GasLiquid and GasLiquidSolid Reactions Performed in Spray Tower

Ind. Eng. Chem. Res. 2005, 44, 9461-9472

9461

Gas-Liquid and Gas-Liquid-Solid Reactions Performed in Spray Tower Loop Reactors Elio Santacesaria,* Martino Di Serio, and Riccardo Tesser Dipartimento di Chimica, Universita` di Napoli, Via Cinthia, Complesso Universitario di Monte S. Angelo, 80126, Napoli, Italy

The behavior of spray tower loop reactors has been examined in details, also by reviewing previous works, with the aim of suggesting useful criteria for the design and simulation of these devices. Different possible situations have been considered and quantitatively interpreted. For gas-liquid systems, for example, physical absorption in the absence of a reaction, absorption with a moderately fast reaction, and absorption with an extremely fast reaction have been studied. Moreover, an attempt to extend the use of spray tower loop reactors to a gas-liquidsolid system has been made with satisfactory results. Introduction Spray tower loop reactors (STLR) are normally composed of two different sections: one characterized by the liquid dispersed phase and another one by a liquid pool collected at the bottom of the reactor. As will be seen, different reactor schemes can be adopted according to the characteristics of the occurring reaction. However, it is important to point out that in this type of gasliquid device the liquid phase is dispersed into the gaseous one instead of the opposite occurring in more conventional systems such as a bubble column or mechanically agitated reactors. STLR are largely used in industry to eliminate pollutants from gaseous streams.1 These reactors can advantageously be used also when dealing with highly exothermic and relatively fast gas-liquid reactions, that is, when mass-transfer limitation could be important. Among the reactions currently performed in industry with this type of reactor, it is worth remembering ethoxylation and propoxylation, used in the production of nonionic surfactants.2,3 The extension of the use of these reactors to other gas-liquid reactions, such as, for example, chlorination, alkylation, and sulfonation, could be possible and in some cases advantageous. It is possible then to extend the use of STLR also to some reactions normally performed in gas-liquid-solid reactors. However, despite some interesting features of the STLR, ethoxylation and propoxylation are the unique examples of industrial application of this type of reactor. One of the main advantages in the use of the STLR in ethoxylation and propoxylation reactions is that gasliquid mass transfer occurs in a separated and confined zone of the reactor, independently of the reaction, which occurs in the liquid phase. A comparison among the performances, respectively obtained in STLR and wellmixed reactors of different size, has recently been reported in the literature.4 It is opportune to point out that well-stirred gasliquid systems have largely been studied,5-7 especially for what concerns mass-transfer behavior. Many papers have also been published on the spray nozzle performances.1 On the contrary, the spray tower loop reactors * To whom correspondence should be addressed. E-mail: [email protected].

have not been studied enough.2,3 In particular, modeling, managing, and optimization of these reactors are lacking. However, in previous works,7-9 it has been demonstrated that the mass transfer is very fast in the small droplets formed at the outlet of a spray nozzle; this results in a reduced volume of the reactor for reaching liquid saturation. This suggests the possibility of usefully extending the use of the STLR to many other gas-liquid and gas-liquid-solid reaction systems, provided that two conditions are respected, that is, (i) the solubility of the gaseous reagent must be high enough for a significant occurrence of the reaction and (ii) the viscosity of the liquid must be sufficiently low in order to have an efficient spraying operation. In the present work, the key factors affecting the performances of these reactors in both gas-liquid and gas-liquidsolid reactions are examined and discussed. For example, when the reaction is very fast, as in the case of the chemical absorption of CO2 in an alkaline aqueous solution, mass transfer and chemical reaction occur together in the drops and an enhancing effect of the reaction on the mass-transfer rate is consequently observed. On the contrary, when the reaction is slower, as for example in the case of the already mentioned ethoxylation, the reaction in the drops can be neglected and two independent zones of the reactor in which mass transfer and reaction occur separately can be recognized. Therefore, modeling, managing, and optimization of a STLR for a gas-liquid system will depend on the rate of the reaction, because the reaction will occur completely, partly, or negligibly inside the drops during their flight. When a solid catalyst is required by the reaction, four different zones of the reactor can be recognized: (i) where gas-liquid mass transfer occurs, (ii) where the liquid containing the dissolved gaseous reagent is accumulated in a reservoir, (iii) where the reaction occurs at the liquid-solid interphase, and (iiii) the heat exchanger for the thermal control on the recirculating liquid. Therefore, for modeling STLR it is necessary to define the following: the geometrical characteristics of the flying drops system, the fluiddynamic behavior of the single drop, the overall masstransfer effect, the kinetics of the reaction, and the heat exchange associated with the phenomena occurring inside and outside the reactor.

10.1021/ie050222b CCC: $30.25 © 2005 American Chemical Society Published on Web 07/09/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005

First, in the present work, the absorption of CO2 in both water and an alkaline solution of NaOH, sprayed in a nozzle of known characteristics, will be described. This completes a previous work by Srinivasan and Aiken,10 which studied the absorption of CO2 in sprayed water concluding that, normally, drops are internally well mixed and mass transfer is consequently very fast. This observation was confirmed by using successfully an equation given by those authors for the description of the mass transfer of ethylene oxide in the ethoxylation reactors. The absorption of CO2 in an alkaline solution shows enhanced mass-transfer rates, as a consequence of the instantaneous chemical reaction. The enhancement factor was correlated to the ratio [OH-]b/ CiCO2 by using a semiempirical correlation. [OH-]b is the bulk concentration of OH- while CiCO2 is the interfacial concentration of CO2. In this work, the two limit cases of the absorption in the presence of the very fast reaction of CO2 with alkaline aqueous solution and of absorption in the presence of a relatively slow reaction, such as ethylene oxide reacting with a fatty alcohol, will be compared. Moreover, when a solid catalyst is used, since the reaction occurs only at the liquid-solid interphase, gasliquid mass transfer can be treated as in the case of physical absorption and gas-liquid slow reaction; in fact, independently of the kinetics, in this case no reaction takes place in the drops. The alkylation of p-cresol with isobutene, catalyzed by acid exchange resins, performed in a STLR will be considered as an example of gas-liquid-solid reactions.11 The relation existing between kinetics and mass transfer in the different zones of the STLR will be examined and discussed also by reviewing what has been published in the past. At last, suggestions for the most suitable criteria that should be used in the design of the STLR will be given. Gas-Liquid Reactions in STRL. Theoretical Background. Gas-liquid reactions have been classified by different authors5-7,12-15 according to their rates, that is, instantaneous, fast, relatively slow, and very slow. To individuate the class of a reaction, it is necessary to compare the observed reaction rates with physical masstransfer rates. As a matter of fact, when the reaction rate is very fast, mass transfer is strongly accelerated. This effect can be quantified through the introduction of the dimensionless parameter the enhancement factor corresponding to E) (absorption rate in the presence of a chemical reaction)/ (the maximum physical absorption rate in the absence of reaction) (CGRl ) 0) (1)

A quantitative approach for the description of a gasliquid well-mixed reactor requires the solution of the following mass balance equations for a generic secondorder reaction of the type A + zB f P,7 where A is the gaseous reagent:

DA(d2CA/dx2) - k2CACB ) 0

(2)

DB(d2CB/dx2) - zk2CACB ) 0

(3)

With the boundary conditions

CA ) CA* ) pA/H (Henry law)

x)0

dCB )0 dx

x)0

CB ) CBl

x ) δL

- DA

( ) dCA dx

x)δL

) k2CACB

{

(1 - g) - δL a

}

(4)

x ) δL

The last boundary condition takes into account the fact that the reaction partially occurs also in the liquid film of depth δL. The solution of the mass balance equation can be obtained only by using a numerical method. For this purpose, it is convenient to introduce into the relationships three dimensionless factors:

Ha ) ZD )

(DAk2CBl)1/2 kL

( )( ) ( )( )

DB CBl )E-1 zDA CA*

M)

1 - g kL a DA

(5)

(6)

(7)

A general solution for these equations is given by Charpentier7 in a plot reporting ZD (a parameter strictly correlated with the enhancement factor El) as a function of the Hatta number Ha. As can be seen, the main factors that must be considered in order to describe gas-liquid well-mixed reactors are as follows: the kinetic law and related parameters, the mass-transfer coefficients, and the gas-liquid interphase area. For fast reactions, stirring is very important because it favors the formation and dispersion of small bubbles of gas by increasing the gas-liquid interphase area. Therefore, bubble columns are, normally, less efficient for the difficulty of obtaining a high interphase area. Many gas-liquid reactions have been studied in well-mixed semibatch or continuous reactors, and Levenspiel and Godfrey12 suggested a method for individuating the kinetic regime of a reaction by using a continuous laboratory reactor. When a gas-liquid reaction is performed in a STLR the situation is quite different. Liquid is forced to pass at a high rate through a spray nozzle. At the outlet of the spray nozzle, a very short and thin liquid sheet is initially formed, and then it rapidly breaks into very small droplets.16,17 The sheet area depends on the type of spray nozzle used, and it is often very low. In any case, the liquid phase is highly dispersed in the gaseous atmosphere and mass transfer mainly occurs at the boundary layer around the small droplets formed by the spray nozzle, although a contribution to the mass transfer could also be given by the liquid sheet emerging from the spray nozzle17 and, to a lesser extent, by the liquid falling film formed on the wall of the reactor, as a consequence of the splashing drops, and by the surface of the liquid pool. However, when the contribution of the liquid sheet is significant, this should be taken into account. Yeh and Rochelle17 have recently suggested the way to calculate the mass-transfer coefficient kL in the liquid sheet emerging from a spray nozzle. Therefore, in STLR used in gas-liquid systems, three different possible situations can be identified: (i) only

Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9463

The relationships suggested by Snirivasan and Aiken10 have been derived by examining many experimental data. However, we have recently compared three different models, the one suggested by Srinivasan and Aiken,10 considering the drops internally well mixed and two others considering the drops internally stagnant.19,20 The gas diffusion in a stagnant spherical drop can be calculated, for example, with the approach suggested by Crank20 based on the molecular transport theory, by integrating the following equation:

[

]

∂CrGR ∂2CrGR 2 ∂CrGR ) DGR + ∂t rd ∂rd ∂rd2

Figure 1. Picture of internally well-mixed droplets formed at the outlet of a spray nozzle according to the model suggested by Snirivasan and Aiken.10

physical absorption occurs in the absence of a chemical reaction; (ii) absorption occurs in the presence of a moderately fast reaction not affecting mass-transfer rate (enhancement factor ∼1); (iii) absorption occurs in the presence of an extremely fast reaction (enhancement factor greater than 1). In the first case, drops will be more or less saturated during their flight according to the efficiency of the spray nozzle and the size of the reactor. In the second case, the flight time is very short with respect to the reaction time; therefore, the reaction occurs only for a negligible amount inside the drops. Thus, in this case, mass transfer and chemical reaction take place in two different zones of the reactor that must be considered separately. Mass transfer occurs almost exclusively during the drops flight, while chemical reaction takes place almost exclusively in the liquid bulk. At last, when absorption of the gaseous reagent occurs in the presence of an extremely fast reaction, chemical reaction occurring inside the drops cannot be neglected. The reaction takes place in the drops together with the mass transfer and can also affect more or less the mass-transfer rate (enhancement factor >1). It has been shown by different authors8,10 that droplets formed at the outlet of an efficient spray nozzle are internally well mixed and mass transfer at the boundary is, therefore, very fast despite the short average flight times of the drops. The mass-transfer coefficient for a small droplet can be calculated by using the relation proposed by Srinivasan and Aiken:10

Sh ) 0.16(Sc)1/2(We)1/2(Re)5/16

(8)

and hence o

kL

( )(

DGR0,16 µL ) DS FLDGR

1/2

)( )

v2FLDS σ

1/2

DSvFL µL

5/16

(9)

The approach of Srinivasan and Aiken10 is based on the Levich theory,18 considering two different zones inside the drop, one near to the free surface of small thickness δ1 in which mass transfer occurs only by molecular diffusion and another larger zone of thickness δ2 . δ1 in which the mass transfer occurs for the whirling motion, as schematized in Figure 1.

(10)

Crank reported an analytical solution of this equation giving the evolution of the internal profile of the gas concentration with time (eq 11) and also the mean adsorbed concentration at the end of the flight time20 (eq 12):

CrGR - CBGR

)

C/GR - CBGR 1+

DS

∞

∑

(- 1) sin

trd n)1 n

CTGR - CBGR C/GR - CBGR

)1-

6

∞

∑

2nrdπ DS 1

π2n)1 n2

(

exp -

(

exp -

) )

4DGRn2π2t D2S

4DGRn2π2tflight D2S

(11)

(12)

Another approach, based on the classical liquid film theory, is the one suggested by Johnson et al.19 for stagnant drops falling in a continuous phase, which allows the calculation of the mass-transfer coefficient kL as

kL ) -

[

]

2πxDGRtflight DS ln 1 tfm DS

(13)

Geometrical and Fluid Dynamic Properties of the Drops System. Drops emerging from a spray nozzle normally have diameters of different sizes. The size distribution can experimentally be determined by using a laser scattering technique. From the distribution, a mean diameter can be calculated. The given distribution is normally determined in a small volume of the spray cone, but this distribution does not change very much by changing the position of the volume sample. This means that coalescence, normally, has a small effect on the drop size distribution. Different types of averages can be made, but Sauter diameter D32 is the most convenient, because the interphase area of a drop (surface/volume) with a given Sauter diameter is coincident with the overall interphase area. At this purpose we can write

DS ) D32 )

∑i nidi3/∑i nidi2 ) Sauter diameter

(14)

The Sauter diameter, normally, obtained for water can be converted in the Sauter diameter of other sprayed liquids by using the following relation reported by Perry and Green:21

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D32 (D32)water

)

( )( )( ) σ 73

0.5

µL 0.1

0.2

0.3

1.0 FL

(15)

The Sauter diameter can be used to calculate the overall surface area of the flying drops:

aG ) 6Qtflight/D32

(16)

and can be assumed as average drop diameter in the calculation of the average flight time, flight path, and kL, too. The Sauter diameter of the drops obtained with the spray nozzle used in this work was for water D32 ) 136.3 µm evaluated for a water flow rate of 1.18 L/min. Some geometrical parameters of the spray nozzles are, normally, furnished by the supplier, corresponding to the form of droplets cone (full cone or hollow cone), as well as the cone width angle (R ) 60°, 90°, 120°). A drop falling into a cylindrical tower can impact both on the free liquid surface and over the internal walls of the reactor. The average flight time is a function of the initial drop velocity and of the average path of the drops (xm). The average path of the sprayed drops, for a cylindrical reactor depends on the following: the distance of the liquid level from the spray (h*); the angle of cone of drops (R); the radius of the reactor (r). By assuming that all the possible paths have the same probability to occur, in a simplified approach, the following general relation can be obtained:

xm ) xr2m + h2m

(17)

with

rm ) r +

[

|h* - r - h°| - (h* - r - h°) 2(h° + r - h*)

)

]

(

)

|h* - h°| - (h* - h°) h* R (18) tan 2 2 2(h° - h*) hm ) h* + |h° + r - h*| - (h° + r - h*) h* + r + h° - h* 2 2(h* - h° - r) (19)

[(

)

]

where

h° )

r tan

; R 2

h* ) h - hL

(20)

All the mentioned geometrical quantities are reported in the scheme of Figure 2. A more rigorous approach, based on the use of a Monte Carlo method, for calculating the average free path of the drops has been described in detail by Dimiccoli et al.8 Change in the drop speed and the drop flight path can be calculated by integrating the following equation derived from the balance of forces acting on the flying droplets:

[

]

(FL - FG) dx 2 FG dx )t g - 3CD + v0 ) v dt FL dt FLDS

( )

where, v0 is the initial drops velocity corresponding to

x

v0. ) φ

(∆P)nozzle × 2 FL

(22)

A coefficient of form CD is calculated by successive approximations being a function of the Reynolds number (Re ) DSνFL/µL), which, in turn, depends on the drop speed (v) that we are estimating. The relation between CD and Re, for a spherical particle falling across a fluid under the influence of an outside force, can be evaluated from data reported by Brown,22 and the following correlation can be obtained:

log(CD) ) 1.355 - 0.806 log(Re) + 0.0817[log(Re)]2 (23)

|h° - h*| - (h° - h*) h* + r - h° -r + 2 2(h* - h°)

(

Figure 2. Geometrical aspects of the spray tower loop reactors.

(21)

The v0 expression is the Bernoulli equation applied between inlet and outlet of the nozzle:

1 1 F v 2 + FLgzIN + PIN ) FLvOUT2 + FLgzOUT + POUT 2 L IN 2 (24) with zIN ) zOUT and vIN2 , vOUT2. A particular solution is of interest, where x (t) ) xm (mean flight path of the drop); the correspondent time (t) is the average flight time (tflight). Mass-Transfer Rates for Gas-Liquid Physical Absorption in the Absence of Chemical Reaction. The models respectively suggested by Snirivasan and Aiken10 for well-mixed drops and by Johnson19 and Crank20 for stagnant drops have been tested, first, in the absorption of CO2 in water, that is, a physical absorption in the absence of chemical reaction. Many experimental runs have been performed in a laboratory STLR absorber. Experimental details are reported elsewhere.8 The runs performed have been simulated by integrating the following mass balance equation from time t ) 0 to t ) mean flight time (internal integration):

dnGCO2 dt

)

kLaG (V Ci - nGCO2) VG G CO2

(25)

Internal integration must be repeated up to the overall process time, that is, until the experimental run is


Figure 3. Example of CO2 absorption simulation. Run performed at 17 °C, PCO2 ) 2.33 bar, PN2 ) 1 bar, liquid volume 1.77 L, h ) 26.6 cm, h - hL)12.4 cm, reactor volume 4 L. A comparison between the models of Snirivasan and Aiken10 and that of Crank.20

Figure 4. Saturation degree of the drop during the flight obtained by calculation for a run of CO2 absorption in water, pCO2 ) 4 bar, T ) 17°C.

stopped (outside integration). Mass-transfer parameters change during the drop flight and must be continuously updated. Drops fall into the liquid pool with a CO2 concentration greater than the one present in the liquid column. Since in these experiments droplets impact on the free liquid surface with high speed, and considering that the liquid level in the reactor is relatively low (less than 15 cm) and liquid recirculation rate is relatively high, we have assumed, for the calculations, the liquid well mixed. Consequently, the reactor outlet concentration will be considered equal to that present, at the same time, in each point of the liquid bulk mass, and it will be updated after any flight time, during the integration. The integration of eq 25 requires the knowledge of kL, aG, and CO2 solubilities. kL and aG can be calculated as described before, while CO2 solubility can be estimated from data reported in the literature.8,23 The Johnson19 and Crank models20 both failed in simulating the experimental runs, as can be appreciated in the example of simulation reported in Figure 3. The model suggested by Snirivasan and Aiken10 performed well, as can be appreciated always in the example of Figure 3, confirming the reliability of the model. It is interesting to observe, as demonstrated in a previous work, that a concentration near to droplet saturation is reached in few milliseconds (4-6 ms) (see Figure 4). The speed of the drops decreases by a factor of 5 during the flight time, that is, from 25 to 5m/s as

Figure 5. Change of the drop speed during the flight.

shown in Figure 5. On the basis of these findings, we can conclude that when a spray nozzle is efficient in producing very small droplets, the gas-liquid masstransfer rate in absorption is very fast. However, a critical value of the mean flight path (in our case 1012 cm) of the drops is necessary in order to achieve satisfactory drop saturation. It is very important to know, for a given spray nozzle, this critical value for optimizing the size of the mass-transfer zone of the absorber. It is also important to select the more suitable type of spray nozzle to be used and to decide how many spray nozzles must be put in a reactor and where. These last aspects will be discussed in a later session. Behavior of Moderately Fast Reactions in STRL. As mentioned, when a moderately fast reaction (Hatta number =1), not affecting mass-transfer rate, is performed in a STLR, the reaction occurs almost exclusively in the liquid bulk and we can recognize two different zones of the reactor, the zone in which gas-liquid mass transfer occurs and another one in which the reaction occurs as schematized in Figure 6. The droplets, saturated with the gaseous reagent, fall on the liquid surface forming a layer that begins to react moving toward the bottom of the reactor. The gaseous reagent concentration profile, along the liquid column, can be calculated together with the temperature profile, by assuming as a first approximation, a plug-flow behavior, considering the high height/diameter ratio adopted in these reactors. These profiles were calculated by integrating the equation of mass and heat balance from the top of the liquid column (z ) 0) to the bottom (z ) hL). Besides, 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:

{

dCGR 4πr2 )r dz Q GR d(FLCPT) dCGR ) ∆H dz dz

(26)

Integration of this system of equations can be made by considering the liquid column divided in N finite elements of equal volume. This procedure of discretization is necessary for increasing the accuracy of the calculations considering that, for a discretization step with N ) 1, the gas-phase behavior can be updated only after

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Figure 6. Scheme of a spray tower loop reactor in which a moderately fast reaction occurs. Drop magnification and evolution with time of internal profiles of gaseous reagent concentration for, respectively, a stagnant and an internally well-mixed drop.

a time equal to the liquid residence time; otherwise, this time becomes 1/N the value of the residence time and the integration is more precise. The integration is obviously possible only if the reaction kinetics is well known, as it occurs, for example, in the case of ethoxylation reactions.24-26 When the reaction is strongly exothermic, as for ethoxylation and propoxylation, the temperature increases, while, the reagent concentration CGR decreases from the top to the bottom of the liquid column, as shown in Figure 6. The effect of temperature on the gas solubility has also been considered in the model. Temperature was measured at the outlet of the reactor and was in good agreement with the calculations. Liquid volume and composition are considered constant during the integration and are updated at the end of each integration step, solving the related mass balance equations. The temperature is adjusted to the desired level by the heat exchanger on the recirculating loop. Heat consumption for the eventual vaporization of the gaseous reagent must be calculated, too. The described model has been satisfactorily tested on both a pilot and different industrial spray loop reactors for different ethoxylation reactions. The mass-transfer model suggested by Snirivasan and Aiken,10 considering liquid drops well stirred, has been used by us also in this case for predicting the ethylene oxide absorption rate with very satisfactory results. The overall model is able to describe the evolution with time of, respectively, the ethylene oxide consumption, the organic substrate conversion, the distribution of the formed ethoxylated oligomers, the ethylene oxide concentration, and the temperature at the bottom of the reactor. Details on the kinetics of the ethoxylation reactions are reported in previous works24-26 as well as the performances of the used STLR industrial reactors.4,8 Absorption in the Presence of an Extremely Fast Reaction Affecting the Mass-Transfer Rate in a STLR. An example of very fast gas-liquid reaction

is the one occurring between CO2 and NaOH dissolved in water. When CO2 (g) is absorbed in a NaOH aqueous solution, the following reactions occur: K1

CO2 + OH- 798 HCO3K2

OH- + HCO3- 798 CO32- + H2O

(27) (28)

which equilibrium constants, at 20 °C and infinite dilution, are6 K1 ) 6.1 × 107 M-1 and K2 ) 5.9 × 107 M-1. The first reaction is rate-determining step and the rate law for the overall process is5,6

rG ) k1[OH-][CO2]

(29)

Kinetic constant (k1) depends not only on the temperature but also on the ionic strength of the solution, as reported by Danckwerts.5 The reaction takes place exclusively in the liquid phase, and being extremely fast, when the reaction is performed in a STLR, it occurs almost completely inside the flying drops. CO2 diffuses from the gas phase into the liquid one and it can be easily demonstrated that the gas side mass-transfer coefficient is at least 2 orders of magnitude greater than the liquid side one.27 Therefore, this mass-transfer contribution can be neglected. In this case, the reacting system is always in a diffusive regime (Ha . 1), the concentration gradient is very sharp closeness to the reaction plane, and the reaction affects the mass-transfer rate, strongly improving it. The introduction of an enhancement factor is necessary for describing the CO2 absorption rates. The mass balance, for an internally well-mixed drop, on the whole spray system, related to CO2 and OH- species can be written as


-V

d[OH-]b ) 2EkLaGCiCO2 dt

(30)

The described approach seems to be similar to the classical one based on the film theory,5,6 when the gas phase is the dispersed phase, but in the case of spray systems, drops could be smaller than the thickness of the hydrodynamic liquid side film; therefore, none of the relations derived from this theory for calculating the enhancing factor can directly be applied to our case. However, absorption and chemical reaction occur together during the drop flight and since the reaction is very fast, after the flight every drop does not contain CO2; therefore, no reaction occurs in the liquid, collected on the bottom of the reactor. Experimental runs can be interpreted by integrating relation 30, repeating the internal integration from time t ) 0 to t ) mean flight time until the integration total time is equal to the experimental final time (outside integration). Also, in this case, mass-transfer parameters must be continuously updated during the internal integration since it depends on both the instantaneous OH- concentration and the instantaneous drop falling rate, which, in turn, change during the flight. As in the previous case of CO2 physical absorption, the liquid column has been considered well mixed for the same reasons explained before. Integration of eq 30, by considering only the internally well-mixed drop model, requires one to know the following: the interfacial area (aG), the liquid-side masstransfer coefficient (kL), the solubility of CO2 in NaOH aqueous solution, and the enhancement factor (E). aG and kL can be determined as described before. For what concerns CO2 solubility, it must be pointed out that very few data for the CO2-NaOH system are available. Nijsing28 and Astarita6 have suggested the use of an empirical correlation of the type

log

(

CCO2i

CCO2i(in H2O)

)

) - kIIi

(31)

also considering the ionic strength of the solution. kI )1.49 × 10-4 (m3 mol-1). In this way, the evaluation of CO2 solubility in NaOH(aq) is possible when the corresponding data of CO2 solubility in water are known.8,23 The enhancement factor (E) can be experimentally evaluated by comparing the measured absorption rate with the one obtained by calculation for internally wellmixed drops when the enhancement factor is put equal to 1. As it can be seen, in Figure 7 the OH- consumption rate calculated with E ) 1 is much lower than the one experimentally measured. As the Snirivasan and Aiken10 model predicts, for both the physical absorption of CO2 and that of ethylene oxide we attribute the experimentally observed difference to an enhancement phenomenon induced by the instantaneous chemical reaction. On the basis of many experimental results, we derived the following semiempirical correlation for calculating the enhancement factor operating in this particular system:

( )

E)A+B

[OH-]b 2CCO2i

) 3.0 + 0.11

( ) [OH-]b 2CCO2i

(32)

The numerical values of A and B, appearing in the correlation, have been determined by mathematical

Figure 7. Simulation of CO2 absorption in an aqueous solution of NaOH.

regression analysis on the experimental data and probably depend on the type of device used. By following the Levich theory, this behavior can be explained by assuming that the reaction mainly occurs in the liquid diffusion zone of the drops (see Figure 1) along a reaction plane contained inside the layer δ1. CO2 concentration is made zero before reaching the agitated internal side. The reaction plane shifting away from the drop core (i.e., toward the gas-liquid interface) increases the slope of the CO2 profile concentration, enhancing the global rate. We observed that the enhancement increases with the ratio COH-/CCO2. By concluding, with respect to the physical absorption, in which the concentration gradient of the absorbed species is extended in the whole diffusive layer (δ1 in Figure 1 ), in the case of chemical absorption, the layer thickness, in which the gaseous reagent concentration is annulled, is smaller and the mass-transfer coefficient is enhanced for a quantity that is inversely proportional to such thickness. The film thickness in which the reaction plane is shifted, corresponding to a portion of δ1 and leading to the enhancement phenomenon, for the Levich theory has dimensions remarkably lower than the one correspondent to the Lewis film theory, and the behavior is, therefore, different. In the runs performed in the STLR, the enhancement factor changes during a drop flight from about 8 to 6.5. Modeling and Optimization of Gas-Liquid STLR. For modeling a gas-liquid STLR, it is important to define whether a reaction occurs inside the drops together with the mass transfer. Therefore, it is important, as for the well-mixed reactors, to classify the reaction as extremely fast, fast, relatively fast, or slow, by determining, for example, the Hatta number. In the case of a relatively fast reaction (Hatta number =1), occurring exclusively in the liquid bulk, the reactor is characterized by the existence of two distinct zones that must be opportunely designed. In one of these zones, gas-liquid mass transfer occurs and the efficiency of the spray nozzle in dispersing the liquid inside the gaseous atmosphere is fundamental. In the second zone, the reaction occurs inside the liquid bulk recirculating at the spray nozzle. To get the best performances, the spray nozzles require an optimal liquid flow rate, that is normally suggested by the supplier as water flow rate. When the liquid is other than water, its viscosity and surface tension can give place to a poor dispersion. Some preliminary runs in the laboratory are necessary in this case in order to individuate acceptable operative conditions. As the optimal liquid flow rate for a spray nozzle

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Figure 8. Schemes of a STLR suitable for the absorption of the gaseous reagent in the presence of a moderately fast or slow reaction.

is fixed, the number of spray nozzles to be used in a reactor can easily be calculated when the kinetics of the reaction is known, by choosing the most convenient liquid residence time. For example, if the kinetics is independent of the gaseous reagent concentration (zero order), it is convenient to choose a residence time sufficient for consuming all the dissolved gaseous reagent along the flowing liquid column. In contrast, when the reaction order for the gaseous reagent is 1 or greater, it is more convenient to maintain a relatively high recirculation rate to keep the concentration of the gaseous reagent in the liquid phase high, thus consequently keeping the reaction rate high. STLR are particularly useful when the reaction occurs in batch conditions with a strong increase in the liquid volume, as it occurs, for example, in ethoxylation or propoxylation reactions. In this case, by keeping constant the liquid recirculation flow rate, mass transfer occurs in a similar way during the whole reaction, but the liquid residence time, in this case, increases more and more. It is possible to realize a compromise by increasing the liquid recirculating flow rate but involving other spray nozzles not used initially. The location of the spray nozzles and the size and shape of the reactor are also important. With eq 21, it is possible to calculate the mean flight path of the drops emerging from a spray nozzle, and with eq 26 to evaluate the level of saturation achieved during the flight as in the example reported in Figure 4. This allows us to determine the minimum void volume Vmin around a single spray nozzle that is necessary for the gas-liquid mass transfer. It is interesting to observe that for small droplets this volume is relatively small, because mass transfer is very fast for both the physical and chemical absorption in the presence of a moderately fast reaction. If the reactor has different spray nozzles and the location of the spray nozzles does not give place to reciprocal interferences, the reactor volume devoted to the mass transfer VMT could be taken 1.5-2 times the ∑Vmin. In the presence of a moderately fast/slow reaction, we need a long residence time to complete the reaction occurring in the liquid bulk. Therefore, a large portion of the reactor should be filled with the recirculating liquid reagent VL in which the reaction occurs.

Therefore, the volume of the reactor would be simply

VR ) VMT + VL + VE

(33)

where VE is the volume destined to the expansion of the liquid as a consequence of the reaction. The most convenient location of the spray nozzles with a cone angle of 90° could be the one reported in Figure 8, that is, produced drops must fill as much as possible the empty part of the reactor. As has been seen, for absorber and reactor design in the presence of a moderately fast reaction, we need to define by calculation the volume of the reactor that is necessary to the spray nozzles to achieve saturation. This is not strictly necessary for reactor simulation, and a simpler procedure can be adopted by assuming that falling drops are completely saturated at the end of their flight. When this does not occur, we can introduce an efficiency factor of the spray nozzles, changing between 0 and 1, giving the average saturation degree (saturation value × efficiency factor) achieved by the drops at the end of the flight. When the reaction is extremely fast, the masstransfer rate is further increased, as a consequence of the reaction (enhancement effect), this last mainly occurring inside the drops. In this case, it is much more convenient to favor the formation of many droplets in which the reaction occurs and the portion of void volume containing drops would be prominent, while the liquid bulk volume can be reduced as in the scheme of Figure 9. Design and simulation both require, in this case, to know the eventual enhancement factor, and preliminary experimental runs of the type previously described are necessary for this purpose. As we have seen, in STLR, according to the reaction rate the reaction occurs inside the drops (extremely fast reaction) or in the liquid bulk (relatively fast or slow reaction), and these two different limit situations suggest the use of two different geometrical structures for the reactors, as the ones respectively outlined in Figures 8 and 9. The schemes of Figure 8, for example, are particularly useful for ethoxylation and propoxylation reactions. Figure 8 (scheme B) has recently been proposed by Fanelli,29 while the scheme of Figure 9 could


Figure 9. Scheme of a STLR suitable for the absorption of the gaseous reagent in the presence of an extremely fast reaction.

Figure 10. Gradients occurring at the interphases of a conventional slurry reactor.

be useful especially for the abatement of pollutants by chemical absorption. Gas-Liquid-Solid Reactions in STRL. Many papers, reviews, and books have been devoted to gasliquid-solid reactors. Considering a gaseous reagent A, in a well-mixed reactor, containing bubbles, all the gradients of Figure 10 must be considered in order to describe kinetic runs.30,31 Considering a reaction of the type A gas + zB f P and a first-order reaction with respect to the gaseous reagent, at a given temperature and by assuming steady-state conditions, we can write

rG ) reaction rate

(34)

) kgaL(pA - pAi) ) gas-liquid mass transfer rate gas side ) kLaL(pAi/H - CGRL) ) gas-liquid mass transfer rate liquid side ) ksas(CGRL - CGRS) ) mass transfer rate from the bulk liquid to the external surface of the solid catalyst ) ηk1asCGRS internal diffusion + chemical reaction By eliminating the common terms we obtain

rG )

pA H H H 1 + + + kgaL klaL ksas ηk1as

(35)

Normally, the gas-liquid gas side resistance can be

Figure 11. Trend of PA/HAr versus 1/m for different reaction orders in a conventional slurry reactor.

neglected, especially when pure gas is used. Then, by substituting as with 6m/Fpdp, a linear relationship is obtained for PA/HrG against 1/m.

(

)

pA Fpdp 1 1 1 ) + + HrG klal 6m ks ηk1

(36)

where m is mass of catalyst/volume of slurry and H is the Henry constant. The effectiveness factor can be calculated in the usual way through the evaluation of the Thiele modulus.30,31 A deviation from the linear trend of PA/HrG against 1/m, as shown in Figure 11, indicates a reaction order different from 1 and with the exclusion of order 0 and 1, requires a numerical approach to calculate the effectiveness factor.30-31 The use of a STLR for performing a gas-liquid-solid reaction gives place, also in this case, to a different behavior. No paper has been published until now on the subject. We can recognize, first, four different zones of the reactor, as schematized in Figure 12 (scheme A): (1) a gas-liquid mass-transfer zone similar to the one described for absorber and gas-liquid reactors in the presence of moderately fast reactions (Hatta number =1); (2) a reservoir for the recirculating liquid; (3) a catalytic fixed bed where the reaction occurs; (4) a heat exchanger for compensating the effect of the exothermicity or endothermicity of the reaction. A catalyst bed can also be put directly inside the liquid reservoir, as shown in scheme B of Figure 2. This reactor scheme is the one adopted by us for performing the alkylation of p-cresol used as reaction test. It would be possible also to put the catalyst before the liquid

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Figure 12. Typical schemes for gas-liquid-solid spray tower loop reactors.

column collected at the bottom of the reactor, as in scheme C of Figure 2. In this case, the system will work like a trickle bed reactor. As has been seen, the sprayed liquid, dispersed in the gaseous atmosphere, normally is rapidly saturated with the gaseous reagent. We can assume, therefore, as a first approximation, the liquid falling on the free surface of the liquid pool completely saturated. Saturated liquid is collected in the reservoir and then fed to the solid catalyst. The reaction occurs on the solid surface. Only two mass-transfer resistances must be considered, in this case, that is, liquid-solid mass transfer and internal diffusion. Normally, the gas concentration is low if compared with the one of the liquid-phase reagent; this means that the conversion per pass of the liquidphase reagent is relatively low also in the presence of a high conversion of the dissolved gas reagent. As mentioned before, a spray nozzle requires a threshold value of the liquid flow rate to obtain a good dispersion of the liquid. In the meantime, the catalytic bed requires an opportune residence time to consume all or a large part of the gaseous reagent. We have, therefore, for a given reactor, the possibility to change the following: the liquid volume, the liquid recirculation flow rate, the catalyst amount, the section of the catalytic bed, the pressure of the gaseous reagent, and the temperature of the reaction. Despite so many variables, when the liquid recirculation rate is relatively high, conversion per pass is low and the system can be considered as a well-mixed reactor with a high gas-liquid mass-transfer rate not limiting reaction rate. As a matter of fact, in Figure 13, the performances respectively obtained, in similar conditions, with a conventional well-mixed reactor and a STLR in the alkylation of p-cresol with isobutene, promoted by an acid exchange resin catalyst, are compared.11 As can be seen, the p-cresol conversion behaviors are quite similar. In particular, the curves of isobutene consumption are comparable considering the different quantities of p-cresol charged into the reactor, that is, 140 g for the well-mixed reactor and 500 g for the STLR corresponding exactly to the same catalyst concentration of 70 g/kg p-cresol. The observed small differences can, probably, be attributed to different values of the liquid-solid mass-transfer coefficients that are normally lower for catalytic beds, as explained in a recent paper.11 p-Cresol used as a liquid reagent has a relatively high viscosity at low temperatures, and good performances of the reactor, comparable with the ones of a slurry reactor, are obtained only at temperatures higher than 70 °C. The possibility of using a STLR for

Figure 13. Comparison of the performances of a conventional slurry reactor and a gas-liquid-solid STRL operating in similar conditions, that is, T ) 72 °C, PIsobut ) 1 bar, and Ccat ) 70 g/kg. Different amounts of p-cresols have been loaded into the two reactors, 140 g in the slurry reactor and 500 g in the STLR.

performing gas-liquid-solid reactions is particularly attractive with respect to the conventional slurry reactors; avoiding the use of a mechanical stirrer that could represents a drawback when there are safety and leakage problems. The design of the gas-liquid-solid STLR is difficult essentially for the choice of the most convenient shape and size of the catalytic bed; these depend on many factors that are interrelated, such as the following: the reaction rate and related kinetics, the fluid dynamic aspects (liquid flow rate and particle size), the eventual internal diffusion, and the exothermicity of the reaction. However, according to the conditions adopted, the catalytic bed can be considered as a plug flow or well mixed. We have seen, in Figure 12 (schemes A-C) that different assembles are possible for gas-liquid-solid STLR. After the choice of the shape, size, and location of the catalytic bed and the size of catalytic particles, the liquid recirculation flow rate must be higher than the threshold value necessary for achieving good efficiency of the spray nozzle. The reservoir capacity must be related to the amount of reagent that must be treated and to the reaction time, while the heat exchanger can be designed in a conventional way. All the aspects related to the catalyst behavior in the described reactors need to be deepened to achieve optimal design and performances.


As seen before, the reactor simulation can be made in a simplified way by introducing a spray nozzle efficiency factor varying from 0 to 1 giving the saturation degree achieved by the drops in the device used. Conclusions As has been seen, spray tower loop reactors can be equipped with efficient spray nozzles that are able to produce very small droplets (100-200 µm) provided that the liquid used has a viscosity and a surface tension comparable with that of water. The mass-transfer rate of the gaseous reagent, in this case, is very fast, and considering only physical absorption, the drops are almost completely saturated during a drop flight of less than 10-15 cm. We have also shown that it is possible to perform conveniently gas-liquid reactions in spray tower loop reactors. The shape and size of the reactors essentially depend on the reaction rate. In fact, extremely fast reactions occur inside the drops emerging at the outlet of the spray nozzle, while moderately fast and slow reactions occur inside the liquid pool collected at the bottom of the reactor. The criteria for modeling and simulating these reactors are now well ascertained. At last, we have shown also the possibility to extend the use of STLR to a gas-liquid-solid system with performances that are comparable with the ones obtained with a conventional well-mixed slurry reactor. Nomenclature aL ) gas-liquid specific interfacial area (cm2 cm-3) aG ) overall interfacial surface area of the drops (cm2) as ) liquid-solid specific interfacial area (cm2 cm-3) CD ) coefficient of form (dimensionless) CA, CB, CGR ) concentration of A, B, and the gaseous reagent (mol cm-3) CAl, CBl, CGRl ) concentration of A, B, and gaseous reagent in the liquid bulk (mol cm-3) CA* ) pA/H ) concentration at the gas-liquid interphase (mol cm-3) CGR ) gaseous reagent concentration inside an internally agitated drop (mol cm-3) CrGR ) gaseous reagent concentration inside the drop at the radium r (mol cm-3) CbGR ) gas concentration at r ) DS/2 (mol cm-3) C*GR ) gas interfacial concentration (mol cm-3) CTGR ) gas concentration inside the drop at the end of the flight (mol cm-3) CGRL ) gaseous reagent concentration in liquid bulk of the slurry system CGRS ) gaseous reagent concentration on the catalyst solid surface CGCO2 ) CO2 drop bulk concentration (mol cm-3) CiCO2 ) CO2 interfacial concentration (mol cm-3) [CO2] ) CO2 concentration (mol cm-3) CP ) specific heat at constant pressure (cal g-1 °C1-) DA, DB, DGR ) diffusion coefficient in liquid phase of A, B, and gaseous reagent (cm2 s-1) DCO2 ) diffusion coefficient of CO2 in the liquid (cm2 s-1) DREACT ) reactor internal diameter (cm) DS ) D32 ) drop mean Sauter diameter (cm) dm ) mean flight path of the drop (cm) di ) ith drop diameter (µm) E ) enhancement factor Eatti ) activation energy of the ethoxylation initiation step (kcal/mol)

Eatti ) activation energy of the ethoxylation propagation step (kcal/mol) Eatt ) activation energy (kcal/mol) H ) Henry constant (atm cm3 mol-1) Ha ) Hatta number g ) acceleration of gravity (cm s-2) h0, h, hL, h, h* ) characteristic height in the spray reactor; see Figure 2 (cm) hm ) vertical component of the drop flight averaged (cm) Ii ) solution ionic strength kg ) gas-liquid, gas side, mass-transfer coefficient kL° ) gas-liquid mass transport coefficient without chemical reaction (cm s-1) kL ) gas-liquid mass transport coefficient with chemical reaction (cm s-1) k1 ) kinetic constants for CO2 chemical absorption in NaOH(aq) (cm3 mol-1 s-1) k2 ) kinetic constants for a generic reaction of second order ki0 ) Arrhenius constant of the ethoxylation initiation step (cm3 mol-1 s-1) kp0 ) Arrhenius constant of the ethoxylation propagation step (cm3 mol-1 s-1) kS ) liquid-solid mass-transfer coefficient (cm s-1) m ) mass of catalyst/volume slurry relazione (g cm-3) ni ) number of drops with diameter ) Di NCO2 ) mass-transfer rate of CO2 (mol s-1) nGCO2 ) CO2 mole in the drop bulk (mol) [OH-] ) OH- concentration (mol cm-3) [OH-]b ) OH- concentration in the liquid bulk (mol cm-3) P ) pressure (atm) PA ) partial pressure of A (atm) PAi ) interfacial partial pressure of A (atm) Q ) recirculating liquid flow rate (cm3 s-1) R ) constant of gas rd ) drop radius ranging from 0 to DS/2 (cm) Re ) Reynolds dimensionless number (DPvFP/µL) rm ) horizontal component of the drop flight averaged (cm) r ) reactor radius (cm) rL, rj ) see Figure 4 rG ) reaction rate (mol s-1 m-3) rP ) drop radius (m) Sc ) Schmidt dimensionless number (µL/FPDGR) Sh ) Sherwood dimensionless number (kLDP/DGR) T ) temperature (°C) t ) time (s) tflight ) average drop flight time (s) V ) liquid volume (cm3) VG ) drop volume (cm3) VLOOP ) reactor loop volume (cm3) v ) drop speed (cm s-1) z ) quote (cm) zi ) ionic charge of the ith species We ) Weber dimensionless number (v2 FP DP/σ) Greek Symbols R ) cone width angle ∆H ) reaction enthalpy (cal mol-1) (∆P)nozzle ) pressure drop of the liquid through the nozzle (Pa) g ) fractional gas holdup in well-mixed gas-liquid reactors φ ) spray efficiency factor (0÷1) µG ) gas viscosity µL ) liquid viscosity (g cm-1 s-1) x ) flying pathway (cm) xm ) mean flight path of the drops (cm) FG ) gas density (g cm-3) FL ) liquid density (g cm-3) FP ) density of catalyst particles (g cm-3) σ ) surface tension (g s-2)

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δL ) thickness of the hydrodynamic liquid film (cm) η ) effectiveness factor of a catalyst

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(18) Levich, V. G. Physicochemical Hydrodynamics; PrenticeHall: Englewood Cliffs, NJ, 1962. (19) Johonson, A. I.; Hamielic, A. E.; Ward, D.; Golding, A. End effect corrections in heat and mass transfer studies. Can. J. Chem. Eng. Sci. 1958, 43 (12), 3141-3150. (20) Crank, J. The mathematics of diffusion; Clarendon Press: Oxford, U.K., 1958. (21) Perry, R. H.; Green, D. W. Chemical Engineer’s Handbook, 6th ed.; McGraw-Hill Book Co.: New York, 1984. (22) Brown G. G. Unit Operations; John Wiley and Sons: New York, 1950. (23) Stephen, H.; Stephen, T. Solubilities of inorganic and organic compounds; Pergamon Press: Oxford, 1963; Vol. 1, Part 1. (24) Di Serio, M.; Tesser, R.; Felippone, F.; Santacesaria, E. Ethylene Oxide Solubility and Ethoxylation Kinetics in the Synthesis of Nonionic Surfactants. Ind. Eng. Chem. Res. 1995, 34, 4092-4098. (25) Di Serio, M.; Vairo, G.; Iengo, P.; Felippone, F.; Santacesaria, E. Kinetics of Ethoxylation and Propoxylation of 1- and 2-Octanol Catalyzed by KOH. Ind. Eng. Chem. Res. 1996, 35, 3848-3853. (26) Di Serio, M.; Tesser, R.; Dimiccoli, A.; Santacesaria, E. Kinetics of Ethoxylation and Propoxylation of Ethylene Glycol Catalyzed by KOH. Ind. Eng. Chem. Res. 2002, 41, 5196-5206. (27) Ranz, W. E.; Marshall, W. R. J. Chem. Eng. Prog. 1952, 48, 141-173. (28) Nijsing, R. A. T. O.; Hendrikas, R. H.; Kramers, H. Absorption of CO2 in jets and falling films of electrolyte solutions with and without chemical reaction. Chem. Eng. Sci. 1959, 10, 88-104. (29) Fanelli, P. U.S. Patent 6,319,999, 2001. (30) Chaudari, R. V.; Ramanchandran, P. A. Three Phase Catalytic Reactors; Gordon and Breach: London, 1983. (31) Chaudari, R. V.; Ramanchandran, P. A. Ing. Eng. Chem. Fundam. 1980, 19, 201.

Received for review February 22, 2005 Revised manuscript received June 8, 2005 Accepted June 8, 2005 IE050222B

GasLiquid and GasLiquidSolid Reactions Performed in Spray Tower

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