Evaluation on intensity of segregation of two-environment model for micromixing.

Takao, Masaharu; Murakámi, Yasuhiro

doi:10.1252/jcej.9.336

Cited by 8 publications

(4 citation statements)

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“…It is found also from this calculation that the condition of ideal mixing is achieved in the experiment using the hydrolysis reaction of ethyl acetate of Eq. (10). As a result, the dimensionless number q is concluded to be useful in correlating the reaction data of irreversible second-order reactions.…”

Section: Methodsmentioning

confidence: 99%

Mixing effect on homogeneous reaction in batch stirred tank reactor.

Murakámi

Takao

Nomoto

et al. 1981

J. Chem. Eng. Japan

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To represent the macro-mixing rate process in a batch reactor, a combined model of the extremes for mixing is proposed by extending the treatment of Miyawaki's model. This model is characterized by the segregation function and has the simplest mixing structure : that composed of both complete segregation and perfect mixing. By equating the intensity of segregation derived for the proposed model to that for the batch mass exchange-type model, the model parameter can be related as a function of macro-mixing time with the mixing parameter of the mass exchangetype model. This treatment of the model is experimentally confirmed by using three kinds of reactions having different rate constants. The mixing parameter of this model calculated from the experimental data of irreversible second-order reactions with different rate constants in a wide range of operational conditions is more successfully correlated to the Reynolds number of the reaction system. Further, the overall reaction performance is found to be characterized by a dimensionless number which is given from both the reaction rate and the mixing parameter.

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Section: Methodsmentioning

confidence: 99%

Mixing effect on homogeneous reaction in batch stirred tank reactor.

Murakámi

Takao

Nomoto

et al. 1981

J. Chem. Eng. Japan

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“…The same analytical result was obtained by Evangelista et al (1969) and discussed in our note. Dankwerts (1958), Brodkey (1966, 1967 Rao and Edwards (1973), Takao and Murakami (1976), Takao et al (1979), Nauman (1981 are among the authors who clearly distinguished between component segregation and degree of segregation based on age, although "the use of the same general terminology for the very different physical process of mixing and self-mixing (or backmixing) has led to some confusion" (Brodkey). Takao and Murakami (1976) derived analytical expressions for Is and J for several models of micromi:ing and concluded that they may or may not coincide depending on the model.…”

Section: National Science Foundation "Sf)mentioning

confidence: 99%

Letters to the editor

et al. 1984

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Recently Chang (1982) reported a numerical method for the estimation of the effectiveness factor for catalyst particles of high Thiele modulus with the Michaelis Menten type kinetics. The report by Lakshmanan (1983) suggested a collocation method with a trial function for the concentration gradient near the catalyst surface. Both methods require a trial and error procedure. In this letter, a simple method using the general modulus (Bischoff, 1965) is suggested and shown to be useful in obtaining the effectiveness for catalyst particles of high Thiele moduli.According to Bischoff (1965), the general modulus, M , with Michaelis Menten kinetics, is where St is the concentration of substrate on the catalyst surface and L is the distance measured from the surface (at L , dS/dr = 0).In the case of high Thiele moduli, the curvature effect on the mass transfer rate in a spherical catalyst particle can be assumed negligible. This is a valid assumption when the thickness of "effective reaction zone" (Paterson and Cresswell, 1971) is very small relative to the particle radius, R, due to a high Thiele modulus. When the above conditions are met, the overall reaction rate per catalyst particle, +overall, can be written (Bischoff, 1965; Moo Young and Kobayashi, 1972) asWe can express the concentration of substrate on the catalyst surface (unmeasurable) asInserting Equation (4) into (3) and using the dimensionless variables defined previously (Chang, 1982; Lakshmanan, 1983), we can derive the implicit function with respect to 7 as follows Equation ( 5 ) is the working equation for the TABLE 1. VALUES 7 values (a) Chang (1982) (b) Nine point collocation (c) This work % difference (Lakshmanan (1983)) 1 (@$-@ x 100, nine point collocation % difference 1(v x 100, this work determination of 7 with given p,@ and Sh.The values of 7 calculated with Equation (5) compare very well with the values reported for the case of 4 = 100. (Chang, 1982; Lakshmanan, 1983). These are shown in Table 1. As can be seen the 7 values calculated fromEquation ( 5 ) agree very well with the values of numerical calculations (Chang, 1983) and with those by nine point collocation (Lakshmanan, 1983). The calculation of 7 with Equation (5) is straightforward and does not require trial and error. In conclusion, Equation (5) can be used successfully in calculating the effectiveness factor for catalyst particles of high Thiele modulus with the Michaelis Menten type kinetics (or the Langmuir type, or the Monod type). NOTATION D = diffusion coefficient k K , = Michaelis Menten constant L to the inside of the particle M = general modulus T = radial coordinate 9 = reaction rate R = radius of a catalyst particle St = the concentration of substrate on the catalyst surface So = the concentration of substrate in bulk stream Sh = Sherwood number V,,, = maximum reaction rate = external mass transfer coefficient = distance measured from the surface Greek Letters 0 = saturation constant 17 = effectiveness factor 4 = Thiele modulus O F~F O R~= 100 Sh = 100; 4 = 100 p = 0.01 ...

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“…(4), (17) and (18) The reaction rate was of the same order as the rate of mixing. The mass exhcnage coefficient of the model kmwas determined so as to fit the experimental data through trial-and-error calculations of Eqs.…”

Section: Integratementioning

confidence: 99%

Mixing effect on irreversible second order reaction in batch stirred tank reactor.

Takao

Yamato

Murakámi

et al. 1978

J. Chem. Eng. Japan

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The mass exchange type "micromixing" model in a flow system is extended to batch mixing rate process accompanying a second-order reaction between miscible reactive fluids A and B. The performance of batch mixing rate process accompanied by reaction and the dimensionless parameter q=krCbolkm are obtained from theoretical analysis of the model. When the value of q becomes less than about 0.1, the mixing effect is negligible on the course of reaction. Through analysis of the mixing characteristics of the model, the mass exchange coefficient km can be correlated with mixing time as follows. Theoretical studies mentioned above are confirmed through experimental studies of the alkaline hydrolysis of ethyl chloroacetate, for which the reaction rate is comparable to the rate of mixing and the infinitely rapid reaction of ammoniumhydroxide and acetic acid. The experimental values of km determined in each experiment show that macromixing due to circulation of the fluid element has a dominant effect on the course of reaction in the experimental condition of 300 < Re < 5000.

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Evaluation on intensity of segregation of two-environment model for micromixing.

Cited by 8 publications

References 1 publication

Mixing effect on homogeneous reaction in batch stirred tank reactor.

Mixing effect on homogeneous reaction in batch stirred tank reactor.

Letters to the editor

Mixing effect on irreversible second order reaction in batch stirred tank reactor.

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