Research on process modeling and simulation of spent lead paste desulfurization enhanced reactor

Lijuan Zhao,Zhe Tan,Xiaoguang Zhang,Qijun Zhang,Wei Wang,Qiang Deng,Jie Ma,De’an Pan,

1 Institute of Circular Economy,Beijing University of Technology,Beijing 100124,China

2 Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China

3 China Ecological Civilization Research and Promotion Association,Beijing 100035,China

Keywords:Chemical reactors Computational fluid dynamics,CFD Simulation Desulfurization Core-shell structure

ABSTRACT In the reaction process of carbonate desulfurization lead paste,the produced PbCO3 is easily wrapped in the outer periphery of PbSO4 to form a product layer,hindering the mass transfer process.Therefore,it is necessary to break the PbCO3 product layer.In this work,the rotor stator-reinforced reactor was selected as the enhanced desulfurization reactor for the purpose of breaking the PbCO3 product layer and promoting mass transfer.The breakage process of the PbCO3 product layer generated during the PbSO4 desulfurization was modeled.Computational fluid dynamics simulation to the rotation conditions was carried out to theoretically analyze the fluid flow characteristics of PbSO4 slurry and the wall shear stress affecting the breakage of PbCO3 product layer.By optimizing the rotation conditions,the distribution ratio of effective rotor wall shear stress range achieved 96.1%,and the stator wall shear stress range reached 99.15%under a rotation of 2000 r.min-1.The research work provides a reference for analysis of the mechanism of product layer breakage in the PbSO4 desulfurization process,and gives a clear and intuitive systematic study on the fluid flow characteristics and wall shear stress of the desulfurization reactor.

1.Introduction

As more and more lead-acid batteries (LAB) are scrapped after being widely used,more than 110 million LAB are currently scrapped every year in China [1].The pyrometallurgical and hydrometallurgical processes are employed by most industries to recycle waste LAB [2].However,the pyrometallurgical processes often require carbonaceous reducing agents and generate waste gases such as sulfur dioxide and carbon dioxide,which could cause serious harm to the environment and human health[3,4].With the increasing requirements for environmental protection,the hydrometallurgy has shown obvious advantages in recycling waste LAB due to its advantages of low energy consumption and low harmful gas emissions[5].Generally,the main component of waste LAB is PbSO4,accounting for about 50% to 70% (mass) [6,7],which is difficult to dissolve in water and acid.Therefore,the use of hydrometallurgical processes to recycle waste LAB requires desulfurization technology[8].At present,the carbonate desulfurization method is widely used,but the desulfurization efficiency is low[9].References reports show that the hydrometallurgical desulfurization process of PbSO4conforms to the core-shell structure,and the important reason for the low desulfurization efficiency is that the PbCO3product layer produced by desulfurization covers the surface of PbSO4[10,11].Simultaneously,the PbCO3product layer hinders the diffusion of the desulfurization agent,so that the inside PbSO4cannot continue to react.Therefore,an effective PbSO4desulfurization method is urgently need to reduce the incomplete desulfurization problem caused by the PbCO3product layer.

In view of the problems caused by PbCO3product layer,desulfurization is mainly carried out by using an enhanced reactor.At present,there are mainly mechanical strengthening methods such as shear,collision,and grinding to break the product layer and improve the mass transfer efficiency.Zhangetal.[10]added grinding media into the intensified reactor to continuously grind and roll the PbSO4particles in high-speed rotation,resulting in the rapid fragmentation of the product layer,and the final lead paste with a sulfur content of less than 0.3%.Pengetal.[12]used a rotating packed bed as an enhanced desulfurization reactor,in which the reactor was rapidly mixed and cut into fine droplets.The results showed that the mass transfer efficiency increased rapidly,and the desulfurization rate of the lead paste reached more than 97.2%in a short time.However,these studies only use experimental methods to break the product layer and promote desulfurization.There are few studies on the mechanism analysis of product layer breakage in the desulfurization process,especially there is no clear and intuitive systematic study on the fluid flow characteristics and wall shear stress of the reactor.

Computational fluid dynamics(CFD)is widely used in fluid simulation and stirred reactor research[13,14].Michaeletal.[15]used CFD to study the turbulent field and droplet characteristics in the high-shear rotor-stator mixer,and the predictions were consistent with related experimental studies[16].Tangetal.[17]studied the influence of the tridimensional rotational flow sieve tray on the gas flow field distribution under different structural parameters and installation methods.It provided a reference for optimizing the structure and installation method of the tridimensional rotational flow sieve tray.Therefore,the use of CFD to study the fluid flow characteristics and wall shear stress in a reactor is an ideal solution.

In this study,CFD was used to study the flow fluid characteristics of the PbSO4slurry and the distribution of the rotor statorreinforced reactor (RS-RR) wall shear stress efficiently breaking the PbCO3product layer during the desulfurization process of PbSO4.Based on the analysis of the relevant experimental research results,the breakage model of the core-shell structure was established.A transient CFD analysis was performed to simulate the breakage conditions of the RS-RR wall shear stress at different rotation speeds,of which results were evaluated according to breakage model.In order to fully confirm the effect of wall shear stress on product layer breakage,the area-weighted average wall shear stress of the rotor and stator was calculated.This work provides an analyze on the mechanism of product layer breakage in the desulfurization process,and gives a clear and intuitive systematic study on the fluid flow characteristics and wall shear stress of the desulfurization reactor.

2.Mathematical Models

2.1.Simulation setup

In this study,the enhanced desulfurization reactor is the RS-RR,and the model is taken from the patent of Panetal.[18],as shown in Fig.1(a).The RS-RR consists of rotor and stator grinding disc with a diameter ofD=25 cm and a height ofH=28 cm.There are three-stage grinding cogging on the surface of the rotor grinding disc with a depth of 14 mm.The direction of the primary and tertiary grinding cogging is the same from top to bottom,and the grinding cogging angle is 5°with the direction of the rotating shaft.The direction of the secondary grinding cogging is opposite to that of the primary and tertiary grinding cogging,and the grinding cogging angle is-5°.The height ratio of the three-stage grinding cogging,that is,H1:H2:H3is 5:4:3,and the grinding cogging number ratio is 2:3:6.Simulation was carried out at 4 different rotation speeds (N=1000,1500,2000,2500 r.min-1).Use the Mesh tool in ANSYS to divide the model,and the mesh types are tetrahedron and wedge,as shown in Fig.1(b).In order to accurately simulate the movement of the wall shear stress in the RS-RR,the mesh around the outlet and the rotor grinding cogging was locally encrypted.Furthermore,the boundary layer mesh was set up near the stator wall to obtain more accurate wall shear stress results.The mesh size is determined by verifying the independence of the mesh,and the specific parameters of the mesh are shown in Table 1.

Table 1 Mesh parameter details

Fig.1.(a) The rotor grinding disc of the RS-RR,and (b) the surface mesh of the RS-RR.

2.2.Model description

When establishing the mathematical model,the following assumptions were made:PbSO4slurry is an incompressible Newtonian fluid with unchanged physical properties and no consideration of vaporization.

Based on the above assumptions,the mass conservation equation for the flow control equation can be expressed as Eq.(1)[19].

where ρ is the density,tis time,υ is the average velocity vector.Xieetal.[20] and Ouyangetal.[21] evaluated the turbulence models such as standardk-ε,achievablek-ε,shear stress transport (SST)k-ω,Reynolds stress model (RSM),etc.The results showed that the SSTk-ω model showed better performance than the standardk-ε,achievablek-ε,and RSM models.Therefore,the SSTk-ω turbulence model was chosen to solve the Reynoldsaveraged Navier-Stokes(RANS)equation.The SSTk-ω shear stress transfer model effectively combines the stability and accuracy of thek-ω model in the near-wall region and the free flow independence of thek-ε model in the far field.Compared with the standardk-ω model,it modifies the formulation of turbulence viscosity and is more suitable for considering the transfer of shear stress in turbulence.Using the SSTk-ω model for simulation of wall shear stress and fluid flow characteristics in RS-RR,more accurate and reliable results can be achieved.The transmission equations of the turbulent kinetic energykand turbulence dissipation rate ε are Eqs.(2) and (3).

whereSkandSω are the source item.

Γkand Γωare diffusivities that representkand ω,and they are derived from Eqs.(4) and (5).

μtis the turbulence viscosity,which is calculated as shown in Eq.(6).

whereSis the strain rate magnitude,α* is given by Eq.(7) below.

σkand σωare Prandtl numbers that representkand ω,and their calculation methods are shown in Eqs.(10) and (11).

The mixed functionF1andF2are given by Eqs.(12),(13),(14),(15),and (16).

The SSTk-ω model is based on the standardk-ω and standardk-ε models.To mix the two models together,the standardk-ε model has been converted to basedk-ω equation,which has led to the cross-diffusion termsDω.Dω is defined as Eq.(26).

2.3.Solution method

The central circular area on the top of the stator grinding disc was set as the velocity inlet,and the velocity direction was along the negative direction of theY-axis.The gap between the rotor and stator grinding disc at the bottom of the model acted as a pressure outlet,and the gauge pressure was 0.In addition,the wall was selected as a stationary wall.Table 2 shows the specific parameters of the boundary conditions.The physical parameters of the PbSO4slurry in the fluid domain are shown in Table 3.The pressure discretization was performed using a secondary order upwind.Select the coupled algorithm to solve the pressure-velocity coupling.Using the SSTk-ω turbulence model with a high degree of stability.The secondary order upwind method was used to solve for the momentum,turbulent kinetic energy,and turbulent dissipation rate.The convergence of the algorithm was verified by monitoring the residuals,and the residual convergence was 10-4.

Table 2 Boundary conditions

Table 3 Fluid physical properties

2.4.The breakage model of core-shell structure

In the RS-RR,the entire desulfurization reaction process can be described as follows.The PbSO4is consumed to form the PbCO3product layer,resulting in the core-shell structure.Under the effect of the RS-RR,the PbCO3product layer decreases,the total diameter of the core-shell structure decreases,and the reaction is completely completed [1].In this study,the shrinking-core &particle model [22] was selected as the desulfurization reaction model of PbSO4,as shown in Fig.2.

Fig.2.The PbSO4 desulfurization model [23]: (a) core-shell structure;(b) shrinking-core &particle mode.

PbCO3is relatively loose and its hardness is lower than that of PbSO4.It is assumed that PbCO3can be completely broken up by each grinding cogging in the RS-RR.Then,the carbonate reacts rapidly with the exposed fresh PbSO4,to generate a new PbCO3product layer.This dynamic process is repeated continuously until the PbSO4is consumed to the median particle size at the limit of hydrometallurgy grinding[24].Liuetal.[25]conducted carbonate desulfurization of PbSO4and provided a large amount of experimental data.Therefore,the desulfurization rate formula (e.g.,Eq.(27)was obtained by fitting the desulfurization experimental data[25],whereR2=0.9996,the fitting effect was better.

wherexBis the desulfurization rate of PbSO4.

The desulfurization rate of single grinding cogging can be obtained according to Eq.(27),as shown in Table 4.

Table 4 The desulfurization rate of single grinding cogging

Further,the dynamic change law of the core-shell structure corresponding to the three-stage grinding cogging was established,including the core radius (Rc),the core-shell structure radius (Rs),and the shell thickness (h),as shown in Fig.3.

Fig.3.The breakage of the PbCO3 product layer.

The continuous breakage of the shell and the continuous consumption of the core will be accompanied by dynamic changes of the core radius(Rc)and the core-shell structure radius(Rs).Assuming that the entire core-shell structure is standard spherical,the desulfurization rate of PbSO4in Eq.(27) can be further written as Eq.(28).

where ρBis density of PbSO4.

Evkinetal.[26] studied the destabilization and fragmentation of thin shells,and the relationship between shell thickness and instability stress could be descripted as Eq.(29).Table 5 is the physical parameters of the PbCO3product layer.The minimum of the external stress required to break the PbCO3product layer is the critical instability stress.

Table 5 The physical parameters of the PbCO3 product layer [27]

whereqcis the criticality instability stress (Pa),Eis the young’s modulus of PbCO3.

Where β is given by Eq.(30).

where v is the poisson’s ratio:Kis the volume modulus,andKis given by Eq.(31).

From Table 4,Eqs.(28)and(29),the criticality instability stress required to break the PbCO3product layer under different speed conditions can be obtained,as shown in Table 6.

Table 6 The criticality instability stress required (Pa)

3.Results and Discussion

The main purpose of this study is to establish a CFD model to simulate the effect of wall shear stress on PbCO3product layer breakage of rotor and stator wall in RS-RR,and to verify the model based on theoretical formula data.The following sections summarize the key features observed from the CFD model,mainly selecting the wall shear stress of the rotor and the stator as the indicators of PbCO3product layer breakage.As shown in Fig.4,the rotor provides wall shear stress to the particles near the wall to break the PbCO3product layer,and then the particles are pushed into the fluid domain under pressure.The fluid is strongly mixed under the action of viscous resistance and the velocity difference between the particles and the fluid.The particles collided under the action of turbulence and then quickly and uniformly disperse with dissipative vortex.Finally,the particles reached the stator wall and experienced violent shear again.

Fig.4.Schematic of the process.

3.1.Fluid domain analysis

As shown in Fig.5,under certain conditions,the fluid flow of PbSO4slurry corresponding to different rotation speeds flow from the inlet into the deflector groove at the top of the rotor.The rotor rotated at a high speed under the action of the motor,driving the fluid to enter the stator and rotor gap through the outlet of the deflector groove.After the fluid collided with the rotor,a portion of it formed eddy current regions of varying sizes in the primary fluid domain,which provides kinetic energy to the fluid and enhances particle collisions in the fluid [28].A portion of the fluid rotated around the rotor grinding cogging and moves upwards,again converging to the top deflector of the rotor.A small portion of fluid flows out along the stator axis.In the case of high-speed rotation,it is easy to cause internal sparseness and external densification,and the mass transfer effect is reduced.While the RS-RR adopts a grinding cogging structure,which can effectively disperse the atomized liquid and enhance the turbulence of the fluid [29].The gap between the rotor and stator results in a continuous PbSO4slurry medium producing a strong lateral mix under high shear stress,and the rotation of the rotor provides a pressure gradient that acts like a centrifugal pump [30].The strong rotational speed causes the particles in the fluid to collide strongly,which enhances the turbulence intensity of the fluid[31],and greatly improves the mass transfer efficiency.The RS-RR speed was set to 1000-2500 r.min-1.The effect of rotation speed on fluid speed is obvious,as the rotor speed increasing from 1000 to 2500 r.min-1,the maximum fluid speed increases from 13.79 to 32.51 m.s-1,an increase of 1.36 times.However,it is worth noting that the maximum speed of the fluid was only increased by 2.68% as the rotation speed increased from 2000 to 2500 r.min-1,so the speed of 2000 r.min-1was more appropriate.

Fig.5.Velocity vector distribution diagrams at different speeds: (a) 1000 r.min-1,(b) 1500 r.min-1,(c) 2000 r.min-1,and (d) 2500 r.min-1.

3.2.Shear stress analysis

Fig.6 is the weighted average wall shear stress of the rotor and stator at different speeds.Fig.6 shows that the weighted average of the rotor wall and stator wall increases with the rotation speed and reaches the maximum value at 2500 r.min-1.This is because a larger rotational speed difference leads to an increase in shear stress as the rotational speed increases.In addition,the huge pressure difference between the rotor wall and the fluid domain pushes the fluid towards the stator wall at high speed.Therefore,it can be seen from the Fig.6 that the wall shear stress of the stator is generally higher than that of the rotor,and the wall shear stress of the stator increased rapidly with the increase of the rotation speed.Therefore,a stator wall material with strong wear resistance should be selected.

Fig.6.Weighted average wall shear stress of rotor and stator at different speeds.

Fig.7 and Fig.8 are the distribution ratio of the wall shear stress of the rotor and stator at different speeds.As expected,the wall shear stress of the stator is significantly higher than that of the rotor,and the stator is able to adequately provide PbCO3product layer breakage.However,due to the wide scope of the shear stress value above mentioned,it is difficult to determine the effective wall shear stress range of the wall.Therefore,in order to ignore the effect of the extreme value,we choose a numerical range which is not only higher than the criticality instability wall shear stress,but also the distribution ratio was more than 1%,as the effective wall shear stress range.Table 7 shows the effective wall shear stress range of the rotor and stator at different rotation speeds.It can be seen from Table 7 that the effective wall shear stress range distribution ratio of the stator wall can reach more than 99.15%.While with the increase of the rotation speed,the effective wall shear stress of the rotor undergoes a series of changes.As the rotation speed increased from 1000 to 2500 r.min-1,the distribution ratio of the effective wall shear stress range on the rotor gradually increased from 86.17% to 97.26%,an increase of 12.87%,and the maximum effective wall shear stress also gradually increased.It can be seen from Fig.9 that the maximum wall shear stress is mainly distributed at the deflector groove,but it is difficult to observe the distribution variation law of wall shear stress with rotation speed.

Table 7 Effective wall shear stress range at different rotation speeds

Fig.8.The distribution ratios of stator wall shear stress at different speeds: (a) 1000 r.min-1,(b) 1500 r.min-1,(c) 2000 r.min-1,and (d) 2500 r.min-1.

Based on Table 7,the contour of the effective wall shear stress distribution area of the rotor is obtained,as shown in Fig.10.Fig.10 shows the effective wall shear stress distribution area contour of the rotor at 1000,1500,2000 and 2500 r.min-1,respectively.The results show that at lower speeds (1000-1500 r.min-1),the area that can provide effective wall shear stress increases significantly in the negativey-axis direction,but changes little in the circumferential direction.This is mainly due to the increased number of grinding cogging on the rotor wall in the axial direction.The distance between grinding cogging become denser,and the grinding cogging shape continues to narrower,resulting in an increasingly strong shear efficiency.As the number of rotor grinding cogging increases,it more obviously that the effective wall shear stress area of the tertiary grinding cogging is higher than that of the primary and secondary.This can be attributed to the narrow cavity in the RS-RR,where the flow rate increases as the flow area decreases [32],resulting in a large speed difference with the wall.Therefore,even if the particles are thicker,the bottom of the rotor(near the tertiary grinding cogging)can still satisfy the wall shear stress of relatively thick particles.It is worth noting that Fig.10 shows the unevenly increasing distribution area of the wall shear stress in the negativey-axis direction.This may be due to an inconsistency in the velocity difference caused by the uneven distribution of the fluid velocity when the fluid flowing along the rotor grinding cogging.As the same rotation speed,the effective wall shear stress distribution area is asymmetrical,that is,it exhibits the characteristics of alternating high and low shear stress.The results of the study[33]show that alternating high and low shears have greater particle shear-breaking capacity than any single shear.In addition,the distribution ratio of higher wall shear stress increases significantly with increasing rotational speed.The wall shear stress distribution characteristics of grinding cogging is that the convexity is significantly higher than that of the recesses.This provides a clear picture of determining the area of the maximum wall shear stress,the breakage mode,and the qualitative comparison of the dominance that affect breaking PbCO3product layer.Fig.10 shows that when the speed was low,the effective wall shear stress area is mainly concentrated in the cogging convexity,and when the speed was increased to 2000 r.min-1,the cogging including the convexity and the recesses has been able to provide sufficient wall shear stress for the breakage.This is in line with the general working principle of high-speed shearing equipment.Moreover,the faster the rotor rotation speed,the greater shear stress of the liquid phase.The liquid phase is decomposed into a finer microcrystalline structure,the liquid-solid contact area increased,the turbulence degree is serious,and the mass transfer performance of the reaction is improved [29].However,Table 7 shows that the distribution ratio of the effective wall shear stress range increased by only 1.16%from 2000 r.min-1to 2500 r.min-1,so in general,the speed of 2000 r.min-1was more appropriate.

Fig.10.The contours of the effective wall shear stress distribution area of the rotor at different speeds: (a) 1000 r.min-1,(b) 1500 r.min-1,(c) 2000 r.min-1,and (d) 2500 r.min-1.

4.Conclusions

The breakage process of the PbCO3product layer generated during the PbSO4desulfurization was modeled in this work.And this study analyzed the distribution of the RS-RR wall shear stress efficiently breaking the product layer and the flow fluid characteristics of the PbSO4slurry during the desulfurization.The analysis results for the fluid flow of PbSO4slurry showed that as the rotation speed increasing from 1000 to 2500 r.min-1,the maximum fluid speed increased from 13.79 to 32.51 m.s-1,an increase of 1.36 times.However,when the rotation speed increased from 2000 to 2500 r.min-1,the fluid speed increased by only 2.68%,so the speed of 2000 r.min-1was more appropriate.The high rotation speed of the RS-RR can cause the PbSO4particles in the fluid to collide strongly,enhance the turbulence intensity of the fluid,and greatly improve the mass transfer efficiency.The CFD simulation results confirmed that high rotation speed of RS-RR can better increase the wall shear stress of the rotor and stator.The effect of speed condition on wall shear stress was systematically studied.Under the optimal parameter of 2000 r.min-1,the distribution ratio of the rotor effective wall shear stress range achieved 96.1%,and the stator effective wall shear stress range reached 99.15%.The present study gives a clear and intuitive systematic study on the desulfurization reactor,and provides a reference on the mechanism of product layer breakage in the desulfurization process,as well as other similar core-shell structure breaking processes.It can provide a clear reference for the internal wall shear stress of the desulfurization reactor,and make up for the disadvantages that it is difficult to observe the internal environment under the current experimental methods.

Data Availability

Data will be made available on request.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was financially supported by the National Key Research and Development Program of China (2018YFC1903603).

Supplementary Material

Supplementary Material to this article can be found online at https://doi.org/10.1016/j.cjche.2023.02.025.