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CORRESPONDENCE Comments on “Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 1. Hydraulic Models” Jun-Hong Qiu College of Chemical Engineering, Zhejiang University of Technology, Hangzhou 310014, People’s Republic of China
Sir: Rocha et al.1 proposed a comprehensive hydraulic model for distillation columns containing structured packings of the corrugated plate type. It was developed from considering the flow channels within the packing as a series of wetted-wall columns and the interaction of falling liquid films with upflowing vapors in them. The model can be used to predict the values of liquid holdup, pressure drop, and flooding capacity. The authors have put forward a good idea for modeling the hydraulic performance of columns equipped with structured packings, and thus their results have been quoted by other researchers such as de Brito et al.2 and Brunazzi et al.3,4 Unfortunately, I find there are some mistakes in their model. 1. Liquid Holdup Assuming that liquid flows on the surface of the structured packing as a film and the wetted-wall flow channel has a diamond-shaped cross section (dealed as a square in fact), Rocha et al.1 gave the holdup equation as follows:
ht ) 4δ/S
(1)
al.1
Rocha et did not describe the derivations of eq 1. After careful analysis, I find eq 1 implies the liquid volume per unit volume of channels. It is well-known that the definition of liquid holdup is the liquid volume per unit volume of packed bed. Although Rocha et al.1 assumed the packed bed consists of a bundle of inclined channels, the volume of channels is obviously not equal to that of the packed bed. This is the reason eq 1 is incorrect and should be corrected. On the basis of the above assumptions, the derived liquid holdup is as follows:
ht ) 4δ(S - δ)/S2
(2)
Substituting δ ) 0 (no liquid) and δ ) 1/2S (channels occupied by liquid completely) into eq 2, the extremes of ht ) 0 and ht ) are achieved. Under normal conditions, δ is much less than S; thus, eq 2 is simplified as
ht ) 4δ/S
(3)
2. Effective Phase Velocities In their paper, effective (or mean) velocities of the gas and liquid were defied by
Uge ) Ugs/(1 - ht) sin θ
(4)
ULe ) ULs/ht sin θ
(5)
Because eq 1 has been corrected as eq 3, eqs 4 and 5 should be correspondingly corrected as
Uge ) Ugs/( - ht) sin θ
(6)
ULe ) ULs/ht sin θ
(7)
Equations 6 and 7 can be strictly derived in accordance with the definitions of effective phase velocities and liquid holdup as well as the above assumptions. The term - ht of eq 6 represents the effective void for gas flow to take into account the presence of liquid film. 3. Static Holdup Film In their paper, the expression for the thickness of the static holdup film was
[
]
1 - cos γ δstat ) 2σ FLg(1 - Fg/FL) sin θ
0.5
(8)
Equation 8 has reasonably considered the buoyancy effect of the gas density, but the correction for the angle of inclination of the corrugations is error and should be changed as
[
]
1 - cos γ δstat ) 2σ FLg(1 - Fg/FL) cos θ
0.5
(9)
When θ ) 0 (cos θ ) 1), eq 9 can be returned to the expression of Shi and Mersmann5 for a horizontal plate, but eq 8 cannot. 4. Dynamic Holdup Film In their paper, the expression for the thickness of the dynamic holdup film was
[
]
ULs δop ) 3µL FLhtgeff sin θ
0.5
(10)
Equation 10 has not taken into account the correction of “effective gravity” geff for the inclination of the channels. On the basis of the classical falling film
10.1021/ie9910773 CCC: $18.00 © 1999 American Chemical Society Published on Web 06/25/1999
Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3187
equation and the definition of effective liquid velocity (eq 7), eq 10 is corrected as
[
]
ULs δop ) 3µL FLhtgeff sin2 θ
0.5
(11)
should be modified. Besides the equations discussed in this paper, the others in their paper such as eqs 9 and 14-19 and the correlations for pressure drop and flooding capacity should also be corrected.
5. Interfacial Area
Literature Cited
The expression for the interfacial area proposed by Rocha et al.1 should be corrected as
(1) Rocha, J. A.; Bravo, J. L.; Fair, J. R. Distillation Columns Containing Structured Packings: A Comprehensive Model for their Performance. 1. Hydraulic Models. Ind. Eng. Chem. Res. 1993, 32, 641. (2) de Brito, M. H.; von Stockar, U.; Bangerter, A. M.; Bomio, P.; Laso, M. Effective Mass-Transfer Area in a Pilot Plant Column Equipped with Structured Packings and with Ceramic Rings. Ind. Eng. Chem. Res. 1994, 33, 647. (3) Brunazzi, E.; Nardini, G.; Paglianti, A.; Petarca, L. Interfacial Area of Mellapak Packing: Absorption of 1,1,1-Trichloroethane by Genosorb 300. Chem. Eng. Technol. 1995, 18, 248. (4) Brunazzi, E.; Paglianti, A. Mechanistic Pressure Drop Model for Columns Containing Structured Packings. AIChE J. 1997, 43, 317. (5) Shi, M. G.; Mersmann, A. Effective Interfacial Area in Packed Columns. Ger. Chem. Eng. 1985, 8, 87.
ae ) 0.90(WeLFrL)0.15 × ap A′deqB′ ReL0.20.4(1 - 0.93 cos γ)(sin θ)0.3
(12)
Equation 12 can be derived from eq 3 and the expression of wetted area for structured packings transformed from that given by Shi and Mersmann.5 6. Conclusion In consideration of the correction of liquid holdup, which is a key expression in the hydraulic model offered by Rocha et al.,1 all equations relative to liquid holdup
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