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Ind. Eng. Chem. Res. 1999, 38, 3188-3189
Rebuttal to the Comments of Dr. Jun-Hong Qiu on “Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 1. Hydraulic Models” J. Antonio Rocha, Jose L. Bravo, and James R. Fair* Separations Research Program, Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
Sir: We are grateful to Professor Qiu for his constructive remarks regarding our paper on hydraulic characteristics of structured packings in distillation service.1 The following responses will be numbered to conform to those numbers used by Professor Qiu.
vertical. Our correlation is favored by phenomenological evidencesthere is lower holdup for higher inclination angles.
1. Liquid Holdup
Equation 8 was used in developing effective velocity relationships (eqs 1 and 2), and either definition of holdup may be used, because we chose to use superficial velocities as correlating parameters. We should point out that values of for structured packings are in the range of 0.90-0.97, depending on sheet metal thickness, and one using holdup data per se will not be misled significantly by using our eq 8.
The comment is made that our eq 10 for static holdup thickness does not use the effective gravity. Gravity always acts downward at 90° inclination and thus does not need to be corrected for that angle. The pull of gravity is always in the vertical direction, and the coordinate system we chose has the horizontal as the plane of reference. We have included the angle correction in the velocity, and thus we do not feel that Professor Qiu’s proposed correction of effective gravity is necessary. In the classical falling film work of Bird et al.,2 the function sin θ is used to correct for inclination of the plate; we have used the correction in defining effective velocity, and to apply twice that correction could lead to errors. Our model gives a reasonable representation of the measured holdup values of Suess and Spiegel3 for Mellapak packings; these values were obtained after submission of our paper.
2. Effective Phase Velocities
5. Interfacial Area
If we apply our definition of holdup to our proposed effective velocities, we obtain the same relationship as given by eqs 6 and 7 of Professor Qiu:
For the effective interfacial area, our eq 12 is given as
Issue is taken with our definition of liquid holdup (eq 8). Our definition is correct based on our analogy to wetted-wall columns formed by the flow channels. If one considers the entire column volume, then the term for total bed void fraction should be added:
ht ) 4δ/S
UGs UGs ) UGe ) 4δ 4δ 1sin θ sin θ S S
(
)
ULe )
(
)
ULs 4δ sin θ S
Accordingly, there is no error in our eqs 1 and 2. 3. Static Holdup Film The static holdup correction proposed by Professor Qiu is in error, we feel. It implies that the static holdup is at a maximum, in fact infinity, for a vertical plate because the cosine is that for 90°. Furthermore, his proposal would have us conclude that the holdup at 0°. inclination is actually the minimum, when realistically it would be at the maximum because of a stacking effect. Perhaps the confusion arises from our definition of the angle being from the horizontal rather than from the * To whom correspondence should be addressed.
4. Dynamic Holdup Film
ae ) ap A′deqB′ 0.76(WeLFrL)0.15 ReL0.20.6(1 - 0.93 cos γ)(sin θ)0.3 whereas the following equation is proposed by Professor Qiu:
ae ) ap A′deqB′ 0.90(WeLFrL)0.15 ReL0.20.4(1 - 0.93 cos γ)(sin θ)0.3 If one analyzes these two expressions, the coefficient makes no difference, because it is absorbed in the constant A′. As far as the difference in the exponent for the void fraction is concerned, this may result from Dr. Qiu’s conversion from superficial velocity to effective velocity, or vice versa, and we feel that our exponent is correct. Practically, the difference can be taken up in
10.1021/ie991075i CCC: $18.00 © 1999 American Chemical Society Published on Web 06/10/1999
Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3189
the correlations fitted to our experimental data, from which the effective area is deduced (see part 2 of our paper4).
dynamic holdup film thicknesses, and effective interfacial area remain unchanged and are recommended for analysis of the various phenomena associated with structured packing performance analysis.
6. Conclusions In response to the comments of Professor Qiu, we can offer the following. His holdup equation is correct for packed columns. Our holdup definition (eq 8) is correct for wetted-wall columns and is approximately correct for packed columns with metallic structured packings. For either definition of volume (channel or column), the derived values and the effective velocities for both phases are the same and correct. Our eq 11 for operational film thickness is correct and follows the classical falling film relationships. Our eq 12 is also correct. The prediction of film thickness for static holdup should employ the sine function, because it is in line with experimental evidence. In summary, our several working equations for effective phase velocity, static and
Literature Cited (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) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley: New York, 1960; pp 37-42. (3) Suess, P.; Spiegel, L. Hold-up of Mellapak Structured Packings. Chem. Eng. Proc. 1992, 31, 119. (4) Rocha, J. A.; Bravo, J. L.; Fair, J. R. Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 2. Mass Transfer Model. Ind. Eng. Chem. Res. 1996, 35, 1660.
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