Effects of Different Gaseous Nozzle Injections on Gasâsolid Dynamic

Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 1055−1067

pubs.acs.org/IECR

Effects of Different Gaseous Nozzle Injections on Gas−solid Dynamic Mixing in FCC Riser Zihan Yan,† Yiping Fan,† Xiaotao Bi,‡ and Chunxi Lu*,† †

Ind. Eng. Chem. Res. 2019.58:1055-1067. Downloaded from pubs.acs.org by IOWA STATE UNIV on 01/17/19. For personal use only.

College of Chemical Engineering, State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China ‡ Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada ABSTRACT: Effects of different gaseous nozzle injections on gas−solid dynamic mixing in FCC riser are experimentally studied by calculating the time fractions of the proposed phases (gas, diluter/denser dispersed particles, and cluster). Generally, a more dispersed particulate phase can be obtained when jets are downward. By analyzing the effects of operating parameters, it is shown that the larger jet/prelift flow momentum ratio increases the proportions of the gas and cluster phases, and the proportion of the useful denser, dispersed particulate phase decreases accordingly when nozzles are upward. For the downward pointed jets, the momentum ratio only affects the radial time fraction distributions of different phases. The cross-sectional time fractions of each phase change little with momentum ratios, indicating a good operational flexibility. To obtain better gas−solid dynamic mixing, suitable setting angle of nozzles is 30−45° when nozzles are mounted downward.

1. INTRODUCTION Fluid catalytic cracking is the key technique for upgrading heavy oil in modern refining engineering. In recent years, the riser reactor is widely used to realize a fast cracking reaction. Generally, four different parts exist in a riser reactor, i.e., the prelift section, the feed injection section, the full reaction section, and the gas−solid separation section.1 In the feed injection section, atomized raw oil is injected into the reactor from the atomizing nozzles to contact with catalyst particles. Cracking reactions occur immediately during the mixing between oil and catalysts. It is reported that more than 50% of the yield of cracking reactions occur in the feed injection zone.2,3 Therefore, the dynamic mixing behavior of nozzle injections and catalyst solids in this region is very important. The flow of gas and solids in FCC riser can be regarded as the fast fluidization of fine particles.4 Both dispersed individual particles and groups of particles (clusters) exist during the whole process.5−7 Many studies have shown that agglomerate particles will influence the contact of jets with solids because of the lower local void volume and larger particle sizes.8−12 Ouyang et al.13 showed that the overall conversion rate in riser reactor decreased with increasing cluster proportions. Breault et al.,14−16 Chalermsinsuwan et al.,17,18 and Subbarao19 found that existing of clusters in fast fluidized beds decreased the mass transfer coefficient. Therefore, in the riser reactor, especially the jet influence zone, if every particle is uniformly covered with a thin layer of atomized feed injection, without particle agglomerates or clusters, an ideal reaction will occur.20−22 That is to say, the dispersed particulate phase is expected to ensure more particles are entrained by feed oil © 2018 American Chemical Society

rapidly and uniformly. However, in most industrial riser reactors, conditions are not perfect. The gas−solid flow behavior in the feed influence zone of FCC riser has been experimentally investigated by Fan et al.23,24 Results showed that the distributions of jet concentration and solid concentration did not match each other. The study of E et al.25 also indicated that the distribution of particles in the jet influence zone was quite different from that in the typical riser. Besides, a numerical calculation method was used by researchers26−30 to investigate the complicated mixing and reaction process in riser reactors. It was concluded that the distributions of particle concentration, jet concentration, and particle temperature were not uniform in the feed mixing region. Yan et al.31 investigated the dynamic mixing of catalysts and jets in the feed influence zone of risers by analyzing the instantaneous concentration of particles. High time fractions of gas phase and cluster phase were found when the injections were upward. Researchers have attempted to obtain a better jet-catalyst mixing in the feed influence region. Maroy,32 Dries,33 and Zheng et al.34 put different inner structures inside the riser to realize a better feed-catalysts mixing. However, some complex internals may cause other unexpected problems such as coking and abrasion. Lomas and Haun35 set the nozzles to a horizontal direction to reduce the jet influence region. But Received: Revised: Accepted: Published: 1055

October 11, 2018 November 28, 2018 November 30, 2018 November 30, 2018 DOI: 10.1021/acs.iecr.8b05033 Ind. Eng. Chem. Res. 2019, 58, 1055−1067

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Industrial & Engineering Chemistry Research

To make a comparison, the cases of upward and downward jets were studied. In most commercial riser reactors, feed nozzles are usually equipped upward, the angle with riser axis is usually 30−40°. Thus, the installation angle of upward nozzles (relative to axis) was chosen to be α = 30° in this study, as shown in Figure 2(a). For the downward jets, we intended to

the nozzles need to be absolutely symmetrically mounted in case the high-speed jets erode the inner surface of the riser. In a patent from Mauleon and Sigaud,36 a new type of downward pointed injection was proposed. Furthermore, effects of different mounted nozzles were studied by Chen et al.37−39 According to their 3D-simulation results, better jet-catalysts mixing was found when the jets were downward. Yan et al.40,41 investigated the matching between jets and catalysts in the FCC injecting region. Moreover, different phases (gas, diluter/ denser dispersed particles and cluster) during the mixing between jet and particles were found.31 Comparisons between upward and downward nozzles were made by calculating the phase time fractions. However, the previous work concentrated on the analysis method, limited operating conditions, and the selection of nozzle setting angles. Therefore, in this paper, we focus on studying the effects of operating conditions on the dynamic mixing of jets with solids in the FCC jet influence zone. The momentum ratio of jet gas to prelift flow K is introduced to reflect the influences of different parameters. In order to have a better understanding of the downward pointed jets, three nozzle setting angles (30°, 45°, and 60°) were selected. The time fractions of the proposed phases in each scheme are calculated to show the gas−solid dynamic behavior. Finally, by analyzing the jet−catalyst dynamic mixing process, cold flow data for model development in FCC riser can be obtained.

Figure 2. Jet injection schemes.

investigate the influence of nozzle setting angles on gas−solid dynamic mixing behaviors. Therefore, three different angles (β = 30°, 45°, and 60°) were used in the experiments, as shown in Figure 2(b). 2.2. Experimental Conditions. FCC equilibrium catalysts with a mean diameter of 65 μm were used in the experiments. The bulk density was ρb = 930 kg/m3 and the particle density was ρp = 1200 kg/m3. Figure 3 presents the particle size distributions.

2. EXPERIMENTS 2.1. Experimental Setup. Experiments were finished in a large scale cold model riser system, whose height was 11 m and inner diameter was 0.186 m, as shown in Figure1. Four nozzles

Figure 3. Particle size distributions of FCC particles.

The prelift gas was atmospheric air. In a cold model experiment, it is hard to use actual feed oil as the injection. Thus, the injection was instead of atmospheric air, similar to the studies of Fan at al.,23,24 E at al.,25 and Yan et al.40,41 This is reasonable because the evaporation of feed oil is usually very fast ( εscr, it is recorded as cluster. If εsi(A2) is near zero, it is recorded as gas phase. For the other case, it is regarded as particulate phase. As the solid holdups of dispersed particles usually have a wide range, it is divided into denser and diluter dispersed particles by using the average value of A2 subsignal. When εsi(A2) < εsi(A2), it is defined as diluter dispersed particulate phase. When εsi(A2) ≤ εsi(A2) < εscr, it is defined as denser dispersed particulate phase. Similar to the previous study, to quantify the results, phase time fractions are employed, as shown in eqs 3−6.

Table 2. Frequency Bands of Detail and Approximation Subsignals j

frequency (Hz)

A1 A2 A3 A4 A5 A6

contained. Instead, some random perturbations as well as useless noise can be removed. In the traditional sensitive analysis used by Manyele et al.,6 to identify clusters, we need to know the consecutive sampling numbers (Ns) above the threshold solids holdup. However, in the jet influence zone, as the velocity of particles is very high, not only can random perturbing be filtered with increasing Ns, perturbations of particles can also be ignored.31 Thus, it is quite hard to obtain reasonable values of Ns under the influence of high speed jets. Fortunately, combining the sensitive analysis method with traditional wavelet decomposition, the problem can be solved. If the original signal is instead near the approximation subsignal, the useless random disturbances can be filtered automatically. Therefore, it is no need to determine Ns. By this way, A2 subsignal of solid concentration signals is chosen (the reason has been described above) for identifying cluster phase under different operating conditions in this study. Equation 2 gives the threshold for cluster identification according to the A2 subsignal.

)

1 2 3 4 5 6

level

For the gas−solid two phase flow in the riser, to form a cluster, there are usually at least 6−10 single particles aggregated together.46−50 In this study, the mean diameter of FCC particles is 65 μm, thus the minimum size of cluster is about 0.4 mm. The optic fiber probe used in the experiment had a diameter of 1.5 mm. Based on the above information, we calculated the maximum possible cluster velocities that are detected by different approximation subsignals, as shown in Table 3. According to the previous study,23,41 the ranges of particle velocities in the injection zone of riser are from 5 m/s up to 11 m/s. Therefore, if the level 2 approximation subsignal A2 is used, most useful information of particles and clusters can be

Fc = Tc/T , Tc =

∑ tci

(3)

Fs = Ts/T , Ts =

∑ tsi

(4)

Fu = Tu/T , Tu =

∑ tui

(5)

Fg = Tg /T , Tg =

∑ tgi

(6)

Where, T is the sampling time; Fc, Fg, Fu, and Fs represent the time fraction of cluster, gas, diluter dispersed particles, and denser dispersed particles, respectively; tci, tgi, tui, and tsi represent the existence time of cluster, gas, diluter dispersed particles and denser dispersed particles, respectively. 1057

DOI: 10.1021/acs.iecr.8b05033 Ind. Eng. Chem. Res. 2019, 58, 1055−1067

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Figure 4. Error bars of cluster time fractions.

Figure 5. Radial time fraction distributions of different phases at 0.185 m above nozzles, α = 30° (a-gas phase, b-cluster phase, c-denser dispersed particulate phase, d-diluter dispersed particulate phase)

this way, useful results can be obtained for engineering reference.

The time fraction distributions of different phases under the influence of upward and downward jets have been compared preliminarily in the previous study. In this paper, we focus on the effects of operating conditions on gas−solid dynamic mixing behaviors in the jet influence region of riser. Under the influence of high speed jets, many parameters can affect the complex gas−solid mixing process.51,52 For example, the density and velocity of prelift flow, the density and velocity of air jets, the solid mass flux and so on. In order to investigate these parameters comprehensively, the momentum ratio of air injection to prelift flow K is introduced, as shown in eq 7. By

K=

Mj Mr

=

Nρju j2AN π

(ρr ur2 + Gsu p) 4 Dr2

(7)

Where, N is the number of nozzles; ρj is the density of jets, kg/ m3; uj is the jet velocity at the exit of nozzles, m/s; AN is the area of nozzle exit, m2; ρr is the density of prelift flow, kg/m3; ur is the superficial gas velocity of prelift flow, m/s; up is the 1058


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velocity of particles, m/s; Gs is the solid mass flux, kg/(m2·s), Dr is the inner diameter of riser, m. In this research, the proposed four phases were distinguished by decomposing the measured instantaneous solid concentrations. In order to know the impact of dynamic errors, the error bars of different time fractions were calculated. As an example, the error bars of cluster time fractions are presented in Figure 4. Results show that most error bars are small, indicating that the method for identifying different phases is reliable.

injections. This cross section is close to the nozzles, most air jets cannot reach riser center under lower momentum ratio conditions. Thus the highest value of Fg appears around the riser wall. When the momentum ratio increases, air jets are easier to get to riser center, the highest Fg is in the center region accordingly. Combining Figure 5(a) with Figure 5(b), it is seen that the radial distribution of cluster time fraction has an opposite trend to that of the gas phase. Under lower momentum ratio conditions, higher cluster time fraction is seen in the riser center. On the contrary, more clusters appear near the riser wall when K is larger. At this cross section, particles cannot mix fully with the injections immediately. A number of particles are pushed to the spaces that are not occupied by air jets. Therefore, the cluster time fraction is higher in these regions. As the gas and cluster time fractions increase with increasing the momentum ratio, the time fraction of denser dispersed particles decreases significantly when K is larger, especially around the riser wall, seen in Figure 5(c). The Cross Section of H−H0 = 0.375 m. Figure 6(a)−(d) show the time fractions of different phases under different momentum ratios at 0.375 m above nozzles. At 0.375 m above nozzles, the highest time fractions of gas phase appear around the radial locations of r/R ≈ 0.5−0.8 under different momentum ratios, as Figure 6(a) shows. In this region, the jet secondary flow occurs.23 Therefore, the gas time fraction is larger near the center of jet secondary flow. During the development of secondary flow, part of the solids are entrained into the injection gas, at the same time, others

4. RESULTS AND DISCUSSION 4.1. Upward Pointed Jets. In most commercial FCC riser reactors, feed nozzles are usually equipped upward with an angle of 30−40° relative to the riser axis. Therefore, for the case of upward pointed injections, we set the angle between nozzles and riser axis to be 30°, as shown in Figure 2(a). Typical cross sections (H−H0 = 0.185, 0.375, and 0.675 m)23 in the jet influence zone are selected to show effects of operating parameters on gas−solid dynamic mixing behaviors. The Cross Section of H−H0 = 0.185 m. The time fractions of proposed four phases under various momentum ratios at 0.185 m above nozzles are shown in Figure 5(a)−(d). When the momentum ratio is low (K = 0.205), most gas phase exists near the riser wall, as shown in Figure 5(a). As the momentum ratio K increases, the gas phase moves toward the riser center. Besides, the time fraction of gas phase increases significantly with the rising K. This result confirms that the existing gas phase is mainly because of the high speed air 1059


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Figure 8. Average time fractions of different phases at 0.185 m above nozzles (α = 30°).

Figure 9. Average time fractions of different phases at 0.375 m above nozzles (α = 30°).

are pushed to the center. As a result, it enhanced the interactions among particles. Thus it is easier to form clusters. The expansion of secondary flow is influenced by the momentum ratio significantly. Therefore, in this region, the radial time fraction distribution of cluster phase varies with K, as shown in Figure 6(b). When the momentum ratio is low, the maximum value of Fc appears around the riser wall. As increasing K, the location of maximum cluster fraction moves toward the riser center.

The Cross Section of H−H0 = 0.675 m. The phase time fractions under various momentum ratios at 0.675 m above nozzles are plotted in Figure 7(a)−(d). In this region, the multiple air jets reach the riser center and mix together. Thus, higher gas time fraction is seen near the riser center. When the momentum of jet injections is larger, it is more difficult for air jets to have a full mix with particles immediately. Thus, the time fraction of the gas phase increases with increasing K, especially around the riser center, as Figure 7(a) shows. 1060


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time fractions are seen near the riser wall. Besides, it is found that the highest value of Fc increases with the rising K, as seen in Figure 7(b). Because the cluster and gas time fractions both increase with improving the momentum ratio, the time fraction of denser dispersed particles decreases when K raises, as shown in Figure 7(c). To show the overall effect of momentum ratio on the dynamic mixing of gas with solids in the jet influence zone, the average values of different time fractions at each cross section are calculated, as seen in eqs 8−11. Fc = Figure 10. Average time fractions of different phases at 0.675 m above nozzles (α = 30°).

Fs =

The jet secondary flow will move toward the riser wall during its development when the injections are upward.40 Part solids are entrained into the injections; clusters form in this process. Thus Fc is higher around the riser wall at this cross section. As mentioned above, the development of secondary flow is influenced by the momentum ratio significantly. Therefore, under lower momentum ratio condition (K = 0.205), jet secondary flow has not reached the riser wall at this height. The highest cluster time fraction appears at the radial location of r/R ≈ 0.5. For other conditions, the highest cluster

Fu =

Fg =

Fci 1 ∑ A i Fci A

(8)

Fsi 1 ∑ A i Fsi A

(9)

Fui 1 ∑ A i Fui A

(10)

Fgi 1 ∑ A i Fgi A

(11)

Where, A is the area of measured cross section and Ai is the integral area of the specific ring region.

Figure 11. Radial time fraction distributions of different phases at 0.185 m below nozzles, β = 30° (a-gas phase, b-cluster phase, c-denser dispersed particulate phase, d-diluter dispersed particulate phase). 1061


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Figure 12. Radial time fraction distributions of different phases at 0.185 m above nozzles, β = 30° (a-gas phase, b-cluster phase, c-denser dispersed particulate phase, d-diluter dispersed particulate phase).

Figures 8−10 show the average phase time fractions in the upward pointed injection scheme. From Figure 8, it is seen that the time fractions of gas and diluter dispersed particles increase with the rising K at 0.185 m above nozzles. The average cluster time fraction does not change significantly with the increase of momentum ratio. Accordingly, the time fraction of denser dispersed particles decreases under higher momentum ratio conditions. It indicates that more proportions of air jets cannot mix fully with particles immediately when K is large in this region. At 0.375 m above nozzles, there is no significant change of average time fractions under various momentum ratios, as Figure 9 shows. In this region, the momentum ratio only affects the radial distributions of different phases. The crosssectional average values of time fractions are similar. At 0.675 m above nozzles, the cluster and gas time fractions both obviously increase as the momentum ratio rises, as seen in Figure 10. In this region, the jet secondary flow keeps expanding and entraining particles. During this process, it is difficult for jet gas to mix uniformly with particles, thus more particles tend to agglomerate together. When the momentum ratio is larger, the influence of secondary flow is more serious. Therefore, the time fraction of denser dispersed particles decreases with increasing K. According to the above analysis, in the upward pointed injection scheme, the proportion of denser dispersed particles which are good for oil-catalyst mixing decreases with raising the momentum ratio in most regions. Accordingly, the cluster and gas time fractions increase when K is larger. Therefore, we

conclude that a larger momentum ratio is negative for the dynamic mixing of oil and catalysts when the jets are upward. 4.2. Downward Pointed Jets. The case of β = 30° was used to investigate the effects of operating parameters on gas− solid dynamic mixing behaviors in the downward feed injection scheme. Three typical cross sections (H−H0 = −0.185, 0.185, and 0.375 m)40 are selected to show the results. The Cross Section of H−H0 = −0.185 m. Figure 11(a)−(d) are the time fractions of different phases under different momentum ratios at 0.185 m below nozzles. In Figure 11(a), we can see that the radial distribution of gas phase time fraction varies with momentum ratios, similar to the distribution of jet eigen-concentration.40 Different from that in the upward injection scheme, the time fraction of gas phase does not increase significantly with raising the momentum ratio in this region. Besides, the time fraction values are very low, usually no more than 2%. For the cluster phase, when the momentum ratio is low, its time fraction distribution has a trend of higher near the riser wall and lower in the center, similar to that in the riser full reaction zone.6 This indicates the downward air injection has little influence on the gas−solids dynamic flow under lower momentum ratio conditions. As K increases, more clusters move toward the riser center, as Figure 11(b) shows. However, the maximum values of cluster time fraction are nearly the same. In the study of Yan et al.,41 the particle concentration in the riser center increases with increasing the jet velocity. Therefore, the distribution of clusters has the same trend. 1062


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Figure 13. Radial time fraction distributions of different phases at 0.375 m above nozzles, β = 30° (a-gas phase, b-cluster phase, c-denser dispersed particulate phase, d-diluter dispersed particulate phase)

Figure 14. Average time fractions of different phases at 0.185 m below nozzles (β = 30°).

Figure 15. Average time fractions of different phases at 0.185 m above nozzles (β = 30°)

In Figure 11(c), it is shown that the time fraction distribution of dispersed particles is contrary to that of cluster phase accordingly. Around the riser center, the time traction of dispersed particulate phase decreases with increasing K, whereas the result is opposite near the riser wall. The Cross Section of H−H0 = 0.185 m. The time fractions of different phases under various momentum ratios at 0.185 m above nozzles are shown in Figure 12(a)−(d). When the momentum ratio is small, the maximum time fraction of gas phase is at r/R ≈ 0.5, while the maximum value moves toward the riser center as K increases, seen in Figure

12(a). In this region, a small part of the high speed jet gas has not mixed fully with particles. Under lower momentum ratios, this part of gas cannot reach the riser center easily, thus the gas phase time fraction at r/R ≈ 0.5 is higher. For the cluster phase, around the riser wall, its time fraction falls as the momentum ratio decreases; while near the riser center, its time fraction increases with rising K. Accordingly, the time fraction of denser dispersed particles reduces when K decreases. 1063


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Figure 16. Average time fractions of different phases at 0.375 m above nozzles (β = 30°).

Figure 19. Comparison of the correlation of denser dispersed particulate phase time fraction with experimental data (α = 30°).

Figure 17. Average time fractions of different phases at 0.185 m below nozzles (K = 1.141).

Figure 20. Comparison of the correlation of denser dispersed particulate phase time fraction with experimental data (β = 30°).

Based on the above results, the cross-sectional average time fractions of proposed four phases under the influence of downward jets are calculated by eqs 8−11, plotted in Figures 14, 15, and 16. Combining Figures 11−13 with Figures 14−16, it is seen that changing of momentum ratio only affects the local distributions of different time fractions when the jets are downward. The cross-sectional time fractions of different phases change little under different momentum ratios. Therefore, combined with the previous studies,53 it is concluded that the momentum ratio will only affect the mixing speed between prelift flow and air jets when nozzles are downward. During the dynamic gas−solid mixing process, the momentum ratio has little influence. In other words, better operational flexibility can be obtained if the nozzles are mounted downward. For the new type of downward pointed injection scheme, appropriate nozzle setting angle needs to be determined before its industrial application. Therefore, three different angles (β = 30°, 45°, and 60°) were used in the experiments to investigate their effects on the dynamic mixing between jets and particles. In order to cover the common industrial conditions, here we chose K = 1.141 to analyze the cross-sectional time fractions of different phases under three nozzle setting angles. Two typical cross sections near the nozzles were selected to show the results, seen in Figures 17−18.

Figure 18. Average time fractions of different phases at 0.185 m above nozzles (K = 1.141).

The Cross Section of H−H0 = 0.375 m. The time fractions of different phases under various momentum ratios at 0.375 m above nozzles are shown in Figure 13(a)−(d). At H−H0 = 0.375 m, the distribution of gas time fraction has a similar trend to that of jet eigen-concentration.40 For the clusters and dispersed particles, their distribution trends vary a little with momentum ratios. This indicates that the influence of jets weakens with the increase of riser height. 1064


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Industrial & Engineering Chemistry Research As shown in Figure 17, at H−H0 = −0.185 m, the time fractions of gas phase for different nozzle setting angles are all very small (under 1%). The time fraction of cluster phase increases with increasing the nozzle setting angles. As increasing the nozzle setting angle, the radial component of jet momentum rises. Under this condition, more particles moved toward the riser center; clusters are easier to form during the movement. Accordingly, the denser dispersed particulate phase decrease as the nozzle setting angle increases. At 0.185 m above nozzles, the gas time fraction is very high for the case of β = 60°, as shown in Figure 18. Under this condition, the high speed air jets gather together in the riser center easily as they move upward. During this process, it is difficult for the jets to have a full mix with the solids soon. On the contrary, the time fraction of cluster phase decreases a little with increasing the nozzle setting angle. Because more gas phase appears when the nozzle setting angle is large, the time fraction of denser dispersed particles falls accordingly. Overall, in order to obtain a better gas−solid dynamic mixing in the downward injection scheme, the angle between nozzles and riser axis should not be too large. Under the conditions investigated in this study, suitable setting angle is 30−45° when the nozzles are mounted downward. 4.3. Correlations of the Time Fraction of Denser Dispersed Particles. In order to present the complex effects of operating parameters on the radial and axial distributions of different phases, empirical expressions are obtained based on experimental results. Here, the time fraction of denser dispersed particles which are good for gas−solid mixing is chosen to be correlated with related parameters. When the jets are upward, the nozzle setting angle is α = 30°. When the jets are downward, we choose β = 30°, as analyzed above. For the upward pointed case (30° upward): ij H yz Fs = 0.301K −0.153 × jjj zzz j H0 z k {

−3.173

ry i × jjj1 − zzz R k {

oil−catalyst mixing, decreases with raising the momentum ratio in most regions. Accordingly, proportions of gas phase and cluster phase increase when the momentum ratio is large. Therefore, larger momentum ratio is negative for the dynamic mixing process of oil and catalysts when the jets are upward. When the nozzles are mounted downward, momentum ratio only affects the local distributions of different time fractions along radial. The cross-sectional time fractions of different phases have little change under different momentum ratios. Therefore, it is concluded that better operational flexibility can be obtained if the nozzles are mounted downward. For the downward mounted injection scheme, to obtain a better gas− solid dynamic mixing process, suitable setting angle of nozzles is 30−45°. In order to reflect the overall effects of parameters on the axial and radial distributions of different phases in the jet influence zone, the time fraction of denser dispersed particles which are good for gas−solid dynamic mixing is correlated with related parameters.

■

Corresponding Author

*E-mail: [email protected]. ORCID

Chunxi Lu: 0000-0002-9803-9119 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge the support from the Postdoctoral Innovative Talent Program by China Postdoctoral Science Foundation, the Science Foundation of China University of Petroleum, Beijing (No. 2462018YJRC016) and the Joint Petrochemical Funds of the National Natural Science Foundation of China (No. U1862202).

−0.092

■

(12)

NOTATION A = total area of the cross section, m2 Ai = the integral area of the specific ring region, m2 AN = the area of nozzle exit, m2 Aj(t) = approximation subsignal Dr = inner diameter of riser, m Dj(t) = detail subsignal dp = mean diameter of particles, m Fc = time fraction of cluster, % Fc’ = first derivative of Fc Fg = time fraction of gas phase, % Fs = time fraction of denser dispersed particles, % Fu = time fraction of diluter dispersed particles, % Gs = solid mass flux, kg/(m2•s) H = axial measuring cross sections, m K = the momentum ratio of jets to prelift flow N = number of nozzles Ns = number of consecutive samples above the threshold solids concentration r/R = relative radial position t = time, s tci = existence time of cluster/agglomerate phase, s tgi = existence time of gas phase, s tsi = existence time of denser dispersed particulate phase, s tui = existence time of diluter dispersed particulate phase, s T = total sampling time, s

For the downward pointed case (30° downward): ij H yz Fs = 0.365K −0.027 × jjj zzz j H0 z k {

−0.491

ry i × jjj1 − zzz R{ k

AUTHOR INFORMATION

0.028

(13)

Figures 19 and 20 plot comparisons of the correlation with experimental data. It is shown that reasonable errors between computed and experimental results are obtained. Based on eqs 12 and 13, local proportions of denser dispersed particles which are good for gas−solid dynamic mixing can be estimated by knowing the momentum ratio of jets to prelift flow.

5. CONCLUSIONS The dynamic mixing between jets and solids in different FCC injection schemes are studied by decomposing the instantaneous solid concentration signals. Effects of operating parameters are studied by introducing the momentum ratio of jets to prelift flow. In order to have a better understanding of the downward injection scheme, three nozzle setting angles (30°, 45°, and 60°) are selected. The gas−solid dynamic mixing process is analyzed by calculating the time fractions of four proposed phases (gas, diluter/denser dispersed particles and cluster). Suitable operating conditions as well as nozzle setting angles are obtained. For the traditional upward mounted injection scheme, the time fraction of denser dispersed particles, which are good for 1065


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uj = air jet velocity, m/s up = particle velocity, m/s ur = prelift flow velocity, m/s V = volume, m3

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GREEK LETTERS α = nozzle setting angle in upward injection scheme β = nozzle setting angle in downward injection scheme σ(A2) = standard deviation of A2 subsignal εscr = threshold for identifying clusters εsi(A2) = local value of A2 subsignal εsi(A2) = average value of A2 subsignal ρb = bulk density, kg/m3 ρj = the density of air jets, kg/m3 ρp = particle density, kg/m3 ρr = the density of prelift flow, kg/m3

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