Flooding of Gas−Solids Countercurrent Flow in Fluidized Beds

Ind. Eng. Chem. Res. 2004, 43, 5611-5619

5611

Flooding of Gas-Solids Countercurrent Flow in Fluidized Beds Hsiaotao Bi,*,† Heping Cui,† John Grace,† Andreas Kern,† C. Jim Lim,† Dan Rusnell,‡ Xuqi Song,† and Craig McKnight§ Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, Canada V6T 1Z4, Syncrude Canada Limited, P.O. Bag 4023, Fort McMurray, Alberta, Canada T9H 3H5, and Syncrude Research Centre, 9421-17th Avenue, Edmonton, Alberta, Canada T6N 1H4

Flooding experiments were carried out in a semicircular pilot-scale cold model of Syncrude’s two fluid cokers. This unit circulates solids downward through a stripper zone and externally back to the top of the vessel, facilitating countercurrent gas/solid contacting. The onset of flooding for FCC particles was determined by analysis of differential pressure signals, supported by visual observations. The solids circulation flux at flooding increased with decreasing superficial gas velocity, with increasing fractional open area, with increasing slot width between adjacent baffles, and with decreasing baffle top included angle. A semiempirical model gives predictions of the onset of flooding that are in good agreement with both cold-flow model results and available commercial data. Introduction Strippers are important components in both fluid catalytic cracking (FCC) and fluid coking. In these units, catalyst or coke particles travel downward through the reactor and then descend through a stripper, where a countercurrent flow of steam strips interstitial hydrocarbons from the surface of the particles. Most of the stripping steam is injected using nozzles or spargers below baffles, which are intended to break up and redistribute rising steam bubbles, reduce backmixing, and improve steam-particle contacting. The need for better stripper performance has led to a variety of baffle designs.1-3 In commercial strippers, a number of operating problems have been identified, most commonly flooding, bridging, and defluidization. Flooding and bridging impede solids circulation; lead to poor gas-solids contacting and hence poor stripping efficiency; and, if pronounced, almost completely stop the circulation of particles, shutting down the process.3,4 Flooding can also be a problem in other applications of fluidized beds, e.g., pressurized fluidized-bed combustion (PFBC) where there are tightly spaced horizontal heat-transfer tubes inside the reactor. The work described in this paper was intended to improve the understanding of flooding behavior in fluidized beds and to provide useful data and guidance for the design and operation of fluidizedbed reactors. Mechanism and Occurrence of Flooding 1. Flooding in Gas-Liquid Countercurrent Flows. The term “flooding velocity” was first used to describe a phenomenon in countercurrent gas-liquid flow through packed towers for which there are at least 10 definitions:5 (a) maximum vapor velocity that a given column can withstand without priming; (b) vapor veloc* To whom correspondence should be addressed. E-mail: [email protected]. † University of British Columbia. ‡ Syncrude Canada Ltd. § Syncrude Research Centre.

ity at which the logarithmic pressure drop-gas velocity curve abruptly turns upward; (c) superficial gas velocity at which marked spraying of liquid occurs; (d) superficial gas velocity at which slight splashing is observed at the top of the packing; (e) superficial velocity at which a liquid layer forms on top of the packing; (f) superficial gas velocity at which liquid builds up to a height of about 1/2 in. above the packing; (g) superficial gas velocity corresponding to the first appreciable liquid carryover; (h) superficial gas velocity corresponding to the second break point in the logarithmic pressure drop vs gas velocity curve; (i) superficial gas velocity at which the measured gas hold-up increases abruptly; and (j) vapor rate at which the height of a transfer unit (HTU), or the height equivalent to a theoretical plate (HETP), reaches a very high value. Definitions c-g are associated with liquid entrainment from the breakup of descending liquid films into droplets. Definitions i and j indicate a change of local structures and deterioration in gas-liquid contacting. In tubes without packings, flooding is often said to occur when the descending liquid film reverses direction and starts to be carried upward as the gas flow rate increases. Just above the flooding velocity, the liquid film oscillates upward and downward. To predict flooding in packed towers, Zenz and Eckert7 proposed the correlation

(

Fg xgD Fl - Fg ug

)

1/2

+

(

Fl xgD Fl - Fg ul

) ( ) 1/2

)

4 tan θ

1/2

(1)

where ug is the upward gas velocity through the slot, ul is the downward liquid velocity through the slot, and θ is the angle of internal friction. Flooding has also been found to be important in flow regime transitions in gasliquid flows.8-10 2. Flooding and Bridging in Gas-Solids Countercurrent Flows. A. Flooding. In gas-solids countercurrent systems containing internals/baffles, “flooding” denotes an unwelcome phenomenon sometimes encountered in commercial units. The following criteria are among those used to identify the onset of flooding: (a) A marked difference exists between the rates of

10.1021/ie030772e CCC: $27.50 © 2004 American Chemical Society Published on Web 05/28/2004

5612 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

steam injected into the stripper and of water condensed from the downstream hydrocarbon products (steam underflow). (b) Poor stripping efficiency leads to higher carry-under of hydrocarbons resulting from reduced catalyst/coke residence times in the stripper and poor steam-catalyst contacting. (c) Detection below the stripper of tracer injected above the stripper increases dramatically.2,4 (d) A region of high voidage develops inside the stripper below the row of baffles where flooding occurs. The high-voidage region can be identified by gamma ray scans of the stripper and/or the solids discharge line or by a dramatic decrease in pressure drop across the flooded portion of the stripper. A criterion for flooding was given by Kwauk6 with flooding defined at the point at which there is a step change of voidage with varying superficial gas velocity for a given solids flow rate, i.e., [∂Ug/∂]Up ) 0, or a step change of voidage as the solids flow rate changes at a constant gas velocity, i.e., [∂Up/∂]Ug ) 0. Senior et al.2 postulated that flooding occurs in FCC strippers when the local downward particle velocity through a baffled section exceeds the upward steam velocity, causing steam to accumulate at the base of the stripper. Assuming uniform distributions of both solids and steam flows over the cross section of the stripper, we can estimate the local downward particle velocity in the narrowest cross section by

vp )

Gs/(1 - φ) FD(1 - B)

(2)

where Gs is the solids flux referred to the cross section of the column in the stripper section, φ is the maximum fraction of the column cross-sectional area occupied by baffles, FD is the density of the dense phase, and B is the volume fraction of the bubble phase. The rising velocity of bubbles relative to the descending solids is expected to be of the form11

ub ) kxgDb

(3)

where Db is the equivalent bubble diameter in the opening or slot. At the flooding point, according to the criterion of Senior et al.,2 ub e vp, so that flooding is predicted when

Gs/(1 - φ) kxgDb e FD(1 - B)

(4)

According to eq 4, flooding can be caused by high catalyst fluxes, small bubbles, large area blockages by baffles, or large bubble hold-ups. This mechanism also suggests that fine particles (“fines”) can lead to flooding by causing smaller bubbles, lower bubble rise velocities, and increased B values. Baffles that redistribute gas as small bubbles and force these to contact catalysts in regions of high solids downward velocity might promote flooding. B. Bridging. If steam bubbles are not well distributed, pockets of catalyst can descend a significant distance before encountering bubbles, leading to defluidized regions that reduce catalyst and steam residence times and lower stripping efficiencies. If defluidization occurs intermittently as a result of locking of particles in constricted regions of a stripper, it can lead to erratic flow behavior, often termed “bridging”, again reported by Senior et al.2 in FCC strippers. When a packet of

Figure 1. Bridging in FCC strippers based on differential pressure measurements (adapted from Senior et al.2).

catalyst forms a bridge as it squeezes between baffles, rising bubbles tend to be caught underneath this “bridge”. The trapped void grows as more bubbles arrive from below, while the catalyst level builds above the bridge. In severe cases, the gas void can grow to the dimensions of the stripper, resulting in a large reduction in catalyst circulation. Eventually, a fault might appear in the bridge, and large clumps of defluidized catalyst then cascade down through the void space. Bridging in commercial strippers can cause poorer stripping and large fluctuations in differential pressure, while also causing spikes in regenerator afterburner and mechanical vibrations.2 Bridging typically starts low in the stripper where gas compression is greatest because of the higher hydrostatic pressure. Defluidization and bridging most frequently occur with deep catalyst beds of low fines content, poor steam distributors, and larger strippers where uniform steam distribution is difficult to achieve. Cold-flow tests2 have shown that some common baffle designs are prone to bridging under normal stripper operating conditions. Figure 1 shows bridging in a cold-model FCC stripper based on differential pressures over the lower stripper section.2 The pressure drop decreased because of the buildup of gas pockets beneath the defluidized catalysts when bridging started and later recovered when the bridge collapsed. This type of behavior has occurred on occasion in Syncrude’s cokers. It has also been observed in the cold-model fluid coker unit described below, especially in the top rows. Comparing the flooding and bridging mechanisms proposed by Senior et al.,2 we find that both are caused by the formation of stagnant zones, leading to dilution below these zones due to the buildup of gas pockets. Flooding can be a smooth process, whereas bridging typically causes erratic fluctuations. Bridging typically starts from the lower section of the stripper, whereas flooding can start on any row of baffles.2 Both can be countered by decreasing the upward gas flow rate and/ or the downward solids flux. Experimental Study 1. Equipment and Particles. Experiments were carried out at UBC under ambient temperature and

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5613

Figure 2. Overall schematic of semicircular fluid coker cold model: (a) side view, (b) front view. All dimensions are in millimeters. (For further details, see Knapper et al.14).

pressure conditions in a semicircular, Plexiglas geometrically scaled cold model of two commercial fluid cokers operated by Syncrude Canada Limited. An overall schematic appears in Figure 2. The diameter of the stripper section is 0.61 m. FCC particles of mean diameter 70 µm and density 1750 kg/m3 were used for modeling purposes. Air was introduced through numerous nozzles located in the feed section, the attrition (transition) section, and the stripper to fluidize the particles. In total, there were originally eight rows of baffles together with several air spargers near the bottom of the stripper. When the unit was operated at steady state, particles traveled downward through the reactor and were then removed through a specially configured exit into a standpipe, from where they passed through a pinch valve and U-bend before being reentrained to the top of the main vessel through a riser and gas-solid separator. The overall solids circulation rate was controlled by the pinch valve and was determined from the pressure drop across a venturi constriction at the top of the riser after calibration using optical fiber probes. The baffles used for most tests were “sheds” with a top included angle of 90°, and an angle of 45° to the horizontal at both sides (see Figure 3b). For some tests, described below, steeper sheds (Figure 3c, d, and f), cylinders of circular cross section (Figure 3e), and flat horizontal plates were also investigated. In all cases, the baffles were horizontal, parallel, and evenly spaced, spanning the entire cross section as shown in Figure 3g. Fouling of the sheds was simulated by gluing flat Styrofoam slabs on the top of the sloping surfaces, thereby increasing φ, the maximum fraction of cross-

sectional area occupied by the fixed baffles, without changing the number of slots. Several differential pressure transducers were set up in the stripper section and transition zone to monitor flooding, as shown in Figure 4. There were two transducers in the baffled stripper section: PC1 across the lower four shed rows and PC2 for the top four rows. The differential pressure transducer in the transition zone between the stripper and feed section is labeled PC3, and another just below the baffled section is designated PC0. Flooding was investigated on the basis of visualization through the transparent front surface and by analysis of the pressure drop across transducer PC2. In the results below, both the superficial gas velocity (Ug) and solids flux (Gs) are referred to the total crosssectional area of the stripper section. 2. Determination of Flooding Conditions in Cold Model Coker Strippers. Figure 5 shows the PC2 pressure drop and its standard deviation over the stripper section as functions of the net solids circulation flux at a superficial gas velocity of 0.12 m/s and a minimum cross-sectional fractional open area (between baffles) of 32%. For normal operation before flooding was reached, neither the time-mean pressure drop over the stripper section nor its fluctuations were sensitive to the net solids flux. However, major changes in the pressure drop and its fluctuations occurred as flooding was approached as the net solids flux increased. The pressure drop over the top stripper section (PC2 in Figure 4) began to drop sharply at a circulation flux of about 36 kg/m2‚s, indicating that the top rows of sheds began to flood. The PC2 pressure drop continued to drop, and eventually, the pressure drop over the bottom

5614 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

Figure 3. Geometries and configurations of baffles tested.

section of the stripper (PC1) dropped sharply at a solids flux of ∼37 kg/m2‚s. Complete flooding of the stripper caused both the PC1 and PC2 pressure drops to fall to low values. From Figure 5, it can be seen that the pressure drop over the reactor section, PC3, was unaffected by flooding in the stripper. To provide consistency, the flooding point in this study is defined as the condition at which the PC2 pressure drop reached onehalf of its original (low-Gs) value at a constant air flow rate. 3. Effects of Operating Conditions and Stripper Configuration on Flooding. Figure 6 shows the effect of the superficial stripping gas velocity, Ug, on the pressure drop. At a higher gas velocity, flooding occurred at a lower solids flux. At low Ug, the pressure drop decreased much more gradually with increasing solids flux, Gs, and flooding occurred more abruptly at higher solids flux. At a higher gas velocity, the pressure drop decreased continuously with increasing solids flux, and the onset of flooding was more gradual. At higher Ug, the interaction between downflowing particles and upflowing gas pockets was more vigorous, so that the

solids hold-up in the stripper did not collapse as abruptly as at lower gas velocities. To explore the influence of the open area of sheds, different open-area fractions were tested. As shown in Figure 7, for each superficial gas velocity, an increase in total open area between sheds delayed the onset of flooding. Flooding occurred at a very low solids circulation flux of 8.2 kg/m2‚s for an open-area fraction of 14%, and at 47 kg/m2‚s for an open-area fraction of 33%, at the same superficial gas velocity of 0.34 m/s. At Ug ) 0.13 m/s, flooding was found to occur at a solids circulation flux of 23 kg/m2‚s for an open-area fraction of 14%, whereas no flooding was observed at a solids circulation flux of 110 kg/m2‚s (the highest achievable flux in our unit) when the open-area fraction was 33%. Visually it was not far off from flooding at 110 kg/m2‚s for Ug ) 0.13 m/s, hence the broken line is used in Figure 7 to indicate the minimum value of flooding for Ug ) 0.13 m/s. The open-area fraction is seen to strongly affect the solids circulation flux corresponding to flooding. Therefore, the shed open area needs to be optimized

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5615

Figure 4. Differential pressure transducers across various stripper sections. Dimensions are in millimeters.

to effectively split bubbles and reduce axial dispersion on one hand while avoiding flooding on the other hand. The effect of the width of the gap between adjacent sheds was investigated by varying the width and number of sheds while maintaining the same total open area between sheds. Three different shed sets (with seven, five, and three sheds in the top row) were tested, with the total shed open-area fraction held constant at 26%. The corresponding gap widths between adjacent sheds were 22, 30, and 51 mm, respectively. The 90°included-angle baffle geometry (Figure 3b) was used in this investigation. Figure 8 shows the solids flux at flooding as a function of the gap width between adjacent sheds for different superficial gas velocities. It is seen that the onset of flooding was delayed for sheds separated by wider gaps at a constant total open area, suggesting that a stripper with wider gaps between larger baffles is more forgiving to high solids downflow. Figure 9 compares the performance of five types of baffles (see Figure 3) for Ug ) 0.13, 0.22, and 0.33 m/s, with total open-area fractions of 31-33%. It is seen that the onset of flooding is influenced by the baffle crosssectional shape. Steeper sheds show a much more gradual decrease of pressure drop with increasing solids flux, leading to flooding at a much higher solids flux. The flat sheds (180° included angle, Figure 3a) usually led to flooding at the lowest solids circulation flux, whereas the steepest sheds (30° included angle) caused flooding at the highest solids circulation flux. Flooding was not observed up to the maximum solids circulation flux of the unit (110 kg/m2‚s) for the steepest sheds at a low gas velocity of 0.13 m/s (Figure 9a). The difference is likely due to less horizontal intrusion into the opening between the baffles by sliding solids as they leave the lower edge of the steeper surfaces, so that more open area is available for the counterflow of gas pockets than

Figure 5. Effect of solid circulation flux on pressure drops and their fluctuations for stripper and reactor sections at a constant superficial gas velocity of 0.12 m/s for 32% open area for 90°included-angle sheds.

for the flat sheds. These results demonstrate that steeper sheds can be advantageous in delaying the onset of flooding. Circular tubes are also relatively effective in delaying the onset of flooding at low gas velocities compared to sheds with included angles greater than 60° (Figure 9a,b). Flooding did not appear for the circular tubes up to the maximum solids circulation flux of the unit at a low gas velocity of 0.13 m/s (Figure 9a). However, at a relatively high gas velocity (0.33 m/s), the circular tubes led to flooding at the lowest solids circulation flux among all the sheds, as shown in Figure 9c. A baffle configuration with 30°-top-included-angle sheds on the top row and simulated fouled sheds on the second row (Figure 3f) was tested to further investigate the effects of baffle configuration on flooding, with a minimum open area of 33%. As evidenced in Figure 10, the onset of flooding occurred at a much lower solids circulation flux for the fouled baffle configuration compared to the configuration with the same minimum open-area fraction and 30° sheds on the top row (Figure 3d), with clean sheds on the second row (no protrusion into the gap from below). Thus, fouling of the second row, leading to a reduction in the gap width and open area for the top row, can easily cause flooding. Modeling of Flooding 1. Model Derivation. Treating flooding in gas-solids strippers as in gas-liquid packed towers, York et al.12 and Papa and Zenz1 extended the flooding correlation of Zenz and Eckert7 (eq 1) to predict flooding in gas-

5616 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

Figure 8. Effects of slot width between adjacent sheds on solids circulation flux at flooding (90°-included-angle sheds; open area ) 26%).

Figure 6. Effect of solids circulation flux on the pressure drop and its fluctuations over the stripper top section for different superficial gas velocities and 32% open area for 90°-included-angle sheds.

Figure 7. Effect of open area on solids circulation flux at flooding at different superficial gas velocities for 90°-included-angle sheds. Broken line indicates the minimum solids flux at flooding as flooding is reached at only 110 kg/m2‚s at 0.13 m/s.

solids strippers. The original correlation was in dimensional form with Imperial units. Rearranged in dimensionless format, it can be written as

[

()]

Ug/(1 - φ) Fg FD xgW

1/2 2/3

(

)

1 Gs/(1 - φ)/FD + 1/3 2 xgW

(

Figure 9. Pressure drop over the stripper top section (PC2) as a function of solids flux for five types of baffles at different superficial gas velocities. Fractional open area ) 31-33% in all cases.

2/3

)

)

1 2 tan θ

1/3

(5)

where Ug is the superficial gas velocity based on the total cross-sectional area of the column, Gs is the solids flux based on the total cross section of the column, W is

the slot width, θ is the internal angle of friction, FD is the bulk density of the dense phase, and Fg is the gas density. In our new model, we consider countercurrent flow in gas-solids transport lines. The average relative velocity between rising gas pockets and descending

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5617

) x∆FF

W Uslug ) 0.23 + 0.13 xgL L

(

(11)

p

Because ∆F/Fp ≈ 1, the last term of eq 11 can be dropped, and the relative velocity is then

Uslip ) Uslug ) (0.23 + 0.13/λ)xgWλ

(12)

where λ ) L/W. Substituting eq 12 into eq 10, one obtains

Gs/FD

xgW(1 - φ) Figure 10. Pressure drop over the stripper top section (PC1 + PC2) as a function of solids flux for two types of baffles at different superficial gas velocity: (A, closed symbols) 30°-top-included-angle sheds on top row, fouled sheds on second row; (B, open symbols), 30°-top-included-angle sheds on top row, clean sheds on second row. Fractional open area ) 31-33% in all cases.

particle dense phase as they travel countercurrently through the narrowest open area can be expressed with the commonly used two-phase theory of fluidization11

Uslip )

(Ug - Umf)/(1 - φ) Vp/(1 - φ) + B (1 - B)

(6)

Note that Ug and Uslip are positive upward, whereas Vp is positive downward. The total absolute momentum flux, M ˙ tot, of gas and particles through the gaps where the open crosssectional area is a minimum is given by

M ˙ tot )

Fg(Ug - Umf)2A B(1 - φ)

+

(1 - B)(1 - φ)

∂M ˙ tot )0 ∂B

(8)

(1 - φ)

+

x x

Fg (Ug - Umf) FD Vp

x

(9)

Fg (Ug - Umf) FD Vp

Fg (Ug - Umf) Uslip ) FD (1 - φ) 1 + F /F

x

g

D

(13)

M ˙ s/FD (0.23 + 0.13/λ)xλ ) xgWD nLWD 1 + F /F

x

(Qg - Qmf) nL(W - WD)

)

g

(14)

D

(0.23 + 0.13/λ)xλ 1 + xFg/FD

g

(10) D

Gas pockets passing through the slots of the baffled stripper section can be considered to travel as plane slugs relative to the descending solids. The velocity of a plane slug through stationary solids in a gap of width W and length L is given13 by

xg(W - WD)

(15)

for the passing of gas pocket at flooding with Qg as the total gas volumetric flow rate in m3/s. Combining eqs 14 and 15 to eliminate WD, one obtains (see Papa and Zenz1)

[

()

(Ug - Umf)/(1 - φ) Fg FD xgW

Substituting eq 9 into eq 6 gives

Vp

x

Equation 13 is similar to eq 1, except that the latter contains the angle of internal friction whereas eq 13 includes the slot length-to-width ratio. Following an approach similar to that of York et al.12 and Papa and Zenz,1 the channel between sheds is divided into two parts, one for downflowing solid dense phase and the other for gas pocket upflow. WD is designated as the effective width of the dense-phase flow stream with a corresponding slot area of AD () nLWD) and (W - WD) is the effective width for the dilute-phase flow stream, with a corresponding area of (AW - AD) [) nL(W - WD)]. The maximum dense-phase mass downflow, M ˙ s, through the slot at flooding is defined by

(7)

leading, after some algebra, to

1+

x

Fg (Ug - Umf) (0.23 + 0.13/λ)xλ ) FD xgW(1 - φ) 1 + F /F

where M ˙ s is the total solids mass flow rate in kg/s and

FDVp2A

where Vp ) Gs/FD. Although we do not know B, it is reasonable to assume that it establishes itself in such a way that the total momentum flux through the gaps is maximized at flooding, i.e.

B )

+

[

]

1/2 2/3

] [

1 Gs/(1 - φ)/FD 21/3 xgW

2/3

)

+

1 (0.23 + 0.13/λ)xλ 2 1 + xFg/FD

]

2/3

(16)

The left-hand sides of eqs 5 and 16 are nearly identical, the only difference being that Ug is replaced by (Ug Umf), but for most cases of practical interest, Ug . Umf. The two equations give similar qualitative results. Both predict that the solids flux at flooding increases with decreasing superficial gas velocity, Ug; with increasing shed opening area, (1 - φ); and with increasing slot width, W. These trends are all consistent with experimental results, presented above. The one parameter that was shown above to have an influence but is excluded from eq 16 is the shape of the baffles. Addition of an empirical term to account for the shed steepness gives

5618 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

[

()

(Ug - Umf)/(1 - φ) Fg FD xgW

[

]

1/2 2/3

+

] [

1 Gs/(1 - φ)/FD 21/3 xgW

2/3

)

1 (0.23 + 0.13/λ)xλ 2 1 + xFg/FD (1.01 + 0.74e

]

-R/25.3

2/3

) (17)

where R is top included angle of the sheds in degrees. 2. Comparison of Correlations with Experimental Data. Equation 5 from Papa and Zenz1 is first compared with our experimental data with the angle of internal friction assumed to be 83° for FCC particles and 70° for coke particles. As seen in Figure 11, eq 5 underestimates the flooding data when an internal friction angle of 83° for FCC is used, but it overestimates most data when this angle is taken as 70°. An internal friction angle of 76° gives reasonable agreement with most of the data. However, data from the smallest slot width do not fall into the same range as those for relatively large open areas and slot widths, implying that the slot length-to-width ratio plays a significant role. A comparison of eq 16 with experimental data obtained with 90° sheds is provided in Figure 11, where Ug* and Up* are the first and second dimensionless groups, respectively, which appear in brackets on the left sides of eqs 5, 16, and 17. It is seen that eq 16 predicts the right order of magnitude, with scatter occurring around the predictions, suggesting that λ is close to the physical ratio of L/W. Equation 5 consistently underpredicts the experimental data. Equation 16 gives better predictions, but eq 17 gives the best agreement with the experimental data, with the effect of the top included angle of the sheds on the onset of flooding well taken into account by the empirical correction term. For the case with 14% open area, all three equations underestimated the flooding points, as seen in Figure 11.

Figure 11. Comparison of predictions from eqs 5, 16, and 17 with experimental flooding data.

Flooding of Commercial Coker Strippers and Its Simulation

Figure 12. Simulated solids circulation flux at flooding versus superficial steam velocity for Syncrude commercial fluid coker stripper based on eq 17 with λ ) L/W. Original open-area fraction ) 50%. Points indicate conditions where flooding did and did not occur. Percentage fouling values are based on end-of-run assessments.

The flooding of Syncrude commercial fluid coker strippers containing eight rows of R ) 90° sheds is next predicted using eq 17. Figure 12 shows the solids flux as a function of superficial gas velocity for various degrees of shed fouling based on eq 17. Two points indicate conditions where flooding did occur and the third where it did not occur in one of the commercial fluid cokers. Consistent with our cold-model experimental results, flooding occurred at a lower solids flux when the shed was seriously fouled. Equation 17 predicts a high solids flux at flooding when the shed is clean (no foulant), falling by one-half when the shed is 30% fouled (i.e., when the total open area is 30% less than that of the original clean sheds). It was found by visual inspection at the end of this commercial run (shutdown for service and cleaning) that shed fouling was less than 40%. Figure 12 predicts that the stripper should not be flooded at a solids flux of 63 kg/m2‚s and a steam superficial velocity of 0.52 m/s, as tested at the end of the run when there was no sign of flooding in the commercial unit. This point is indicated by the square symbol in Figure 12. At the end of the run, as indicated by the filled and open circular points, severe fouling of the stripper was identified, with ∼74%

and >85%, respectively, of the minimum open area between sheds blocked off, determined after the unit had been shut down and cooled. Some of this fouling might have occurred during the late stages of these runs, so it is impossible to determine precisely the fouled area when flooding first occurred, but fouling likely blocked close to 74 and 85% of the original open area, respectively, for these two runs. The unit was found to be flooded according to pressure drop signals over the stripper section. This is consistent with the prediction in Figure 12, in which operations at Gs ) 43 kg/m2‚s and Ug ) 0.24 m/s, as well as Gs ) 26 kg/m2‚s and Ug ) 0.18 m/s, fall into the flooding zone when the stripper is 74 and 85% fouled, respectively. Although three commercial data points are too few to draw conclusions, it is encouraging that eq 17 provides consistent predictions of flooding with respect to the available findings for large commercial fluidized-bed reactors. In a gas-liquid packed tower, the gas flow rate is generally maintained at about 80% of the flooding rate to maximize the contacting efficiency while avoiding flooding. In gas-solids strippers, it is clear from visual observations of the UBC cold-model unit that the gassolids contacting is improved with increasing stripping-

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5619

air flow rate as long as flooding is avoided. As in gasliquid packed towers, operating close to, but safely below, the flooding condition, say, at ∼80% of flooding, would be desirable for a gas-solids stripper to minimize carry-under. The danger of fouling is clearly illustrated in Figure 12. If the operation is set at 80% of flooding at the start of the run with clean sheds, the operation will fall into flooded operation when only 10% of the open area is blocked by fouling of the sheds. Therefore, both accurate prediction of flooding and prevention or minimization of fouling are required to operate the stripper in the most efficient manner. Conclusion Flooding in fluidized beds has been investigated by analysis of pressure drop and pressure fluctuations. Flooding was found to be affected by superficial gas velocity, open-area fraction, open slot width, and baffle shape. Higher superficial gas velocities and smaller open-area fractions lead to flooding at lower solids circulation fluxes. Steeper sheds delay flooding. For the same open-area fraction, an increase in the slot width between baffles delays flooding. A top row of clean sheds with fouled sheds on the next lower row can lead to premature flooding compared to clean sheds with the same open area. A theoretically based equation describing flooding has been developed with an empirical addition to account for the influence of the baffle top included angle. This equation provides reasonable predictions in comparison with both cold-model data and limited commercial data. Acknowledgment The authors are grateful to Syncrude Canada Limited for sponsoring this work and for permission to publish the results. We are also grateful to A. Donald, B. Knapper, K. Mansaray, and P. Ronan for assistance with the experiments. Nomenclature A ) total cross-sectional area of column, m2 AD ) slot area for the passage of solids dense phase, m2 AW ) total slot area, m2 b ) dimensionless factor D ) equivalent column diameter, m Db ) bubble diameter, m g ) gravitational acceleration, m/s2 Gs ) net solids downward flux based on total cross-sectional area, kg/m2‚s L ) length of the slot, m Le ) effective length of the slot, m M ˙ tot ) total momentum flux through minimum open crosssectional area, N Qg ) volumetric gas flow rate, m3/s ub ) bubble rise velocity, m/s ul ) actual liquid downward velocity, m/s ug ) gas rise velocity based on slot open area, m/s Ug ) superficial gas velocity in stripper section based on total cross section, m/s Up ) superficial particle velocity, m/s Uslip ) relative velocity between gas pocket and particle dense phase, m/s

Ug* )

()]

[

Up* )

1 Gs/FD/(1 - φ) 21/3 xgW

(Ug - Umf)/(1 - φ) Fg FD xgW

[

0.5 2/3

]

2/3

Vp ) superficial particle velocity ) Gs/Fp, m/s vp ) particle velocity ) [Vp/(1 - φ)]/(1 - B), m/s W ) effective slot width of baffles, m WD ) effective slot width for the passage of solid dense phase, m M ˙ s ) solids mass flow rate, kg/s Greek Letters R ) top included angle of sheds, degrees  ) cross-sectional average voidage B ) volume fraction of gas pocket/bubble phase λ ) length-to-width ratio of slot ) Le/W φ ) maximum cross-sectional shed area fraction θ ) angle of internal friction for particulate material, degrees FD ) density of dense phase, kg/m3 Fg ) gas density, kg/m3 Fl ) liquid density, kg/m3 Fp ) particle density, kg/m3

Literature Cited (1) Papa, G.; Zenz, F. A. Optimize performance of fluidizedbed reactors. Chem. Eng. Prog. 1995, 91 (4), 32. (2) Senior R. C.; Smalley, C. G.; Gbordzoe, E. Hardware modifications to overcome common operating problems in FCC catalyst strippers. In Fluidization IV; Fan, L. S., Knowlton, T. M., Eds.; Engineering Foundation: New York, 1998; p 25. (3) McKeen, T.; Pugsley, T. S. Simulation of cold flow FCC stripper hydrodynamics at small scale using computational fluid dynamics. Int. J. Chem. React. Eng. 2003, 1, A18. (4) Rivault, P.; Nguyen, C.; Laguerie, C.; Bernard, J. R.; Aquitaine, E. Countercurrent stripping dense circulating beds: Effect of the baffles, In Fluidization VIII; Large, J. F., Laguerie, C., Eds.; Engineering Foundation: New York, 1995; p 491. (5) Silvey, F. C.; Keller, G. J. Testing on a commercial scale packed tower. Chem. Eng. Prog. 1966, 62 (1), 68. (6) Kwauk, M. Generalized fluidization. Sci. Sin. 1963, 12 (4), 587. (7) Zenz, F. A.; Eckert, C. A. New chart for packed tower flooding. Pet. Refin. 1961, 40 (2), 130. (8) Wallis, G. B. One-Dimensional Two-Phase Flow; McGrawHill: New York, 1969. (9) Bi, H. T.; Grace, J. R. Regime transitions: Analogy between gas-liquid co-current upward flow and gas-solids upward transport. Int. J. Multiphase Flow 1996, 22 (Suppl), 1. (10) Wo¨lk, G.; Dreyer, M.; Rath, H. J. Flow patterns in small diameter vertical noncircular channels. Int. J. Multiphase Flow 2000, 26, 1037. (11) Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: Cambridge, U.K., 1963. (12) York, J. L.; Barberio, J. T.; Samyn, M.; Zenz F. A.; Zenz, J. A. Solve all column flows with one equation. Chem. Eng. Prog. 1992, 88 (10), 93. (13) Clift, R.; Grace J. R.; Weber, M. E. Bubbles, Drops and Particles; Academic Press: New York, 1978. (14) Knapper, B.; Berruti, F.; Grace J. R.; Bi, H. T.; Lim, C. J. Hydrodynamic characterization of fluid bed cokers. In Circulating Fluidized Bed Technology VII; Grace, J., Zhu, J., de Lasa, H., Eds.; CSChE: Ottawa, Canada, 2002; p 263.

Received for review October 22, 2003 Revised manuscript received March 3, 2004 Accepted March 9, 2004 IE030772E