Comprehensive Mass Transfer Model for Distillation Columns

Oct 12, 2006 - DiotisalVi 2, Pisa I-56126, Italy, Laboratory for Process Equipment, Delft UniVersity of Technology, 2628 CA. Delft, The Netherlands, a...
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Ind. Eng. Chem. Res. 2006, 45, 7967-7976

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Comprehensive Mass Transfer Model for Distillation Columns Equipped with Structured Packings Lorenzo Del Carlo,†,‡ Z ˇ arko Olujic´ ,‡ and Alessandro Paglianti*,§ Department of Chemical Engineering, Industrial Chemistry and Materials Science, UniVersity of Pisa, Via DiotisalVi 2, Pisa I-56126, Italy, Laboratory for Process Equipment, Delft UniVersity of Technology, 2628 CA Delft, The Netherlands, and Department of Chemical, Mining and EnVironmental Engineering, UniVersity of Bologna, Viale Risorgimento 2, Bologna I-40136, Italy

A new mechanistic model for the evaluation of mass transfer performance in columns equipped with structured packings is proposed. The model is developed by taking into account the interactions of falling film with the gas phase, and thus, it includes the effects of both the physical properties of the working fluids and the geometrical characteristics of the packings. The model does not introduce any adjustable parameter but relies on the semiempirical equations developed earlier for the prediction of the pressure drop and the mass transfer coefficients in absorption processes. The model has been validated using experimental data obtained under total reflux conditions with different systems at different operating conditions, including the conventional and high capacity packings of different specific surface areas and different corrugation angles. The results indicated that simple mechanistic models can be used with confidence to describe the fluid dynamics within the packings. The adoption of the present model is suggested for systems for which experimental data are not available, while for experimentally tested systems, higher prediction accuracy could be obtained using different models, based on a larger number of adjustable parameters that have to be tuned on the experimental data. The knowledge of the liquid film hydrodynamic behavior can also allow understanding of the reasons for some observed deviations in performance such as the efficiency “hump” occurring at specific operating conditions in distillation columns. 1. Introduction In the last decades, researchers and manufacturers have studied and developed new types of column internals to improve performances for distillation processes. One of the most important improvements has been the introduction of structured packings, especially for vacuum applications.1,2 Although the structured packings are adopted worldwide, the models for the design of the columns are not yet fully reliable.3 Recently, to improve the modeling accuracy, some approaches based on the neural network4,5 have also been suggested. Unfortunately, the neural-network models are not broadly established, because so far their applicability to commercial-scale apparatuses has not been verified.6,7 Beside the question on the more appropriate modeling approach for designing distillation columns, other questions are still to be further clarified. For instance, the effective surface area available for the mass transfer is an essential parameter for predicting mass transfer performances, but a satisfactory method for its evaluation has not been identified.8 Also, the analysis of the relations published in the open literature9-12 shows that a good agreement cannot be found on the effects of superficial velocity, viscosity, density, and surface tension of the liquid phase on the effective surface area. Currently, the effective surface area is evaluated by correlations that are all based on the study of the falling film fluid dynamic,13 but important differences distinguish them. For gauze packing, in some equations the total geometrical surface is assumed to be * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: +39-051-2090403. Fax: +39-051-6347788. † University of Pisa. ‡ Delft University of Technology. § University of Bologna.

wetted,14 but this hypothesis is removed when sheet metal structured packings are used.15 In some cases, the interfacial mass transfer area and the wetted area are supposed to overlap,16,17 while others include a correction accounting for the flow instabilities between the sheets.11 Finally, some empirical relations take into account the effect of the liquid load only,18 or all relevant parameters, relying on a well-established correlation developed originally for random packings but adapted to consider appropriately the ordered geometry of structured packings, including the effect of the corrugation angle.19 Other important open questions concern the relative magnitude of the mass transfer resistance in the liquid phase. In some published models, the liquid resistance is assumed to be small,20 while some authors suggest that the correlation of the experimental data can be improved if a nonnegligible resistance in the liquid phase is assumed.8,21 Also, most of the published models for liquid mass transfer coefficients are based on the penetration theory,14,22 while others suggest that, for evaluating the liquid-side mass transfer coefficient, the liquid-film thickness has to be modeled.23,24 The gas-side mass transfer coefficient is usually evaluated using equations derived from those proposed by Johnstone and Pigford,9,14,20,22,25 and an acceptable agreement among the proposed correlations can be found. Some improvements have been suggested to remove the hypothesis of laminar flow, for introducing the effects of drop formation and film detachment26 or by using the penetration theory.12 Finally, to design distillation columns, the prediction of the fluid-dynamics behavior of the two phase mixture is also required. The correct prediction of the two-phase fluid dynamics is important, not only for the evaluation of the packing pressure drops but also because the mass transfer performance, e.g., HETP, changes if the column operates at a load close to the

10.1021/ie060503z CCC: $33.50 © 2006 American Chemical Society Published on Web 10/12/2006

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Table 1. Factors Suggested by Brunazzi and Paglianti24 to Be Used in Eq 7 for Corrugated Sheets Packings angle of flow channel from horizontal (deg)

c3

c4

c5

γ (deg)

45° 60°

16.43 16.43

0.915 0.915

0.09 0.09

60° 69°

flooding conditions.27 The mixture fluid dynamics is also significant to understand the effect of the working pressure on the mass transfer performances. In some cases, the experimental results show that mass transfer performance improves with increasing pressure,27 while above a critical value, the efficiency decreases with increasing pressure.28,29 In this paper, a simple model for evaluating both the fluid dynamics and the mass transfer efficiency of distillation columns equipped with structured packings is presented. The model has been tested on the basis of a number of experimental data, including that obtained most recently with a high-specific-area, high-capacity structured packing using a total reflux pilot-scale distillation column available at the Delft University of Technology30 as well as those available in the open literature. The aim of the paper is to show that structured packing efficiency can be predicted with good accuracy using only the geometrical characteristics of the packings without introducing any empirical parameter for tuning the model. 2. Proposed Model The separation performance of distillation columns is usually expressed as the number of equilibrium stages required at a given reflux ratio to achieve the desired degree of separation. For columns equipped with structured packings, the mass transfer efficiency must be known to enable translation of the number of equilibrium stages into corresponding bed height. A common measure of the packing efficiency is the packing height equivalent to an equilibrium stage or theoretical plate (HETP), defined according to the two-film theory, as

(

)

USL ln λ USG HETP ) +λ λ - 1 kGae kLae

(1)

where λ is the well-known stripping factor, i.e., the ratio of the slopes of equilibrium and operating lines in the McCabe (y-x) plot representing a given test system, USG (m/s) is the superficial vapor velocity, USL (m/s) is the superficial liquid velocity, kG (m/s) and kL (m/s) are the vapor-side and the liquid-side mass transfer coefficients, respectively, and ae (m2/m3) is the effective specific (wetted) area. A recent thorough evaluation of the predictive models for structured packings has indicated that no satisfactory method is available for estimating the effective area under actual operating conditions.8 In the present modeling approach, some of the previous results obtained on the study of the absorption process in columns equipped with structured packings have been used. In particular, for working conditions falling below the flooding point, when the two-phase mixture flows as a stratified regime, the effective surface area available for the mass transfer has been calculated from the experimental liquid holdup values16 as

(

) (

de sin ϑ 1.5 FLg ae ) hL ag 4 3µLUSL

)

0.5

(2)

where ag (m2/m3) is the geometric specific surface area,  (m3/ m3) is the void fraction, ϑ (deg) is the angle of the inclined

flow channel with respect to the horizontal axis, hL (m3/m3) is the liquid holdup, and FL (kg/m3) and µL (Pa s) are the density and the viscosity of the liquid phase, respectively. The characteristic hydraulic diameter of the channel, de (m), is defined as

de )

4 ag

(3)

The expression for the liquid holdup is31

( )

c2 hL ) c1a0.83 g (3600USL)

µL µL,0

0.25

(4)

where µL,0 is the viscosity of water at 20 °C and the constants c1 and c2 differ, depending on the liquid load:

c1 ) 0.0169 and c2 ) 0.37 for USL < 0.011 m/s c1 ) 0.0075 and c2 ) 0.59 for USL > 0.011 m/s Equation 4 is strictly valid only for Mellapak packings, but in order to arrive at a model with a small number of adjustable parameters, it has been used also for the analysis of other types of structured packing. The vapor-phase mass transfer coefficient is described using the following equation,14 0.33 ShG ) 0.054Re0.8 G,eff ScG

(5)

where ShG is the Sherwood number, ScG is the Schmidt number, and ReG,eff is the Reynolds number based on the relative effective velocity between the two phases:

Urel )

USG (1 - hL) sin ϑ

+

USL hL sin ϑ

(6)

For the liquid-phase mass transfer coefficient, the following equation is used,24

ShL ) c3

Gzc4 Kac5

(7)

with

Ka )

σ3FL

(8)

µL4g

and

Gz ) ReLScL

δ sin γ Hel

(9)

where σ (N/m) is the surface tension, g (m/s2) is gravitational acceleration, δ (m) is the liquid film thickness, and Hel (m) is the height of the packing element. The factors c3, c4, and c5 and the effective liquid flow angle γ (deg) have been estimated on the basis of previous results.24 The corresponding values are shown in Table 1. Under the hypothesis of negligible shear stress at the interface between vapor and liquid phases, the film thickness, δ, can be estimated from24

δ)

(

USL 3µL FLg sin γ hL sin γ

)

0.5

(10)

Ind. Eng. Chem. Res., Vol. 45, No. 23, 2006 7969 Table 2. Experimental Database packing

system

Mellapak 752.Y

cyclohexane-n-heptane methanol-water chlorobenzene-ethylbenzene chlorobenzene-ethylbenzene cyclohexane-n-heptane i-butane-n-butane chlorobenzene-ethylbenzene

1.013 1.013 0.1, 0.4, 0.96 0.1, 0.4, 0.96 0.34, 1.65 6.9, 11.4 0.96

chlorobenzene-ethylbenzene chlorobenzene-ethylbenzene chlorobenzene-ethylbenzene cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane chlorobenzene-ethylbenzene

0.1 0.1, 0.96 0.1, 0.96 0.33, 1.63, 4.14 0.33, 1.63, 4.14 0.33, 1.63, 4.14, 6.8, 11.2, 20.4 0.33, 1.63, 4.14 0.17, 0.33, 1.03, 4.14 0.17, 0.33, 1.03, 4.14 0.17, 0.33, 1.03, 4.14 0.17, 0.33, 1.03, 4.14 1.03 0.33, 1.03, 4.14 0.33, 1.03, 4.14 1

Mellapak 452.Y Mellapak 250.Y

Mellapak 350.Y Mellapak 500.Y Flexipac 2 Gempak 2A Intalox 2T Maxpak B1-250 B1-250M B1-350 B1-350M B1-400 B1-250.60 B1-400.60 A3-500

operating pressure (bar)

origin present data present data Sulzer Chemtech33 Sulzer Chemtech33 Fitz et al.28 Fitz et al.28 Rocha et al.20 Gualito et al.34 Rocha et al.20 Rocha et al.20 Rocha et al.20 Rocha et al.20 Rocha et al.20 Rocha et al.20 Rocha et al.20 Olujic et al.27 Olujic et al.27 Olujic et al.27 Olujic et al.27 Olujic et al.3 Olujic et al.3 Olujic et al.3 Shilkin and Kenig35

Table 3. Physical Properties for the Systems Used system

pressure (bar)

FG (kg/m3)

µG (kg/m/s)

DG (m2/s)

FL (kg/m3)

µL (kg/m/s)

DL (m2/s)

σ (N/m)

λ

cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane cyclohexane-n-heptane chlorobenzene-ethylbenzene chlorobenzene-ethylbenzene chlorobenzene-ethylbenzene i-butane-n-butane i-butane-n-butane i-butane-n-butane i-butane-n-butane methanol-water

0.17 0.33 1.013 1.03 1.65 4.14 0.1 0.4 0.96 6.9 11.4 20.7 27.2 1.013

0.66 1.19 3 3.53 5.45 13.4 0.39 2 3.26 17 30 58 85 1.15

6.67E-06 6.94E-06 8.09E-06 7.78E-06 8.33E-06 9.17E-06 7.82E-06 8.50E-06 9.37E-06 8.40E-06 9.00E-06 9.80E-06 1.02E-05 1.21E-05

1.33E-05 1.14E-05 4.53E-06 4.17E-06 3.06E-06 1.39E-06 2.73E-05 1.50E-05 4.09E-06 7.97E-07 5.49E-07 3.56E-07 2.91E-07 3.70E-05

659 657 658 625 609 561 927 905 858 523 487 426 383 854

4.67E-04 4.31E-04 2.87E-04 2.97E-04 2.31E-04 1.61E-04 4.01E-04 3.20E-04 2.50E-04 1.10E-04 8.80E-05 6.20E-05 4.90E-05 3.17E-04

2.31E-09 2.72E-09 4.35E-09 4.44E-09 6.11E-09 9.17E-09 4.42E-09 6.00E-09 7.55E-09 1.05E-08 1.38E-08 2.08E-08 2.68E-08 7.25E-09

0.018 0.017 0.0154 0.014 0.012 0.008 0.026 0.022 0.018 0.0073 0.0048 0.0021 0.0011 0.021

0.884 0.905 0.934 0.934 0.945 0.962 0.994 0.996 0.997 1.3 1.23 1.15 1.10 0.675

If the shear stress cannot be neglected, e.g., for high-pressure applications, the film thickness can be estimated using a procedure proposed by Brunazzi and Paglianti,32

δ)

τi + 2µL

x( ) [

]

τi 2 ULe dP + 4 FLg sin ϑ 2µL dy chan 3µL 2 dP F g sin ϑ 3µL L dy chan

[

( ) ( ) ]

(11)

where τi (Pa) is the shear stress at the vapor-liquid interface, (dP/dy)chan (Pa/m) is the pressure drop per meter flow channel length, and ULe (m/s) is the effective liquid velocity. 3. Experimental Database The experimental data considered in this study are summarized in Table 2, which includes information on the packing type and size, test system, and operating conditions. New are data obtained recently in Delft, with Mellapak 752.Y packing, using cyclohexane/n-heptane and methanol/water systems at atmospheric pressure, respectively. Chlorobenzene/ethylbenzene data for the same packing are from the Sulzer tests as well as the data for Mellapak 452.Y packing.33 Conventional Mellapak 250.Y performance data, including high-pressure operation, come from Fractionation Research Inc. (FRI) tests described in the open literature.20,28,34 For conventional and high-capacity Montz packings, the experimental data were obtained using

facilities available at the Separations Research Program (SRP) at the University of Texas at Austin.3,27 For the Koch and Jaeger packings, the experimental data are available in the open literature.20 Table 3 contains all relevant physical properties of the different tests systems, which were used as the basis for model validation purposes. 4. Results and Discussion Figure 1a shows a comparison of predicted and measured efficiencies of Mellapak 752.Y, expressed as a function of the F factor. The latter, i.e., the product of the superficial vapor velocity and the square root of the vapor density, is a common measure for the vapor load of a column. In the case of total reflux operation, a change in vapor load is accompanied by a change in the liquid load proportional to the product of vapor superficial velocity and the ratio of vapor and liquid densities. Figure 1a shows that, for both test systems, the present model follows in the trend but slightly overpredicts the measured efficiency, which, however, is on the safe side. The corresponding parity plot shown in Figure 1b includes also the Sulzer data on the chlorobenzene/ethylbenzene (CB/EB) system at three operating pressures shown as lines. Each of the experimental sets shown in Figure 1b is characterized by similar behavior; the lower experimental values of the HETP are approximately on a line parallel to the 45° line; at a critical point, the increment of the experimental HETP is much higher than the increment

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Figure 3. Parity plot of computed HETP vs experimental HETP for column equipped with Mellapak 250.Y packing. Error mean square ) 15%.

Figure 1. Comparison between measured and calculated data for column equipped with Mellapak 752.Y packing: (a) HETP vs F factor and (b) parity plot including additional data. Error mean square ) 14%. Figure 4. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-250 packing. Error mean square ) 21%.

Figure 2. Parity plot of computed HETP vs experimental HETP for column equipped with Mellapak 452.Y packing.

of the calculated HETP. The strongly deviating points are those measured close to the flooding point of the packing. Indeed, by approaching the flooding point, the model tends to underestimate the strongly increasing experimental values of HETP because it is based on the hypothesis that the two-phase mixture flows on the packing as a stratified flow, which is valid for the preloading region only. In the loading region, especially close to the flooding conditions, this is certainly not the case. As can be seen from Figure 1a, within the normal operating range, the HETP values of cyclohexane-n-heptane and methanol-water systems are predicted with sufficient accuracy by the present model. The data for the chlorobenzene-ethylbenzene system, which show a particular trend, indicate that the capability of the model to catch the experimental data depends, to some extent, on the operating pressure. Indeed, at a pressure of 0.4 bar, the model predicts the experimental values with good accuracy, whereas at lower and higher pressures, the model tends to overestimate the experimental data. The confirmation for the observed trend of the experimental data for the chlorobenzene-

Figure 5. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-250M packing. Error mean square ) 16%.

ethylbenzene system and the corresponding model performance can be found in Figure 2, which shows corresponding data obtained at Sulzer with Mellapak 452.Y packing. The analysis of the Mellapak 250.Y is restricted to the data range falling below the flooding condition. Moreover, only the data measured above an F factor > 0.5 m/s (kg/m3) have been considered, because of the strong detrimental effect of the liquid maldistribution associated with very low liquid load experienced at low vapor loads. The experimental results are compared with the model predictions in Figure 3. Despite the scatter of the data, the accuracy of the model can be considered acceptable, since the error mean square is ∼15%. To verify to which extent the proposed model is suitable for other types of structured packings, it has been applied also to the Montz B1 packings family. The results obtained with the packings B1-250 and B1-250M27 are shown in Figures 4 and 5, respectively. The geometrical difference between the two

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Figure 6. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-350 packing. Error mean square ) 13%.

Figure 9. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-250.60 packing. Error mean square ) 12%.

Figure 7. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-350M packing. Error mean square ) 7.5%.

Figure 10. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-400.60 packing. Error mean square ) 21.5%.

Figure 8. Parity plot of computed HETP vs experimental HETP for column equipped with Montz B1-400 packing. Error mean square ) 6.5%.

packings is related to the bottom part of the element that, for the B1-250M, is a smooth long bend,27 whereas in the case of the conventional B1-250 packing, the change in gas flow direction at the transition between packing elements is sharp, i.e., 90°. This rather small difference in corrugation geometry influences strongly the pressure drop and, consequently, the capacity of the packing. However, the mass transfer efficiency, as measured with the cyclohexane/n-heptane system at different operating pressures, appeared to be affected to a lesser extent, mainly in the preloading region.27 To exclude detrimental end effects, for the B1-250M, the analysis is limited to an F factor < 2.5 m/s (kg/m3). As can be observed from the comparison between the experimental data and the computed values of HETP shown in Figures 4 and 5, for both Montz B1 packing types, the proposed model overestimates the experimental value of the HETP. In this case, the model inaccuracy is most likely to ascribe to both eq 4 and to the factors of Table 1, since they

Figure 11. Parity plot of computed HETP vs experimental HETP for column equipped with various packings.

have been experimentally obtained for the Mellapak family. Encouragingly, when increasing the specific area, the HETP overestimation turns almost negligible, as can be observed from the comparison between experimental and calculated values for the B1-350 and B1-350M packings shown in Figures 6 and 7, respectively. The same trend is confirmed by the analysis of the results relevant to the conventional B1-400 packing shown in the Figure 8. Finally, the data for Montz B1-250.60 and B1-400.60 packings have been analyzed in order to investigate the capability of the model to account for the effect of the corrugation angle. The comparisons between experiment and model shown in Figures 9 and 10 indicate that, in this case, the model seems to underestimate the experimental values of the HETP and the error increases with decreasing operating pressure and increasing specific surface of the packings, respectively.

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To extend the model validation to other commercial structured packings, the experimental data published by Rocha et al.20 have been analyzed. Figure 11 shows a comparison between calculated and measured HETP values. As can be observed, the error seems to be acceptable for all the packings analyzed. In view of the overall agreement between calculated and measured efficiencies for practically all commercially available packings, obtained with different systems and different operating conditions, the predictive accuracy of the proposed model is quite acceptable. This is surprising to some extent, if we consider the fact that the model does not require any adjustable parameter and relies on the mass transfer coefficients and effective area correlations developed originally for absorption columns equipped with conventional Mellapak type structured packings. Furthermore, the present model can be also adopted to estimate the liquid composition along the distillation column. In Figure 12, the experimental data of the liquid molar composition for different values of the F factor in a column working at atmospheric conditions with a mixture of chlorobenzene/ethylbenzene35 are shown together with the model predictions. As can be seen, the model predicts the experimental trend very well for all three values of the F factor. It is worth noticing that good predictions have been obtained also in the case of F factor ) 1.113 Pa1/2, while, for such a condition, a large overestimation of the chlorobenzene (CB) composition was obtained in previous works.35 It is worth observing that, to date, the available models have been developed for working conditions where negligible interactions between the vapor and the liquid phases could be assumed. Some empirical corrections have been proposed34 for taking into account the effects of the interfacial shear stress when the columns work at high pressure, but how to model the interactions is still an open question. In the present approach, the gas-liquid shear stress has been taken into account;32 therefore, the mass transfer performances can be predicted even for high-pressure applications, without introducing adjustable parameters. In the case of high-pressure applications, a correct comparison between experimental data and theoretical results has to consider the effects of the premature flooding occurring in some parts of the packed bed.29,36 The experimental values of HETP measured at the bottom and the top of the column36 and the relevant values of the liquid holdup computed with the present model are shown in Figure 13. It can be observed that the theoretical flooding of the column occurs at F factor ) 0.72 Pa1/2. Approximately at the same working conditions, the experimental HETP starts to assume different increasing values, depending on the measurement point, while very similar values were obtained for lower F factors. Finally, the theoretical model indicates that, if the F factor > 0.72 Pa1/2, the flooding of some channels within the bulk of the structured packing could occur. This theoretical result agrees with the explanations for the presence of the efficiency “hump” that has been ascribed to a liquid backmixing36 due to the building-up of the liquid phase. Figure 14 shows a parity plot comparing the experimental critical F factor and the corresponding data evaluated with the present model. The experimental data have been published by Fitz et al.28 for the system isobutane/n-butane in a column equipped with Mellapak 250.Y, by Olujic et al.27 for the system cyclohexane/n-heptane in a column equipped with B1-250M, and by Fair et al.22 for the same system but equipped with B1250. The experimental values of HETP have been obtained by plotting the HETP against the F factor and selecting, as the

Figure 12. Comparison of calculated and experimental chlorobenzene (CB) concentration profiles: chlorobenzene/ethylbenzene system, and Montz A3500 packing.

critical condition, the value of the F factor above which the HETP starts to increase, indicating the presence of the efficiency “hump”. The computed values have been estimated as the maximum F factor above which the liquid holdup tends to 1 (see Figure 13). The accuracy of the model seems to be acceptable for all analyzed systems. If the analysis of the HETP is limited to the working conditions falling below the above-cited critical point, the model predicts the value of HETP with sufficient accuracy, (see Figure 15). A large error arises only for a very low value of the F factor, ∼0.2, which is probably due to the fact that corresponding liquid flowrate is so small that it induces a severe maldistribution of the liquid over the packing.

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Figure 13. Experimental data of HETP and computed values of liquid holdup vs F factor: working pressure 20.7 bar, i-butane-n-butane system, and Mellapak 250.Y packing. Open circles indicate experimental data measured at the column bottom, and filled circles indicate experimental data measured at the column top.

Figure 15. Experimental and computed HETP vs F factor: Mellapak 250.Y packing, pressure 20.7 bar, and i-butane-n-butane system.

of the knowledge of the liquid holdup, the inaccurate evaluation of this parameter could induce an imprecise evaluation of the mass transfer efficiency of the analyzed packing. The estimated packing efficiencies have been compared with experimental data collected with different structured packings working with different systems, and the overall predictive accuracy of the proposed system has been shown to be acceptable for conceptual design purposes. The link between the mechanistic model for the fluid dynamics of the falling liquid film and the models for evaluating liquid and gas mass transfer coefficients allows for the explanation of the origin of the “efficiency hump” observed in some occasions. Most probably, the observed strong drop in mass transfer efficiency is due to a partial flooding of the packing, which gives rise to maldistribution and liquid backmixing. Acknowledgment

Figure 14. Parity plot of computed critical working conditions vs experimental critical conditions for column equipped with Montz B1250M, Montz B1-250, and Mellapak 250.Y packings. Error mean square ) 8%.

5. Conclusions The present work was aimed at the development and validation of a simple but comprehensive predictive method to estimate the HETP of distillation columns equipped with structured packings. The proposed method is based on effective area and mass transfer coefficient equations developed originally for Mellapak type structured packings used in absorption columns, which implies a stronger contribution of the liquid-side resistance than anticipated in the case of mainly vapor-side controlled distillation applications. Most importantly, the proposed method does not require any additional adjustable parameter. The model does not contain tuning parameters, but it is based on the evaluation on the fluid-dynamic behavior of a falling film. Therefore, it can be strictly applied only when the liquid flows as a stratified film. Because the evaluation of the film characteristics is based

Dedicated to Professor Giuliano Nardini on the occasion of his 70th birthday. The technical support of Sulzer Chemtech is gratefully acknowledged. Appendix The following example shows how the model suggested in the present work can be applied to the separation of ethylbenzene-styrene mixtures for the evaluation of the column HETP. The system and the working conditions are equal to those used by Billet and Schultes.12 Let’s assume that the top product contains a molar fraction of ethylbenzene equal to 99%, and the bottom product has a molar fraction of styrene equal to 99.9%. The column works under reflux ratio r ) 6, and the top pressure is equal to 66.7 mbar, with an average relative volatility, R, of 1.37. The analyzed packing is a Montz B1-400. In the following, the height equivalent to a theoretical plate is computed. The influence of the composition of the mixture has been evaluated by dividing the column into two sections, as suggested by Billet and Schultes.12 In the first section, the liquid molar fraction of ethylbenzene is in the range of 99-80% with an average slope of the equilibrium line m ) 0.7737.

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The physical properties used are

It is now possible, from eq 5, to evaluate the vapor-phase mass transfer coefficient MV ) 105.98 kg/kmol ML ) 105.95 kg/kmol FV ) 0.290 kg/m3 FL ) 840.1 kg/m3 µV ) 7.31 × 10-6 Pa s µL ) 0.426 × 10-3 Pa s DV ) 31.9 × 10-6 m2/s DL ) 3.154 × 10-9 m2/s σ ) 24.01 × 10-3 N/m

molecular weight of vapor molecular weight of liquid density of vapor density of liquid dynamic viscosity of vapor dynamic viscosity of liquid diffusivity in vapor diffusivity in liquid surface tension of liquid

ScG )

0.33 ShG ) 0.054Re0.8 G,eff ScG )

0.054 × 27190.8 × 0.790.33 ) 27.93 kG )

The geometrical characteristics of the packing are

capacities in the first section superficial velocity vapor phase superficial velocity liquid phase molar vapor flow molar liquid flow

Ka )

USG ) 4.57 m/s USL ) 1.36 × 10-3 m/s V˙ ) 423.96 kmol/h L˙ ) 364.40 kmol/h

The hydraulic diameter de and the liquid holdup hL can be calculated from eqs 3 and 4.

de )

4 4 × 0.96 ) 9.75 × 10-3 m ) ag 394

( )

µL c2 hL ) c1a0.83 g (3600USL) µL,0

0.25

δ)

(

(3600 × 1.36 × 10-3)0.37

)

0.25

(

) ( ) ( ) ( 0.5

840.1 × 9.81 3 × 4.26 × 10-4 × 0.00136

(24.01 × 10-3)3840.1 (0.426 × 10-3)49.81

) 3.599 × 1010

(

(

)

0.5

)

3 × 0.426 × 10-3 1.36 × 10-3 ‚ 840.1 × 9.81 sin 60 3.51 × 10-2 sin 60

FL(4δ) ReL )

(

)

0.5

)

8.95 × 10-5 m

)

USL hL sin γ ) µL

(

)

1.36 × 10-3 3.51 × 10-2 sin 60 ) 32 0.426 × 10-3

840.1(4 × 8.95 × 10-5)

)

0.5

) 0.81

ae ) 0.81 × 394 ) 319.14 m2 It is important to notice that, if the effect of the surface-tension gradient is taken into account, as proposed by Billet and Schultes,12 a reduction of the value of the interfacial area of ∼9.3% is obtained. For evaluating the Reynolds number of the gas phase, the relative velocity between the vapor and liquid phases has to be computed with eq 6.

USG

USL ) Urel ) + (1 - hL) sin ϑ hL sin ϑ 4.57 + (1 - 3.51 × 10-2)0.96 sin 45 0.00136 ) 7.03 m/s 3.51 × 10-2 × 0.96 sin 45 ReG,eff )

)

3µL USL FLg sin γ hL sin γ

)

9.75 × 10-3 sin 45 0.03511.5 × 4 × 0.96

µL4g

) 3.51%

The interfacial area for mass transfer can be calculated from eq 2

de sin ϑ 1.5 FLg ae ) hL ag 4 3µLUSL

σ3FL

Since the analyzed packing has an angle of flow channel from horizontal equal to the angle of the Mellapak 250.Y packing, in the following the slope of the steepest descendent line with respect to the horizontal axis, γ, has been assumed to be equal to 60°:

) 0.0169 × 3940.83 × 4.26 × 10-4 10-3

ShGDG 27.93 × 31.9 × 10-6 ) ) 0.091 m/s de 9.75 × 10-3

The liquid-phase mass transfer coefficient can be evaluated from eq 7

ae ) 394 m2/m3  ) 0.96 m3/m3 Hel ) 0.197 m ϑ ) 45°

packing specific area void fraction element height angle of flow channel from horizontal

µG 7.31 × 10-6 ) ) 0.79 FGDG 0.29 × 31.9 × 10-6

UrelFGde 7.03 × 0.29 × 9.75 × 10-3 ) ) 2719 µG 7.31 × 10-6

ScL )

µL 0.426 × 10-3 ) ) 160.77 FLDL 840.1 × 3.154 × 10-9

Gz ) ReLScL

δ sin γ ) Hel 32 × 160.77 ×

8.95 × 10-5 sin 60 ) 2.02 0.197

Because of the physical similarities between Mellapak 250.Y and Montz B1-400 packings, the coefficients c3, c4, and c5 of eq 7 have been assumed to be equal to those experimentally obtained for the Mellapak family.

2.020.915 Gzc4 ) 3.51 ShL ) c3 c ) 16.43 × 5 Ka (3.599 × 1010)0.09 kL )

ShLDL 3.51 × 3.154 × 10-9 ) ) 3.09 × 10-5 m/s 4δ 4 × 8.95 × 10-5

Finally, the values of the packing height equivalent to a theoretical plate can be computed as

λ)m

423.96 V˙ ) 0.7737 × ) 0.9 L˙ 364.4

Ind. Eng. Chem. Res., Vol. 45, No. 23, 2006 7975

HETP )

(

(

)

USL ln λ USG ln 0.9 +λ ) × λ - 1 kGae kLae 0.9 - 1

)

4.57 1.36 × 10-3 ) + 0.9 × 0.091 × 319.14 3.09 × 10-5 × 319.14 0.296 m

The number of theoretical stages per unit height are equal to 1/0.296 ) 3.38. Nomenclature ae ) effective area, m2/m3 ag ) packing specific area, m2/m3 c1 ) constant in eq 4 c2 ) constant in eq 4 c3 ) constant in eq 7 c4 ) constant in eq 7 c5 ) constant in eq 7 D ) diffusivity, m2/s de ) equivalent diameter of the channel, m (dP/dy)chan ) pressure drop in the channel, Pa/m F factor ) gas capacity factor ) USGFG0.5, m/s(kg/m3)0.5 g ) gravitational constant, m/s2 hL ) liquid holdup in column, m3/m3 Hel ) element height, m HETP ) height equivalent to a theoretical plate, m HTU ) height of transfer unit, m k ) mass transfer coefficient, m/s m ) slope of the equilibrium line, dimensionless L˙ ) molar liquid flow, kmol/h ML ) molecular weight of the liquid phase, kg/kmol MV ) molecular weight of the vapor phase, kg/kmol N ) number of theoretical stages, dimensionless ULe ) effective liquid velocity, m/s USL ) superficial velocity, liquid phase, m/s USG ) superficial velocity, vapor phase, m/s V˙ ) molar vapor flow, kmol/h Greek Symbols R ) relative volatility, dimensionless δ ) liquid film thickness, m  ) void fraction, m3/m3 γ ) slope of the steepest descendent line with respect to the horizontal axis, deg λ ) stripping factor, dimensionless µ ) dynamic viscosity, Pa‚s µL,O ) dynamic viscosity of water at 20 °C, Pa‚s ϑ ) angle of flow channel from horizontal, deg F ) density, kg‚m-3 σ ) surface tension of liquid, N/m τ ) shear stress, Pa Subscripts bot ) bottom CB ) chlorobenzene G ) gas i ) interfacial L ) liquid top ) top Dimensionless Groups Gz ) Graetz number, Gz ) ReLScL((δ sin γ)/Hel) Ka ) Kapitsa number, Ka ) σ3FL/µL4g ReG,eff ) gas Reynolds number, ReG,eff ) FGdeUrel/µG

ReL ) liquid Reynolds number, ReL ) FL(4δ)(USL/(hL sin γ))/ µL Sc ) Schmidt number, Sc ) µ/FD ShG ) gas Sherwood number, ShG ) kGde/DG ShL ) liquid Sherwood number, ShL ) kL(4δ)/DL Literature Cited (1) Meier, W.; Stoecker, W. D.; Weinstein, B. Performance of a new, high efficiency packing. Chem. Eng. Prog. 1977, 73 (11), 71. (2) Billet, R.; Mackowiak, J. Application of modern packings in thermal separation process. Chem. Eng. Technol. 1988, 11, 213. (3) Olujic, Z.; Seibert, A. F.; Fair, R. Influence of corrugation geometry on the performance of structured packings: An experimental study. Chem. Eng. Prog. 2000, 39, 335. (4) Whaley, A. K.; Bode, C. A.; Ghosh, J.; Eldrige, R. B. HETP and pressure drop prediction for structured packing distillation columns using a neural network model. Ind. Eng. Chem. Res. 1999, 38, 1736. (5) Pollock, G. S.; Eldrige, R. B. Neural network modelling of structured packing height equivalent to a theoretical plate. Ind. Eng. Chem. Res. 2000, 39, 1520. (6) Larachi, F.; Grandjean, B. P. A. Comments On “Neural Network Modeling of Structured Packing Height Equivalent to a Theoretical Plate” and “HETP and Pressure Drop Prediction for Structured Packing Distillation Columns Using a Neural Network”. Ind. Eng. Chem. Res. 2000, 39, 4437. (7) Eldridge, R. B. Response to Comments from Larachi and Grandjean on “Neural Network Modeling of Structured Packing Height Equivalent to a Theoretical Plate” and “HETP and Pressure Drop Prediction for Structured Packing Distillation Columns Using a Neural Network”. Ind. Eng. Chem. Res. 2000, 39, 4438. (8) Wang, G. Q.; Yuan, X. G.; Yu, K. T. Review of mass transfer correlations for packed columns. Ind. Eng. Chem. Res. 2005, 44, 8715. (9) Bravo, J. L.; Rocha, J. A.; Fair, J. R. A comprehensive model for the performance of columns containing structured packings. Inst. Chem. Eng. Symp. Ser. 1992, 128, A439. (10) Spiegel, L.; Meier, W. Correlations of the performance characteristics of the various Mellapak types (capacity, pressure drop and efficiency). Inst. Chem. Eng. Symp. Ser. 1987, 104, A203. (11) 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. (12) Billet, R.; Schultes, M. Predicting mass transfer in packed columns. Chem. Eng. Technol. 1993, 16, 1. (13) Shi, M. G.; Mersmann, A. Effective interfacial area in packed columns. Ger. Chem. Eng. 1985, 8, 87. (14) Bravo, J. L.; Rocha, J. A.; Fair, J. R. Mass transfer in gauze packings. Hydrocarbon Process. 1985, 64, 91. (15) Fair, J. R.; Bravo, J. L. Distillation columns containing structured packings. Chem. Eng. Prog. 1990, 86, 19. (16) 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. (17) Nardini, G.; Paglianti, A.; Petarca, L.; Viviani, E. Sulzer BX gauze: Fluodynamic and absorption of acid gases. Chem. Eng. Technol. 1996, 19, 20. (18) Olujic, Z. Development of a complete simulation model for predicting the hydraulic and separation performances of distillation columns equipped with structured packings. Chem. Biochem. Eng. Q. 1997, 11, 31. (19) Olujic, Z.; Behrens, M.; Colli, L.; Paglianti, A. Predicting the efficiency of corrugated sheet structured packings with large specific area. Chem. Biochem. Eng. Q. 2004, 18, 89. (20) Rocha, J. A.; Bravo, J. L.; Fair, J. R. Distillation columns containing structured packings: A comprensive model for their performance. 2. Masstransfer model. Ind. Eng. Chem. Res. 1996, 35, 1660. (21) Segado, A. R.; De La Fuente, F. C.; Aguilar, A. M. Laboratory data of structured gauze packings as a base for scale-up in distillation. Chem. Eng. Commun. 2002, 189, 1470. (22) Fair, J. R.; Seibert, A. F.; Behrens, M.; Saraber, P. P.; Olujic, Z. Structured packing performancesExperimental evaluation of two predictive models. Ind. Eng. Chem. Res. 2000, 39, 1788. (23) Shetty, S.; Cerro, R. Fundamental liquid flow correlation for the computation of design parameter for ordered packings. Ind. Eng. Chem. Res. 1997, 36, 771.

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(24) Brunazzi, E.; Paglianti, A. Liquid-film mass transfer coefficient in a column equipped with structured packings. Ind. Eng. Chem. Res. 1997, 36, 3792. (25) Johnstone, H. F.; Pigford, R. L. Distillation in a wetted wall column. Trans. Am. Inst. Chem. Eng. 1942, 38, 25. (26) Olujic, Z. Development of a complete simulation model for predicting the hydraulic and separation performances of distillation columns equipped with structured packings. Chem. Biochem. Eng. 1997, 11, 31. (27) Olujic, Z.; Seibert, A. F.; Kaibel, B.; Jansen, H.; Rietfort, T.; Zich, E. Performance characteristics of a new high capacity structured packing. Chem. Eng. Process. 2003, 42, 55. (28) Fitz, C. W.; Kunesh, J. G.; Shariat, A. Performance of structured packing in a commercial-scale column at pressure of 0.02-27.6 bar. Ind. Eng. Chem. Res. 1999, 38, 512. (29) Nooijen, J. L.; Kusters, K. A.; Pek, J. J. B. The performance of packing in high-pressure distillation applications. Inst. Chem. Eng. Symp. Ser. 1997, 142, 885. (30) Olujic, Z.; Behrens, M.; Spiegel, L. Experimental characterisation and modelling of the performance of a large specific area high capacity structured packing. Ind. Eng. Chem. Res., under revision. (31) Suess, P.; Spiegel, L. Holdup of Mellapak structured packings. Chem. Eng. Process. 1992, 31, 119.

(32) Brunazzi, E.; Paglianti, A. Mechanistic Presure Drop model for columns containing structured packings. AIChE J. 1997, 43, 317. (33) Sulzer Chemtech Ltd. Structured packings for distillation, absorption and reactiVe distillation; Rep. No. 22.13.06.40-I.05.50; Sulzer Chemtech Ltd.: Winterthur, Switzerland, 2003. (34) Gualito, J. J.; Cerino, F. J.; Cardenas, J. C.; Rocha, J. A. Design method for distillation columns filled with metallic, ceramic, or plastic structured packings. Ind. Eng. Chem. Res. 1997, 36, 1747. (35) Shilkin, A.; Kenig, E. Y. A new approach to fluid separation modelling in the columns equipped with structured packings. Chem. Eng. J. 2005, 110, 87. (36) Zuiderweg, F. J.; Olujic, Z.; Kunesh, J. G. Liquid backmixing in structured packing in high-pressure distillation. Inst. Chem. Eng. Symp. Ser. 1997, 142, 865.

ReceiVed for reView April 21, 2006 ReVised manuscript receiVed July 19, 2006 Accepted September 7, 2006 IE060503Z