually used to represent the separation performance of filters.
η ( % ) = 1 − ( Cout Cin ) × 100 (2) Here Cout and Cin are the dust concentrations in the outlet and the inlet of the C-CGBF, respectively. In order to determine the outlet dust concentrations, a stream of the outlet gas is isokinetically drawn off by an out-stack sampling system, shown in Figure 1. Due to the diameter of the outlet duct used in this study is merely 215 mm; therefore, only one sampling position in the centerline of the outlet duct is adopted. The sampling position is fixed in a vertical pipe section. And the position is at about 12 diameters downstream and 8 diameters upstream of
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the bends. Furthermore, the mouth of the sampling probe is 8 mm in diameter and is sharp edged and tapered to avoid the turbulence around the inlet of the probe. The sampling gas is led through a filter cylinder in which the dusts are captured. The time for sampling is fixed at 30 min for collecting efficient samples and reducing the accidental errors caused by the operation and the sampling pipe. And then they are weighed; hence the collection efficiency is obtained. The precision grade of the instruments used in the sampling system is listed in Table 1. The time point to which the collection efficiency corresponds is noted by the mid-point in the sampling time. Table 1. The main instrument characteristic in the sampling system. Number in Figure 1
Instrument name
Precision grade (%)
(19)
sampling probe
1.00
(20) (22)
filter cylinder pressure gauge
0.20 0.25
(23)
air flowmeter
1.50
2.4 The measurement and control of the granules circulation flux The volume method is employed to determine the granules circulation flux Ws in the CCGBF. The time t spent by a given volume V of the collector granules downwards flowing out of the feeder hopper is recorded by a seconds-counter. As the bulk density ρb of the filter media is known, Ws can be calculated by:
WS = ρbV t (3) As mentioned in section 2.1, the granules circulation flux is controlled more sensitively and flexibly by adjusting the gas flowrate of the transporting air in the pneumatic valve, while the overall flowrate of the regenerating gas Qr in the riser is maintained at 98 m3/h. Figure 4 shows that more transporting air through the V valve would result in a high granules circulation flux until the flowrate of the transporting air increases above 12 m3/h. This limitation is mainly
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caused by the pressure balance between the material sealing height and the riser-spouted bed regeneration system. Therefore, all the relative operating parameters for assessing the C-CGBF are listed in Table 2.
Figure 4. The granules circulation flux at different flowrates of the transporting air in the V valve
Table 2. Operating parameters for assessing the C-CGBF using the FCC catalyst particles. Inlet gas flowrate
Superficial inlet velocitya
Superficial cross-flow velocityb
Inlet dust concentration
Granules circulation flux
m3/h
m/s
m/s
g/m3
kg/s
1
800
8.54
0.21
6.19
0.22
2
800
8.54
0.21
17.87
0.22
3
800
8.54
0.21
29.24
0.22
4
800
8.54
0.21
57.6
0.22
5
1400
14.95
0.37
16.71
0.22
6
800
8.54
0.21
29.24
0
7
800
8.54
0.21
29.24
0.04
8
800
8.54
0.21
29.24
0.10
9
800
8.54
0.21
29.24
0.15
10
800
8.54
0.21
29.24
0.24
Test
a
Based on the cross-sectional area of the inlet duct of the C-CGBF
b
Based on the equivalent area of the cross-flow (Johnson screen) section of the built-in granular bed
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2.5 A real-time monitoring method on the granules circulation flux Solids (particles and granules) circulation flux has significant influences on most gas-solids processes including the moving granular bed32-35 and the circulating fluidized bed49, 50. However, there are still no reliable and simple approaches in published studies for monitoring the instantaneous variation of the solids circulation flux during operation. In order to observe the real-instantaneous variation of the granules circulation flux in the C-CGBF, two pressure taps are set at the wall of the riser as shown in Figure 1. One tap is 0.5 m away from the top of the pre-lift section; the distance between two taps is 4 m. The pressure drop between the 4 m riser ∆Pr is recorded continuously at 1 HZ by another AZ82062 digital manometer. ∆Pr is theoretically analyzed as:
∆Pr = ρ gh + f g + f s (4) Where, ρ is the average density of the gas-solids flow in the 4 m riser, ρ =kWs / Qr ; fg is the friction loss caused by the pneumatic gas; fs represents the pressure loss due to the collision between the solids and the riser wall, as well as the collision between the solids themselves. fs can be viewed as a function of the dynamic head of the gas-solids flow, f s =ξs ⋅ ρ ut2 2 . Therefore
∆Pr is rewritten by: ∆Pr = Ws k ( gh + ξ ut2 ) Qr + f g (5)
Given the correcting coefficient k, the frictional coefficient of the solids motion ξs and the terminal velocity of the collector granules ut are constants depending on the collector granules and the dimensions of the riser; thus, there is a linear relationship between ∆Pr and Ws, with an intercept of fg.
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The experimental data is plotted in Figure 5. It is clearly shown that the pressure drop of the 4 m riser has a good linear variation with the granules circulation flux. If the granules circulation flux is fixed at 0 kg/s, the pressure drop of the 4 m riser is about 0.17 kPa, merely caused by the pneumatic gas flowing through the 4 m riser. In this way, the real-time monitoring on the granules circulation flux is easily realized by continuously measuring the pressure drop of the 4 m riser during operation.
Figure 5. Relationship of the pressure drop of the 4 m riser and the granules circulation flux
3. Results and discussion 3.1 Effect of inlet dust concentration The static pressure drop ∆P of the C-CGBF at different operating times at Q=800 m3/h and Ws=0.22 kg/s in different inlet dust concentrations Ci is plotted in Figure 6. The initial average
pressure drop is about 0.9 kPa and it is mainly caused by the inlet gas flowrate (velocity). The pressure drop under the investigated concentrations increases slightly with time after the FCC catalysts introduced into the C-CGBF at t=1000 s. However, the gradient of the pressure drop declines gradually, especially during the initial increase stage (about 1000~3000 s). After 3000 s, however, the gradient keeps nearly unvaried at a relatively low constant. As to the traditional barrier filters including the FB regime in this scheme, the pressure drop undoubtedly increases
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due to the bed voids gradually filled by the filtered FCC catalyst particles. Whereas, under the MB regime, the fine FCC catalyst particles filtered by the granular bed are continuously transported out from the filter bed by the downward flow granules. In other words, the duration time for the increasing of the hold-up of the FCC catalyst particles in the filter bed is quite short. A balance between the FCC catalyst particles settling in and carried out is then reached. For the MB regime, once the balance condition is achieved, the FCC catalyst particles are transported out by the spent granules as soon as it settles in the granular bed; as a result, the hold-up of the FCC catalyst particles in the filter bed stays comparatively unchanged; therefore, the static pressure drop assumes a comparatively steady profile.
Figure 6. Static pressure drop at different operating times (inlet dust concentrations).
It is clearly observed that the dust aggregation forms on the screen wall during the course of experiments. It is a possible reason for why the static pressure drop still increases slightly after 3000 s. Although the filter cake with a certain thickness benefits to high collection efficiency, an excessive formation of the dust aggregation always results in some undesirable conditions including the shut down as well as the filter cleaning. Fortunately, parts of the filter cake are substantially scraped by the gas vortex motion in the first annular space. The swirl flow sweeps past the surface of the outer screen wall, bring about a shear on the particle agglomerates
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adhering to the screen wall. Thereby the formation of the particle agglomerates is considerably restrained. The thickness and solidity of the dust aggregation are greatly influenced by the swirlflow intensity, the cross-flow gas velocity, the inlet dust concentration and the cohesive characteristic of the dust particles. If increasing the inlet dust concentration, the pressure drop and its gradient present a relatively great value, as illustrated in Figure 6. In such a high inlet dust concentration, more fine FCC catalyst particles with several micrometers are carried into the filter bed by the cross-flow gas, resulting in a high depositing rate and a high balance hold-up of the FCC catalyst particles therein. A high inlet dust concentration is also benefit to the formation of the filter cake. In consequence, the pressure drop caused by the gas flowing through the C-CGBF is inevitably increased. As illustrated in Figure 6 and Figure 7, the collection efficiency of the C-CGBF is generally above 98%; meanwhile, the pressure drop is generally less than 1.5 kPa. The collection efficiency remains stable with time and increases with the inlet dust concentration. In regard to the FB regime, the hold-up of the FCC catalyst particles in the filter bed inevitably increases during operation. The bed voids are congested by the FCC catalyst particles sequentially; therefore, the dust separation performance is anticipated to be enhanced. Although the fine FCC catalyst particles filtered by the granular bed are continuously carried out, the balance hold-up of the FCC catalyst particles are raised by high concentrations, so as to the voidage in the filter bed decreases. The separation efficiency increases with more FCC catalyst particles settling in the filter bed. Besides, the filter cake is also strengthened in the condition of the high inlet dust concentration. It is noted that, the agglomeration of the fine particles is strengthened in a high concentration; thus, the centrifugal separation is also intensified22. As a result, the total collection
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efficiency increases. As analyzed above, it is benefit for improving the collection efficiency by increasing the inlet dust concentration for the C-CGBF system. Whereas, a high inlet dust concentration potentially results in a poor operation with a rapidly and continuously growing pressure drop, even unplanned shutdown, although these conditions are not observed at this granules circulation flux (Ws=0.22 kg/s). However, the adhesiveness among fine particles become apparent if they are just a few micrometers in diameter. Consequentially, the flowing-performance of the particles under the gravity is greatly weakened. If the hold-up of the FCC catalyst particles is above a critical value, it is hard to be carried out by the downward flow granules, especially under low granules circulation fluxes. As a result, the fine FCC catalyst particles settling in the filter bed will gradually block the downward flow granules and thoroughly transform the MB operation into the FB operation.
Figure 7. Collection efficiency at different operating times (inlet dust concentrations).
3.2 Effect of inlet gas flowrate In order to investigate the effects of the swirl flow and the cross-flow velocity, the inlet gas flowrate is increased to 1400 m3/h. The initial pressure drop is relatively large under a high gas
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flowrate (velocity), as illustrated in Figure 8. The sequence of the pressure drop for Q=1400 m3/h, however, presents the same profiles as that under Q=800 m3/h.
Figure 8. Static pressure drop at different operating times (inlet gas flowrates).
Figure 9 shows the collection efficiency at different operating times under different inlet gas flowrates. The separation efficiency declines if increasing the inlet gas flowrate to 1400 m3/h. The dust aggregations are probably destroyed by a high inlet gas flowrate, and then the separation contribution by the filter cake is reduced. On the other side, the high inlet gas flowrate leads to a high superficial cross-flow gas velocity, which intensifies the re-entrainments of the fine FCC catalyst particles settling in the filter bed, and then decreases the collection efficiency of the C-CGBF. Besides, if the cross-flow velocity is too high, the downward movement of the collector granules in granular bed may be difficult because of the increase of friction force between the collector granules and the screen wall. On the other hand, the capacity of the granular bed filter may be relatively small if the cross-flow velocity is too low.
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Figure 9. Collection efficiency at different operating times (inlet gas flowrates)
3.3 Effect of granules circulation flux Granules circulation flux has significant influences on the pressure drop, the collection efficiency, as well as the energy consumption of the regenerating system in the C-CGBF. Under the FB regime (Ws=0 kg/s), the pressure drop increases rapidly/linearly with operating times when introducing the FCC catalyst particles in the inlet, as illustrated in Figure 10. At the same time, the pressure drop of the 4 m riser at Ws=0 kg/s fluctuates around 0.17 kPa as shown in Figure 11. With the voids in the filter bed gradually filled by the FCC catalyst particles, the collection efficiency of the C-CGBF is expected to be elevated. However, if the pressure drop approaches to a critical value, the C-CGBF must be shut down and the filter cleaning is required. On the other hand, except for Ws=0.04 kg/s, the pressure drop of the C-CGBF under the MB regime presents only slight increase over the course of experiments. As to the granules circulation flux Ws=0.04 kg/s, the pressure drop of the 4 m riser is stabilized at about 0.45 kPa in the beginning. With the fine FCC catalyst particles settling in the filter bed, the pressure drop of the 4 m riser decreases gradually from 0.45 to 0.17 kPa, as shown in Figure 11. It is obviously revealed that the granules circulation flux gradually decreases from 0.04 to 0 kg/s. The fact that fine particles continue to accumulate in the granular bed suggests that the filter is essentially
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Industrial & Engineering Chemistry Research
clogged by the dust particles and the downward granular flow is unable to transport the FCC catalyst particles out as fast as they deposit. When the operating regime is thoroughly transformed into the FB regime at t=10000s, the pressure drop of the C-CGBF increases rapidly/linearly with the operating times, as shown in Figure 10. The gradient of the pressure drop of the C-CGBF becomes considerably larger than that under the MB regime. Under other three circulation fluxes (Ws≥0.10 kg/s) in Figure 11, on the other hand, the pressure drop of the 4 m riser remains essentially steady before and after introducing the dust particles, which means that a stable granules circulation flux is obtained. It is a highly desirable circumstance for the CCGBF. The result suggests that there must be a notable critical granules circulation flux Wsc (0.04