Levenspiel

Levenspiel, O., Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972. 

D. Kiinii and O. Levenspiel, Fluidicyation Engineering 2nd ed., Butterworth-Heinemaim, Boston, Mass., 1991. 

D. Kiinii, K. Yoshida, and O. Levenspiel, "Axial Movement of Solids ia Bubbting Fluidized Beds," presented at I. Chem E Tripartie Chemical Eng Conference—Eluidi tion Series, Montreal, Canada, Sept. 1968. 

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

For details beyond the scope of this subsection, reference should be made to Kunii and Levenspiel, Fluidization Engineering, 2d ed., But-terworth Heinemann, Boston, 1991 Pell, Gas Fluidization, Elsevier, New York, 1990 D. Geldart (ed.). Gas Fluidization Technology, Whey, New York, 1986 and the vast number of papers published in periodicals, transcripts of symposia, and the American Institute of Chemical Engineers symposium series. 

The bubble model (Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969 Fig. 17-14) assumes constant-sized bubbles (effective bubble size d ) rising through the suspension phase. Gas is transferred from the bubble void to the mantle and wake at... 

FIG. 17-14 Biihhling-hed model of Kunii and Levenspiel. dy = effective hiih-ble diameter, = concentration of A in hiihhle, = concentration of A in cloud, = concentration of A in emulsion, y = volumetric gas flow into or out of hiihhle, ky,- = mass-transfer coefficient between bubble and cloud, and k,. = mass-transfer coefficient between cloud and emulsion. (From Kunii and Leoen-spiel, Fluidization Engineering, Wiley, New York, 1.96.9, and Ktieger, Malahar, Fla., 1977.)... 

Octave Levenspiel "Chemical Reaction Engineering," John Wiley Sons, New York, 1962. 

Caution must be exereised when the rate equations with gas phase reaetions are expressed in terms of the partial pressure as eompared to eoneentration. This is beeause eaeh rate gives different aetivation energy for the same data and for the same reaetion. Levenspiel [4] suggests that tlie differenee ean be ignored for reaetions with reasonably high aetivation energies as the amount is only a few kJ. 

For an ideal gas at both constant temperature and pressure, but with changing number of moles during reaction, Levenspiel relates that... 

Levenspiel considers the cases where the relationship between concentration and conversion of reacting specie is not obvious, but depends on a number of factors. 

Levenspiel, O., The Chemical Reactor Omnibook, OSU Book Stores, Ine., 1993. 

Consider a series of eontinuous flow stirred tank reaetors of equal size with inlet and exit eonversions as Xg and X. The intermediate optimal eonversions Xj, Xj, X3. . . X . . . X i ean be determined, whieh will minimize the overall reaetor size. Levenspiel [1] has shown... 

Figure 6-23. Solution of mass and energy balanoes for reversible exothermio reaotion. (Source 0. Levenspiel 3rd ed. Chemioal Reaotion Engineering, John Wiley and Sons, 1999.)...

Equation 6-136 is the basis for the r - T - X ehart as developed by Levenspiel [11]. Assuming that tliere is no produet reeyele (Gj = 0) and that the reaetion is unimoleeular reversible reaetion (Or = 1), Equation 6-136 beeomes... 

Additional data (rate eonstants taken from Levenspiel [11]) ... 

Mae Mullin and Weber [1] introdueed the eoneept of the RTD in the analysis of ehemieal reaetors, and Danekwerts [2] developed this eoneept further in his elassieal paper, whieh has sinee formed the basis of various investigations involving flow systems in ehemieal and bioehemieal reaetors. Levenspiel [3], Levenspiel and Bisehoff [4], Himmelblau and Bisehoff [5], Wen and Fan [6], and Shinnar [7] have given extensive treatments of this subjeet. 

Danckwerts [2] also obtained steady state solutions based on the same boundary conditions and various studies have since been performed by Taylor [19], Arts [20], and Levenspiel and Smith [21],... 

The inverse of the Bodenstein number is eD i/u dp, sometimes referred to as the intensity of dispersion. Himmelblau and Bischoff [5], Levenspiel [3], and Wen and Fan [6] have derived correlations of the Peclet number versus Reynolds number. Wen and Fan [6] have summarized the correlations for straight pipes, fixed and fluidized beds, and bubble towers. The correlations involve the following dimensionless groups ... 

Figure 8-32. Correlation for the dispersion of fluids flowing in pipes. (Source Levenspiel, 0., Ind. Eng. Chem., 50, 343, 1958.)...

Levenspiel [3] has given a family of Gaussian curves, and the equations representing these curves are given in Table 8-7. 

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