5496
Ind. Eng. Chem. Res. 2004, 43, 5496-5506
“Choking” Revisited Wen-Ching Yang* Science and Technology Center, Siemens Westinghouse Power Corporation, Pittsburgh, Pennsylvania 15235
The classical “choking” phenomenon was revisited in this paper in light of confusion in the open literature. A coherent development was elucidated, with support of experimental data, to clarify the ever-present confusion in vertical pneumatic transport of solids. The importance of the distinction between the “small particles” and “large particles” in their manifestation of flow phenomena in vertical solids transport, especially at close to “choking” where low voidage and high solids concentration prevailed, was emphasized. A new operating map, which could be doubled as a regime transition map, was proposed for operating risers of circulating fluidizedbed systems. The “choking” and “nonchoking” transition proposed by Leung in 1980 was also reexamined. Introduction At the 10th International Conference on Fluidization held at Beijing, China, in 2001, there was an impromptu and heated discussion focused on the “choking” phenomenon in vertical pneumatic transport of solid particles. The confusion stems primarily from the misunderstanding of different “choking” definitions now being employed in the literature without proper qualifications and from the complex phenomena observed in pipes of different sizes and particles of different properties. There are no ambiguities when “choking” is applied in the context of vertical pneumatic transport where the phenomenon was first described and the terminology “choking” was first proposed. It is when “choking” is employed in the context of “fast fluidization” in risers of circulating fluidized beds (CFBs) that confusion and disagreement are aroused. Here the term “fast fluidization” is also enclosed in quotation marks because its definition is also in dispute and that adds to additional complications. The term “choking” was first coined by Zenz1 in 1949 to describe a phenomenon observed in vertical pneumatic transport of solid particles in pipes of usually small diameter. Because the primary application was to transport solids from one location to a different location, there was no need to study the gas and solids flow patterns or their temporal and spatial distributions inside the pipe. The only operating parameter of importance and concern was the total pressure drop across the vertical transport line. Thus, the focus of pneumatic transport studies was to develop correlations for proper predictions of the total pressure drop in vertical pneumatic transport lines. Vertical pneumatic transport lines can be employed as efficient chemical reactors as well. Risers of CFBs are prime examples. The only differences are that the risers in CFBs are usually larger in diameter and the solids employed are usually smaller and lighter such as fluid catalytic cracking (FCC) catalysts. For application as chemical reactors, studies of gas and solids flows inside the vertical risers are imperative. Now we know that the gas-solid two-phase flow inside the risers is heterogeneous in nature and can be in various regimes * To whom correspondence should be addressed. Fax: 412256-2121. E-mail:
[email protected].
depending on the solids volume fraction and operating velocity. Solid particles can flow as individual particles when the flow is dilute, or they can aggregate into clusters or streamers when the solids fraction is high. Depending on the solids fraction in the risers, the solid particles do not always travel upward. At high solids concentration, while particles move at high speed upward in the core region, considerable downward flow of solid particles occurs near the wall in a now familiar core-annular structure and thus creates an intensive solids backmixing. It also has been reported that under some operating conditions there can be core-annular flow with solid particles moving upward at all radial locations.2,3 To qualify the new flow regimes observed in risers of CFBs, the term “choking” was employed to describe phenomena in risers of CFBs, which were quite different from the classical “choking” originally defined by Zenz1 in 1949. Adding to the confusion is also the fact that the data available in pneumatic transport studies are mostly from larger and denser particles normally classified as Geldart group B and D powders4 while the particles employed in risers of CFBs are usually smaller and lighter particles such as FCC catalysts, normally classified as Geldart group A powders.4 The flow characteristics of group A powders4 in large risers and group B and D powders in small vertical pipes are quite different. Using the same terminology, “choking” without qualifications to describe phenomena observed in vertical transport for both classes of particles with widely different flow characteristics will invariably result in confusion. In this paper, I will attempt to provide a historical review on the development of “choking” and to discuss its potential applications in predicting the flow regime transitions in risers of CFBs. New correlations are also proposed for flow regime transitions in risers of CFBs. Historical Account of “Choking” As mentioned earlier, the term “choking” was first coined by Zenz1 in 1949 (see also work by Zenz and Othmer,5 1960) to describe a phenomenon associated with dilute-phase vertical pneumatic conveying. It is usually discussed with the help of a plot of pressure drop per unit length of pipe versus superficial gas velocity with solids flux as a parameter, as shown in Figure 1. Supposing that, at the solids flux of W1, the conveying
10.1021/ie0307479 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/20/2004
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5497
Figure 1. Schematic representation of flow characteristics in vertical solids transport.
velocity is slowly decreased, the operation of the transporting line will follow the line CDE. At point D, the pressure loss due to the solids head starts to exceed that of the fluid frictional loss. Further reduction in the fluid velocity will cause the pressure drop to increase rapidly. The classical definition of “choking” is thus, in Zenz and Othmer’s own words, “As point E is approached, the solids velocity has decreased to such an extent that the fluid has difficulty in supporting the high flowing density of solids, and, eventually, at point E the entire suspension collapses and is then transported up the tube in slug flow. This collapse of the dispersed flowing suspension into a condition of slug flow is referred to as choking. The solids flow rates at the choking points represent the saturation carrying capacity of the fluid stream at the corresponding superficial velocities.” Zenz and Othmer5 also said that “If pressure restrictions do not exist, it is perfectly feasible to operate smalldiameter vertical lines in slug flow, e.g., at gas velocities below the choking point. .... Such operation will cause violent vibration in large-diameter conduits owing to the relatively large change in inventory as slugs are ejected, whereas in small-diameter, relatively long lines, a fairly smooth transition from disperse flow to dense-phase or mass-lift operations could occur with slugging conditions going almost undetected.” In studying vertical pneumatic transport for chemical reactor applications, Yousfi and Gau6 proposed four different flow regimes: dilute phase flow, concentrated phase flow, slug flow, and fluidized-bed flow. They described the transition to “choking” as, translating from French in the original article, “We call choking the limiting condition beyond which these (solid) slugs appear. The gas ceases at that point to be able to maintain the particles under the form of a suspension. The limiting concentration of the suspension at the moment the (solid) slugs appear, is the choking concentration.” They went on to say that “... according to our definition, choking corresponds to a state in which the solids’ slugs extend over an entire pipe cross section. This determination of the choking conditions is therefore visual.” On the basis of this description, “choking” defined by Yousfi and Gau6 is exactly similar to that of
Zenz and Othmer.5 Yousfi and Gau6 also proposed a “choking” correlation based on their data and hydrodynamic stability analysis of vertical transport as
S ) (1 - )Frd
(1)
Frd ) Ut2/gdp
(2)
where
Equation 1 does not have a solution for Frd < 4S, which means that in this case “choking” due to the formation of solid slugs does not occur and there is a direct transition from the dilute phase pneumatic transport to the dense phase transport without “choking”. The constant, S, was determined to be 35 using polystyrene as the experimental particles. The Yousfi and Gau6 criterion of “choking” can thus be rewritten as
Frd ) Ut2/gdp g 140
(3)
The criterion served well for their own data and the data by Yerushalmi et al.7 but failed for other data sets, e.g., data of the 41 µm glass particles by Lewis et al.8 and the 270 µm alumina particles by Carotenuto et al.9 The major weaknesses of the criterion are that the effect of the particle diameter appears at both the numerator and denominator and that the important variable, the pipe diameter, is not in the correlation. It is reasonable to expect that when the pipe diameter is increased, the solid slugs will become unstable. Thus, the particles, which exhibit “choking” in a smaller diameter pipe, will not do so in a larger one. On the basis of the maximum stable bubble size theory of Harrison et al.10 (see also work by Davidson and Harrison,11 1963), Yang12 proposed the following “choking” criteria:
FrD ) Ut/xgD > 0.35
(4)
Yang’s criterion12 maintains that the slugging type of pneumatic transport can be eliminated simply by
5498 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
increasing the diameter of the transport line or by decreasing the particle size and density. A dramatic demonstration of Yang’s criterion12 was supplied by Carotenuto et al.9 in their experiments. For 95 µm alumina particles, they were able to smoothly make the transition from dilute phase transport to the turbulent flow regime without passing through the “choking”. When they increased the particle diameter to 270 µm, the turbulent flow regime was not attained. As the flow velocity was increased over the terminal velocity of the particles, “all the solids formed a compact region over a gas plug which grew so as to cause bulk entrainment of the whole bed”. Yousfi and Gau6 predict no “choking” for the 270 µm alumina particles, while Yang’s criterion12 correctly predicts the slugging type of transport. Yang’s “choking” criterion12 was the basis of Leung’s proposal13 in 1980 to demarcate the boundary between “choking” (“slugging”) and “nonchoking” (“nonslugging”) systems (see also work by Leung14). Smith15 considered the “choking” of the flow in the vertical pneumatic transport of solids to arise from the growth of bubbles in the transporting mixture to a size near to that of the conduit. He argued that stable slugs could not travel at a velocity higher than the wave propagation velocity and, for “choking” to occur, the slug must be stable with the following criterion
Utn-1n(1 - )/xgD g
x
Fj - Fg 2.0Fj
(5)
where n is the exponent in the Richardson and Zaki correlation.16 Available literature on “choking” and the saturation carrying capacity at “choking” up to 1983 was critically reviewed by Yang.17 Continuing development after 1983 is reviewed in the following sections. Classical “Choking” The “choking” just reviewed in the last section is customarily called the classical “choking” to differentiate from other types of “choking” introduced subsequently in the literature by other researchers. The classical “choking” first defined by Zenz1 was observed usually for pipes of small diameter, usually less than 10 cm in diameter, with relatively large and/or dense particles applicable mostly in pneumatic conveying. Under those conditions, solids do collapse into slugs and thus the term “choking”. Most of the data employed to develop the classical “choking” correlations were data where solids did collapse into slugs spanning the complete cross section of the pipe at “choking”. Thus, the correlations developed for classical “choking” strictly can only be applied for systems where solids collapse into slugs at “choking”. As Zenz1 pointed out, if pressure restrictions do not exist, a vertical pneumatic transport line could very well operate in slug flow conditions under “choking”. Thus the name “choking” does not necessarily mean that the vertical transport line is actually choked and inoperable. This unfortunate choice of terminology did indeed cause much confusion in the literature, especially in the discussions of flow regimes in risers of CFBs. In 1985, Satija et al.18 employed the statistical parameters of pressure fluctuations to study the transition from the dilute phase flow to the dense phase flow. Slugging dense phase flow was observed for fine sand, coarse sand, and spent FCC particles. The “choking”
transitions for those particles were described well by the criteria proposed by Yousfi and Gau6 and Yang12 and partially by Smith.15 They concluded that the power spectral density function and the standard deviation of pressure fluctuations could be effectively used to accurately determine the “choking” transition. Their suggestion provided the first objective experimental technique to study the classical “choking” phenomena quantitatively. In their study on the fluid dynamic similarity of CFBs in a 20 cm diameter vessel, Chang and Louge19 described their encounter with “choking” as follows. “In our facility, it is unambiguously accompanied by loud banging noises and shaking of the riser, which result from the passage of slugs there. ... The onset of choking with plastic and steel powders is well predicted by the correlation of Yang (1983).” By matching of five similarity criteria with different gas mixtures and solid particles of various sizes and densities, their experiments employing plastic, glass, and steel powders allowed them to achieve fluid dynamic similarity with hightemperature CFB risers of 0.32, 0.46, and 1 m diameter. They went on to speculate that “Risers of larger diameter exhibited incipient choking characterized by a gradual collapse of the suspension originating from the base of the riser, and by considerably more intense pressure fluctuations.” Classification of “Choking” In 1993, Bi et al.20 classified the types of “choking” into type A “accumulative choking”, type B “blower/ standpipe-induced choking”, and type C “classical choking”, after extensive review of literature information. Type C “choking” is essentially the classical “choking” we just discussed. Type A “choking” occurs when the saturating carrying capacity of a vertical transporting tube, such as the riser in a CFB, is reached and further attempts to increase the solids flux result in accumulation of solids, and hence a dense region at the bottom of the transport tube. Thus, type A “choking” is called “accumulative choking”. Other types of “choking” induced by the deficiencies of equipment and design in the system are all lumped into type B. For fluid dynamics intrinsic to vertical pneumatic transport of solids, we will exclude type B “choking” from our discussion because they are so equipment and system dependent. An exhaustive review and compilation of literature data on type A ”accumulative choking” and type C “classical choking” has recently been published by Xu et al.21 with a comparison of data with available correlations in the literature. Important Distinction between Type A “Accumulative Choking” and Type C “Classical Choking” Historically, most data for classical “choking” were from visual observations with little rigorous quantitative criteria. Though data for type A “accumulative choking” were based on a better quantitative experimental analysis, a uniform criterion is still lacking. More rigorous experimentation following that by Bai et al.22 is recommended. Experimental Elucidation of Type A “Accumulative Choking” and Type C “Classical Choking”. The distinction between type A “accumulative choking”
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5499
Figure 3. Determination of choking velocities, UcA and UcC, and corresponding voidages in the riser from Bai et al.22 Figure 2. Pressure drop fluctuations at various heights in the riser from Bai et al.22
and type C “classical choking” is best elucidated by the excellent experimentation carried out by Bai et al.22 in 1998. The existence of saturation carrying capacity was also amply demonstrated in their experiments. The experiments were carried out in their high-density CFB facility with spent FCC catalyst particles of mean diameter 70 µm and density 1600 kg/m3. During the experiments, the gas velocity in the riser, the pressure drop across the solids-supplying downcomer, the differential pressure drops at various heights of the riser, and the pressure drop across the entire riser were continuously recorded. Typical instrumentation responses are reproduced in Figures 2 and 3, with authors’ permission. For the detailed experimental setup, experimental procedure, and results, the original paper should be consulted. At t ) 0, the valve between the solids-supplying downcomer and the riser was opened while the gas velocity in the riser was preset, in this case at 7.2 m/s. Gradual opening of the valve increased the supply of solids into the riser and thus the solids flux in the riser. This can be seen from the increases in the pressure drop across the riser (Figure 3), very nearly proportional to the solids holdup in the riser. Because no particles were returned to the top of the downcomer, the solids inventory in the downcomer decreased, as could be seen from the decreases in the downcomer pressure drop, ∆Pd, with time shown in Figure 3. Further opening of the valve between the downcomer and the riser increased the solids flow from the downcomer to the riser and thus increased the solids flux in the riser. Eventually, at time t1 (see Figures 2 and 3), a sharp increase in the pressure at the bottom of the riser was noted due to accumulation of solids and the formation of a dense phase region. This initial accumulation of solids and formation of a dense phase region at the bottom of the riser correspond to the point of type A “accumulative choking”. A similar description can also be found in Xu et al.21 Type A “accumulative choking” also is the demarcation of
transition from dilute phase pneumatic transport to fast fluidization. The discussion on the definition of fast fluidization is presented in a later section. Beyond the type A “accumulative choking” point, further opening of the valve between the downcomer and the riser did not increase the solids flow because the riser now reached the saturation carrying capacity of the solids. This can be seen readily from Figure 3, in which the solids level in the downcomer falls linearly with time, indicating the constant solids flow rate at the saturation carrying capacity of the riser. The accumulation of solids in the riser and the increase of the dense region in the riser continue, however, as indicated by the pressure drop across the riser (Figure 3). The solids flow rate can be calculated from the slope of the pressure drop across the downcomer as shown in Figure 3. With continuing increases in the height of the dense region at the bottom of the riser, a point is eventually reached where gas slugs form at the bottom and rise through the dense bed like that of a conventional slugging bed. When the slugging develops over the whole riser, shown at point t ) t2 in Figures 2 and 3, this point can be taken to be the classical “choking” or type C “classical choking”. At this point, the local differential pressure drop fluctuates between two values corresponding to a solids holdup of 0 and that of a packed bed at minimum fluidization as shown in Figure 2. It is important to note that the procession from type A “accumulative choking” to classical “choking” took only about 15 s in the experiments of Bai et al.22 Without careful experimentation, it may not be possible to distinguish between these two types of “choking”. This is quite possibly the biggest reason why there is so much confusion in the literature data on “choking”. The solids flux in the riser at the classical “choking” point was observed by Bai et al.22 to be 206 kg/m2‚s at a choking velocity of 2.4 m/s and as high as 618 kg/m2‚ s at a choking velocity of 3.5 m/s. These high solids fluxes are usually not attainable in the risers of most of the experimental CFBs reported in the literature.
5500 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
Figure 4. Comparison of data from Bai et al.22 with various models. Solid and open points represent data for UcA, GsA and UsC, GsC respectively.
Thus, most of the “choking” data sets reported in the literature for Geldart group A powders such as FCC catalysts are pertaining to type A “cumulative choking” rather than classical “choking”. The aforementioned experiment did not return particles to the top of the downcomer. If particles were returned to the top of the downcomer, appropriate operating conditions and the solids inventory in the circulation loop could be selected such that the CFB system could have a stable operating system with a fast fluidized bed, either slugging or not, with different bed heights in the riser. Consensual Definition of Fast Fluidization. After considerable confusion and controversy, there is now a consensus in the research community that fast fluidization in risers of CFBs is when the risers have a coexistence of a dense phase transport region in the lower part and a dilute phase transport region in the upper part (Rhodes and Wang,23 1998). Because of the simultaneous coexistence of the dense and dilute phase transport regions, the fast fluidized beds often exhibit the characteristic S-shaped axial solids concentration profile proposed by Li and Kwauk.24 By this definition, the fast fluidization regime is bounded at the lower limit by type A “accumulative choking” and at the upper limit by classical “choking”. This can be elucidated more clearly by the data obtained by Bai et al.22 and plotted in Figure 4. This type of flow regime diagram was first suggested by Takeuchi et al.25 in 1986 and adapted by Yang26 in 1993. Extension of Classical “Choking” Correlations to Risers of CFBs On the basis of the historical review presented in the previous sections, application of correlations developed on the basis of classical “choking” is strictly limited to systems where “choking” is manifested by solid slugs across the entire cross section of the pipe. These systems usually consist of a pipe of small diameter and generally with particles of large sizes and densities similar to that
in vertical pneumatic conveying applications. For these systems, the resulting slugging transport is more akin to the type B slugging bed where flat-nosed solid slugs and flat-nosed gas slugs, extending across the entire pipe cross section, are observed. Successful application of classical “choking” correlations in risers of CFBs with large diameter vessels and small and light particles, such as FCC catalysts, reported in the literature was considered to be coincidental by Wang and Rhodes.27 However, because the most popular classical “choking” correlations, those by Yousfi and Gau,6 Yang,17 and Smith,15 were developed on the basis of the stability of gas bubbles and solid slugs in vertical pneumatic transport, the successful applications of these correlations in risers of CFBs might be more than coincidental. This is best demonstrated by the recent data from Bai et al.22 employing a FCC catalyst of 70 µm mean particle size and 1600 kg/m3 particle density. Those data are plotted in Figure 4 for comparison with the correlations proposed by Yousfi and Gau6 in eq 6 and Yang17 in eqs 7 and 8.
UcC
xgdp
) 32Redp-0.06
2gD(cC-4.7 - 1) (UcC - Ut)2
( ) () Gs FgUcC
) 6.81 × 105
0.28
Fg Fs
Gs ) (UcC - Ut)Fs(1 - cC)
(6)
2.20
(7) (8)
The correlations as shown in Figure 4 are quite reasonable. We can expect that the slugging transport resulting from the FCC particles cited here will be similar to that of the type A slugging bed with roundnosed gas slugs. The question of whether the classical “choking” phenomenon represents a genuine fluid dynamic instability in a vertical solids suspension or is simply due to a local flow disturbance is also a point of contention in
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5501
the literature. This question has just been answered recently by Du et al.28 In their study, the nonintrusive electrical capacitance tomography based on the neural network multicriteria optimization image reconstruction technique was used to probe the mechanism of “choking” by examining a real-time, quasi-3D cross-sectional flow structure of a CFB riser. The experimental evidence indicated that such flow structure variations were not appreciably affected by the solids feeding patterns with or without a gas or solids distributor or by the gas humidity. The result seems to indicate that the classical “choking” phenomenon indeed represents a genuine fluid dynamics instability in vertical solids transport. This powerful nonintrusive experimental technique will break new grounds in future experimental studies and accelerate the development of fundamentals in vertical solids transport systems. Type A “Accumulative Choking” and the Incipient Fast Fluidization Boundary
Laminar layer: at y+ < 5
(9)
Buffer layer: u + ) -3.05 + 5.0 ln y+
at 5 e y+ e 30 (10)
Turbulent core: u+ ) 5.5 + 2.5 ln y+
at y+ > 30
(11)
where +
u ) u/u* y+ ) yu*/υ
dimensionless velocity
(12)
modified Reynolds number (13)
u* ) Uave(f/2)1/2
friction velocity
u/Uave ) 5(f/2)1/2
(14)
For the development of the incipient fast fluidization boundary, only the laminar layer is of interest. We are assuming that the downflow solids in the annulus of the core-annular structure in the riser of a CFB are restricted to the laminar layer. Thus, to prevent the dense region to build up at the bottom of the riser, the gas velocity at the outer boundary of the laminar layer has to be high enough to transport the net solids flux
(15)
The local gas velocity, u, should be capable of carrying the imposed net solids circulation flux, which equals its saturation carrying capacity, here expressed as its carrying capacity at choking, or
GsC ) Fs(1 - c)(u - Ut)
In 1993, Yang26 proposed the incipient fast fluidization boundary to demarcate the flow regime between the dilute phase pneumatic transport and the fast fluidization in a flow regime diagram similar to that of Figure 4. Phenomenologically, the incipient fast fluidization boundary is similar to type A “accumulative choking”. At the incipient fast fluidization boundary, a dense phase starts to form at the bottom of the riser. Further reduction in the gas velocity or a further increase in the solids flux results in coexistence with both dilute and dense phases in the riser and thus the fast fluidized bed. A mechanistic model based on the universal velocity distribution for turbulent flow in circular tubes was also proposed to calculate the incipient fast fluidization boundary or the type A “accumulative choking” boundary. The model proposed by Yang26 is briefly recapped here. The complete velocity profile for turbulent flow in circular tubes can be expressed as
u+ ) y+
imposed by the operating conditions. At a constant solids circulation flux, the minimum gas velocity required to transport the solids would be when the gas is transporting at its saturation carrying capacity. Thus, the incipient fast fluidization velocity is defined as the gas velocity at the outer boundary of the laminar layer, i.e., at y+ ) 5, where the net solids flux equals the saturation carrying capacity. Mathematically, it can be derived as follows. The local gas velocity at the outer boundary of the laminar layer, where y+ ) 5, can be determined as
(16)
Combining eqs 15 and 16, we have
Uave ) [GsC/(Fs(1 - c)) + Ut]/[5(f/2)1/2]
(17)
The voidage at choking, c, can be calculated from the choking correlation suggested by Yang17 and given in eq 7. The friction coefficient, f, can be calculated from
f ) 0.079Re-0.25
for 3000 < Re < 100 000
(18)
This model is slightly different from the one originally proposed by Yang26 in 1993. The original model does not allow the downflow of solids in the annulus before the incipient fast fluidization boundary is reached. By treatment of the solids downflow annulus as part of the laminar layer and consideration of the net solids upflow, the difference between the solids upflow and downflow, at the outer boundary of the laminar layer, the same model applies for cases with solids downflow close to the wall. One important distinction should be noted here. The saturation carrying capacity of the gas is applied here for the velocity at the outer boundary of the laminar layer, i.e., at y+ ) 5, and not for the average riser operating gas velocity, Uave. Their relationship is expressed in eq 15. Correlations with Literature Data for Type A “Accumulating Choking” or Incipient Fast Fluidization Distinctions between Small and Large Particles. The difference in the behavior of small and large particles in vertical pneumatic transport is well-known. This difference is even more pronounced at high solids concentrations. Especially at low gas velocities approaching “choking”, the descending motion of the particles along the pipe walls and cluster formation lead to results that are markedly different from those for small and large particles. Yousif and Gau29 found that, for large particles, the slip velocity between the gas and particles was about 1-4 times the terminal velocity of the particles depending on the properties of the particles, the solids concentration, and the gas velocity. For small particles, the experimental relative velocity between gas and solids was from 8 to 40 times the terminal velocity of the particles for a 55 µm FCC
5502 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
Figure 5. Empirical correlation for type A “accumulative choking” (incipient fast fluidization boundary) based on all literature data for particles with Ar < 25.
catalyst and from 50 to 300 times for a 20 µm FCC catalyst. In their study, they classified 20 and 55 µm FCC catalysts as small particles and 118, 143, and 183 µm glass balls and 290 µm polystyrene particles as large particles. Literature information available so far seems to indicate that Geldart group A powders are small particles and groups B and D particles are large particles. This distinction is important and will be evident when we analyze the “choking” data from the literature to be described next. Type A “Accumulative Choking” or Incipient Fast Fluidization Correlation for Small Particles. Figure 5 shows the plot of transport velocity versus solids flux at the incipient fast fluidization (or type A “accumulative choking”) based on the data compiled by Xu et al.21 for particles with an Archimedes number of less than 25. The data set designations in the figure are those of Xu et al.21 Those particles are mostly various FCC catalysts. It can be seen that the solids flux at incipient fast fluidization can be uniquely related to the gas velocity. The empirical correlation can be simply expressed as
GsA ) 3.8364UcA2.4938 for Ar < 25 with confidence level R2 ) 0.9549 (19) where GsA is in kg/m2‚s and UcA is in m/s. These data came from nine different research groups with riser diameters from 50 to 150 mm and mostly Geldart group A powders with an Archimedes number of less than 25. Equation 19 was also used to compare with the data from Bai et al.22 in Figure 4. Alternatively, the mechanistic model proposed by Yang26 for incipient fast fluidization can be applied. If the solids circulation flux, GsA, is known, the incipient fast fluidization velocity, Uave, can be obtained by solving eqs 7 and 17 simultaneously. If the operating gas velocity, Uave, is known, theoretically the choking void-
age, c, can be calculated from eq 7 and the solids circulation flux from eq 17. However, because of the sensitivity of the thickness of the laminar boundary layer (eq 9) during the development of the model, sometimes a negative solids circulation flux will be obtained. To circumvent this problem, eqs 7 and 17 should always be solved simultaneously even if the operating gas velocity is known, by assuming a solids circulation flux and then solving for the incipient fast fluidization velocity until the calculated velocity equals the known operating velocity. When Yang’s model is employed,26 the incipient fast fluidization velocities, or type A “accumulative choking” velocities, are compared with the experimental data compiled by Xu et al.21 in Figure 6. It can be seen that the calculated incipient fast fluidization velocities are within (30%. This model was also used to compare with the data from Bai et al.22 in Figure 4. Type A “Accumulative Choking” or Incipient Fast Fluidization Correlation for Large Particles. For large particles, there is no unique empirical correlation like that of the small particles shown in Figure 5. However, Yang’s correlation26 for incipient fast fluidization velocities, or type A “cumulative choking” velocities, can also be applied. The results are shown in Figure 7. The accuracy is within (40%. In 1993, Yang’s model26 was applied to data sets on incipient fast fluidization by Monceaux et al.,30 Rhodes and Geldart,31 Takeuchi et al.,25 Arena et al.,32-34 Li et al.,35 Jiang et al.,36 Zhang et al.,37 and Hirama et al.,38,39 with similar accuracies of (30%. Those data sets include materials of glass beads, FCC catalysts, silica sand, alumina, iron concentrate, and pyrite cinder with particles ranging from 38 to 105 µm and particle densities from 750 to 4510 kg/m3. Discussions Operating Map for a Riser of CFB. For vertical pneumatic transport lines, the general operating char-
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5503
Figure 6. Comparison of calculated incipient fast fluidization velocities from Yang’s model26 with experimental type A “accumulative choking” velocities for particles with Ar < 25.
Figure 7. Comparison of calculated incipient fast fluidization velocities from Yang’s model26 with experimental type A “accumulative choking′′ velocities for particles with Ar > 25.
acteristics are usually presented as a pressure drop per linear pipe length versus conveying velocity plot like that shown in Figure 1. If the solids transport rate is expressed as a solids flux based on the unit crosssectional area of the pipe, nomenclature more close to that employed in CFB systems, the operating map for a vertical pneumatic transport line can be readily transposed to an operating map of a CFB system as shown in Figure 8 (see work by Yang,40 2001). Figure 8 is similar to Figure 4 and is also similar to the regime diagram originally suggested by Takeuchi et al.25 in 1986, except with additional important information on
the mean axial voidage and pressure drop in the riser. With the availability of correlations to calculate the incipient fast fluidization boundary, or the type A “accumulative choking” boundary, and the classical “choking” boundary, Figure 8 can be readily constructed for risers of different CFB systems. With additional information of the voidage and pressure drop, Figure 8 is valuable in improving the understanding of system operating characteristics and system operation in risers of CFBs. Reexamination of “Choking” and “Nonchoking” Transitions. In 1980, Leung13 proposed the “choking”
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Figure 8. Example of an operating map for a riser of 0.1 m diameter operating at atmospheric pressure with air and a FCC catalyst of 57 µm diameter and 1500 kg/m3 density.
and “nonchoking” systems based on Yang’s criterion12 expressed in eq 4. On the basis of experimental data of Bai et al.22 and Du et al.,28 we know that all vertical transport systems, including the Geldart group A powders such as FCC catalysts, eventually reach the “choking” point at low velocities. At the “choking” point, the slugging transport for Geldart group A powders resembles the slugging beds with round-nosed gas slugs (type A slugging beds), while for Geldart groups B and D particles, the slugging beds with square-nosed gas and solid slugs (type B slugging beds). The fast fluidization region, the region between the incipient fast fluidization boundary and the classical “choking” boundary (see Figures 4 and 8), becomes smaller with decreasing riser diameter and with increasing solids particle size and density; i.e., it is harder to have a fast fluidization region with smaller diameter risers and with particles of large sizes and densities. If the particle and riser sizes employed are such that they fit Yang’s criterion12 expressed in eq 4, it would no longer be possible for the system to have a fast fluidization region. In this case, the incipient fast fluidization boundary coincides with the classical “choking” boundary and the system exhibits the so-called “choking” transition in Leung’s classification. The flow inside the riser goes directly from the dilute phase to classical “choking”. Equation 4 is thus a criterion to determine whether the CFB system is going to have a fast fluidization regime or not. This characteristic might be the reason the incipient fast fluidization boundary was sometimes mistaken to be the classical “choking” boundary in the literature. Conclusions Classical “choking” phenomenon was revisited in this paper in light of confusion in the open literature. The new classification of “choking” into types A-C was also reviewed. It was also pointed out that type A “accumulative choking” was phenomenologically similar to the incipient fast fluidization boundary proposed by the author in 1993.26 To avoid further confusion in the
“choking” discussion, it is proposed to use the term “incipient fast fluidization boundary” rather than “type A accumulative choking”. A coherent development was elucidated in this paper to clarify the ever-present confusion in the literature regarding the “choking” phenomena in vertical pneumatic transport lines and risers of CFB systems. Experimental data were cited to support this development. The importance of the distinction between the “small particles” and “large particles” in their manifestation of flow phenomena in vertical solids transport, especially close to the “choking” point where high solids concentration prevailed, was emphasized with support of experimental data. For “small particles”, with characteristics close to those of Geldart group A powders, a unique empirical equation between the gas velocity and the circulating flux exists at the incipient fast fluidization boundary. For “large particles”, with characteristics similar to those of Geldart groups B and D particles, no such correlation is apparent. For both classes of particles, the correlation based on the universal velocity distribution for turbulent flow in circular tubes proposed by Yang26 in 1993 is applicable for calculation of the incipient fast fluidization boundary. A new operating map, which can be doubled as a regime transition map proposed by Takeuchi et al.,25 is proposed for operating risers of CFB systems. The operating map, which can be transposed from a map similar to Figure 1 for vertical pneumatic transport, contains additional important information of the voidage and pressure drop. The “choking” and “nonchoking” transition proposed by Leung13 in 1980 based on Yang’s “choking” criterion12 expressed in eq 4 was reexamined. The fast fluidization region, the region between the incipient fast fluidization boundary and the classical “choking” boundary (see Figures 4 and 8), becomes smaller with decreasing riser diameter and with increasing solids particle size and density. It is harder to have a fast fluidization region with smaller diameter risers and with particles of large sizes and densities. If the particle and riser sizes
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5505
employed are such that they fit Yang’s criterion12 expressed in eq 4, it is no longer possible to have a fast fluidization region for the system. In this case, the incipient fast fluidization boundary coincides with the classical “choking” boundary. Thus, eq 4 can be employed as a criterion to determine whether a CFB system can have a fast fluidization regime. This unique flow characteristic might be the reason the incipient fast fluidization boundary was sometimes mistaken to be the classical “choking” boundary in the literature. Because of the complexity of the choking phenomena and the uncertainties during observation, the effect of temperature, pressure, and particle size distribution have so far eluded a meaningful quantitative analysis. Acknowledgment Experimental data provided by Dr. Issangya and permission to use their data and illustrations contained in their paper Bai et al.22 are very much appreciated. Notation Ar ) Archimedes number, Ar ) dp3Fg(Fs - Fg)g/µ2 D ) diameter of the riser or vertical transport tube dp ) particle diameter f ) gas friction factor Frd ) Froude number based on the particle diameter, defined in eq 2 FrD ) Froude number based on the pipe diameter, defined in eq 4 g ) gravitational acceleration Gs ) solids circulation flux GsA ) solids circulation flux at incipient fast fluidization or type A “accumulative choking” GsC ) solids circulation flux at “choking” n ) exponent in the Richardson and Zaki correlation16 ∆Pd ) pressure drop across the downcomer Re ) Reynolds number, DUaveFg/µ Redp ) Reynolds number based on the particle diameter, dpUaveFg/µ S ) constant defined in eq 1 t, t1, t2 ) time u ) local gas velocity Uave ) average superficial gas velocity in the riser or vertical transport tube UcA ) choking velocity for type A “accumulative choking” or incipient fast fluidization UcC ) choking velocity for classical “choking” or type C “classical choking” Ut ) terminal velocity of a single particle u+ ) dimensionless gas velocity defined in eq 12 u* ) friction velocity W, W1, W2 ) solids flux y ) distance measuring the normal to solid boundary y+ ) dimensionless distance or modified Reynolds number defined in eq 13 Fg ) density of the fluid Fs ) density of solids Fj ) average density of the gas-solid suspension in the column µ ) gas viscosity ν ) kinematic viscosity of air (or fluid) c ) voidage at choking
Literature Cited (1) Zenz, F. A. Two-Phase Fluid-Solid Flow. Ind. Eng. Chem. 1949, 41, 2801.
(2) Issangya, A. S.; Bai, D.; Bi, H. T.; Lim, K. S.; Zhu, J.; Grace, J. R. Suspension Densities in a High-Denisity Circulating Fluidized Bed Riser. Chem. Eng. Sci. 1999, 54, 5451. (3) Reddy Karri, S. B.; Knowlton, T. M. Wall Solids Upflow and Downflow Regimes in Risers for Group A Solids. In Circulating Fluidized Bed Technology VII; Grace, J. R., Zhu, J., de Lasa, H., Eds.; Canadian Society of Chemical Engineering: Ottawa, Canada, 2002; p 310. (4) Geldart, D. Types of Gas Fluidization. Powder Technol. 1973, 7, 285. (5) Zenz, F. A.; Othmer, D. F. Fluidization and Fluid-Particle Systems; Reinhold Publishing Corp.: New York, 1960; p 319. (6) Yousfi, Y.; Gau, G. Aerodynamics of the Vertical Flow of Concentrated Gas-Solid SuspensionssI. Flow Regimes and Aerodynamic Stability. Chem. Eng. Sci. 1974, 29, 1939 (in French). (7) Yerushalmi, J.; McIver, A. E.; Squires, A. M. The Fast Fluidized Bed. Proceedings of the Joint AIChE-VTG Meeting, Munich, West Germany, 1974. (8) Lewis, W. K.; Gilliland, E. R. Bauer, W. C. Characteristics of Fluidized Particles. Ind. Eng. Chem. 1949, 41 (6), 1104. (9) Carotenuto, L.; Crescitelli, S.; Donsi, G. High Velocity Behavior of Fluidized Beds: Characterization of Flow Regimes. Ing. Chim. Ital. 1974, 10 (12), 185. (10) Harrison, D.; Davidson, J. F.; de Kock, J. W. On the Nature of Aggregative and Particulate Fluidization. Trans. Inst. Chem. Eng. 1961, 39, 202. (11) Davidson, J. F.; Harrison, D. Fluidized Particles; Cambridge University Press: Cambridge, U.K., 1963; p 84. (12) Yang, W. C. A Criterion for “Fast Fluidization”. Proceedings of the Third International Conference on the Pneumatic Transport of Solids in Pipes (Pneumotransport 3), Bath, England, 1976; pp E5-49. (13) Leung, L. S. The Ups and Downs of Gas-Solid Flow: A Review. In Fluidization; Grace, J. R., Matsen J. M., Eds.; Plenum Press: New York, 1980; p 25. (14) Leung, L. S. Vertical Pneumatic Conveying: A Flow Regime Diagram and a Review of Choking versus Nonchoking Systems. Powder Technol. 1980, 25, 185. (15) Smith, T. N. Limiting Volume Fractions in Vertical Pneumatic Transport. Chem. Eng. Sci. 1978, 33, 745. (16) Richardson, J. F.; Zaki, W. N. Sedimentation and Fluidization: Part I. Trans. Inst. Chem. Eng. 1954, 32, 35. (17) Yang, W. C. Criteria for Choking in Vertical Pneumatic Conveying Lines. Powder Technol. 1983, 35, 143. (18) Satija, S.; Young, J. B.; Fan, L. S. Pressure Fluctuations and Choking Criterion for Vertical Pneumatic Conveying of Fine Particles. Powder Technol. 1985, 43, 257. (19) Chang, H.; Louge, M. Fluid Dynamic Similarity of Circulating Fluidized Beds. Powder Technol. 1992, 70, 259. (20) Bi, H. T.; Grace, J. R.; Zhu, J. X. Types of Choking in Vertical Pneumatic Systems. Int. J. Multiphase Flow 1993, 19 (6), 1077. (21) Xu, G.; Nomura, K.; Gao, S.; Kato, K. More Fundamentals of Dilute Suspension Collapse and Choking for Vertical Conveying Systems. AIChE J. 2001, 47 (10), 2177. (22) Bai, D.; Issangya, A. S.; Grace, J. R. A Novel Method for Determination of Choking Velocities. Powder Technol. 1998, 97, 95. (23) Rhodes, M. J.; Wang, X. S. Defining Fast Fluidization. In Fluidization IX; Fan, L. S., Knowlton, T. M., Eds.; Engineering Foundation: New York, 1998; p 133. (24) Li, Y.; Kwauk, M. The Dynamics of Fast Fluidization. In Fluidization; Grace J. R., Matsen, J. M., Eds.; Plenum Press: New York, 1980; p 537. (25) Takeuchi, H.; Hirama, T.; Chiba, T.; Biswas, J.; Leung, L. S. A Quantitative Regime Diagram for Fast Fluidization. Powder Technol. 1986, 47, 195. (26) Yang, W. C. Incipient Fast Fluidization Boundary and Operational Map for Circulating Fluidized Bed Systems. In Circulating Fluidized Bed Technology IV; Avidan, A. A., Ed.; AIChE: New York, 1993; p 62. (27) Wang, X. S.; Rhodes, M. J. On the Use of Choking as a Boundary for Fast Fluidization. Chem. Eng. Commun. 2002, 189 (2), 223. (28) Du, B.; Warsito, W.; Fan, L. S. Electrical Capacitance Tomography Studies of Choking Phenomenon in a Gas-Solid Circulating Fluidized Bed. AIChE J. 2003, submitted for publication.
5506 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 (29) Yousfi, Y.; Gau, G. Aerodynamics of the Vertical Flow of Concentrated Gas-Solid SuspensionssII. Pressure Drop and Relative Gas-Solid Velocity. Chem. Eng. Sci. 1974, 29, 1947 (in French). (30) Monceaux, L.; Azzi, M.; Molodtsof, Y.; Large, J. F. Particle Mass Flux Profiles and Flow Regime Characterization in a PilotScale Fast Fluidized Bed Unit. In Fluidization V; Ostergaard, K., Sorensen A., Eds.; Engineering Foundation: New York, 1986; p 337. (31) Rhodes, M. J.; Geldart, D. The Hydrodynamics of ReCirculating Fluidized Beds. In Circulating Fluidized Bed Technology; Basu, P., Ed.; Pergamon Press: Toronto, 1986; p 193. (32) Arena, U.; Cammarota, A.; Pistone, L. High Velocity Fluidization Behavior of Solids in a Laboratory Scale Circulating Bed. In Circulating Fluidized Bed Technology; Basu, P., Ed.; Pergamon Press: Toronto, 1986; p 119. (33) Arena, U.; Cammarota, A.; Maximilla, L.; Pirozzi, D. The Hydrodynamic Behavior of Two Circulating Fluidized Bed Units of Different Sizes. In Circulating Fluidized Bed Technology II; Basu, P., Large, J. F., Eds.; Pergamon Press: Oxford, U.K., 1988; p 223. (34) Arena, U.; Malandrino, A.; Marzocchella, A.; Massimilla, L. Flow Structures in the Risers of Laboratory and Pilot CFB Units. In Circulating Fluidized Bed Technology III; Basu, P., Horio, M., Hasatani, M., Eds.; Pergamon Press: Oxford, U.K., 1991; p 137. (35) Li, J.; Tung, Y.; Kwauk, M. Axial Voidage Profiles of Fast Fluidized Beds in Different Operating Regions. In Circulating Fluidized Bed Technology II; Basu, P., Large, J. F., Eds.; Pergamon Press: Oxford, U.K., 1988; p 193.
(36) Jiang, P.; Inokuchi, K.; Jean, R.; Bi, H.; Fan, L. S. Ozone Decomposition in a Catalytic Criculating Fluidized Bed Reactor. In Circulating Fluidized Bed Technology III; Basu, P., Horio, M., Hasatani, M., Eds.; Pergamon Press: Oxford, U.K., 1991; p 557. (37) Zhang, H.; Xie, Y.; Chen, Y.; Hasatani, M. Mathematical Modeling for Longitudinal Voidage Distribution of Fast Fluidized Beds. In Circulating Fluidized Bed Technology III; Basu, P., Horio, M., Hasatani, M., Eds.; Pergamon Press: Oxford, U.K., 1991; p 151. (38) Hirama, T.; Takeuchi, H.; Chiba, T. Regime Classification of Macroscopic Gas-Solid Flow in a Circulating Fluidized Bed Riser. Powder Technol. 1992, 70, 215. (39) Hirama, T.; Takeuchi, H.; Chiba, T. On the Definition of Fast Fluidization in a Circulating Fluidized-Bed Riser. In Fluidization VII; Potter, O. E., Nicklin, D. J., Eds.; Engineering Foundation: New York, 1992; p 313. (40) Yang, W. C. From Pneumatic Transport to Circulating Fluidized Beds: The Importance of Operating Maps. In Fluidization X; Kwauk, M., Li, J., Yang, W. C., Eds.; United Engineering Foundation: New York, 2001; p 333. (41) Bi, H. T.; Fan, L. S. Regime Transition in Gas-Solid Circulating Fluidized Beds. AIChE Annual Meeing, Los Angeles, Nov 17-22, 1991; Paper 101e.
Received for review October 2, 2003 Revised manuscript received January 5, 2004 Accepted January 13, 2004 IE0307479
