A Generalized Method for Predicting the Minimum Fluidization Velocity - C. Y. WEN and Y. H. YU

8/12/2019 A Generalized Method for Predicting the Minimum Fluidization Velocity - C. Y. WEN and Y. H. YU

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( E i j k t CijkJ presented here is equal to the E used byLu and Wang 3 ) . This has the advantage that in theabsence of quaternary data, the corresponding jkl maybe set to zero to obtain a better approximation than bysetting (Eijkl C i j k l ) to zero.N O T A T I O Na interaction coefficientAC ternary coefficientD binary four-suffix coefficientE quaternary coefficientA G ~ ~molar excess Gibbs free energyi, i, k 1 m, n, p index representing componentsn molesP =pressureR gas constant

binary two- and three-suffix coefficient

T absolute temperaturex mole fractiony activity coefficientLITERATURE CITED1. Benedict, M. C. A. Johnson, E. Solomon, and L.C. Rubin,2. Jordan, D., J. A. Gerster, A. P. Colburn, and K. Wohl,3. Lu C.-H. and Y.-L. Wang, Znd. Eng. Ch em . Fundamentals,4. Marek, J., Chem. Listy, 47, 739 (1953); Collection Czech.5. Redlich, O., and A. T. Kister, Znd. Eng. Chem., 40, 345-3486. Wohl, K., Trans. Am . Inst. Chem. Eng., 42, 215-249 (April,7. Chem. Eng. Progr., 49, 218-219 (April, 1953).

Trans. Am. Inst. Chem . Engrs., 41, 371-392 (1945).Chem. Eng. Progr., 46, 601-613 (December, 1950).3, 271-272 (August, 1964).Chem . Commun., 19 , l ( 1954).

1948).1946).

A Generalized Method for Predicting the MinimumFluidization Velocity

C. Y. WEN and Y. H. YUWest Virginia University, Morgantown, West Virg in io

In a recent article Narsimhan (18) presented a gen-eralized expression for the minimum fluidization velocityby extending the correlation proposed by Leva, Shirai,and Wen 14 ) into intermediate and turbulent flow re-ions. Based on a similar approach by employing the&ed-bed pressure drop equation of Ergun 7) , an expres-sion for the minimum fluidization velocity quite differentfrom that of Narsimhan has been obtained 2 3 ) .It is the purpose of this communication to comparethese two correlations and to examine the validity andapplicability of each.The generalized expression given by Narsimhan con-sists of three equations [Equations ( 6 ) , (9) , and (11) inhis communication (18)1.The correlation obtained by Wen and Yu 23) can berepresented by

N R ~ ) ~ ~d(33.7) + 0.0408 N G ~ 3.7 (1)For nonspherical particles, the particle diameter p is de-fined as the equivalent diameter of a spherical particlewith the same volume. As an approximation, the particlediameter may be calculated from the geometric mean ofthe two consecutive sieve openings without introducingserious errors 2 6 ) .The major differences between the two correlations arethe minimum fluidization voidage emf and the shape factor4 .1. Narsimhan considered that for sphericalemf has the value of 0.35 and is independent of e parti-cle diameter, provided that the wall effect can be neg-lected. From the literature data 16, 20, 24), as well as

trrticles

from the experimental data of the present investigation2 3 ) , emf for spherical particles can be shown to varyfrom 0.36 to 0.46. Different average values of emf have

V Van Heerden, et a l . Z Z )0 Fancher and Lewis 9)o.ol ars imhan s corr e la t ion I

0 001 aooz 0.004 aoi aoz 03dp (in.)

986 emfFig. 1. Correlation of voidage shape factor function -(1 - e m f ) 2Page 610 A.1.Ch.E. Journal May, 1966


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002

00100080 006

V

0.004o LIYO, e i 1 151

S h i m (21)van Heerden, et 1 221Brownel l nd K o t 2 51F o o c h a r and L e w i s 9 )Norsrmhanr C o r r e l a t i o n

I o0 5 0 6 0 7 0 8 0.9 1.0 11 1.2 1.3 1.40001

( - Em f )+s

- 14

(1 --Emf)Fig. 2. Corre la t ion o f vo idage shape fac to r f u nc t io n -@S

been reported, such as, 0.386 21) , 0.40 4 ) , or 0.422 3 ) .Therefore, the value of 0.35 used by Narsimhan forspheres seems to be too small.nonspherical particles, Narsimhan consideredthat Emf depends on the particle diameter if it is less than0.02 in. On the other hand, if greater than 0.02 in., heconsidered that Emf is independent of particle diameter.From Figures 1 and 2, Narsimhans correlations forsmall particles are seen to be valid only for a limitednumber of t he experimental data points. Owing to thelack of li terature data, the validity of Narsimhans correla-tion for large particles cannot be tested. Narsimhan usedonly seven data points to establish his correlation.It is believed that if the wall effect can be neglected,

e m f should depend only on the shape factor regardless ofthe diameter of the particle. In Figure 3, E m f are plottedvs. +s for spherical as well as nonspherical particles. Al-though some scattering may be observed, a general trendis seen to exist between m f and +s. The following twoapproximate relations are obtained which cover the d,range from 0.002 to 1.97 in., emf from 0.385 to 0.935, dsfrom 0.136 to 1.0, and with a particle diameter to columndiameter ratio ranging from 0.000807 to 0.25.

2 . For

( 1 m f ) / ( d J s 2 E m f 3 ) = 11 2 )l / + smy 3) = 14 3)

In order to compare the validity of Equation (1) andthat of Narsimhans correlation, the deviations based on

Shirai (21) 0 Fan(8a )v Van Haerden, a t a l . (22) Brownel l and K at z( 5)m Oman and Watson 19) 0 Fancher and Lewis 9)

I I I I I / I

n10 - I

:I

IId3 Io2 10 10 I0 Io3 oI I I I 1Id3 Io2 10 I 10 I0 Io3 oN d m f

Fig. 4. A genera l i zed co r re la t ion fo r m in imum f lu id iza t ion ve loc i t y .

284 points appearing in Figure 4 are computed. The re-sults are given in Table 1. Equation 1) gives an overallstandard deviation of 34 and an average deviation of25 based on 284 points available in the literature RSshown in Figure 4.An overall standard deviation of 46and an average deviation of -t 34 are obtained fromNarsimhans correlations based on 267 data points tested.The difference in the number of data points tested for thevalidity of the two correlations is due to the lack of infor-mation pertaining to the shape factor. The proposed cor-relation represented by a single relation in Equation 1)does not require this information and covers the widestN R e ) f range, from 0,0 01 to 4000, heretofore at tempted.The advantages of Equation 1) over the Narsimhanscorrelations may be summarized as follows: 1) Equation1) is considerably simpler. (2) Equation 1) givesgreater accuracy. ( 3) Equation (1) may be expressed ina convenient graphical form such as shown in Figure 4for a rapid estimation of the minimum fluidization veloc-ity.

TABLE .COMPARISONF EQUATION1 ANDNARSIMHANSORRELATIONSStandard devi- Standard devi-No. of ations based ations based onParticle data on Narsimhans Equation 1 ,characteristics points correlations,

Spherical 55 43.4 34.1Nonsphericald p < 0.02 in. 203 38.6 37.6dp > 0.02 in. 9 135.3 21.3Overall standard deviation: 46 34f* Calculation based on 267 data points.t Calculation based on all the 284 data points.

A.1.Ch.E. Journal Page 611ol. 12, No. 3


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ACKNOWLEDGMENTFoundation Grant GP 560.This work was supported in part by the National Science

N O T A T I O Ntp particle diameter, Lf ) function of ( )g acceleration du e t o gravity, L/02G,f minimum fluidization flow rate, M/L20N c a Galileo number 4 3 f ps f)g/pzN R e particle Reynolds number 4 f V / p

N R e ) m f partic le Reynolds number a t onset of fluidiza-N R e t particle Reynolds number at terminal falling

pf fluid density, M/L3ps particle density, M/L3p fluid viscosity, M/LBemf minimum fluidization voidage4 ssurface area of sphere having the same volume as particle

tionvelocitysuperficial fluid velocity, L/0

surface area of particle

LITERATURE CITED1. Baerg, A.. 1. Klassen, and P. E. Gisher, Can. J. Res., F28,287 [igso j.2. Berl., E. Catalog of Ditt and Frees, Wiesbaden (1930).3. Blake, F. C., Trans. Am. Inst. Chem. Engrs., 14, 415( 1922).

(1961).537 (1947).

4. Bransom, S. H., and S. Pendse, lnd. Eng. Chem., 53, 5755. Brownell, L. E. and D. L. Katz, Chem. E n g . Progr., 43,

6. Brownell, L. E. H. S. Dombrowski, and C. A. Dickey,7 . Ergun, S . and A. A. Oming, lnd. E ng. C b m . , 41, 11798 . Fan, L. T., and C . J. Swartz, Can. J . Chem . Eng., 37, 204

ibid., 46,415 (1950).(1949).(1959).8a. Fan, L. T., Kansas State Univ. BuU., 43, 4 (1959).9. Fancher, G. H. and J. A. Lewis, lnd. Eng. Chem., 25,

10. Fetterman, C. P., M.S. thesis, Univ. Washington, Seattle,11. Furukawa, J., T. Ohmae, and I. Ueki, Chem. High Poly-12. Johanson, L. N., Unclassified Rept. HW-52891, General13. Kelly, V. P., M.S. thesis, Univ. Idaho, Moscow (1958).14. Leva, Max, T. Shirai, and C. Y. Wen, Genie Chim., 75(2),15. Leva, Max, M. Weintraub, M. Grummer, M. Pollchik, and16. Lewis, W. K. E. R. Gilliland, and W. C. Bauer, Ind. Eng.17. Miller, C . O., and A. K. Logwinuk, ibid. , 43, 1220 (1951)18. Narsimhan, G., A.1.Ch.E. J . 11, No. 3, 550 (1965).19. Oman, A. O. , and K. M. Watson, Natl. Petrol. News, 36,20. Shannon, P. T., Ph.D. thesis, Illinois Inst. Technol., Chi-

1139 (1933).(1958).mers, Tokyo 8(2),111 (1951).Electric Co. (September, 1957).

33 (1956).H. H. Storch, U . S . Bureau Mines Bull. 504 (1951).Chem. ,41, 1104 (1949).

R795 (1944).

cago 1961).21. Shirai, T., Fixed Bed, Fluidized Bed, and the Fluid Re-sistance. Heat Transfer and Mass Transfer of a SingleParticle: Res. Rept., Tokyo Inst. Technol., Japan 195z).22. Van Heerden, C., A . P. P. Nobel, and D. W . Van Krevelen.Chem. Eng. Sci. 1, No. 1 37 ( 1951).23. Wen, C. Y., and Y. H. Yu, Chem. Eng. Progr. SymposiumSer. No. 62, 62 1966).24. Wilhelm, R. H. and M. Kwauk, Chem. E n g . Progr., 44.-201 (1948).16.307 (1952).25. Yagi, S. I . Muchi, and T. Aochi, Che m . Eng. J a p a n) ,26. Yn, Y. H., M.S. thesis, West Virginia Univ., Morgantown1965).

Scale-Up of Residence Time DistributionsD. S. AMBWANI and R. J. ADLER

Case Insti tute o f Technology, Cleveland Ohio

Residence time distributions are valuable for under-standing the performance of many continuous flow sys-tems and for formulating mathematical models of suchsystems. The residence time distribution Y X ) referredto in this communication is defmed as: Y X)dX is thefraction of th e inflowing (outflowing) stream which willspend (has spent) a time between X and X + dX in thesystem. Fo r ideal cases such as plug flow, perfectly stirredvessels, laminar flow, etc., t he residence time distr ibu-tions may be obtained analytically. However, in many

cases of practical interest, it is necessary to determine thedistr ibutions experimentally. This study investigates thepossibility of determining residence time distributions ofprocess systems from experimental tests performed on suit-ably scaled laboratory models.

CRITERIA FOR MODELSAs early as 1953 the conditions under which residencetime distributions of large systems can be predicted fromPage 612 A.1.Ch.E. Journal May, 1966

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A Generalized Method for Predicting the Minimum Fluidization Velocity - C. Y. WEN and Y. H. YU