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Ind. Eng. Chem. Res. 1996, 35, 1660-1667
SEPARATIONS Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 2. Mass-Transfer Model J. Antonio Rocha,† Jose L. Bravo,‡ and James R. Fair* Separations Research Program, The University of Texas at Austin, Austin, Texas 78758
This is the second part of a two-part paper dealing with the fluid mechanics and mass transfer in structured packings for distillation column service. The first part elucidated pressure drop, flooding, and liquid holdup. The second part covers the generation of effective interfacial area and provides a general correlation for predicting the mass-transfer efficiency as a function of surface type, packing geometry, phase flow conditions, and fluid properties. The mass-transfer model has been tested against a variety of commercial structured packings, for distillation pressures ranging from 0.33 to 20.4 bar. In all cases the fit of the data is excellent, with the possible exception of the highest pressures, where additional factors of axial mixing appear to have an effect. In the first part of this paper (Rocha et al., 1993), models were developed for predicting liquid holdup, pressure drop, and flooding in distillation columns containing structured packings. The various commercially-available packings were described, and the design correlations developed were based on rational, mechanistic models that provide a very good representation of experimental observations in larger diameter columns. In part 2 attention will be given to methods for predicting the mass-transfer performance of the same types of packings. In the present work the two-resistance approach will be used, with the assumption of thermodynamic equilibrium at the phase interface. This should make the model useful for either rate-based or equilibrium stagebased computational routines; its basic ingredients are the gas (or vapor) phase mass-transfer coefficient, the liquid-phase coefficient, and the effective interfacial area. Concepts and methods developed in part 1 will be retained, since the interconnected relationships between film thickness, liquid spreading, and liquid holdup are important considerations for interphase mass transfer. Also, the model will be developed along modular lines such that as new packing materials and geometries are introduced they can be accommodated without major changes in the basic approach. Previous Work In a previous paper (Bravo et al., 1985), the present authors proposed an interphase transport model based largely on earlier studies of wetted-wall columns. The gas-phase transfer coefficient was included in a correlation of dimensionless groups:
Shg ) C1RegmScgn
(1)
where the characteristic lengths in the Sherwood and * To whom correspondence should be addressed. E-mail:
[email protected]. † Present address: Celaya Tecnologico, Celaya, Mexico. ‡ Present address: Shell Development Co., Houston, TX.
a
b
Figure 1. Fractional surface coverage of representative packings, for the cyclohexane/n-heptane system. Points are calculated by the Shi-Mersmann relationship (eq 10); lines are based on eq 2.
Reynolds groups were defined on the basis of packing geometry. For the available data base, values of C1 ) 0.0338 and m ) 0.8 were found, with n being taken as 0.333. For the liquid phase, a simple penetration model was used, with exposure time based on liquid flow across one corrugation face of the packing. In order to calculate heights of transfer units, it was necessary to assume complete wetting of the packing surface. This was a reasonable assumption, since the commercial-scale data base available at the time covered only gauze-type packings and the capillarity expected would cause uniform spreading of the liquid on both sides of a
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a
c
d
e
f
Figure 2. Comparison of measured and predicted HETP values for Flexipac 2 and Gempak 2A. Cyclohexane/n-heptane system, total reflux, SRP data: (+) predicted; (o) measured. Table 1. Characteristics of Several Structured Packingsa surface area, void surface enhancement m2/m3 fraction e factor FSE Flexipac-2 Gempak 2A Gempak 2AT Intalox 2T Maxpak Mellapak 250Y Mellapak 350Y Mellapak 500Y Sulzer BX
233 233 233 213 229 250 350 500 492
0.95 0.95 0.95 0.95 0.95 0.95 0.93 0.91 0.90
0.350 0.344 0.312 0.415 0.364 0.350 0.350 0.350
a
Note: All packings listed have a corrugation angle with the horizontal of 45° except Sulzer BX, which has a 60° angle.
corrugated piece. With this assumption, the values of C1 and m given above were found to be very close to those determined much earlier for tubular wetted-wall columns. In later papers, Fair and Bravo (1987, 1990) discussed the expected incomplete wetting of the surfaces of sheetmetal corrugated packings and proposed that at a nearflood condition the effective interfacial area should be about the same as the specific surface area of the
packing. Below the flood point, the following empirical equation was suggested, based on total reflux distillation studies:
ae/ap ) β ) 0.50 + 0.0058 (% flood)
(2)
% flood ) (Fs/Fs,flood × 100)L/G)constant
(3)
where
In the same references the authors pointed out that the value of β should be a much stronger function of liquid rate than gas rate, as has been found in many studies of random packings (for a summary of such studies, see Charpentier, 1981). Thus, eq 2 would be more properly restated in terms of liquid rate; such a relationship can easily be deduced from loading/flooding measurements. In a related investigation, McGlamery (1988) observed that indeed gauze surfaces do not wet completely, especially for aqueous liquids. While the liquid might spread to cover the entire surface, a portion of the surface would become stagnant and thus not participate
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b
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d
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Figure 3. Comparison of measured and predicted HETP values for Intalox 2T and Maxpak. Cyclohexane/n-heptane system, total reflux, SRP data: (+) predicted; (o) measured. Table 2. Data Bank for Model Testing column diameter, m
system
pressure, bar
cyclohexane/n-hexane
0.43
0.33, 1.63, 4.14
o/p-xylenes ethylbenzene/styrene methanol/ethanol chlorobenzene/ethylbenzene
0.07, 0.25, 1.00 0.50 0.50 1.0
0.021, 0.39, 1.0 0.066, 0.13 1.0 0.10, 0.96
i-butane/n-butane
12
6.8, 11.2, 20.4
in the mass-transfer process. The extent of this nonactive area was found not to be a strong function of liquid rate. Importantly, values of β would be less than unity for at least a portion of the operating range of liquid and gas flows. Only two other studies of structured packing efficiency have been reported. In 1987 Spiegel and Meier used the form of eq 1, with m ) 0.8 and n ) 0.333, but with C1 to be determined experimentally. They assumed that the mass-transfer resistance in the liquid phase is either negligible or readily incorporated into the coefficient C1. They found interfacial area to be a
packing
source
Flexipac 2, Gempak 2A, Gempak 2AT, Intalox 2T, Maxpak, Sulzer BX Sulzer BX Sulzer BX Sulzer BX Mellapak 250Y, Mellapak 350Y, Mellapak 500Y Intalox 2T
Univ. of Texas Sakata (1972) Billet (1969) Billet (1969) Spiegel and Meier (1987) Rukovena and Strigle (1991)
function of liquid rate according to
ae ) A1(rLULS)0.2
(4)
with the value of A1 to be determined experimentally. Thus, the Spiegel and Meier method does not provide a priori values for new designs but is useful for interpolating and extrapolating available data. Importantly, these authors provided information on several different sizes of a sheet-metal packing, Mellapak. The other paper dealing with structured packing efficiency was by Billet (1988); this paper deals largely
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Figure 4. Comparison of measured and predicted HETP values for three sizes of Mellapak. Chlorobenzene/ethylbenzene system, total reflux, Spiegel and Meier (1987) data: (+) predicted; (o) measured.
with random packings but does include a model that can be applied to structured packings. A form of eq 1 was used, with experimental data needed to evaluate the constants. Billet took n ) 0.667 and determined C1 and m from measurements. Structured packings considered by Billet were Gempak 2AT, Mellapak 250Y, Montzpak B1-300, and Ralupak 250YC.
are defined as before:
Gas-Phase Transfer
Liquid-Phase Transfer
In the present work, the wetted-wall relationship (eq 1) has been retained, with adjustments in the hydraulic diameter as discussed in part 1. Thus, dimensionless Sherwood, Reynolds, and Schmidt numbers are combined:
The penetration model for predicting the liquid-phase mass-transfer coefficient has been retained, but with the recognition that for some systems the exposure time cannot be taken as a simple function of liquid rate and corrugation length. Because the contribution of the liquid to the overall resistance is generally small in distillation operations, a simple approach to estimating the coefficient has usually been acceptable. As noted above, some researchers have even assumed that the liquid side resistance can be neglected. Recent studies at The University of Texas indicate that, for cases where liquid resistance is significant, the penetration approach can be used, with a modified
(
)( )
kgS (Uge + ULe)FgS ) 0.054 Dg µg
0.8
µg DgFg
0.33
(5)
where the characteristic length S is the side dimension of a corrugation cross section, and the effective velocities
Uge )
Ugs (1 - hL) sin θ
ULe )
ULs hL sin θ
(6)
(7)
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b
b
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Figure 5. Comparison of measured and predicted HETP values for Intalox 2T at higher pressures. Isobutane/normal butane system, total reflux. Experimental work at FRI, Rukovena and Strigle (1991): (+) predicted; (o) measured.
exposure time:
te ) S/CEULe
(8)
where CE is a factor slightly less than unity to account for those parts of the packed bed that do not encourage rapid surface renewal. Experiments with the oxygenair-water system show that, for the several well-known structured packings, CE ∼ 0.9 (Murrieta, 1991). Thus, the departure from the previously published model (Bravo et al., 1985) is not great. Accordingly, the liquidphase mass-transfer coefficient may be calculated by the relationship:
(
kL ) 2
)
DLCEULe πS
Figure 6. Comparison of measured and predicted HETP values for Sulzer BX. Cyclohexane/n-heptane system, total reflux, SRP data: (+) predicted; (o) measured.
far from simple; such factors as initial liquid distribution, radial migration of liquid in the bed, surface wettability, and surface texturing must all enter into the consideration. Problems of achieving uniform liquid distribution throughout a packed bed have been discussed by many authors, with a good practical summary provided by Kunesh et al. (1987). The estimation of interfacial area has been discussed in part 1 of this series, since it is a critical parameter for liquid holdup and film thickness. The extensive studies of Shi and Mersmann (1985) were accepted as reasonable for hydraulic considerations and are accepted here for the case of sheet-metal structured packings:
1/2
(9)
Interfacial Area The wetted-wall relationship (eqs 1 and 5) provides a value of the gas-phase transfer coefficient but must be coupled with a value of the effective interfacial area in order to be useful for packed column analysis and design. The evaluation of effective surface coverage is
ae ) FSE aF Re
29.12(WeLFrL)0.15S0.359 0.2 0.6
L
(1 - 0.93 cos γ)(sin θ)0.3
(10)
where the factor FSE accounts for variations in surface enhancement (lancing, fluting, etc.) and the contact angle γ accounts for surface material wettability. For sheet-metal packing,
cos γ ) 0.9
for s < 0.055 N/m
(11)
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Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1665
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Figure 7. Comparison of measured and predicted HETP values for Sulzer BX. Several systems, total reflux, data of Billet (1969): (+) predicted; (o) measured.
cos γ ) 5.211 × 10-16.835σ
for σ > 0.055 N/m (12)
Values of FSE, (void fraction), and θ (corrugation angle) for some common packings are shown in Table 1. The surface enhancement factor FSE represents an adjustable parameter based on observations of liquid flow on the surfaces (McGlamery, 1988) as well as the relative performance of the surfaces under distillation conditions. It might be noted here that on the basis of eqs 10-12 and for the same flows, phase properties, and packing dimensions, a water system wets a metallic surface about 23% as well as an organic liquid wets the same surface. The dependence of β on liquid rate, computed from eq 10 for the cyclohexane/n-heptane system, is illustrated for two packings in Figure 1; the values of β from eq 2 are shown for comparison. The parameter is liquid Reynolds number, defined as follows:
ReL ) 4dULeFL/µL
(13)
It should be noted that β can have a value greater than 1.0 at high loadings. This is due to rippling in the liquid film and the shearing of liquid from the packing surface at high vapor velocities. The liquid removed is dispersed as droplets, with high surface to volume ratios. The Shi-Mersmann relationship does not deal with the problem of maldistribution of liquid in the packed bed. Thus, in an analysis of performance data, it is necessary to make at least a subjective judgement regarding the degree of uniformity of liquid flow, with greater reliance given to those data for which at least 100 pour points/m2 were contained in the liquid distributor design. As mentioned, Shi and Mersmann did not evaluate gauze surfaces, and for the present work, the gauze wetting has been correlated by:
β ) ae/ap ) 1 - 1.203(ULS2/Sg)0.111
(14)
As opposed to the case for sheet-metal materials, the
gauze does not show an increase in the value of β when liquid rate is increased. Overall Transfer Rate On the basis of conventional definitions of transfer units,
HOG ) HG + λHL
)
Ugs ULS +λ kgae kLae
(15) (16)
where kg, kL, and ae are obtained from eqs 5, 9, and 10, respectively, except for Sulzer BX where eq 14 was used for ae. The term λ is the ratio of slopes, equilibrium line to operating line. For a point in the column where both of these lines may be considered straight, a value of HETP (height equivalent to a theoretical plate) may be calculated:
ln λ HETP ) HOG λ-1
(17)
Validation of Model A data bank for validating the mass-transfer model has been assembled and is described in Table 2. It will be noted that the conditions for the tests cover a wide variety of column sizes, test mixtures, packing types, and packing sizes. The equipment and experimental methods for procuring The University of Texas data were given in part 1 of this paper. For all studies at least 100 pour points/m2 were provided by the top distributor. Observed values of HETP have been taken from the data bank and compared with values predicted by eq 17. Representative comparisons are shown in Figures 2-8. The fit is reasonably good, with the following exceptions. For the gauze surfaces (Sulzer BX) the
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1666 Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996
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Figure 8. Comparison of measured and predicted HETP values for Sulzer BX. o/p-Xylene system, total reflux, data of Sakata (1972): (+) predicted; (o) measured.
degree of wetting in the studies by Billet and Sakata appears to be higher than that achieved in The University of Texas equipment. It is quite possible that the area discount given in eq 14 is too severe. Research in progress is designed to clear up this point. Also, the model fails to represent the data for the butanes system at the highest pressure operated (20.4 bar). As discussed by Kurtz et al. (1991), this may be due to axial mixing effects that would not be covered by the model described in the present paper. Zuiderweg and Nutter (1992) have presented evidence that under high-pressure conditions packed columns can exhibit significant vapor backmixing. On the other hand, recent data for an equivalent structured packing (Fitz et al., 1995) indicate that the model does indeed represent the efficiency of that packing at higher pressure conditions. There is a continuing debate over whether structured packings should be specified for columns operating at pressures higher than about 5-10 bar. Conclusions A fundamental approach has been used in developing the mass-transfer model; in particular, separation of interfacial area from the mass-transfer coefficient has been preserved, and independent work by Shi and Mersmann has been utilized for evaluating the effective interfacial area. Only metal surfaces have been evaluated for structured packing mass transfer, but work reported recently by Uresti-Melendez et al. (1994) indicates that the same model may be used for structured packings fabricated from ceramic materials. The model has been integrated with those for predicting liquid holdup, pressure drop, and flooding capacity of structured packings of the corrugated metal type. It takes into account the texturing of the packing surface as well as the wettability of the surface material when in contact with various types of liquids. It has been
validated for distillation systems at operating pressures ranging from 0.02 to 4.14 bar. In principle, it should also be applicable to absorption and stripping systems where transfer is largely unidirectional. It does not account for axial mixing effects, although these are implicitly included in holdup predictions under high loading conditions and at lower pressures. Acknowledgment This work was supported by the Separations Research Program at The University of Texas at Austin. The authors are grateful to Messrs. Bobby Reeves and Joe Snyder for obtaining the large-scale distillation data and to Mr. Carlos Murietta for making available his results for oxygen-air-water mass transfer in structured packings. Nomenclature ae ) effective area (1/m) ap ) packing surface area (1/m) A1 ) constant in eq 4 CE ) correction factor for surface renewal C1 ) constant in eq 1 deq ) equivalent diameter (m) Dg ) diffusion coefficient, gas phase (m2/s) DL ) diffusion coefficient, liquid phase (m2/s) Fs ) gas flow factor ()Ugs(rg)0.5) [m/s (kg/m3)0.5] FrL ) Froude number for liquid FSE ) factor for surface enhancement G ) mass velocity of gas (kg/m2 s) hL ) fractional holdup of liquid HG ) height of a gas-phase-transfer unit (m) HL ) height of a liquid-phase-transfer unit (m) HOG ) height of an overall transfer unit, gas-phase basis (m) HETP ) height equivalent to a theoretical plate (m) kg ) mass-transfer coefficient, gas phase (m/s) kL ) mass transfer coefficient, liquid phase (m/s)
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Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1667 L ) mass velocity of liquid (kg/m2 s) m ) exponent in eq 1 n ) exponent in eq 1 Reg ) Reynolds number for the gas ReL ) Reynolds number for the liquid Shg ) Sherwood number for the gas S ) side dimension of corrugation (m) te ) exposure time, penetration model (s) Uge ) effective gas velocity (m/s) Ugs ) superficial gas velocity (m/s) ULe ) effective liquid velocity (m/s) UL, ULS ) superficial liquid velocity (m/s) WeL ) Weber number for the liquid Greek Letters β ) ratio of effective to total packing surface area γ ) contact angle (deg) δ ) thickness of film (m) ∆ ) increment ) void fraction of packing θ ) angle with horizontal for falling film or corrugation channel (deg) λ ) ratio of slopes, operating line to equilibrium line µg ) gas viscosity (kg/m‚s) µL ) liquid viscosity (g/m‚s) π ) 3.1416... Fg ) gas density (kg/m3) FL ) liquid density (kg/m3) σ ) surface tension (N/m) Dimensionless Groups CaL ) ULµL/Fgc ) Capillary number for liquid FrL ) UL2/Sg ) Froude number for liquid Reg ) UgsSFg/µg ) Reynolds number for gas ReL ) ULSFL/µL ) Reynolds number for liquid WeL ) UL2FLS/σgc ) Weber number for liquid Subscripts S-M ) Shi-Mersmann stat ) static op ) operating
Literature Cited Billet, R. Optimization and Comparison of Mass Transfer Columns. Inst. Chem. Eng. Symp. Ser. 1969, 32, 4-42. Billet, R. Relationship Between Residence Time, Fluid Dynamics and Efficiency in Counter Current Flow Equipment. Chem. Eng. Technol. 1988, 11, 139-148.
Bravo, J. L.; Rocha, J. A.; Fair, J. R. Mass Transfer in Gauze Packings. Hydrocarbon Proc. 1985, 64 (1), 91. Charpentier, J.-C., Mass Transfer Rates in Gas-Liquid Absorbers and Reactors. In Advances in Chemical Engineering; Drew, T. B., Cokelet, G. R., Hoopes, J. W., Vermeulen, T., Eds.; Academic Press: New York, 1981; Vol. 11, pp 2-133. Fair, J. R.; Bravo, J. L. Prediction of Mass Transfer Efficiencies and Pressure Drop for Structured Tower Packings in Vapor/ Liquid Service. Inst. Chem. Eng. Symp. Ser. 1987, 104, A183. Fair, J. R.; Bravo, J. L. Distillation Columns Containing Structured Packings. Chem. Eng. Prog. 1990, 86 (1), 19. Fitz, C. W.; Shariat, A.; Spiegel, L. Performance of Structured Packing at High Pressure. Presented at AIChE Meeting, Houston, TX, March 20, 1995. Kunesh, J. G.; Lahm, L.; Yanagi, T. Commercial Scale Experiments that Provide Insight on Packed Tower Distributors. Ind. Eng. Chem. Res. 1987, 26, 1845-1850. Kurtz, D. P.; McNulty, K. J.; Morgan, R. D. Stretch the Capacity of High-Pressure Distillation Columns. Chem. Eng. Prog. 1991, 87 (2), 43. McGlamery, G. G. Liquid Film Transport Characteristics of Textured Metal Surfaces. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, 1988. Murrieta, C. Liquid Phase Mass Transfer in Structured Packing. Separations Research Program report, The University of Texas at Austin, Austin, TX, October 1991. 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. Rukovena, F.; Strigle, R. F. Paper presented at Houston AIChE Meeting, March 1991. Sakata, M. Tests of 1000, 250 and 70 mm Diameter Columns with Koch Sulzer Packing. Plant Test Report No. 22; Fractionation Research, Inc.: Stillwater, OK, 1972. Shi, M. G.; Mersmann, A. Effective Interfacial Area in Packed Columns. Ger. Chem. Eng. 1985, 8, 87. Spiegel, L.; Meier, W. Correlations of the Performance Characteristics of the Various Mellapak Types (Capacity, Pressure Drop, Efficiency). Inst. Chem. Eng. Symp. Ser. 1987, 104, A203. Uresti-Melendez, J.; Alvarado, F. J.; Rocha, J. A. Effect of Packing Material in Distillation with Structured Packings. In Separation Technology; Vansant, E. F., Ed.; Elsevier Science: Amsterdam, The Netherlands, 1994; pp 153-162. Zuiderweg, F. J.; Nutter, D. E. Evidence of Vapour Backmixing in Packed Columns in the Case of High Pressure Distillation. Inst. Chem. Eng. Symp. Ser. 1992, 128, A481.
Received for review January 18, 1996 Accepted March 7, 1996X IE940406I X Abstract published in Advance ACS Abstracts, April 15, 1996.
