Polyethoxylation and polypropoxylation reactions:Kinetics,mass transfer and industrial reactor design

E.Santacesaria *,R.Tesser ,M.Di Serio

1 Eurochem Engineering srl.,Via Codogno 5,IT-20139 Milan,Italy

2 University of Naples “Federico II”,Department of Chemical Sciences,Via Cinthia,IT-80126 Naples,Italy

Keywords:Ethoxylation Propoxylation Kinetics Mass transfer Spray tower loop reactor

A B S T R A C T Ethoxylation and propoxylation reactionsare performed in the industry to produce mainly non-ionic surfactants and ethylene oxide(EO)–propylene oxide(PO)copolymers.Both the reactions occur in gas–liquid reactors by feeding gaseous EO,PO or both into the reactor containing a solution of an alkaline catalyst(KOH or NaOH).Non-ionic surfactants are produced by using liquid starters like fatty alcohols,fatty acids or alkyl-phenols,while when the scope is to prepare EO–PO copolymers the starter can be a mono-or multi-functional alcohol of low molecular weight.Both reactions are strongly exothermic,and EO and PO,in some conditions,can give place to runaway and also to explosive side reactions.Therefore,the choice of a suitable reactor is a key factor for operating in safe conditions.Acorrect reactor design requires:(i)the know ledge of the kinetic law sgoverning the rates of the occurring reactions;(ii)the role of mass and heat transfer in affecting the reaction rate;(iii)the solubility of EOand POin the reacting mixture with the non-ideality of the reacting solutions considered;(iv)the density of the reacting mixture.All these aspects have been studied by our research group for different starters of industrial interest,and the data collected by using semibatch well stirred laboratory reactors have been employed for the simulation of industrial reactors,in particular Gas–Liquid Spray Tower Loop Reactors.

1.Introduction

Polyethoxylation and polypropoxylation reactions are normally performed,in industry,for preparing non-ionic surfactant and polymers[1–3].Both the reactions are highly exothermic(~83.7 kJ·mol?1)and requires an efficient heat exchange to avoid the hazard of runaway that is particularly dangerous for the possible intervention,at high temperature,of explosive side reactions related to ethylene or propylene oxide decomposition[4,5].In all cases the reaction needs a starter,that is,a molecule having a more or less acid terminal proton.The starter can be a hydrophobic molecule,in the case of producing surfactants or a hydrophilic molecule of low molecular weight for producing polymers.

Polyethoxylation and polypropoxylation are normally promoted by an alkaline catalyst like KOH,NaOH or related alkoxides previously dissolved in the starter.The reaction is normally studied in laboratory by using well-mixed semibatch reactors.Ethylene oxide(EO)or propylene oxide(PO)or both are gradually added to the solution of an alkalinecatalyst in the liquid starter previously heated at the reaction temperature,normally kept in a range of 120–200 °C.EO and PO,in the mentioned conditions of temperature,quickly evaporate and are partitioned between gas and liquid phases.The reaction occurs in liquid phase between the starter and the gaseous reagent dissolved into the starter.The pressure of the gas phase is kept constant at a level of 0.2–0.5 MPa by continuously feeding the alkylene oxide reagent.To study the reaction kinetics,it is important, first of all,to create a large gas–liquid interface area to avoid masstransfer limitation.Moreover,considering that the reaction occurs in the liquid phase,it is opportune to know how the EO and PO solubility changes by changing pressure,temperature and chemical composition of the reaction environment.It is opportune to achieve the EO,PO solubility data by experiments independent of the kinetic study or by using predictive methods.Another important point to be considered in the kinetic study is that the volume of the reaction mixture increases as the polyalkoxylation reaction proceeds.As a consequence,it is necessary to know how the density of the liquid phase changes with the reaction extent and the temperature.A kinetic model,for interpreting correctly the behavior of the polyalkoxylation reactions,must consider both the mentioned effects and must be developed on the basis of the alkoxylation reaction mechanism.In this review,the kinetic approach for the ethoxylation and propoxylation of many different starters,performed in laboratory semibatch gas–liquid well-stirred reactors,is described in detail together with the agreement achieved between the developed kinetic models and the experimental obtained results.Then,it will be shown how the kinetic models and related parameters can be usefully employed for simulating the behavior of industrial reactors,in particular,the Spray Tower Loop Reactors.

2.Kinetics in the Literature

A lot of kinetic runs have been performed in laboratory by the research group of the authors by using different starters and alternatively EO or PO.The different runs have been performed with the aim to evaluate:

1)the effects of both the acidity of the starter and the nucleophilicity of the corresponding anions[6–8].

2)the effect of the type of involved hydroxyls using respectively 1-and 2-octanol as starters[9].

3)the effect of low molecular weight hydrophilic and polyfunctional starters,such as ethylene and tetraethylene glycols[10].

4)the behavior of propylene oxide in comparison with ethylene oxide[9,10].

More details about the performed runs are reported in Fig.1.

2.1.Laboratory reactor for studying the kinetics

The kinetics of polyalkoxylation have been studied by using a thermostated well-mixed semibatch reactors equipped with a magnetic driven stirrer sucking the gas and dispersing it in small bubbles inside the liquid phase.The large interface area developed by stirring avoids reaction rate suffered from mass transfer limitation.EO or PO are pressurized in a bottle with nitrogen and automatically fed to the reactor kept at constant moderate pressure of 0.2 or 0.3 MPa.Small samples of the reacting liquid were withdrawn at different times and analyzed by HPLC.A scheme of the employed apparatus is in Fig.2.

3.Alkoxylation Reaction Mechanism(SN2)

The catalyst precursor KOH or NaOH is added to the starter and reacts with it forming in situ the true catalyst and water.Water must be removed by heating under vacuum the reaction mixture,because,it acts as an undesired starter giving place to a side reaction.Then,when the reaction temperature is reached,ethylene or propylene oxide or both are added and the polymerization reaction starts.The initiation step occurs with an SN2 mechanism followed by further reaction steps of propagation occurring with the same mechanism.The product is formed thanks to the proton transfer reaction that is an equilibrium fast reaction.The described reaction mechanism is summarized in the scheme of Fig.3[11].

This is a living polymer because no termination occurs and in the presence of the catalyst the reaction starts again when we add ethylene or propylene oxide.The reaction can be definitively stopped only by neutralizing the alkaline catalyst with an acid.

4.Polyalkoxylation Kinetic Model Describing a Semibatch Wellstirred Reactor

On the basis of the described mechanism a kinetic model can be written.We can define first of all,an equation describing the substrate consumption and then a series of equations describing respectively the formation and disappearing of any single oligomer and,at last,an equation giving the overall consumption of the alkylene oxide.Then we can consider also the eventual contribution of the mass transfer limitation by equating the overall reaction rate to the mass transfer rate.If the reactor is not perfectly isothermal we have to evaluate also the change of temperature inside the reactor by solving the heat balance equation reported in Fig.4.

To solve this system of differential equations we need to know,first of all,the expressions of the reaction rates that are present in the system.Considering the reaction mechanism we can write for the initiation and propagation rates second order kinetic law s,such as

Fig.1.List of the performed kinetic runs and the related scope.

Fig.2.Scheme of the laboratory reactor for studying polyalkoxilation reactions.A=Computer,B=Computer interface,C=on–off solenoid valve,D=EO bottle,E=Pressure transducer,F=Manometer,G=Line for samples,H=Jacketed reactor,I=Freezing coil,L=Holed stirrer,M=Magnetic driven stirrer,N=Thermocouple.Reprinted with permission from[7]Copyright(1992)American Chemical Society.

Fig.3.Polyalkoxylation reaction mechanism.

Fig.4.Kinetic model describing a semibatch well-stirred reactor.

Moreover,as the reaction products are obtained through the proton transfer equilibria,we assume all these reactions at equilibrium and introduce the corresponding equilibrium constants.

Initial conditions are:t=0,[RXH]=[RXH]°,[RX(AO)iH]=0,nAO=0,T=Ti.

But we have some other problems to solve before starting with the calculations:

1)The concentrations appearing in the expressions of the kinetic model change along the time,not only as a consequence of the reaction but also because the liquid volume of the reacting mixture changes during the reaction.

2)The solubility of the alkylene oxide changes,too,with the pressure,temperature and polymer composition,and we need to know how this change occurs.

3)At last,the catalyst is partitioned between the unreacted starter

anion and the growing chains ethoxylated anions.

This last problem can be solved by introducing in the catalyst mass balance a reasonable approximation expressed by these relations:

As a consequence we have:

where B°is the overall catalyst concentration.Densities and solubilities must be determined with independent experiments[11,12]or by predictive calculations as described in the following chapter.

5.Effect of Density Change on the Kinetics

As before mentioned,we have to evaluate how the density changes as a function of the number of adducts and of the temperature by interpolating,for example,the experimental data with a polynomial empirical expression like the following one:

The values of the coefficients A to E,experimentally determined for some different substrates,are reported in Table 1.

6.Effect of AO Solubility on the Kinetics

The alkylene oxide solubility in the reaction mixture can be considered as a pseudo-binary system:one component being the alkylene oxide and the other a more or less ethoxylated substrate considering the average number of ethoxy groups[12,13].The vapor phase can normally be considered ideal,but the liquid phase is usually,characterized by high non-ideality,therefore,the equilibrium alkylene oxide molar fraction in liquid phase is given by the Raoult equation,while the Antoine equation can be used for determining the corresponding equilibrium vapor pressure:The interpretation of experimental data can be made by using the Wilson or the NRTL methods that performsvery well.Hereare reported,as example,the Wilson equations containing the binary interaction parameters Λ12and Λ21:

Then,the binary interaction parameters can be correlated with the average number of alkylene oxide groupsnAO:

In Table 2 the parameters experimentally found for different substrates are reported.

In the absence of experimental data,the well-known predictive methods such as UNIFAC or ASOG can be used.

7.Effect of the Catalyst Anion Nucleophilicity and Starter Acidity

The molecule acidity and the different nucleophilicity of the starter anions have a dramatic effect on the kinetic behavior[11],as it can be appreciated in Fig.5.

Table 1Empirical parameters to describe the densities of different hydrophobic substrates and related ethoxylated mixtures[11,12]

Fig.5.The effect of acidity of the starter and of nucleophilicity of the corresponding anion on the ethoxylation activity(1 atm=101.325 kPa)[11].

In Fig.5,the kinetic behavior observed for respectively 1-dodecanol,dodecanoic acid and nonylphenol are reported for comparison.Dodecanol has a quasi linear trend of the ethylene oxide consumption,nonylphenol shows two consecutive linear trends,while,dodecanoic acid has an initial curve going toward a plateau followed by a linear trend in which the reaction rate increases very much with respect to the initial reaction rate.It has been observed that dodecanoic acid[8]gives place initially to a reaction that is not catalyzed by KOH.The reaction initially is promoted by the acidity of the starter and the reaction,therefore,occurs also in the absence of KOH.When the first adduct completely neutralized the dodecanoic acidity,the reaction,catalyzed by KOH,starts with a rate similar to the one observed for dodecanol.This behavior can be well appreciated in Fig.6.

Fig.6.Peculiar kinetic behavior of fatty acids in the ethoxylation.Reprinted with permission from[8]Copyright(1994)American Chemical Society(1 atm=101.325 k Pa).

In Fig.7,the kinetic behavior of dodecanol observed in three different runs,performed at 2×105Pa of pressure and at three different temperatures is reported[7].In the same figure an example of oligomer distribution related to Run 1 is also reported.Points are experimental data,lines are calculated with the previously described kinetic model.

Only three parameters are necessary to describe the ethoxylation of a starter constituted by a primary alcohol like dodecanol,because,initiation rate is approximately equal to the rates of all the successive propagation steps.Moreover,the proton exchange equilibrium constant is a unique value independently of chain length and temperature.Therefore,the kinetic parameters experimentally determined for dodecanol are[7]:

The behavior of the kinetic and equilibrium constant with the temperature can be appreciated in Fig.8.

In Fig.9,the kinetic behavior of nonylphenol[6]for some runs performed by changing both the temperature and the pressure are reported.In the same figure,an example of oligomer distribution related to run 4 is also reported.As before,points are experimental;lines are calculated always with the previously described kinetic model but with different kinetic parameters.

In this case,the initiation rate is clearly different from the successive propagation steps.This occurs,because,the nonylphenol hydroxyl has a greater acidity and the corresponding anion has a lower nucleophilicity than the primary alcohol formed in the successive propagation steps.Therefore,the initiation kinetic constant is different from the constants of the propagation steps.

Hence,two different kinetic constants and related activation energies and a proton transfer equilibrium parameter and related enthalpy change are necessary,in this case,to describe all the nonylphenol ethoxylation kinetic runs.

Fig.7.The kinetic behavior of the starter dodecanol at different temperatures and catalyst concentrations.Reprinted with permission from[7]Copyright(1992)American Chemical Society(1 bar=105 Pa).

Kinetic parameters determined

Fig.8.Arrhenius and Van't Hoff plots for the parameters of dodecanol ethoxylation.Reprinted with permission from[7]Copyright(1992)American Chemical Society.

It is interesting to point out that the difference in the kinetic constant of the initiation step with respect to the propagation one has a dramatic effect on the oligomers distribution,as shown in Fig.10.As it can be seen,in this figure,1-dodecanol show sabroaden oligomers distribution and alargeamount of un-reacted alcohol if compared with nonylphenol[13].

8.Propoxylation Mechanism and the Kinetics of PO with EO

On a theoretical basis the asymmetric characteristics of the propylene oxide molecule could generate,when ring opening reaction occurs,a primary or a secondary alcohol,as a consequence of the nucleophilic attack to respectively the methylene group 1 or the methyne group 2.

But by 13C NMR analysis,it is possible to demonstrate that the contribution of route 2 is negligible.Therefore,reaction with PO gives place exclusively to a secondary alcohol.In order to compare the reactivity of primary and secondary alcohols in both ethoxylation and propoxylation,a series of runs have been made using respectively 1-and 2-octanol as starters in both ethoxylation and propoxylation[9,14,15].The results can be appreciated in the plots of Fig.11.

Fig.9.The kinetic behavior of the starter nonylphenol at different temperatures,pressures and catalyst concentrations(KOH=0.015 mol/0.785 mol of NP(run 1,2,3),KOH=0.083/0.759 of NP(run 4)).Reprinted with permission from[6]Copyright(1990)American Chemical Society(1 bar=105 Pa).

As it can be seen,two limit conditions of reactivity can be recognized in Fig.11 corresponding respectively to the reaction of a primary alcohol with EO(higher activity)and to the reaction of a secondary alcohol with PO(lower activity).These two systems,although having different reactivities,are quite similar in behavior,because the hydroxyl that formed after any step of polymerization has the same characteristics,that is,the primary alcohol reacting with EO remains primary,while the secondary alcohol reacting with PO remains secondary.The consequence is that there is no difference between initiation and propagation kinetic constants.On the contrary,when asecondary alcohol(2-octanol)is subjected to ethoxylation,a primary alcohol is formed.In this case,initiation and propagation constants are different,but the propagation constant is equal to the one observed for the system starting with a primary alcohol.In the case of a primary alcohol submitted to propoxylation,from a primary alcohol a secondary one is obtained,and again,the initiation has a constant different from propagation,but the propagation step constant is the same as the system starting from secondary alcohol.In other words,at a given temperature only 4 kinetic parameters can describe with a satisfactory approximation all the kinetic behaviors of the considered systems.In conclusion,when a change occurs from primary to secondary alcohol or vice versa we need at least two kinetic constants to describe the system but one only parameter is necessary when no change occurs.So,we can identify four different occurring reactions with their own kinetic behavior and related kinetic constant:

Fig.10.The effect of the difference in the kinetic constant of initiation and propagation on the oligomers distribution[13].

Fig.11.Kinetic behavior observed for the reaction of 1-and 2-octanol with respectively ethylene and propylene oxide[18].

The kinetic constants for each reaction type are reported in Table 3.

For what concerns the proton transfer equilibrium constants,these parameters seem independent of temperature and chain length and the values experimentally found are:

Table 3Kinetic constants for describing all the reaction occurring in the ethoxylation and propoxylation of both 1 and 2 octanol

The effect of the type of hydroxyl on the EO and PO activity can be well appreciated in the Arrhenius plot of Fig.12.As it can be seen,we can write that k11＞＞k12＞k21＞＞k22.

Again,it is opportune to point out that as in the previous examples for simulating all these systems we need to evaluate,with independent experiments,how density changes with the polymerization degree and the temperature,evaluating the parameters of an empirical polynomial correlation.For example,the densities parameters determined by regression for both 1-an 2-octanol reacting with ethylene or propylene oxide are reported in Table 4.

For completing the kinetic analysis,we have also to evaluate the EO/PO solubilities in both the starter and the corresponding ethoxylated mixture.In this case,the solubility values have been estimated by using the predictive method UNIFAC,and the obtained values for a pressure of 0.2 MPa are reported in Table 5.As it can be seen,PO is twice more soluble than EO,and this represents a problem for the safety of the reactors working with PO.

Fig.12.A comparison of the activity found for the ethoxylation and propoxylation of 1-and 2-octanol respectively.Reprinted with permission from[9]Copyright(1996)American Chemical Society.

Table 4Empirical parameters for determining the density of the mixtures of oligomers obtained by ethoxylation and propoxylation of 1-and 2-octanol

Table 5Solubilities of EO and PO in 1-and 2-octanol and related oligomers mixtures determined by UNIFAC

9.Effect of Using Low Molecular Starters

9.1.Ethoxylation of ethylene glycol and tetraethylene glycol

Let us consider now the effect on the kinetics of low molecular weight hydrophilic starters.In Fig.13,the kinetic runs of polyethoxylation using respectively ethylene glycol and tetraethylene glycol,as starters at different temperature are reported[10].From these figures it is possible to observe that the reaction rate is slightly declining with the starter ethylene glycol,while is just a straight line starting with tetraethylene glycol.The conclusion is that in the first case,we need at least two kinetic parameters for the complete simulation,while in the second case,one only parameter is enough.In Fig.14 are reported,in an Arrhenius type plot,the kinetic constants of the initiation and propagation reactions for the polyethoxylation of ethylene glycol.Initiation and propagation constants are equal for tetraethylenglycol corresponding to the propagation constant of ethylene glycol.

On the same plot are reported for comparison also the kinetic constants determined for the ethoxylation of 1-octanol and 1-dodecanol.As it can be seen,the data points fall on the straight line,confirming that the propagation constant is approximately the same for a primary alcohol independently of the type of starter(hydrophobic or hydrophilic)and of the chain length.

The best fitting kinetic parameters are:

Fig.14.Arrheniustype plot for the ethoxylation of ethylene glycol.The plot is valid also for the starter tetra-ethylene glycol.Reprinted with permission from[10]Copyright(2002)American Chemical Society.

9.2.Propoxylation of ethylene glycol

The reaction of PO with ethylene glycol[10]gives place to an asymmetric mono-adduct(A1).A further reaction with propylene oxide can give two types of bi-adductsonesymmetric(S2)and another asymmetric(A2).The asymmetric compound A2 follow s two different growing routes,while S2 has only one possibility of reaction as can be seen in the scheme of Fig.15.

The kinetic model of propoxylation is slightly different with respect to the model initially described in this work.By considering the mechanism reported in Fig.15,we have one initiation rate but two different propagation routes,one followed by the symmetric molecules and another one followed by the asymmetric molecules.Therefore,we can write:

Initiation

Asymmetric propagation,

Fig.13.Ethoxylation of low molecular weight starts,that is,ethylene glycol and tetra-ethylene glycol.Reprinted with permission from[10]Copyright(2002)American Chemical Society.

Fig.15.Ethylene glycol propoxylation reaction scheme.Reprinted with permission from[10]Copyright(2002)American Chemical Society.

Table 6Best fitting kinetic parameters found for the propoxylation of ethylene glycol

Symmetric propagation

Propylene oxide consumption:

Despite this apparent complexity,the necessary kinetic constants at a given temperature are only two:kppand kps.The best kinetic parameters,determined by regression on the experimental data,are reported in Table 6.In the same table are also reported the proton transfer equilibrium constants.Ke3can be assumed equal to 2Ke2considering that the symmetric propoxylated species have two secondary hydroxyl groups.Therefore,we need just 2 equilibrium parameters Ke1and Ke2.

In Fig.16,an Arrhenius type plot related to the kinetic constants of ethylene glycol propoxylation is reported.In the same plot are also reported the kinetic constant respectively obtained for the reaction of propylene oxide with respectively 1-and 2-octanol.As it can be seen,also in this case the kinetic constants have comparable values confirming that the activity is strongly affected by the type of hydroxyls but poorly by the chain length.

10.Ethoxylation–Propoxylation Reactors

Fig.16.Arrhenius type plot of ethylene glycol propoxylation.Reprinted with permission from[10]Copyright(2002)American Chemical Society.

Fig.17.Simplified schemes of the reactors most used in industry in polyalkoxylation processes[18].

In Fig.17,the simplified schemes of the reactors most used in industry in polyalkoxylation processes are reported[18].The first three are the schemes of Semibatch Stirred Tank Reactors(SSTR)mainly employed for small-scale productions.As it can be seen,the three schemes differ only for the adopted heat exchange system.The 4th one,Venturi Loop Reactor(or Buss reactor),was born as hydrogenation reactor,in which hydrogen gas was sucked by the Venturi tube.It has been then adapted to alkoxylation,but EO and PO are sucked as liquid into the Venturi tube and there vaporize with an exceptional increase of volume.This gas is pressurized into the mixer and gives place to a high gas–liquid interface area inside the reactor.Therefore,this reactor can be considered as a well-mixed gas–liquid reactor and treated with models similar to the already seen isothermal laboratory reactors[15].The only problem of this reactor is the project of the Venturi tube suitable for this specific application[16].

In all the described reactors,for favoring EO or PO mass transfer,the gas is bubbled into the liquid phase.On the contrary,the Spray Tower Loop Reactors(or Pressindustria-Scientific Design reactors)are singular,because in these reactors the liquid is sprayed in an atmosphere of gaseous EO or PO,that is,the liquid is the dispersed phase[17–20].Recently,Desmet-Ballestra launched a Hybrid Spray-Venturi Loop Reactor that coupled the advantages of the Venturi Loop Reactor with those of the Spray Tower Loop Reactor.

11.Modeling of the Spray Tower Loop Reactor(STLR)

In Fig.18,a Spray Tower Loop Reactor is sketched.There are two distinct zones of the reactor:the mass transfer zone and the reaction zone.In the mass transfer zone,the gaseous reagent diffuses into the fine droplets emerging from the spray nozzles.Then,the droplets,more or less saturated with EO or PO,arrive on the top of the liquid pool and start to react.Passing from the top to the bottom of the liquid phase bulk the EO/PO concentration is reduced as a consequence of the reaction according to a Plug Flow pattern.In the meantime,the temperature increases from the top to the bottom due to the reaction heat released.Passing the liquid phase through the external heat exchanger the desired reaction temperature is restored.In optimal conditions,the droplets are completely saturated and contain EO or PO corresponding to their solubility at the reaction temperature.

The saturation level of the drops can be evaluated with a rigorous approach to calculate the average alkylene oxide concentrationat the end of the drop flight by solving the following differential equation:

Fig.18.The scheme of a Spray Loop Reactor with the magnification of the sprayed liquid drops.

w here t corresponds to flight time of the drops going from 0 to the average flight time tfm.To make the integration we have to know:(i)the equilibrium solubility of AO();(ii)the average specific surface of the drops(alm),(iii)the average flight time(tfm),(iv)the average liquid side mass transfer coefficient(klm)and(v)the AO concentration in the recirculated sprayed liquid entering into the spray nozzle().The parameter klmand almare estimated with the methods described later in the text.The EO consumption during the absorption into the drops is negligible because the flight time is very small if compared with the residence time of the liquid pool.

The drops,more or less saturated with AO,fall on the liquid surface forming alayer that begins to react and moves to ward the bottom of the reactor.The AO concentration along the liquid column can be calculated together with the temperature profile,by assuming the approximation of a plug- flow behavior and by integrating the equation of mass and heat balance from the top of the liquid column(z=0)to the bottom(z=hL).The assumption of a plug flow-like behavior is justified by the observation that the increase of the temperature from the top to the bottom is in agreement with the extent of AO conversion per passage and by the observation that by increasing the residence time of the liquid inside the reactor the difference increases.Then,by assuming a pseudo steady-state condition for the mentioned profiles,the mass and the heat balance can be expressed with the following ordinary differential equations:

The integration of this system of equations can be made by considering the liquid column divided into N vertical slides that are integrated as standalone reactors keeping boundary conditions between them.This procedure of discretization is useful for increasing the accuracy of the calculations.The advantage is that the integration duration to have the new concentration and temperature profile is N time lower.In particular,also the gas-phase behavior can be updated after a time equal to 1/N the value of the residence time.This feature has shown improvement especially during fast transients and instability condition simulation.Normally values of N=10 or 20 are enough for obtaining satisfactory results.

For working in optimal conditions it is necessary:

1)To know for a given spray nozzle how fast is the EO/PO mass transfer rate,that is,what is the degree of saturation of the droplets falling on the liquid column.

2)To evaluate the optimal residence time of the liquid inside the reactor on the basis of the conversion per pass.

3)To know what is the temperature profile inside the liquid column.

As we have no information about the performances of the in-line spray nozzles,we have studied this specific problem for answering to the question:how much saturated are the drops falling on the liquid column?For studying all these aspects as pray tower loop laboratory reactor schemed in Fig.19 have been developed.As it can be seen,in the reactor there is only one spray nozzle inserted in a cylindrical reactor of well-known geometry.A recirculation pump and a heat exchanger allow control over the reaction temperature.

This reactor has been employed for studying and comparing:

(i)the absorption of CO2in an alkaline solution.

(ii)the absorption of ethyleneoxidein dodecanol,containing KOHas catalyst.

The scope is to compare the rates of these two reactions whose kinetics are quite different but well-know n,to establish the performance of the spray nozzle in saturating the droplets.The reaction of CO2is an extremely fast reaction,normally occurring inside the boundary liquid film and characterized by the presence of an enhancement factor greater than one,while polyethoxylation is a relatively slow reaction,occurring in the liquid bulk,which enhancement factor is equal to about 1.We have experimentally determined, first of all,the droplets size distribution by employing a Laser Scattering technique and feeding water at the spray nozzle(see Fig.20).In this way,we evaluated the Sauter Mean Diameter of the drops.

The Sauter mean diameter obtained by using water was then corrected for obtaining the corresponding value for the starter dodecanol,then from the Sauter diameter we determined the specific surface area and hence the overall surface area of the flying drops.Then,we examined the geometry of the system[17,20]to evaluate both the average flight time and the average path length of the drops before the impact on the liquid surface or on the walls of the reactor(see Fig.21).

Fig.19.Scheme of a Laboratory Spray Tower Loop Reactor.Reprinted with permission from[19]Copyright(2000)American Chemical Society.

The motion of the drops had been considered uniformly accelerated with a speed determined by integrating the following equation:considering both the effect of the gravity and that of afriction coefficient CDfunction of the Reynolds number.vois the initial drops velocity corresponding to:

Fig.20.Determination of drop size distribution with a Laser Scattering Technique and evaluation of theaverage Sauter diameter d32.Reprinted with permission from[19]Copyright(2000)American Chemical Society.

Fig.21.Determination of the Average Path Length of the drops on the basis of geometrical aspects.Reprinted with permission from[20]Copyright(2005)American Chemical Society.

The length of the path has been calculated on the basis of geometrical aspects as the distance of the liquid level,the angle α of the spray cone of drops and the reactor diameter.

The problem of a gas diffusion in a spherical drop has already been treated in the literature:one case considering the drop internally well-mixed[21],and another case considering the drop internally stagnant[22,23].The mathematical description is summarized in Fig.22.

Both the proposed models have been tested to describe respectively the absorption of CO2in water and in an alkaline solution and the adsorption of EO in dodecanol+KOH catalyst.In Fig.23 some results obtained for the physical absorption of CO2in water are reported.In the first plot are shown some calculations to evaluate how the drop saturation occurs along the time by respectively assuming that the drop is either well-mixed or stagnant.In the same plot,is reported also an estimation of the drop speed during their flight.As can be seen,the drop life is of the order of some milliseconds.In the second plots,the simulations of two performed experimental run as examples.As is seen the simulation is satisfactory if we consider the drops internally well-mixed,while the agreement for the stagnant model ispoor.In conclusion,the drops emerging from the spray nozzles are internally turbulent.

Let us consider now the behavior of CO2absorption in a sprayed alkaline solution.As previously mentioned,the reaction of CO2with NaOH solution has been largely studied by many different researchers[23–25],but nobody studied this reaction in a spray tower loop reactor.The CO2absorption in this case is the consequence of the two extremely fast reactions:

Fig.22.The problem of gas diffusion in a spherical drop and the solutions in the literature.

Fig.23.Kinetics of physical absorption of CO2 in water.Comparison of the models with drops stagnant and internally well-mixed.Reprinted with permission from[19]Copyright(2000)American Chemical Society.

The kinetic law for the overall absorption is of the second order,while the mass transfer rate can be expressed as reported in the following expression containing the enhancement factor E:

In Fig.24 the collected experimental points and the calculated simulation line by assuming the drops well-mixed are reported.In the same plot for comparison,is also reported the physical absorption of CO2in water,that is,absorption in the absence of the reaction.

Fig.24.Kinetics of CO2 absorption in an alkaline solution.Reprinted with permission from[19]Copyright(2000)American Chemical Society.

As it can be seen,the effect of the reaction on the mass transfer rate is dramatic.For describing correctly the experimental curves we have introduced an enhancement factor correlation that is a function of both the alkalinity of the solution and of the CO2solubility:

For physical absorption in water E=1.

Some ethoxylation runs have been performed in a Pilot Spray Tower Loop Reactor by using dodecanol and nonylphenol respectively as starters.The runs,reported in Fig.25 have been interpreted with the already described kinetic model by using the parameters found as the best for these reactions.Again,we have considered the drops either well mixed or stagnant.As it can be seen,the best agreement has been obtained by considering the drops internally well mixed in both cases.In the same slide are also reported,as example,the simulations of the evolution of the EO pressure in the reactor and of the temperature measured at the bottom of the liquid column.As can be seen,the agreement of the kinetic model is excellent.

The same kinetic model has then been used also for simulating an industrial reactor running.The reaction in industrial reactors is characterized by three different periods that we can call:(1)Peaking;(2)Reacting and(3)Cooking.Peaking corresponds to the feeding of a small pulse of EO and has the scope to check the functionality of the reactor.As a matter of fact during the peaking(C8:Which is correct:peaking,or picking?)period the pressure increases after the EO pulse addition and then decreases as a consequence of the EO reaction.Then,EO is fed with a constant flow rate until the amount of the corresponding number of adducts desired is reached.At this point starts the cooking period in which all the EO accumulated in the reactor must be eliminated by the reaction.All the mentioned operations have been successfully simulated with the described model and also the temperatures,measured at the bottom of the liquid column,are well- fitted,too.A correct simulation of the EO concentration respectively at the head and at the bottom of the liquid column is very important for safety purpose having the scope to estimate what is the accumulation of ethylene oxide inside the reactor.

12.Conclusions

The kinetics of ethoxylation and propoxylation have been studied by using many different starters.Ethoxylation and propoxylation have been classified as relatively slow gas–liquid reactions with a Hatta Number?1.As a consequence,the two films theory can be applied for interpreting mass transfer rates.Venturi Loop Reactors(VLR)are characterized by a dispersion of the gas(EO and/or PO)into the liquid and mass transfer occurs together with the reaction.The kinetic behavior of this reactor is similar to the one of well-mixed semibatch reactors.

A rigorous mathematical model has been developed to simulate the Spray Tower Loop Reactors for determining:

(i)The degree of saturation of the drops;

(ii)The amount of reaction occurring inside the liquid column;

(iii)The change of temperature along the liquid column.

The model has shown that with efficient spray nozzles the drops are completely saturated at the end of their flight.This allows to greatly simplify the mathematical model.The developed model has amoregeneral use because can be applied also to the modeling of spray tower absorber.

Nomenclature

AiPre-exponential factor of the initiation reaction,cm3·mol?1·s?1

[AO] Concentration of the alkylene oxide in the liquid phase,mol·cm?3

ApPre-exponential factor of the propagation reaction,cm3·mol?1·s?1

aLor almAverage specific interfacial surface area of drops,cm2·cm?3

atTotal interfacial surface area of flying drops,cm2

B° Catalyst concentration,mol·cm?3

CAOBulk AO concentration,mol·cm?3

CDFriction coefficient

CpLiquid specific heat,J·g?1·°C?1

DEOEO diffusion coefficient,cm2·s?1

D32Sauter diameter,cm

diDiameter of i fraction drops,cm

E Enhancement factor

g Gravity acceleration,cm2·s?2

J Gas–liquid mass transfer rate,mol·cm?3·s?1

KeEquilibrium constants of the proton exchange reaction

kiConstant rate of initiation,cm3·mol?1·s?1

kLklm=Average mass transfer gas–liquid coefficient,cm·s?1

kpConstant rate of propagation,cm3·mol?1·s?1

nAOAverage number of alkylene oxide units for starter molecule

niNumber of drops with diameter di

P Total gaseous pressure,MPa

QlLiquid re-circulation rate,cm3·s?1

Re Reynold Number(D32vρ /μ)

[RXH°] Initial starter concentration,mol·cm?3

[RXH] Starter concentration,mol·cm?3

[RX?M+]Concentration of the ionic form of the starter,mol·cm?3

[RX(AO)iH]Oligomer concentration with i adducts of AO in the chain,mol·cm?3

[RX(AO)i?M+]Concentration of the ionic form of the oligomer concentration with i adducts of AOin the chain,mol·cm?3

r Reactor radius,cm

rAORate of substrate consumption in spray tower loop reactor,mol·cm?3·s?1

riRate of oligomer “i” formation or consumption,mol·cm?3·s?1

roRate of substrate consumption in semibatch conditions,mol·cm?3·s?1

Sc Schmidt Number(μ/ρ DA)

Sh Sherwood Number(kLD32/DA)

T Temperature,K

t Time,s

tfmAverage flight time,s

VLLiquid volume,cm3

v Drops velocity,cm·s?1

v0Initial drops velocity,cm·s?1

We Weber Number(v2ρ D32/σ)

x Flying pathway,cm

xAOAO liquid phase molar fraction

xmAverage path of sprayed drops,cm

yAOAO gas phase molar fraction

z Spray tower loop reactor length,cm

α Spray cone width angle

βLkLaL=Overall gas liquid mass transfer coefficient,s?1

γAOAO activity coefficient in liquid phase

ΔH Reaction enthalpy change,kJ·mol?1

ΔEiActivation energy of the initiation reaction,kJ·mol?1

ΔEpActivation energy of the propagation reaction,kJ·mol?1

ΔP Pressure drop of the liquid through the nozzle,MPa

μGGas viscosity,Pa·s?1

μLLiquid viscosity,g·cm?1·s?1

ρ or ρLLiquid density,g·cm?3

ρGGas density

σ Surface tension,g·s?2

φ Spray efficiency factor(dimensionless)

Acknowledgments

Thanks are due to the valuable help of all the students of Master Degree that worked on the topic.Thanks are due to Pressindustria,Scientific Design and Desmet Ballestra for the financial support to the researches described in this work.