Influence of Chemical Parameters on Micromixing in a Continuous

27 Influence of Chemical Parameters on Micromixing in a Continuous Stirred Tank Reactor Downloaded by UNIV OF OTTAWA on November 23, 2014 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch027

ANDRÉ ZOULALIAN and JACQUES VILLERMAUX Département de Génie Chimique, Ecole Nationale Supérieure des Industries Chimique, 1, rue Grandville, 54042 Nancy, France

The state of micromixing in a CSTR was experimentally investigated through its (marked) influence on the selectivity of consecutive competitive reactions A + B = R, R + B = Sin the liquid phase. An experimental segregation index was defined. The influence of the following parameters was investigated: stirring, space time, viscosity, ultrasounds, concentrations, temperature, nature of the reaction, and contacting of reactants. Segregation becomes more important as k C exp(E/RT) increases;C = total concentration, and Ε = experimental activa tion energy. Micromixing results from a combination of reaction and molecular diffusion in the ultimatefluidaggregates having a size below the turbulence concentration microscale, which can be estimated by this method. Thus, the usual assumption of maximum mixedness in the design and use of the CSTR for com plex reactions may be quite erroneous. The CSTR is not well suited to kinetic studies of complex reactions unless experimental conditions ensuring a perfect micromixing are determined. 1

0

0

T

he question of the influence of micromixing on the extent of chemical reactions in continuous reactors has been the subject of many investigations. Most of the studies are theoretical and rather academic ones (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14). Several authors have attempted however to study this problem in an experimental way (15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,26,27,28, 29, 30, 31). In a previous work (29), we demonstrated experimentally that if the residence time distribution (RTD) and the batch kinetics are accurately known, it is possible to deduce the state of mixing of the fluid from chemical con version measurements. For moderately dispersed R T D and single reactions, segregation effects are usually very small (a few per cent) and consequently of little practical importance; this is a fortunate result for the designer. The sensitivity to mixing effects can become much more important if we use a reactor having a broad R T D and use another chemical characteristic: the product distribution (selectivity) in a system of multiple reactions. This led us to study the selectivity of consecutive competitive reactions of the type 348

In Chemical Reaction Engineering—II; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

27.

zouLALiAN AND viLLERMAux

Micromixing in a CSTR

349

Downloaded by UNIV OF OTTAWA on November 23, 2014 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch027

A + B = R , R + B = S i n a continuous stirred tank reactor (CSTR). In this case, an elementary calculation shows that at total conversion of Β—initially in defect—the selectivity in the production of R strongly depends on the micromixing state and may vary in a range of 100% between the maximum mixedness limit and the total segregation limit (batch reactor selectivity). In particu lar, we were asking the following questions: (1) Are micromixing and macromixing tied together in a CSTR? (2) Is it possible to influence only the first one, and if so, in varying which physicochemical parameters? (3) Is a CSTR a well suited tool for the determination of the kinetics of complex reactions in the liquid phase? (4) Does the chemical study of segregation effects allow the estimation of a micromixing scale? In addition to the answers to those questions, the surprising results we obtained eventually led us to a new appraisal of micromixing phenomena, discussed below.

Figure 1.

Experimental reactor (linear dimensions in mm)

The Experimental Reactor The reactor is a vertical cylindrical tube fixed on its base to a strap includ ing the various feed inlets and the mechanical agitation device (Figure 1). The upper side of the reactor is a piston through which the fluid flows out. In Chemical Reaction Engineering—II; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

350

CHEMICAL

REACTION ENGINEERING

II

The displacement of the piston allows the geometric reacting volume to be varied. When ionic reactants are used, their outlet concentration is measured by an electrical conductivity probe. The temperature of the fluid can be con trolled and measured by a thermocouple.


Residence Time Distribution Except at the lower stirring speeds (N < 60 rpm) for which the mixing time is clearly perceptible, the experimental R T D is undistinguishable from a pure exponential decay (Figure 2). The mean residence time and the space time (calculated from the volume and the flow rate) agree within 2%. Because of accuracy limitations in the measurements of volumes, flow rates, and slopes, such an uncertainty has no systematic character and is usual in experimental R T D determinations. We thus consider below that the reactor behaves as a perfect macromixer. Choice of the Chemical Reactions—Definition of an Experimental Micromixing Index To investigate the influence of micromixing on the reactor performance, three liquid phase reactions have been selected: (1) A single second-order reaction: A + Β ->R + Τ The well known alkaline hydrolysis of ethyl acetate: CH —COOC2H5 + O H " ^ C2H5OH + C H 3 C O O -

(1)

3

(2)

Two consecutive competitive second-order reactions A + B - > R + T, R + B - + S + T

The alkaline hydrolysis of glycol diacetate : CH COOCH —CH —OOC—CH s

2

2

3

+ OH" Λ CH —COO—CH —CH —OH 3

2

2

)

+ CH -COO" I C H C O O — C H — C H — O H + OH~ OH—CH —CH —OH + CH —COO" J 3

3

2

(3)

2

2

The iodination of p-cresol:

C H 3, - -( ^ 0 Ο^ V - o- O HH + 1+ 2 I.

>»

2

(2

)

3

^ H a - ^ r y ^ OH + cCH 3

HI

(3) CH -^Ô^-OH 3

+ I

2

> C H - ^ 0 ^ - O H 3

+ HI

I The products were analyzed by conductimetry (OH"), chromatography (glycol acetate) and/or spectrophotometry (iodoparacresols). The initial reactant concentrations were in the range of 0.1 to 0.4M (Reactions 1 and 2) and 10" to 5 X 10" M (Reaction 3). Experimental details are given else4

4



27.

zouLALiAN AND viLLERMAUx


351

Figure 2. An example of RTD—experimental conditions: Ν = 1400 rpm; V = 492 cm ; Q = 0.495 cm 1 sec; τ = V / Q = 994 sec; t = 982 sec; deviation: 1.2%. 3

3

where (32). Before continuous processing, careful batch experiments were done to determine the kinetic constants. The best results are summarized below: Reaction 1 : ki = 2.635 Χ 10 exp £ -

11400 ± 200 RT

τ>

0

7

•·

ο

ι ι „ tor

J

Γ

1

0

0

0

Reaction 2: k = 1.1 X 10 exp 1, X V. 10 , Λ « exp IΓ k7 = 1.4

1

8

2

±

,/

^

7

x

1/mole/si

2

0

0

0

, /

l/mole/s
0 as m -» 0 and X —» 1 as m —> oo. On a purely phenomenological basis, a function exhibiting such a behavior is:


4

1

0

2

)

X = 1 — exp [— m/m ] G

(6)

It is reasonable to suppose that X takes intermediate values between 0 and 1 when the diffusion time equals the reaction time (m = 1). We shall thus make the additional assumption that ra « 1. From Equation 5 we are led to identify m to BY: 0

m = kxCotf/D = BY = BkiCo exp [E/RT]

(7)

In this case, we should verify that k /D (1) varies as exp [ E / R T ] , Ε 5-6 kcal/mole; (2) only undergoes a slight increase as a function of the vis cosity; (3) decreases in the presence of ultrasounds. The Ε value is of the order of magnitude of the activation energy of the diffusivity of solutes in aqueous solutions, and this might account for point ( 1 ). On the other hand, one might expect that 1 / D is proportional to the viscosity of the solution. The addition of sodium polyacrylate increases the shear vis cosity but may lead to the formation of a microphase through which small molecules can diffuse as in the pure solvent. This has been proved by Huizenga 2



27.


357

et al. (36, 37) for sodium ions and might account for point ( 2 ) . This statement is still speculative and should be checked experimentally. The following expression has been proposed by Corrsin (38) in the case of liquids:

S = [^+K -)


1 8

V

, , 2

logSc]

(8)

where I is the concentration fluctuations microscale. The influence of the viscosity ν is weak since it figures in the second term which only amounts for a few percent of the first one (see below). The role of ultrasounds (point 3 ) can be understood if we imagine that they produce an increase of ε, which represents the kinetic energy dissipation per unit mass. Of course, these crude arguments need to be refined, and we can imagine the actual processes occurring in the segregated regions to be far more complex, depending on the nonuniform turbulence pattern in the reactor. On the whole, we can consider that the above interpretation is not inconsistent with our experi mental observations. If we accept it, we can estimate an order of magnitude of λ. From Equation 7 it results that: λ

= BD exp (E/RT)

2

(9)

Taking D = 7 . 2 Χ 1 0 " cm /sec (aqueous diffusivity of glycol diacetate calcu lated from the Wilke and Chang ( 3 9 ) formula) and Ε = 5 kcal/mole, we obtain at room temperature: 6

2

λ = 3.3 X 10~ cm 3

This value is not unrealistic but is difficult to compare with the microscale I given by Equation 8 because the energy dissipation term ε is not known. In this respect, it would be interesting to carry out direct measurements of the concentration fluctuations in the reacting fluid. Conversely, if we assume that λ and I are of the same order of magnitude, we can estimate ε. We shall use the Corrsin formulas, as reported by Brodkey (40). The wave number k can be expressed by the approximate relation: 0

ko where L

s

=

(χ/5) Ls" 1

is the segregation macroscale.

Then:

Taking L ~ 2 cm ( 1 / 3 - 1 times the blade width according to Ref. 41), ν = 1 0 " cm /sec, λ = 3 . 3 Χ 1 0 " cm, D = 7 . 2 Χ 1 0 " cm /sec, one obtains Sc = 1 3 8 8 and s

2

2

3

6

2

ε = 23000 cm /see 2

3

The second term in Equation 1 0 represents only 2 % of the sum, justifying the fact that the dependence of λ on the viscosity is weak. A typical value of ε is reported by Evangelista et al. (42) in a commercial application as ε = 2 0 0 0 0 cm /sec , in excellent agreement with the above estimation. 2

2

3


358

CHEMICAL REACTION ENGINEERING

II

θ near 20 C C near 0.4 mole/l M near 1

0.60

e

0

Reacteinte fed into zone

Μ (2

ο +


0.40

0.20

02

0.4

0.6

0.8

1

Figure 8. Variation of the segregation index X as a function of the volume ratio 7 = Vj/fVi + Vs). Zone 1: containing the stirrer; Zone 2: free of mechan ical stirring. The reactants are fed alternately into the two zones. For a reactor volume, V = 450 cm , the total dissipation of kinetic energy amounts to 3

Vç>e = 450 X 2.3 Χ ΙΟ4 Χ 10"7 « 1 watt

It is interesting to compare this value with the energy consumption (43) : Ρ = 4>pATW

(11)

Under typical conditions, Ν = 10 rps, D , agitator diameter = 6 cm. Re = D N/v = 36000 so that Φ is nearly constant and can be estimated to Φ 6 for a two-blade turbine in the turbulent domain (44). With these values, one obtains: a

2

&

Ρ = 4.7 watts The efficiency of the turbulent production is thus: η » Vçe/P « 0.2 a reasonable value (Corrsin cites η = 0.5 from work in pipe flows, as reported in Ref. 42). Of course, because of the crudeness of our assumptions, such estimations can only yield an order of magnitude. Two Micromixing Zones Reactor We now present the results of experiments which prove that the micromixing state in the inner volume of the reactor can be made locally variable. The reactor volume was divided into two zones by a metallic screen or a layer


27.



359

of glass beads, allowing a perfect global macromixing of the fluid, as checked by the R T D . The first zone (1) (volume V ) contained the stirrer whereas the second one (2) (volume V ), was free of mechanical stirring. Figure 8 reports the variation of the segregation index X at the outlet of the reactor as a function of the ratio: γ = V / ( V + V ), the reactants being alternately fed into the first or the second zone of the reactor. The results clearly show that the second zone (no mechanical stirring) is more segregated than the first one, as could be expected. t

2

2

1

2


Conclusion (1) Micromixing is not only the result of hydrodynamic phenomena. It must not be considered (as many authors have done) as a physical framework in which chemical reactions take place. On the contrary, it can exist as irre ducible coupling between reaction and diffusion, which gives rise to the segre gation phenomenon. The intensity of segregation is then a function of concen tration and depends on the size of the ultimate clumps of fluid. Chemical performance measurements thus appear to be a possible tool for studying turbu lence phenomena. (2) Thus, the usual and implicit assumption of perfect micromixing in the design and use of the CSTR for complex reactions may be quite erroneous, especially in viscous media, even if the R T D seems to be ideal and if the mechanical stirring power is high. We emphasize that a strong dependence of selectivity on segregation effects may however arise even for moderately rapid reactions in low viscosity media as those used in the present investigation. (3) The CSTR is not well suited to kinetic studies of such complex reactions in the liquid phase (especially if selectivity measurements are to be carried out), unless experimental conditions ensuring maximum mixedness are defined. Preliminary experiments and the use of the general correlation we have proposed may help find these conditions. Fortunately segregation effects are probably less severe in gases, so that the above restrictions do not seem to entirely apply to the widespread gas phase kinetic measurements using a CSTR. This point deserves special study. Nomenclature A Β R Τ Β Ci

ethyl acetate ( Reaction 1 ) glycol diacetate (Reaction 2) paracresol ( Reaction 3 ) sodium hydroxide (Reactions 1 and 2) iodine ( Reaction 3 ) ethanol (Reaction 1) glycol monoacetate (Reaction 2) monoiodoparacresol ( Reaction 3 ) sodium acetate (Reactions 1 and 2) hydriodic acid (Reaction 3) constant, sec concentration of reactant i, mole/liter initial concentration of reactant i CAO +

C-BO

molecular diffusivity, cm /sec agitator diameter, cm wave number (turbulence theory), cm" kinetic constants, liter/mole/sec 2

1


360

CHEMICAL REACTION ENGINEERING

I L m = k C \ /D M Ν Ρ Sc Τ V, ν , V X Y = k C exp (E/RT) s

1

χ

2

t


2

0

0

II

Taylor turbulent concentration microscale, cm segregation macroscale, cm dimensionless criterion C /C rotation speed of the stirrer, sec" or min" power consumption of the stirrer, watts Schmidt number absolute temperature, °K volumes of reaction zones, cm segregation index correlation parameter, sec" B 0

A 0

1

1

3

1

Greek Letters γ ε

volume ratio turbulent kinetic energy dissipation rate per unit mass, cm /sec dynamic viscosity, cp characteristic dimension of the microsegregated regions, cm kinematic viscosity, cm /sec density, gram/cm space time, sec power number 2

η λ ν Ρ τ Φ

3

2

3

Literature Cited 1. Chen, M. S. L., Fan, L. T., Can. J. Chem. Eng. (1971) 49, 704. 2. Costa, P., Trevissoi,C.,Chem. Eng. Sci. (1972) 27, 653. 3. Curl, R. L., A.I.Ch.E.J.(1963) 9, 175. 4. Danckwerts, P. V., Chem. Eng. Sci. (1958) 8, 93. 5. Kattan, Α., Adler, R. J., Chem. Eng. Sci. (1972) 27, 1013. 6. Ng, G. Y.C.,Rippin, D. W. T., 3rd Europ. Symp. Chem. Reaction Eng., P mon Press, Oxford, p. 161, 1965. 7. Nishimura, Y., Matsubara, M., Chem. Eng. Sci. (1970) 25, 1785. 8. Rietema, K., Advan. Chem. Eng. (1964) 5, 237. 9. Rippin, D. W. T., Chem. Eng. Sci. (1967) 22, 247. 10. Trealeaven, C. R., Tobgy, A. H., Chem. Eng. Sci. (1972) 27, 1497. 11. Villermaux, J., Devillon, J.C.,5th Europ. 2nd Intern. Symp. Chem. Rea Eng., B-l-13, May 1972. 12. Villermaux, J., Zoulalian, Α., Chem. Eng. Sci. (1969) 24, 1513. 13. Weinstein, H., Adler, R. J., Chem. Eng. Sci. (1967) 22, 65. 14. Zwietering,. T., Chem. Eng. Sci. (1959) 11, 1. 15. Aubry,C.,Thesis, Université de Nancy, 1972. 16. Constantinides, Α., M.S. Thesis, Ohio State University, 1964. 17. Devillon, J.C.,Thesis, Université de Nancy, 1972. 18. Geurden, J. M. G., Thoenes, D., 5th Europ. 2nd Intern. Symp. Chem. Rea Eng., B-l-35, May 1972. 19. Harada, M., etal.,J. Chem. Eng.Japan(1968) 1, 148. 20. Hatate, Y., et al., J. Chem. Eng.Japan(1971) 4, 348. 21. Leitman, R. H., Ziegler, Ε. N., Chem. Eng. J. (1972) 3, 245. 22. McWharf, J. E., Ph.D. Thesis, University of Rochester, 1967. 23. Methot, J.C.,Roy, P. H., Symp. Kinetics Catalysis, Reactor Design, 21 Chem. Eng. Conf., 1971. 24. Paul, E. L., Treybal, R. E., A.I.Ch.E.J.(1971) 17, 718. 25. Ross, J. M., O'Brien,G.,Ph.D. Thesis, University of Pennsylvania, 1966. 26. Treleaven, C. R., Tobgy, A. H., Chem. Eng. Sci. (1973) 28, 413. 27. Worrel, G. R., Eagleton, L.C.,Can.J.Chem. Eng. (1964) 42, 254. 28. Zoulalian, Α., Thesis, Université de Nancy, 1969. 29. Zoulalian, Α., Villermaux, J., Chim. Ind. Génie Chim. (1970) 103, 973.


27. ZOULALIAN AND VILLERMAUX

30. 31. 32. 33. 34. 35. 36. 37. 38. 39.


40. 41. 42. 43. 44.


361

Zoulalian, Α., Villermaux, J., Chem. Eng. J. (1970) 1, 76. Hovorka, R. B., Ph.D. Thesis, Case Institute of Technology, Cleveland, Ohio, 1961. Zoulalian, Α., Ph.D. Thesis, Université de Nancy, 1973. Okada, K., et al., Chem. Eng. Sci. (1972) 27, 259. Beek, J., Jr., Miller, R. S., Chem. Eng. Prog. Symp. Ser. (1959) 55 (25), 23. Paul, E. L., Ph.D. Thesis, New York University, 1968. Huizenga, J. R., etal.,J. Amer. Chem. Soc. (1950) 72, 2636. Huizenga, J. R., et al., J. Amer. Chem. Soc. (1950) 72, 4228. Corrsin, S., A.I.Ch.E. J. (1964) 10, 870. Wilke, C. R., Chang, P., in "The Properties of Gases and Liquids," 2nd ed., R. C. Reid and T. K. Sherwood, Eds., McGraw-Hill, New York, p. 549, 1966. Brodkey, R. S., "The Phenomena of Fluid Motions," Addison Wesley, Reading, Mass., Chap. 14, 1967. Rao, Μ. Α., Brodkey, R. S., Chem. Eng. Sci. (1972) 27, 137. Evangelista, J. J., Katz, S., Shinnar, R., A.I.Ch.E.J.(1969) 15, 843. Uhl, V. W., Gray, J. B., "Mixing, Theory and Practice," Vol. 1, Academic Press, New York, p. 123, 1966. Uhl, V. W., Gray, J. B., Op. Cit. p. 134.

RECEIVED January 2, 1974.


Influence of Chemical Parameters on Micromixing in a Continuous

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