Numericalsimulation ofmicromixing effect on the reactive flow in a co-rotating twin screw extruder☆

Hao Tang,Yuan Zong,Ling Zhao*

State Key Laboratory ofChemicalEngineering,East China University ofScience and Technology,Shanghai200237,China

1.Introduction

The co-rotating twin-screw extruder(CoTSE)is very attractive reactor for reactive extrusion(REX)due to its self-wiping performance and modular design characteristic.The reactions in a CoTSE can be classi fied into two categories:single componentreaction,such as bulk polymerization,and multicomponent reaction,such as synthesis of urethanes,co-polymerizations and grafting reactions.For the former,studies were mainly focused on the macromixing and temperature in the extruder[1,2].For the latter,in most cases,multicomponent reactions take place on the interface between striation structure and its area is increased with deforming and reorientation during laminar mixing[3].Once the mixing time has the equivalent magnitude with reaction times or longer than that,incomplete localmixing of the reactants will signi ficantly affect the course ofreaction or even makes the conversion independent on Damköhler number[4,5].Therefore,detailed information of the mixing phenomena is important for the controlofreaction in REX process.

From a view ofhydrodynamics,the essence of the multicomponent reactive extrusion is a combination ofmass and momentum transfer in laminar regime.Like other reaction process,mixing between reactants is the precondition for the occurrence ofreaction.To reduce the computing load,traditionalapproaches simplify the geometry ofextruder into idealchemicalreactor models based on chemical reaction engineering theory and employ the residence time distribution(RTD)as a measure of axialmixing performance.While this measure is not very usefulfor the laminar mixing ofviscous fluids because it provides little information on transverse mixing[6],which is of more interest for the micromixing of reactive species.Since reaction occurs at the interface between striations,pioneering micromixing work of Ottino proposed a lamellar mixing modelwith alternating lamellar structure to describe the distribution of multicomponent concentration in reactive flow[7,8].In this model,the striation thickness and average deformation rate were utilized as a measure of mixing state[9–11].This approach is proved feasible in the analysis of relationship between molecular weightdistribution and micromixing in a CoTSE[12].

However,the lamellar micromixing modelsimpli fies the mixing as one-dimensionalconvection and diffusion problembecause of the complexity in describing flow dynamics in the screw channel[13].With the development of computational capabilities,approaches based on computational fluid dynamics(CFD)theory allow to solve these reactivemixing problems in a three-dimensionalway[14].Thus,more realistic flow patterns can be obtained[15].Various simulations have been reported for the reactive extrusion flow in recent decades,such as peroxide-initiated degradation of polypropylene and polymerization ofε-caprolactone in CoTSE[16–19].While most of these investigations were only concerned with macromixing and research on micromixing was rarely reported.It is reported that the inadequate mixing between the polymers and initiators can signi ficantly in fluence on the molecular weightdistribution(MWD)[20],which was ubiquitous in multicomponentreactions[2].Consequently,micromixing behavior should also be taken into consideration in the three dimensionalsimulation of REX.

Generally,there lies three decisive factors for the reactive-mixing process,i.e.,macromixing state,which can be measured by RTD,degree of segregation,and earliness/lateness of mixing[21].In the present paper,numericalsimulation with three-dimensionalmixing analysis was performed for the REXprocess.Effectofoperationalparameters,including initial species distribution,screw rotating speed and speci fic throughput,on product quality were numerically investigated and their relationships with these three factors were discussed.The aim of this study is to geta grasp on the REX process fromthe view ofchemical reaction engineering and find the decisive factors in the controlling of product quality.

2.Numerical Simulation

2.1.Modelreactions

Competitive-parallelreaction has been widely used in the investigation of micromixing in reactor[5,11,22].In order to obtain realistic results in extruders,the competitive-parallelpolymerization ofpolyurethane is employed in this work.The modeling reactions are:

where species A is–R-OH(1,4-butane diol,BDO),species B is–R′-NCO,i.e.,the prepolymer ofdicyclohexylmethane 4,4′-diisocyanate(H12MDI)and polyester(Mn=1000 g·mol-1),species D is –R″-NCO,i.e.,the prepolymerof4,4′-diphenylmethane diisocyanate(MDI)and polyester(Mn=1000 g·mol-1)[23,24].k1and k2are the rate constants ofreaction(a)and(b),respectively.Both reactions are second-orderreactions with suitable catalysts.According to k=5.45×109[Cat]exp.(-Ea/RT),where[Cat]=4.75 × 10-4mol·L-1and Ea=48.5 kJ·mol-1(Ref[23]),the reaction constantis in the range of10-1–10-2L·mol-1·s-1.Thus,k1=0.16 L·mol-1·s-1and k2=0.016 L·mol-1·s-1are set in the model.

2.2.Simulation methods

In practicalprocess,the barreltemperature is usually kept at a constantto ensure stable extrusion.By this way,the temperature rise in reactive extrusion becomes small and its effect on the process can be neglected.Thus,incompressible non-Newtonian flow,pseudo-steady state and isothermalcondition are assumed for the numericalsimulation.The governing equations are as follows:

Continuity equation:

Navier–Stokes equation:

where p is the pressure in extruder,is the localvelocity.ηis the viscosity of system.The constitutive equation of reaction system is regressed by literature data[23]:

where a=1.24 is the Yasuda index,n′=0.42 is the power law index,τ=0.014 s is the relaxation time constant and˙γis the shear rate.

The molecular weight(MW)ofprepolymer is 7.2 kg·mol-1,at that range,the zero-shear viscosity of reaction system is[25]:

In practical polymerization,zero-shear viscosity is yielding 0.1–105Pa·s.During the simulation in this work,it ranges from 0.1–10 Pa·s.That makes Reynolds number ranges from 0.02–2.

The mass balance of species i gives the following convection–diffusion equation:

whereρis the density of mixture,ωiand Diare the mass fraction and the molecular diffusivity for species i in the mixture,and Rirepresents the net mass rate of reaction(s)for species i,which could be estimated as follows:

where Miis the mole mass ofspecies i,υijis the stoichiometric coef ficient of the i-th species in the j-th reaction.For reactants,υij＜ 0,for products,υij＞ 0,and rjis the molar reaction rate of reaction j.

Divide both sides of Eq.(6)by Mi,the laminar diffusion equation of species concentration can be reformed into:

By solving the above equations,the characteristics of the flow regime and species transport can be obtained.The dimension of ciin Eq.(8)is[mol·m-3],and we convertitinto[mol·L-1]for convenience.

2.3.Simulation details

Fig.1 illustrates the geometrical features of three-dimensional model.The origin of coordinates is at the center of one of the screw inlets,and the extrusion direction is along the negative Z-axis.Screw elements are right-handed with 40 mm pitch and 60 mm length.Forlaminar flow,the length ofdevelop section is Ldevelop=0.05Re×D≈4 mm[26].Thus,two 10 mmlong flow domains withoutscrews are added before the inlet and after the outlet separately to ensure that the flow is fully developed.In the present simulation,two feeding streams are introduced into extruder through inlet 1 and inlet 2 separately.Two planes are chosen as sample planes,i.e.,plane y/D=0.38 in the middle of the screw chamber and plane|Z|/L=0.75 approaching the outlet,where D=42 mm is the barreldiameter and L=80 mm is the axial length of flow domain.Besides,a sample line from(0,16 mm,0)to(0,16 mm,-80 mm)is created to investigate the local properties along the axialdistance.

Both inlets have the same flow rate.Differentspecies concentrations are given for both inlets in order to investigate the reaction extentin accompany with convection–diffusion process.In practicalprocess,the initial concentration of diolor diisocyanate is 3.12 mol·L-1[23–25].Thus,the concentrations of–OH and –NCO are set as 2 mol·L-1with consideration ofprepolymerization before reactive extrusion.The feeding streams are shown in Table 1.In this way,generation ofa lamellar structure for species concentrations can be displayed during extrusion.

Fig.1.Geometricalfeatures ofsimulated screw(a)constrains of screws and(b)three-dimensionalmodel.

Table 1 Reactant concentrations imposed on two inlets(mol·L-1).

No-slip condition is imposed on the screws and barrelsurfaces.The barrelis static and the screws are set as moving wallat certain rotating speed.The simulation work is performed on commercialCFD platform POLYFLOWbased on finite element method.To eliminate the possible negative volume meshes arising due to screw rotating,the mesh superposition technique(MST)was implemented:fluid mesh elements obey the conservation equations,while the mesh elements occupied by moving screws are forced to rotate as rigid bodies[27].Thus,threedimensional finite element meshes are constructed covering moving parts and flow domain(Fig.2),the flow domain is discretized into 48 k hexahedral elements and each screw is divided into 40 k hexahedral elements.All the properties including velocity,species,pressure and viscosity,etc.are coupled with each other in the simulation to ensure convergence.The convergence ofcalculation is achieved until the residuals are less than 0.0001.TypicalCPUtime for an FEMtask on a workstation with 8 processors is around 1.6×104s.The mixing task is implemented with particle tracking analysis.The trajectories of 5000 marker particles are calculated per case in order to ensure the accuracy of the statisticalresults[28,29].Allthese particles are volume less,massless and independent from each other[30].Initially,these particles are randomly released at the inlet plane.The particles released at inlet 1 and inlet 2 can be distinguished with different colors,seen in Fig.3.In the computationalcode,these particles are assigned as“1”and “0”,respectively.Then their trajectories are calculated from the flow field.By this way,the materialdeformation can be estimated via the displacements of particle pairs,and the RTD can be obtained by the statistics of particle lifetime at outlet plane.Typical CPU time for a mixing task on a workstation with 8 processors is 1.4×103s.

2.4.Characterization ofmicromixing

Convection,diffusion and reaction determine the effectofmixing on the course of chemical reaction[6].Thus,the characteristic reaction time and mixing time need to be evaluated.

The characteristic reaction time is de fined as[10]:

The characteristic micromixing time with diffusion mechanism is de fined as[10]:

whereαis the deformation rate ofstriation and s0is the initialstriation thickness.The micromixing time in the present simulation of the order of magnitude 1–10 s.Apparently,the micromixing time has similar magnitude to the characteristic main reaction time,indicating the signi ficance of spatialmixing performance on the reactions.

Fig.2.Finite element meshes of(a)screws and(b)flow domain.

Fig.3.Initialdistribution ofparticles.

When multiple reactions take place between two reactant fluidsand once these reactions proceed to a considerable extent before homogeneity is attained,productdistribution willbe affected by the segregation status of the flow[31].Here we adoptsegregation scale and segregation intensity to characterize the mixing flow.The former measures the region size ofhomogeneous concentration and the latter re flects the spatialuniformity of the concentration[32,33].Reduction ofsegregation scale and segregation intensity represent the homogenization process[34].Segregation scale Lsis de fined as follows[32,35]:

where

R(|r|)is the correlation coef ficientbetween concentration ofpairs of particles separated by|r|and M=NP(NP-1)/2 is the numberofpairs,where NPis the number ofparticles,andis the sample variance.The cj′and cj″denote the concentrations ofboth particles in the j-th pair.cpis the concentration ofa certain particle which equals to either 0 or 1 and remains constant since the diffusion vanishes.

The segregation intensity Isegis the standard deviation of the concentration around its mean,and is de fined as follows[33,34]:

whereis the variance of a completely segregated system andis the measured variance.xjdenotes the concentration of j-th element in the extruder and N is the number of elements.The concentration of these elements willbe homogenized due to convection and diffusion effect.

Another important factor in micromixing is the earliness/lateness of mixing,i.e.,whether fluid mixes early or late as it flows through the vessel.Formulticomponentreaction,the mixing ofreactantis the prerequisite for reaction,which is related to the premixed condition.In the simulation,the earliness/lateness ofmixing is controlled by the reactant concentrations imposed on two inlets(seen in Table 1).

2.5.Characterization ofreaction

In order to quantify the reaction extent,firstly,the area-averaged features of i-th species on a plane is de fined as[19]:

where Ajand cijare the area and the concentration ofspecies i at cell j.

Conversionand selectivityofspecies A can be calculated by the following equations:

where,1 mol⋅L-1and

2.6.Evaluation ofsimulation results

The evaluation of simulation results includes two aspects:veri fication and validation[36].Veri fication evaluates the uncertainty in numericalsimulation.Here,mesh independency was checked.Validation means comparison between simulation and experiment.To prove the versatility of numerical methods,RTD and species distribution were compared with different sizes ofextruders.

2.6.1.Veri fication

In the simulation,mesh size is extremely importantto ensure the accuracy ofspecies transportation.Fig.4 shows the meshes at a cross section normalto the extrusion direction with three mesh sizes in mesh independency check.The total element quantities are 41 k,88 k and 190 k for schemes a,b and c,respectively.

Feeding①with Q/n=7000/30 were employed in mesh check,where the reactants are initialsegregated in different inlets,as seen in Table 1.Fig.5(a)illustrates the velocity on the sample line and Fig.5(b)shows the evolution of average conversion along axial distance with three mesh sizes.The curves ofmeshes b and c are very close in both figures,while perceptible difference could be recognized between results frommesh a and others.With compromising consideration ofcomputationalload and accuracy,mesh size b is chosen as an optimized mesh for the simulation work.

Fig.4.Meshes at a cross section normalto the extrusion direction.

Fig.5.Mesh independency check(a)Velocity distribution on sample line 1.(b)Average conversion evolution along the axialdistance.

Fig.6.Validation ofsimulation on RTD(a)Element geometry(b)RTD curves.

2.6.2.Validation

In order to test the capabilities and accuracy ofnumericalmethods,RTD of a flow through KD2 structure(two pairs of 60/4/32 kneading disks with D=35 mm)is simulated and compared with that in literature[30],as shown in Fig.6a.In Zhang's experiment[30,37],the test elements were installed in the mixing section ofextruderand two probes were located atthe upstream and downstream.Anthracene was chosen as the tracer and the in-line fluorescentlightmeasuring system was developed to measure the local RTD at probe locations.Then the RTD between them was calculated by a deconvolution method[38].

The experimentalmaterialis polystyrene and its constitutive equation can be represented by Carreau model[30]:

The flowrate is 3.06×10-6m3·s-1and rotating speed is 120 r·min-1in the simulation according to literature[30].Agood agreementis found in the comparison ofboth work(Fig.6b).And the relative error is less than 5%.

Besides,distribution ofspecies is also validated by comparing the deformation ofstriation between the simulation work and the experiment work of Kalyon[39].The geometry ofscrew elements is full flightelements,diameter and pitch respectively in 50.8 mm,and the operational conditionsare identicalto literature[39]in the simulation.Fig.7a shows the initialposition ofstriation.Fig.7 panels b and c illustrate simulated and experimentalshapes ofstriation after halfrevolution ofscrews,respectively.The agreementbetween those shapes seems fine.The above validations indicate thatthe employed numericalmethod is feasible and the parameters de fined in numericalanalysis are reasonable.

3.Results and Discussion

3.1.Flow pattern in CoTSE

Fig.7.Spatialdistribution oftracer in extruder after 1/2 revolution.(a)Initialposition,(b)simulated result,and(c)experimentalresult.

In twin screw extruders,the distribution of fluid elements is improved due to relative movement between both screws and barrel,which have signi ficant in fluence on flow behavior.In order to trace the transfer movement of species,species A is introduced into inlet 1 with a concentration of 2 mol·L-1.The screw rotating speed is 30 r·min-1and both inlets have the same flow rate of 3500 mm3·s-1.Fig.8 gives the distribution evolution ofspecies A atdifferent axiallocations.Obviously,it can be seen that the flow is transferred from one screw to the other because the other screw picks up the materialand drags it away from intermeshing region.As a result,species A is delivered in a“”pattern with helical flow and new materialinterfaces are generated with each screw revolution[40,41].With the development ofmaterialexchange and accumulation of the mixing effect,the distribution ofconcentration gradually becomes uniform along the extrusion direction as seen after plane|Z|/L=0.75.

3.2.Effect offeeding condition

For continuous process,the initialspecies distribution is determined by the feeding condition.In orderto clarify the interaction between flow field and reactions,here the species are fed through different inlets,which can be regarded as completely separated condition[42–44].Table 1 shows the initialspecies distributions of various feedings.The flow rate is set as 3500 mm3·s-1for each inlet and rotating speed equals to 30 r·min-1for allcases.

Fig.9 illustrates the concentration distribution of main product(C)and side product(E)on plane y/D=0.38 with various feedings.The results clearly illustrate the sensitivity of species C and E to the premixing status of their relevant reactants.It is noticed that the concentration of species E is improved in Fig.9b compared with that in Fig.9a,indicating that prior mixing between species A and D is bene ficialto the side reaction.The same observation can be made for the concentration distribution ofspecies C and E in Fig.9c and d compared with that in Fig.9a,which implies that the initialhomogeneous distribution of the reactants can simultaneously promote the main and side reactions to a certain extent.

Table 2 provides reaction results on plane|Z|/L=0.75.From the table,it can be seen that the lowest averaged conversion is found in the case with feeding condition①,this is caused by the initialcondition ofspecies.In that condition,species A is completely separated from B and D,and the insuf ficientmixing between these reactants can decrease the reaction rate.Higher conversion and lowestselectivity under feeding condition②is caused by the only premixing ofspecies A with species D atthe inlet,hence the side reaction is enhanced while the main reaction is suppressed.Better mixing of the reactants under feeding conditions③and④leads to higher reaction conversions.And the highestlocalreactant concentrations in the case with feeding condition④are responsible for the highest conversion.Moreover,it is also observed that the selectivity of the cases with feeding condition ①,③and④is very close.This can be attributed to the fact that the mixing ofspecies B and D are identicalin these cases.

Fig.10 gives the yield ofspecies C(Φ)along the extrusion direction,which is the productofselectivity and conversion.As far as feeding conditions③and④are concerned,earlier mixing between reactants results in a jump in the yield of species C,and then the growth is gradually weakened approaching the outlet since the reactant A is exhausted.The curves with feeding conditions①and②are almost overlapped in the inlet section due to their low conversions.Downstream,the differences between the two curves become larger attributing to their distinguishing selectivity.

The above discussion reveals differentmicromixing behaviors of the fluids.Flow through the inlets at feeding conditions①,②and④,is often called “macro fluid”,where fluids are completely segregated.When identical flow through both inlets,like feeding condition③,is called “micro fluid”,and fluids will be in the state of maximum mixedness during being transported.These two groups of fluids restrict earliness/lateness ofmixing,which is also a prominent issue for other reactors.The above observations con firm that earliness/lateness of mixing has a determined effect on the localconcentration distribution,which can further affect the conversion and selectivity for these multicomponent reactions in CoTSE.It also provides an evidence that attentions should be paid to the feeding condition in order to achieve the desired reaction results in the REX process.

3.3.Effectofrotating speed

Fig.11 illustrates the productdistributions at various screw rotating speeds with feeding condition②.The flow rate is fixed at 3500 mm3·s-1per inlet.With increasing rotating speed,the concentration ofspecies C is improved while the concentration ofspecies E is decreased,indicating that the main reaction has been enhanced while the side reaction has been suppressed on the contrary.

Fig.11 panels a and b show the selectivity and conversion evolution along the axialdirection atvarious rotating speeds.In order to illustrate the mixing effect on reaction,fully premixed case with feeding condition ③ and rotating speed of 30 r·min-1is provided for comparison.The reaction conversion and selectivity along the extrusion direction are found increasing with the increase ofscrew rotating speeds,indicating that higher screw rotating speed is bene ficialto the proceeding of reaction under the given feeding condition.Besides,apparent distinct can be noticed between premixed case and non-premixed cases.The selectivity for the premixed case keeps a high value in the all range,which proves the importance of reactant segregation on the reactions.

Fig.8.Distribution ofspecies A along extrusion direction at n=30 r·min-1.

Fig.9.Distributions of species C(left)and E(right)on plane y/D=0.38 with(a)feeding①,(b)feeding②,(c)feeding③and(d)feeding④.

Table 2 Average concentrations,selectivity and conversion on plane|Z|/L=0.75.

Fig.10.Effect of feeding condition on yield ofspecies C.

The"product gap",Δφ,is de fined to demonstrate the difference of yields between premixed and segregated feeding:whereϕpremixis the yield of the case with premixed feeding.The yield difference along the extrusion direction is shown in Fig.12c.At the beginning ofextrusion,the rise oftargetproductin the micro fluid is larger than thatin the macro fluid due to the earliness ofmixing between reactants.With the developmentof flow and accumulation ofmixing effect,this difference reaches its maximum.Then,the gap between mixed and non-mixed cases declineswith the consumption ofreactants.The smaller rotating speed,the bigger gap is found.

RTDis typically employed as a measure ofa kinematic description of flow,to understand the axialmixing in the reactor.Fig.12d describes the local RTD at plane|Z|/L=0.75 at different speeds.There is no obvious effect ofrotating speed on the RTD pro file shape.Moreover,the mean residence time is found slightly reduced,which is 11.58 s,10.56 s and 9.64 s with the increasing ofrotating speed.Change to the results of reaction extent,it is clearly insuf ficient to analyze the reactive-mixing flow only by RTD.Because RTD is only a good measure for macromixing and becomes invalid in the characterization of micromixing.Hence,statisticaldescription of mixture is processed to analyze the degree of segregation in the extruder.Fig.12e shows the evolution of segregation scale along extrusion direction.The segregation scale presents a sharp decline in allcurves near the entrance section,illustrating that the region size with homogeneous concentration is decreased rapidly.It is also found the segregation scale oscillates in the remaining section,which may be caused by the stretching,folding and reorientation of the striations during extrusion[45].Approaching the outlet,the segregation scale at higher speed is found smaller than thatatlower speed.Fig.12fshows the evolution ofsegregation intensity along extrusion direction.All curves show a decreasing trend.The higher the screw rotating speed,the quicker the curve goes down.Lower value ofsegregation intensity is obtained at higher speed near the outlets.Itshows thatrotating speed is more relevantto micromixing rather than macromixing and higher rotating speed can achieve more uniformdistribution ofspecies in the extruder.The results also illustrate thatthe scalarmixing analysis is a necessary supplementfor the characterization ofreactive-mixing in REX.

Fig.12.Effect ofrotating speed on(a)selectivity,(b)conversion,(c)yield difference,(d)RTD,(e)segregation scale and(f)segregation intensity.

3.4.Effectofspeci fic throughput

Ithas been reported thatthe speci fic throughput,de fined as the ratio between flow rate Q and rotating speed n,has signi ficant in fluence on partialas wellas overallresidence time/revolution/volume distribution[37].However,notmuch is mentioned aboutits effecton reaction.Since the REX process is determined by a combination of mixing,reaction kinetics and residence time in the channelof fluid element,itis ofinterest to figure out the relationship between speci fic throughput and reactions.

Fig.13 provides the species distribution of C and E at y/D=0.38 at the same speci fic throughputwith feeding condition②.Itcan be seen that both the concentrations of species C and E in the whole extruder are reduced with increasing flow rate,which is due to the decrease of residence time.

Fig.14 panels a and b show the selectivity and conversion evolution along the extrusion direction.The resultofconversion indicates thatreactions are suppressed with increasing flow rate.However,the reaction selectivity is increased with increasing screw rotating speed.There may be two possible reasons behind this phenomenon:(1)The local micromixing status in extruder may not change at the same speci fic throughput,while the time to achieve the same micro-mixing status is shortened with higher flow rate.Thus,the side reaction is suppressed.(2)The micromixing ofreactive flow is enhanced by the increasing rotating speed with identical speci fic throughput.The yield difference along the extrusion direction is shown in Fig.14c.Allcurves show a trend from increase to decline as except.Moreover,the yield difference is decreasing with the increase of flow rate.That is because shorter residence time leads to shorter reaction time,and hence the yields with premixed and segregated feeding are decreased.

To con firm the true reason behind the improvement of reaction selectivity,here we analyze the effectofspeci fic throughputon the mixing performance of flow firstly.With the increasing of flow rate and rotating speed while the speci fic throughput remains constant,the RTD curve shifts to the left and becomes narrower as expected,as seen in Fig.14d.The mean residence timesare 21.40 s,10.56 s and 7.14 s with increasing flow rate.As the mixing performance is concerned,it is interesting to find thatthe curves ofsegregation scale and segregation intensity are almost superimposed on a single master one(Fig.14e and f).Therefore,we can conclude that the same speci fic throughput bring about differences in the duration of mixing while identity in micromixing status.And it gives the answer that the improved selectivity is mainly attributed to the shortened reaction time rather than the mixing performance.Combined with the results in Section 3.3,it con firms that the mixing is closely dependent on the speci fic throughput instead of simply rotating speed,and the reaction extent is the consequence of both mixing and residence time.

3.5.Reactive-mixing flow in extruder

To compare the signi ficance of the effects offeeding,rotating speed and flow rate on reactions,an orthogonaltestis performed.Each factor has three levels and the interaction of feeding condition and rotating speed is considered(Table 3).The results oforthogonaltest are listed in Table 4.Columns 6 and 7 show levelerrors,the deviations are quite small.While,the same outcomes are found in columns 3 and 4,indicating that the interaction between feeding condition and rotating speed can be neglected,columns 3,4,6 and 7 could be regarded as level error columns.It can be concluded that sequence of signi ficance of these factors on the reaction yield is feeding condition＞flow rate＞rotating speed,based on the range and sum ofsquare ofdeviations analysis.The F examination tells both the differences of flow rate and feeding condition are highly signi ficant(P＜0.01),and the difference of rotating speed is also remarkable(P＜0.1).

Fig.13.Distributions of species C(left)and E(right)on plane y/D=0.38 at speci fic throughput of(a)3500/15,(b)7000/30,(c)10500/45.

It should be pointed out that screw rotating speed may have different effects on reaction according to the micro-mixing behavior of the fluid.For macro fluid,increasing rotating speed enhances the micromixing,which can compensate the shortening ofresidence time and results in a higher reaction extent;for micro fluid,increasing rotating speed only reduces the reaction time,leading to lower reaction extent.The orthogonaltest proves that when the screw rotating speed is low,micro fluid status is more bene ficialfor the reaction because macro fluid takes long time for micro-mixing.When the screw rotating speed is extremely increased,higher than the studied speed,the micro-mixing time may be greatly shortened and the signi ficance of rotating speed can be strengthened.However,in order to ensure enough reaction time,lower rotating speed is more reliable.In brief,the highly signi ficant differences of feeding condition and flow rate on reaction yield can be attributed to their relationship with earliness ofmixing and residence time,respectively.The effect of rotating speed relies on the micro-mixing status of the fluid.

4.Conclusions

Numericalmodeling ofreactive extrusion systems is ofgreatinterest since it provides an accessible way to choose favorable operationalconditions froma practicalpointofview.In the presentpaper,effects ofinitialspecies distribution,screw rotating speed and speci fic throughput on the multicomponent reaction were numerically investigated.In accordance with the above discussions and analysis about their effects and interaction,the following conclusions are drawn.

The results show that RTD alone is inadequate to characterize the mixing status in REX process.Micro-mixing status of fluids,i.e.,micro fluid and macro fluid,which controls earliness/lateness ofmixing,has the highest priority in affecting the flow field and the product quality.

The analysis ofsegregation degree,including segregation scale and segregation intensity,shows thatatthe same flow rate,effective mixing resulted from higher screw rotating speed can compensate the shortening of residence time and promote the proceeding of reactions with macro fluid feeding.On the contrary,prominent effect of increasing screw rotating speed decreases the reaction time with micro fluid feeding.

Fig.14.Effect of speci fic throughput on(a)selectivity,(b)conversion,(c)yield difference,(d)RTD,(e)segregation scale and(f)segregation intensity.

Table 3 Factors and levels in orthogonaltest

Table 4 The results oforthogonaltest

The relationship between flow rate and rotating speed is identi fied by speci fic throughput.The mixing performance keeps unchanged at the same speci fic throughput,while higher flow rate and rotating speed lead to signi ficantdecrease ofproducts due to the reduction ofreaction time.

In order to discriminate the signi ficance of these operationalconditions on the reaction,orthogonaltest is performed and the results confirmed that the initialspecies distribution and flow rate play decisive roles in the yield controlling.

Nomenclature

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