Characterizing the catalyst fluidization with field synergy to improve the amine absorption for CO2 capture☆

Yunsong Yu ,Chen Zhang ,Zaoxiao Zhang,2, *,Geoff Wang

1 School of Chemical Engineering and Technology,Xi’an Jiaotong University,Xi’an 710049,China

2 State Key Laboratory of Multiphase Flow in Power Engineering,Xi’an Jiaotong University,Xi’an 710049,China

3 School of Chemical Engineering,The University of Queensland,St Lucia,QLD 4072,Australia

ABSTRACT There are great interests to capture the CO2 to control the greenhouse gas emission.Amine absorption of CO2 is being taken as an effective way to capture CO2 in industry.However,the amine absorption of CO2 is cost-ineffective due to great energy consumption and solution consumption.In order to reduce the capture cost,catalyst fluidization is proposed here to intensify the mass transfer and heat transfer.Catalyst fluidization with field synergy and DFT model is developed by incorporating the effects of catalyst reaction kinetics,drag force and multi-field into the mass transfer,heat transfer,fluid flow and catalyst collision.Experiments with an improved distributor are performed well to validate the model.The reaction kinetics is determined by the DFT simulation and experiment.The mass transfer coefficient in the fluidized reactor is identified as 17% higher than the conventional packed reactor.With the field synergy of catalyst fluidization,the energy consumption for CO2 desorption is reduced by 9%.Stepwise operation and inclination reactor are used to improve catalyst fluidization process.

Keywords:CO2 capture Catalyst fluidization Mass transfer DFT Energy consumption Field synergy

1.Introduction

With the environmental burden of the greenhouse gas effect,it attracts great attentions to mitigate the CO2in the world [1,2].As Intergovernmental Panel on Climate Change estimates,to keep the concentration of CO2stable,the emission of CO2should be decreased by 30% to 80% before 2050 [3].In order to target this goal,the main CO2emission from industry,such as power plant and chemical industry,should be focused on seriously[4,5].Amine absorption of CO2is regarded as the most feasible way to achieve the CO2mitigation goal for the industry [6-9].However,substantial capture cost in the amine absorption of CO2due to energy consumption and solution consumption significantly cuts off its industry application priorities [10,11].

The amine absorption of CO2usually occurs in the conventional packed reactor.In order to solve the problem of high cost,the technical route is to develop the new solvent to reduce the solvent consumption and increase the loading.However,it is normally expensive and difficult to develop a new solvent to simultaneously satisfy the requirement of high mass transfer performance and low desorption energy consumption [12,13].Thus,other potential technologies are eagerly required to improve the amine absorption of CO2.Catalysts like compounds with Al and Ti have been developed to enhance the CO2desorption by reducing the mass transfer resistance[14-16].These catalysts have increased the mass transfer coefficient by 16%.How to effectively utilize the catalysts is still ongoing.Fluidization being taken as an effective intensification method[17,18]has shown the great potential to intensify the catalyst performance.Thus,the idea of this work is to develop the catalyst fluidization process to improve the amine absorption of CO2.

Since fluidization is a typical phenomenon in the gas and solid phase system[19-21],it is feasible to extend the particle fluidization to the catalyst fluidization for improving the conventional amine absorption of CO2.By this extension,the drag force produced in the fluidization is expected to improve the interactive effects between CO2and amine solutions.This is feasible by considering that the drag force has been proven as an effective method to make the bed expansion [22]and produced the slip velocity as large as 0.4 m·s-1[20].All the results above suggest that catalyst fluidization is possible to enhance the CO2desorption in the amine solutions.This can reduce the CO2capture cost,especially cut off the amount of energy and solution consumption.

Fig.1.Catalyst fluidization to reduce the CO2 capture cost.

During the catalyst fluidization for desorption of CO2,the key point is to characterize the effects of catalyst fluidization on the desorption process.The field synergy theory and Density Functional Theory(DFT)[23-26]are able to be extended to characterize the catalyst fluidization effects by considering that it can include the multi-field effects,which are important phenomena in the catalyst fluidization.It is obvious that catalyst fluidization will make the multi-field effects more complicated induced by catalyst motion and collision.The field synergy theory has just the right ability to quantify the complicated multi-field effects since it can incorporate all the field information.

Fig.2.Transition state of CO2-MEA-catalyst.

Thus,the technical route here is to use the catalyst fluidization to enhance the reaction kinetics,mass transfer and heat transfer in the amine absorption of CO2.It is anticipated that the catalyst fluidization can improve the synergy effects and provide the great mass transfer coefficient.Additionally,the catalyst fluidization is expected to increase the gas and liquid volume ratio and thus reduce the solution consumption amount.Finally,the energy consumption is anticipated to be reduced since the desorption efficiency is improved and the desorption temperature can be decreased in the regeneration process due to catalyst effects.The overall route is depicted in Fig.1.

2.Reaction Kinetics Model

The catalyst like Gamma-Alumina intensifies the reaction.In order to determine the reaction kinetics,the DFT model is developed for the CO2-amine and catalyst system.The DMol3 module is used and Geometry Optimization is firstly done for the reaction kinetics calculation.The RMS convergence is set as 0.01 HaThe SCF tolerance reaches at 1×10-4.The transition state is determined by the Complete LST/QST.The function used here is GGA and BP.According to the energy at the transition state (Fig.2),the activation energy and reaction rate constant are obtained.The reaction order is considered by the stoichiometric of the reaction.In order to validate the simulation results,the experiment is performed in a 250 mlvessel.The CO2concentration is monitored by the IRMS gas analyzer.The catalyst is stirred by the magnetic device.According to the curve of desorption efficiency versus time,the reaction kinetics is obtained.The results are given in Table 1.As shown in Table 1,the simulation results fit the experiment data with only 5.68%activation energy error.The obtained reaction rate is larger than that of CO2-MEA system [27].This result demonstrates the intensification effect of the catalyst,which is also the reason for the decrease of the activation energy compared with no catalyst system.

Table 1 Reaction kinetics intensified by the catalyst

3.Fluidization with Field Synergy Model

The drag force is an important parameter for the catalyst fluidization.Here,by referencing the drag force model in the literature [28],the CO2and amine concentration is used to revise the model,which incorporates the chemical reaction effects into the drag force model,which is developed as

where F is the drag force and ε is the void fraction.y and y0refer to the CO2concentration and initial CO2concentration,respectively.C and C0respectively represent the amine concentration and initial amine concentration.

The conventional drag force Fdis given as [28].

The field synergy factor f is developed to quantify the field synergy effects during the fluidization process.The multi-fields including fluid flow field,concentration field and temperature field influence the catalyst fluidization.Here,the multi-field effects are quantified by the synergy angles,which produces the f as

where n is the field number,θiis the synergy angle between the multi-fields,which is given as

Here,U is the velocity vector,which is obtained by the continuity,momentum and energy model below.A represents the vectors,such as velocity gradient,concentration gradient and temperature gradient.

Compared with the conventional fluidization model,the fluidization with field synergy model here incorporates the multifield information to describe the fluidization process,which characterizes the fluidization in the field synergy view.Compared with the typical field synergy theory,the integration of synergy effects is considered in the field synergy factor,which offers the strategy to correlate the multi-fields by energy dissipation and energy accumulation.This field synergy factor includes the nonlinear characteristic during coupling the multi-fields.

The gas phase continuity equation is developed by considering the fluidization to increase the drive force as

where N is the CO2amount at no fluidization state,which is correlated with the obtained reaction kinetics at catalyst condition in Table 1.Nfis used to incorporate the fluidization on the mass transfer,which is developed as

Here,V is the volume and a is the effective interface area,which is determined by the Onda’s equation [29].

The gas phase momentum equation is revised by adding the drag force between the gas and fluidized catalyst,which is being given

where p is the pressure.τgis the stress-strain tensors,which are correlated with viscosity,void fraction,gas velocity and unit tensor.upis the catalyst motion velocity.

The gas phase concentration is developed by considering the CO2amount in the solution,which is

The gas phase temperature is determined by the heat transfer amount,which is being given

where cpgand αgare respectively the thermal capacity and thermal diffusivity and Tgis the gas temperature.Qgrefers to the heat transfer amount.Considering the catalyst fluidization enhances the heat transfer between gas and liquid phases,the Nusselt number is revised by including the catalyst drag force,which is developed as

where Nu0is the Nusselt number corresponding to no fluidization,which is obtained by referencing the literatures [30,31].

According to the CO2mass conservation,the liquid phase continuity equation is developed as

The liquid phase momentum equation is revised by adding the drag force into the conventional force Flincluding gravity,interface drag force between gas and liquid phases and body force,which is given as

Additionally,the interface drag force between gas and liquid phases Fiis revised by considering the catalyst fluidization producing the velocity slip,which is established as

Here,Fi,0is the interface drag force between gas and liquid two phases without fluidization (in the conventional packed reactor),which is calculated by the literature model [32].

The liquid phase concentration equation is developed based on the CO2conservation between gas and liquid phases,which is being given

Table 2 Experiment conditions

Fig.3.Catalyst motion route in the reactor.

Fig.4.Improved distributor.

Fig.5.Mass transfer coefficient in the fluidized catalyst system.

Fig.6.Catalyst fraction(a),catalyst holdup(b)and catalyst expansion(c)and their synergy effects in the fluidized reactor.

where Dlis the diffusivity in the liquid phase.

The liquid phase temperature is determined by the reaction heat and heat transfer amount,which is being given

where Qris the total reaction heat,which is determined by the typical reaction heat under the catalyst enhancement.

The catalyst continuity equation is developed as

The catalyst momentum equation is developed by considering the interactive effects between gas and catalyst and liquid and catalyst,which is being given

The granular energy equation is developed by incorporating the collisional dissipation of catalyst energy,energy exchange between gas and catalyst and gas and liquid phases,which is being offered

where collisional dissipation of catalyst energy of epcis determined by referencing the literatures [19].

Energy exchange between gas and catalyst is given as

Likewise,energy exchange between liquid and catalyst is given as

The catalyst shear viscosity,granular bulk viscosity,catalyst pressure and radial distribution function are cited from the literatures [33-35].

In order to solve the model,SIMPLE algorithm is used to solve the differential equations and additional source term method is used to improve the convergence[36,37].Since the numerical solution is much more difficult for the gas-liquid-solid three phases cases in the fluidized reactor,the initial parameters are set by referencing the parameter distributions obtained in the packed reactor in the literatures [38].This can further increase the solution speed due to that these parameter distributions are more close to that in the fluidized reactor than the conventional uniform initial parameters set.Three grid systems of 88×12,120×14 and 152×18 are used to test the grid independence and it is found that the temperature difference is within 0.4%.Thus,with the calculation precision,grid system of 88×12 is finally used to save the computation time.

4.Model Validation

In order to test the model,the simulation results are compared with the experiment data.The experiment conditions are listed in Table 2.In the experiment,the gas analyzer GE-MG and BT100s pump made by Trover Company are used.Here,CO2loading of 0.45 mol·mol-1MEA is used to desorb the CO2in the catalyst environment.The MEA rich solution flux is 24 L·h-1.The catalysts with diameter of 3 mm and 6 mm are used in the reactor with 0.27 m static catalyst height.

The typical catalyst motion is monitored by the high speed camera during the period of 5 s to 30 s.The results agree well with the simulation catalyst motion route in the reactor in Fig.3,which validates the fluidized model accordingly.Moreover,the curve of catalyst motion route is similar to that solid motion one in the typical fluidized bed[21],which also qualitatively assures the accuracy of the model.

Fig.7.Catalyst fraction at 0.1 m·s-1 (a) and 0.15 m·s-1 (b) in the fluidized reactor.

In order to keep the uniform liquid distribution,an improved distributor is designed as Fig.4.The idea is to use the cover to firstly distribute the amine solutions and after that the grooves start to distribute the liquid again.Considering the CO2desorption in the fluidized catalyst state,the mass transfer coefficient is compared against the experiment data.As shown in Fig.5,the mass transfer coefficient shows good agreement with the experiment data in the different catalyst amounts.Additionally,the simulation result is further compared against the MEA rich solution desorption of CO2at 358 K in the literature[15].The higher mass transfer coefficient is obtained here due to the fluidization enhancement against the literature data,which further qualitatively validates the fluidized model.

5.Results

5.1.Effects of fluidization on catalyst and synergy

In the fluidization state,the catalyst distribution in the fluidized reactor is not as uniform as that in the packed reactor.The catalyst fraction is used to quantify the catalyst distribution in the fluidized reactor,which is offered in Fig.6(a).As shown in Fig.6(a),the catalyst fraction increases in the bottom section of the fluidized reactor and starts to decrease from the 0.3 m position away from the bottom.This suggests that the force on the catalyst reaches at the relatively steady state in the section around 0.3 m.This steady state compromises the catalyst collision,gas and catalyst interactive force,liquid and catalyst interactive force and gas and liquid interactive force due to gas and liquid countercurrent flow and catalyst upward flow and catalyst gravity.These results show the similar trend to the CO2capture in the bubbling state due to comparable flow pattern [22].Due to the fluidization,the synergy effects in the upper section (0.55 m to 0.75 m) of the reactor is improved greatly with the field synergy factor above 1.0.The main reason is that catalyst fluidization offsets the liquid turbulence in the upper section of the reactor,which is quite usual phenomenon in the packed reactor.

Similar to gas and liquid interactive effects in the packed reactor,the catalyst holdup is still observed as the typical phenomenon in the fluidized reactor.The corresponding catalyst holdup is provided in Fig.6(b).As shown in Fig.6(b),the catalyst holdup increases as the static catalyst height increases from 0.27 m to 0.33 m and decreases from 0.33 m to 0.39 m.It indicates that sufficient catalysts reduce the amine solution films in the catalyst surface,which reduces the catalyst holdup.This catalyst holdup is lower than that in the conventional packed reactor,which gives evidence that lower mass transfer resistance is obtained in the fluidized reactor.As for the synergy effects,the larger field synergy factor produces the greater catalyst holdup,which means good synergy has been reached in the catalyst holdup of 6% to 9%.Increasing the static catalyst height increases the field synergy factor from 0.7 to 1.2,suggesting that good synergy can be improved by increasing the static catalyst height in the fluidized reactor.

In the fluidized reactor,the static catalyst expands from the down section to the upper section.The expansion ratio of the catalyst is given in Fig.6(c).As shown in Fig.6(c),at the static catalyst height of 0.27 m,the expansion ratio falls into the range of 1.0 to 2.7.These expansion ratios agree well with the literature data[22]since similar conditions are kept.As presented in Fig.6(c),at the gas velocity of 0.05 m·s-1,the expansion ratio is 1.0,which corresponds to no fluidization state.As the gas velocity increases from 0.05 m·s-1to 0.19 m·s-1,the expansion ratio increases by 2.7 times,which assures good fluidization state to reach high mass transfer performance.As the catalyst expands gradually,the field synergy factor firstly increases and then starts to decrease.The best synergy reaches with the field synergy factor of 1.13 corresponding to the expansion ratio of about 2.2.

Fig.8.CO2 concentration (a) and its distribution (b) and loading (c) along the fluidized reactor.

The catalyst expansion agrees well with the catalyst fraction distribution.The catalyst fraction in the reactor is influenced by the gas velocity.Here,the catalyst fraction at 0.1 m·s-1and 0.15 m·s-1are studied in Figs.7(a) and (b).As shown in Fig.7(a)and (b),the catalyst rises to 0.5 m at 0.1 m·s-1gas velocity and rises up to 0.6 m at 0.15 m·s-1due to strong drive force at 0.15 m·s-1.The catalyst accumulation zone is found in the right bottom of the reactor because of the zigzag catalyst motion pattern,which agrees with the results in Figs.3 and 6(a).

5.2.CO2 capture performance in the fluidized reactor

The CO2concentration in the fluidized reactor is given in Fig.8(a).It is quite clear that the CO2concentration increases from the bottom to the top of the fluidized reactor as the CO2absorption occurs in the MEA solutions.As the gas velocity increases from the 0.098 m·s-1to 0.196 m·s-1,the average CO2concentration along the reactor height direction increases by about 13%.This is due to the fact that high gas velocity produces the strong turbulence for the CO2diffusion and evacuation.Additionally,high gas velocity makes the gas residence time shorter,which results in more desorption of CO2in the fluidized reactor.

The CO2concentration distribution can be found in Fig.8(b).As shown in Fig.8(b),the highest CO2concentration is produced in the top section of the reactor.This is attributed to that catalyst enhances the CO2desorption and CO2accumulates in the top section of the reactor.As shown in Fig.8(b),the CO2distribution shows the relatively uniform characteristic due to catalyst effects occurring mostly in the bottom section of the reactor.It is noted that the CO2concentration is a little higher in the zone of about 0.3 m height direction and close to the wall.The reason is that the force on the catalyst reaches at the relatively steady state,which agrees with the result in Fig.6(a).Due to the steady state of catalyst,the longer CO2desorption process is obtained,which provides the higher CO2concentration.

Fig.9.Flow characteristic (a) and flow field (b) and upward circulation flux (c) in the fluidized reactor.

The CO2loading in the fluidized reactor is illustrated in Fig.8(c).As shown in Fig.8(c),the average CO2loading is about 0.11 mol·mol-1to 0.33 mol·mol-1,which is about 15% lower than that in the packed reactor [39].It is clearly observed that the CO2loading decreases by 23% as the gas velocity increases from 0.098 m·s-1to 0.196 m·s-1.This is probably due to that higher mass transfer interface area is obtained.Moreover,as catalyst size increases from 3 mm to 8 mm,the average CO2loading decreases by 40.5%.This is attributed to the fact that 3 mm catalyst provides more cross-section area due to catalyst collision in the fluidized state.Simultaneously,small catalyst provides large gas and liquid contact area,which decreases the loading of MEA solutions.

Flow characteristic of CO2absorption in the fluidized reactor is seriously influenced by the catalyst fluidization.The corresponding results are given in Fig.9(a).As shown in Fig.9(a),the clear pictures at 5 s,15 s,20s,25 s and 30 s are obtained by high speed camera.The fluctuation of interface is obviously observed and simulated in Fig.9(a).This is due to the fact that the catalyst fluidization shows the zigzag flow pattern.The clear zigzag flow pattern clearly states that this flow characteristic intensifies the mass transfer easily.Compared with the conventional packed reactor,the zigzag flow characteristic is more effective to enhance the CO2desorption in the MEA solutions.

The full fluid flow field is provided in Fig.9(b).As shown in Fig.9(b),the high fluid velocity starts from the bottom section with 0.1 m·s-1,which then decreases gradually.In the center section up to 0.5 m reaction height direction,the fluid field is found to produce the Z shape fluid field,which agrees with the zigzag flow pattern.More importantly,the two velocity peaks are identified in the 0.7 m height direction,which validates the surface interface of the catalyst fluidization.

Due to the fluidization effects,there is upward circulation flux for MEA solutions in the fluidized reactor.The results are given in Fig.9(c).As shown in Fig.9(c),the upward circulation flux increases from 8 kg·m-2·s-1to 28.25 kg·m-2·s-1in the fluidized bottom section and middle section.However,the upward circulation flux starts to decrease from the middle section of 0.46 m.This is probably due to the fact that in the top section,the downward force becomes dominant against the upward force for the MEA solutions.Additionally,as the drag force increase,i.e.,the Cdincreasing from 1 to 3,the upward circulation flux increases rapidly.This is attributed to the fact that large drag force makes the MEA solution torsion and circulation more easily.

The temperature distribution in the fluidized reactor influences the CO2desorption.The temperature distribution in the fluidized reactor is offered in Fig.10 (a) and (b).As shown in Fig.10 (a),the temperature bulge phenomenon is observed as the same as that in the packed reactor with packing height of 0.75 m.It is interesting that the maximum temperature bulge in the fluidized reactor is reduced to 12.5 K compared with that of 18.5 K in the packed reactor.This result indicates that heat transfer is improved in the fluidized reactor since gas and liquid phases have more heat transfer area due to catalyst fluidization.This good heat transfer favors the CO2desorption in the fluidized reactor.The temperature distribution in Fig.10(b) also offers that the high temperature zone is produced in the catalyst motion direction,which suggests that catalyst fluidization produces additional energy supply route for the CO2desorption.This is reasonable that catalyst motion enhances the convective heat transfer by the catalyst collision.Additionally,compared with catalyst motion shown Fig.3,the high temperature zone is also observed as well fitting the catalyst motion.The result can be explained by the fluid field in Fig.9,which is found to produce the Z shape.

6.Discussions

Fig.10.Temperature (a) and its distribution (b) in the fluidized reactor.

Fig.11.CO2 desorption in the fluidized reactor with the inclination angle.

Fig.12.Drag force in the fluidized reactor.

In order to provide the sufficient contact of the gas and liquid phases in the CO2desorption process,the technical route to make reactor inclination is discussed in Fig.11.However,the CO2desorption efficiency rapidly decreases below 80%after the inclination angle is above 4 degrees.This is attributed to that the wall flow phenomenon becomes stronger and stronger as the inclination angle increases.Thus,the CO2desorption efficiency is further discussed in the inclination angle of 4°.As shown in Fig.11,the CO2desorption efficiency is 5% higher that of no inclination case at the high gas flux of 1.5 m3·h-1to 2.0 m3·h-1,which suggests that inclination offers more contact area by changing the force balance in the fluidized reactor.

Drag force,as the important parameters for the fluidization in the fluidized reactor,is offered in Fig.12.It is clearly found that the drag force between gas and catalyst increases as the slip velocity increases from 0.1 m·s-1to 0.6 m·s-1.At the void fraction of 0.4,the drag force reaches as high as 35,600 kg·m-2·s-1,which shows the same magnitude of order as that in the literature [20].However,as the void fraction increases to 0.8,the drag force becomes as low as 380 kg·m-2·s-1to 883 kg·m-2·s-1.This is attributed to that the catalyst tends to follow the gas motion at the high void fraction.The catalyst collision probability becomes larger at the low void fraction,which makes the drag force hard to be balanced by other forces like gravity and inter-phase forces.

Fig.13.Gas and liquid volume flow rate ratio and energy consumption.

Fig.14.Mass transfer enhancement by catalyst fluidization.

Table 3 Reaction free energy

The gas and liquid volume flow rate ratio is given in Fig.13.According to the gas and liquid volume flow rate ratio,the energy consumption is calculated by the reaction heat,sensible heat and evaporation heat.The energy consumption amount is provided in Fig.13.As shown in Fig.13,the fluidization averagely increases the gas and liquid volume flow rate ratio by 10%in the amine mass fraction of 20% to 40%.Corresponding to the higher gas and liquid volume flow rate ratio,the sensible heat is reduced accordingly due to less amine solutions.The reaction heat is also reduced due to the catalyst enhancement.Thus,the energy consumption amount is reduced by 9%compared with the CO2desorption without fluidization.The main reason is that the mass transfer coefficient is enhanced by more than 11% as shown in Fig.14.Additional reason is that the reaction free energy is reduced at the fluidization state compared with the no fluidization one.The results are given in Table 3.As shown in Table 3,the reaction free energy of MEA system is reduced by 10% due to the catalyst fluidization.For the MDEA system,the reaction free energy is reduced by 9.6%.For the H-ZSM-5 catalyst,the same reaction free energy reduction by the DFT model is identified in Table 3.The HZSM-5 enhances the stronger CO2desorption than the gamma Alumina since it has produced the better field synergy effects by the higher field synergy factor.The energy consumption for the catalyst fluidization is negligible since the gas and liquid volume flow rate ratio is significantly increased and the reactor diameter can be decreased due to good mass transfer coefficient (Fig.14).It is worth noting that amine mass fraction as high as 50% can be used in the fluidized reactor by considering that good heat transfer and high gas and liquid volume flow rate ratio are obtained.This will probably compromise the problems of reaction heat accumulation and corrosion that occur in the high mass fraction amine absorption of CO2in the conventional packed reactor [40].

Fig.15.Stepwise and steady operation.

Finally,in order to well utilize the fluidization to intensify the CO2desorption,the stepwise operation is compared with the steady operation in Fig.15.The average maximum rising distance of the catalyst is kept as the same 0.6 m.It is interestingly found that the CO2removal efficiency can be increased by 12% through the stepwise operation.This is attributed to that stepwise operation makes the fluidized catalyst damp in the reactor,which offers more contact area compared against the steady operation.The details will be studied in the future.

7.Conclusions

In order to reduce the cost of amine absorption of CO2for effective greenhouse gas mitigation,catalyst fluidization was successfully developed to intensify the mass transfer and heat transfer.Catalyst fluidization with field synergy and DFT model was accurately developed to describe the effects of the catalyst fluidization and multi-field on the mass transfer,heat transfer and fluid flow,which were well validated by the experiments with an improved distributor.It was interestingly found that the mass transfer coefficient in the fluidized reactor was 17% higher than the conventional packed reactor.The energy consumption for CO2desorption was reduced by 9% through catalyst fluidization.Stepwise operation and inclination reactor were proposed to improve the catalyst fluidization process.