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A Shortcut Method for the Estimation of Structured PackingsHEPT in Distillation

By Francisco Carrillo, Ana Martín and Antonio Roselló*

A shortcut method to calculate HETP for metal structured packings is proposed. The method is a simplification and extension ofLockett's equation for sheet packings, based on the Bravo, Rocha and Fair model. It is applicable at vacuum or pressuredistillation of organic or aqueous mixtures in columns of sheet and gauze packings. The necessary variables are specific surface ofpacking, density of vapor and liquid and flow (when gauze packings are being considered). No estimation of hydrodynamicconditions is necessary.

1 Introduction

There are several models in the literature to describe theperformance of columns with structured packings. Equationsor diagrams for pressure drop and capacity have beenproposed, with acceptable results. In contrast, the predictionof efficiency is a question without an adequate solution so far.The models to estimate HETP or HTU are based on the two-film theory. Therefore, their application involves calculationsof the effective interfacial area and resistances in both phases.This implies dealing with several equations and a lot ofproperties [1].

In the first model for structured packings [2] the gauzepacking is visualized as a series of completely wetted channels,where the vapor flows in the same way as in a wetted-wallcolumn, the interfacial area being equated to the specificsurface area of packing and the mass transfer coefficient beingexpressed by a relationship similar to the correlation forwetted-wall columns. The liquid-side mass transfer coefficientwas based on the penetration theory, being the exposure timethe ratio between the effective liquid velocity through thechannel and the length of corrugation. This model wasadapted to sheet-metal surfaces using a ªdiscount factorº (infact, the effective fraction of interphase) [3]. Bravo, Rochaand Fair have recently developed a quite complex solution [4]for the mass transfer in beds of structured packings, startingfrom their hydraulic model for these devices. The interfacialarea is related to liquid holdup, a variable to be included inmass transfer coefficients [5].

This Bravo-Rocha-Fair rigorous treatment would be asound estimation of the ªbasicº HETP, an efficiency at totalreflux, without maldistribution in beds, but it is not able tocorrelate all the data in the literature. Moreover, a reliableresult is not possible without a good prediction of theproperties of mixtures, a huge problem with diffusivities or

aqueous systems. For these difficulties it is worth using lesscumbersome solutions to obtain a confident result. A typicalsimplification of the rigorous treatment is to supposenegligible liquid resistance. Nevertheless, problems relatedto effective interface remain and it is necessary to introducesome empirical parameters.

Furthermore, shortcut methods are recommended forseveral purposes, even when more accurate solutions areavailable [5]: designs for ideal or close-to-ideal systems, or forsystems for which equilibrium data are unavailable, scopingstudies for preliminary costs, etc. Harrison and France [6]proposed for structured packings a very simple rule of thumb,stating three HETP for three crimp heights. The equation is,after Kister1):

HETP = 100 / a + 0.102 (1)

Lately, Lockett [7] has developed a shortcut method basedon the Bravo-Rocha-Fair model which is applied to a specificsheet packing (Flexipac). The correlation starts with a size ofpacking and a flow (F at 80 % flood). This first equation isextended to correlate data with other sizes of Flexipac. Using aflooding correlation [7], an expression for HETP at totalreflux and stripping factor equal to 1 is obtained, HETP beinga function of the nominal specific surface of packing, densityof vapor, density and viscosity of liquid. Lockett claims that hismethod has a similar accuracy to that of the model it is basedon. Also, its possible limitations: so, Lockett advises to becautious with aqueous systems, given the poor wetting which isassigned to these mixtures.

2 Analysis of Data

Information about HETP in the literature is not related tocommercial columns but to pilot plants (diameter up to 1.05m) where binary mixtures were distilled at pressures between

Chem. Eng. Technol. 23 (2000) 5, Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2000 0930-7516/00/0505-00425 $ 17.50+.50/0 425

±

[*] Dr.-Chem. F. Carrillo, Dr.-Chem. A Martín, Prof. Dr.-Chem. A. Roselló,Department of Chemical Engineering, University of Seville, C/Prof.García Gonzalez s/n (Faculty of Chemistry), 41012 Seville, Spain.

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±

1) List of symbols at the end of the paper.

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5 atm and 5 mmHg. The typical function of efficiency is HETP= f (load), without reference to the composition or thetemperature which would be necessary to calculate physicalproperties.

There are different shapes for the function, but a generalenough rule would be that HETP increases when F or Cincreases, the variation being very sharp above the loadingpoint. But even this simple statement has exceptions, some ofwhich involve difficult explanations.

The influence of packing and pressure will now beconsidered using data for a given mixture. The most studiedsystems have been chlorobenzene-ethylbenzene and cyclo-hexane-heptane.

From these data some conclusions can be reached:± The two types of structured packings (gauze and sheet)

show a different behavior: for sheet packings, the change ofHETP with flow is often small. HETP may even besupposed to be constant over a wide range of flow. For thegauze type, the decrease of efficiency when flow increases isalways significant.

± HETP shows a strong dependence on the specific surface ofpacking, decreasing when the surface increases; but there isnot a sole function for all packings.

± The relationship between efficiency and pressure iscomplicated. Often, HETP is greater at higher pressures,but it is frequent to find similar HETP with very differentpressures. It is also possible to find a greater HETP atvacuum.

± Estimations using Lockett's equation give conservativeresults, with calculated HETP 50 % higher than experi-mental ones, as is shown in Fig. 1.

3 Developing a New Method for Sheet StructuredPackings

Lockett's equation is a suitable start for a rapid estimationof HETP, because it is simple enough, using only four variableswith good possibilities of being accurately calculated and itsdeviation from empirical results does not bend in a particulartendency related to packing or pressure. Moreover, it is easy tosimplify the equation without loss of accuracy using rl

0.5

instead of (rl±rv)0.5 and taking (ml/mv)0.06 as a constant. Avalueof 0.63 in I.S is suggested.

Differences between Lockett's solution and the newequation are less than 5 %, as can be seenin Fig. 2.

Although the solution would strictly bevalid only for operations at 80 % flood, itsapplication is extendible to a wide rangeof flow, where a constant efficiency versusflow rate can be assumed for sheetpackings.

In order to obtain a new factor in thissimplified Lockett's equation, the relation

' � HETPexp����lp

a 1�0:78�v�l

� �0:25105:8 10ÿ4 a

� �2

(2)

is calculated for chlorobenzene-ethylbenzene and cyclo-hexane-heptane systems, with different packings and pres-sures. Results for average ' are given in Tab. 2.

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Figure 1. Experimental HEPT and calculated HEPT by Lockett's equation.

Figure 2. Differences between Lockett's equation and its modification.

Table 1. Systems used in Fig. 2.

n0 System P (mmHg) n0 System P (mmHg)1 Cyclohexane-Heptane 3146 9 O-Xylene-P-Xylene 3002 Argon-Oxygen 1572 10 Toluene-Octane 2003 Chlorobenzene-Ethylbenzene 1013 11 Ethylbenzene-Styrene 1004 Methanol-Ethanol 1013 12 Argon-Oxygen 525 Ethanol-Water 1013 13 Chlorobenzene-Ethylbenzene 256 Argon-Oxygen 786 14 Decane-trans-Decaline 207 Methanol-Water 760 15 O-Xylene-P-Xylene 168 Acetone-Water 760 16 trans-Decaline-cis-Decaline 10

Table 2. Factor for the simplified Lockett's equation (in brackets, number ofexperimental points).

Pressure (bar) 4.14 1.63 0.96 0.33 0.10

Chlorobenzene-Ethylbenzene

5.69 (11) 5.17 (9)

Cyclohexane-Heptane 5.37 (35) 5.40 (28) 5.41 (20)

Differences are small enough and a unique average' for allpressures may be proposed: ' = 5.40 (+/±20 %).

Fig. 3 is a parity plot where experimental and calculatedHETP are compared, including data of organic and aqueousmixtures.Themajorityofdatahasadeviationsmallerthan25%

Figure 3. Parity plot of experimental and calculated HEPT.

The chosen value for ' would not be suitable fornonmetallic surfaces. It is known that the packing materialinfluences efficiency: HETP with a metal packing can be halfthat of a polypropylene packing [1]. Hence,' > 5.40 for plasticpacking. But at the moment it should be set aside for furtherconsideration because there are few data in the literature ofceramic or plastic structured packings.

4 Gauze Packings

In spite of their wide specific surfaces, structured packingsmade from metal gauze are used nowadays less than sheet

packings, because of their higher operational cost. The bulk ofthe data in the literature has been obtained in columns withSulzer BX.

As HETP of gauze packings changes sharply with flow rates,it is necessary to know how this variation behaves in order toestimate efficiency for any flow. A simple dependence may beproposed up to the loading point:

HETP = A F (3)

There is a dependence of ' on pressure, increasing whenvacuum increases. Nevertheless, it appears preferable tomaintain a unique power and to introduce the influence ofpressure, if necessary, through . A value of 0.42 for issuggested, and the following relationship between P and ':

' � 7:12 P33:08 � P

(4)

Sulzer CY and Goodloe packings show the same tendencywith reference to variations of with flow, but the power of Fis higher (between 0.50 and 0.77). These changes in are,probably, attributable to the growing influence of the liquidflow rate when significant differences in the vapor-liquidsurface are possible: at vacuum and when involving packingswith high specific surfaces to be wetted.

Also a datum of HETP at a flow F* must be known toestimate HETP for other flows. F* has to be between theloading point and a flow rate high enough to avoid thenonfulfilment of the previous relation. Considering the rangeof flows in the data of the literature, F* = 1.5 m/s (Kg/m3)0.5 isused. The following equation matches experimental effi-ciences of BX packing acceptably, as can be seen in Fig. 4.

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Figure 4. Parity plot for BX gauze packing.

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HEPTBX �P ����

�lp

�2712�82:0 P� 1�1:505�v

�l

� �0:25 !2 F0:42

(5)

�P; in mmHg�

Received: June 15, 1999 [CET 1123]

Symbols used

a [m2/m3] specific surface area of packingA [m/(m/s.(kg/m3)0.5)] constantC [m/s] flow parameterD [m] diameter of columnF [m/s (kg/m3)0.5] vapor load factorg [m/s2] gravitational accelerationHETP [m] height equivalent to a

theoretical plateHTU [m] height of a transfer unitP [mmHg] pressureZ [m] height of column

Greek symbols

ml [Pa.s] liquid viscositymw [Pa.s] water viscosity�v [kg/m3] vapor density�l [kg/m3] liquid density' [±] factor in the simplified

Lockett's equation [±] power of F factor

References

[1] Gualito, J. J.; Cerino, F. J.; Cµrdenas, J. C.; Rocha, J. A., Ind. Eng. Chem.Res. 36 (1997) pp. 1747±1757.

[2] Bravo, J. R.; Rocha, J. A.; Fair, J. R., Hydrocar. Proc. 64 (1985) Jan., pp. 91±95.

[3] Fair, J. R.; Bravo, J. L., Chem. Eng. Prog. 86 (1990) Jan., pp. 19±29.[4] Bravo, J. R.; Rocha, J. A.; Fair, J. R., Ind. Eng. Chem. Res. 35 (1996) pp.

1660±1667.[5] Billet, R.; Schultes, M., Chem. Eng. Technol. 16 (1993) pp. 1±9.[6] Frank, O., Chem. Eng. 84 (1977) March, No. 6, pp. 110±128.[7] Harrison, M. E.; France, J. J., Chem. Eng. (1989) Apr., pp. 121±128.

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