Effect of wetting efficiency on selectivity in a trickle bed reactor

Shorter Communications

d(mo) modified Thiele modulus R

absorption rate in the presence of immobilized enzyme, kmol/mss Ro absorption rate in the absence of immobilized enzyme, kmobmsls X dimensionless distance, z/S Y. dimensionless concentration, C,JCA~ ‘? distance from gas-liquid interface, m

Greek symbols 6 void fraction in slurry phase 6 liquid-film thickness, m 7) catalyst effectiveness factor Subscript A absorbing component i gas-liquid interface

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REpERBNCX.8 [l] Sada E., Kumazava H. and Butt M. A., Chem. Engng Sci. 1977 32 970. [2] Alper E.. Wichtendahl B. and Dcckwer W.-D., C/rem. Engng Sci. 1980 35 217. [3] Deckwer W. D. and Alper E., Chem-kg-Technik 1980 52 219. [4]. Satterlield C. N. and Huff G. A., C/rem. Engng Sci. 1980 35 19s. [S] Zaidi A., Louisi Y., Ralek M. and Deckwer W.-D., Germon Chem. Engng 1979 2 94. [6] Wichtendahl B.. Diplomarbeit, Universitit Hannover 1979. f7] Dnnckwerts P. V., Gus-Liquid Reactions. McGraw-Hill, New York 1970. 181 Alper E. and Deckwer W. D., unpublished. 191 Aluer E., Lohse hf. and Deckwer W. D., Chem. Engng Sci. 1980 35 2147. [lo] Nysing R. A. T. 0. and Kramers H., Chem. Engng Sci. 1959 10 88.

Effect of wetting efficiency OIIselectivity in a trickle bed reactor (Received 6 May 1980; accepted 10 October 1980) An important factor that intluences the performance of trickle bed reactors is the partial wettin of the outer surface of the catalyst particles. This partial wetting of the catalyst bed, termed here as the wetting efficiency I, is defined as the fraction of particle external surface covered by liquid. Expressions for calculatin8 the overall effectiveness factor as a function of the Thiele modulus 4, the wetting efficiency f and the Biot numbers in the &as and liquid covered parts of the particle have been recently proposed[l]. Only the case of first-order reaction has been treated. The scope of this work is to consider the effect of f on the selectivity of consecutive first-order reactions (Wheeler type III):

-g=c+2)

Idry fraction (3c)

-$=&-b)

x=0.

f
Equations (1) and (2) were solved by separation of variables to yield, d = 2 7. cos [(n - I)?ry][exp [+((a - 1)2a* f &*) (x -2)] It-1 f exp l( -X&l - I)%? + &%)I m b = .z, E. cos Kn - l)wl[exp (VW - U2?r2+ 4&x -2))

A%Bh-C.

(4)

2

TEEORF,TlCALMODEL In a previous paper it has been shown that the effect of particle shape on the effectiveness factor of partially wetted particles is insignificant. Therefore, it is assumed that the particle is an infinitely long, two dimensional slab, completely filled with liquid. The mass balance inside the catalyst particle is expressed by the equations: 2 $-$++$,%

fexp(- d/((n- l)*d + ob%)I+ 42t

&,*

a.

The coefficients 7’,, and E. may be calculated following the Fourier series approximation proposed by Herskowitz[l]. Their values are the solutions of the following sets of linear algebraic equations:

=o

$+$-@zzb+&2a=0.

(2) Expressions for calculating Fii, Gij, Ifi, di and gi are given in Table 1. The selectivity of the desired component R may be defined as:

Subject to the boundary conditions: da db -_=-_=(J ax ax

x=l

(W

aa ab -_=-_=O JY ay

y=O.y=l

(3b)

(8)

-$=R,(l-(1)

wetted fraction

-g=&(-b)

O
The result of the integration is: 1

x=0

“iG-Tb

El

112I-

ev

( - 242)

l-exp(-24,)

(9)

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Shorter Communications Table 1. Expressions of coefficients in eqn (9)

i-2,5....

,

j-2,3,..

i=Z,3..

where

ILLUSTRATING EXAMPLE

The selectivity is computed for a system where A is a gaseous component and B is a nonvolatile component. In this system Q*= 0. The solution of the sets in eqn (8) was carried out by the

....

Gauss-Jordan elimination procedure and the Gauss-Siedel method. The number of terms in the series in eqn (8) was varied from 10 to 50. Increasing the number of terms beyond 20 resulted in a change of less than 1% in the calculated values of the selectivity. Both methods of computation gave similar results which are plotted in Fig. 1. They indicate a significant effect of f on S. Hence the wetting efficiency may become an important factor that affects not only the overall effectiveness factor but also the selectivity. MORDECHAY Deportment uj Chemical Engineering Ben Curion University of the Negeu Beer Sheua, Israel

0.6

HERSKOWITZ

NOTATION 07

06

1

05

0.6

07 Wetting

Fig.

0.6 efficiency,

0.9 f

I. Effect of wetting efficiency on selectivity.

1.0

intraparticle concentration of reactant A, C,lC, intraparticle concentration of reactant B, CJC, intraparticle concentration of reactants A and B, mole/l concentration of reactants A and B in equilibrium with their concentration in the gas, mole/l constants defined in eqn (6) and Table I effective diffusivity in the liquid-filled pores of the catalyst, cm’/s constants defined in eqns (5) and (7) wetting efficiency, dimensionless coefficients defined in eqn (6) and Table I constants defined in cqn (7) and Table I coefficients defined in eqn (7) and Table I coefficients defined in eqn (7) and Table 1 mass transfer coefficient in the liquid-covered part of the particle, cm/s mass transfer coefficient in the gas-covered part of the particle, cm/s intrinsic rate constants, s-’ depth and width of the slab, cm selectivity defined in eqn (II) constants defined in eqas (4) and (6) distance on the X coordinate, X/L. distance on the X coordinate, cm distance on the Y coordinate, Y/L. distance on the Y coordinate, cm

Shorter Communications

Greek symbols LI Biot number for mass transfer on the gas-covered part of particle, k,L/D, fl Biot number for mass transfer on the liquid-covered part of the particle, k&D, y ratio of bulk liquid concentrations, CJC, S ratio of effective diffusivity coefficients, DJD,. LT ratio of Thiele moduli, (&/$,)2 E particle porosity 4, Thiele modulus, L(kl/D1,~“*

CES

Vol.36. No. 61

1101

$2 Thiele modulus, Z&1Dz,)“2 I$J Thiele modulus, Z&/Q,)“2

Subscripts 1 reactant A 2 reactdnt 6

REFERENCES [I]

Herskowitz

M., Chem. Engng Sci. in press (1981).