MAY 1986 ISSN 0018-8190

HydrocarbonProcessing

REFLUX AND SURFACE TENSION EFFECTS ON DISTILLATION

Reflux and surface tensioneffects on distillationTheoretical and experimental data suggesthow to set reflux ratio for the most efficientdistillation separation in packed towers.Surface tension effects also are considered

T. D. Koshy and F. Rukovena, Norton Co., Akron, Ohio

EASY SEPARATION SYSTEMS (those with relative volatili-ties of approximately 2.0 or greater) are influenced signifi-cantly by reflux ratio. Theoretical relations suggest the bestseparation efficiency occurs when X, the ratio of the slopes ofthe equilibrium and operating lines (mG\{/L\), is approxi-mately 1.0. Then, experimental data are obtained to relate Xto its equivalent reflux ratio.

2.0

1.5

1.0

0.5

o o0 a

o°0

Total refluxPartial reflux, L/D = 1.0

\10.30.2

Cs at midpoint, ft/s

-Packed tower rectification of methanol-water.

0.4

2 3 456 810-1 2 3 456 810°

Slope ratio X

Fig. 2—Relationship among variables.

2 3 4 56 810

More difficult separation systems (relative volatility closeto 1.0) have more uniform separation efficiencies over theentire concentration range (i.e., X has a lesser influence).

A difference in surface tension can explain some differ-ences in efficiencies. Comparing two easy separation sys-tems, one with a negative surface tension gives a lower sepa-ration efficiency than another with a positive surfacetension.

Operating efficiency. The operating efficiency of packedtowers is generally expressed as Height Equivalent to a The-oretical Plate (HETP) or Height of a Transfer Unit (HTU).But note, a minimum HETP or HTU represents a maxi-mum separation efficiency.

The effect of reflux ratio is shown in Fig. 1, a plot ofHETP versus a vapor capacity factor CY These data are fora methanol-water binary distillation at atmospheric pres-sure. The upper plot is for total reflux. The lower plot is foran internal reflux ratio, L\i/G\, of 0.5. The HETP is signif-icantly larger for total reflux than for partial reflux.

These data were obtained at Norton Company's Cham-berlain Laboratories in Stow, Ohio. The distillation towerhad a diameter of 381 mm and was filled with a 3,048-mm-deep bed of No. 25 IMTP stainless steel packing. Additionaruns were made to examine the relation between HETP ana*"reflux ratio. Further, HETP measurements were conductedat a fixed boil-up rate to eliminate the effect of Cy on HETP.

Theoretical analysis. A generalized (HTU)(X; correlationassuming a two-resistance theory1-2 is given as follows:

(HTU)0(; = (HTU)C; + X(HTU),. (1)

If the equilibrium curve and the operating line are as-sumed to be straight lines over a single stage, the followingrelation is obtained:

HETP = (HTU)oo(ln X)/(X - 1) (2)

Then define

and

(3 = (HTU)L/(HTU)G

£ = HETP/(HTU)C;

Combining the foregoing equations gives:

£ = ( l + X / 3 ) ( l n X ) / ( X - 1)

(4)

(5)

Fig. 2 shows a plot of £ as a function of In X for variousvalues of /3. For a fixed (8, the minimum £ is determined bysetting the first differential of Eq. 5 to zero (i.e., d£/dX = 0).This gives:

/3 = (X - 1 - X In X)/(X In X - X2 + X) (6)

Substituting Eq. 6 into Eq. 5 gives:

L,,, = ( lnX) 2 / (X - 1 - In X)

Table 1 shows the variation of £,„,„ with j3 and X.

Finding minimum HETP. If (HTU)(, is assumed to be a con-Reprinted from HYDROCARBON PROCESSING, May 1986

Copyright* 1986 by Gull Publishing Co., Houston, Texas.All rights reserved. Used with permission.

stant, it follows from Eq. 4 that having a minimum £ alsomeans there is a minimum value for HETP. And since X,and to some extent /?, varies over the range of concentrationfor which HETP is measured, values of/? and X must be ob-tained experimentally.

The righthand term of Eq. 2, (In X)/(X - 1), approaches'.0 as X approaches 1.0. Therefore, Eq. 2 suggests HETP

^approaches (HTU)OG; and it is feasible to correlate HETP asa function of the physical properties. It is customary to usepublished correlations5"' to evaluate (HTU)oo using Eq. 1.

Relative volatility, a, relates the vapor and liquid phasecompositions of the more volatile component in a binaryseparation, i.e.,

y = ax/[I + (a - l)x] (8)

Here, a is not necessarily a constant.On the other hand, if a is assumed to be constant over a

small range of composition, the slope of the equilibriumcurve can be given as follows:

dy/dx = m = a / [ l + (a - \)x]2 (9)

Then when x —> 1, m —*• I/a (10)

and when x —> 0, m —> a (11)

Thus, for liquid phase compositions between x = 0 andx = 1.0, m lies between ex and I/a.

Difficult separations (those binary systems whose a. val-ues are not significantly larger than 1.0), have values of mthat do not greatly differ from 1.0. This also implies the in-ternal reflux ratio, L\i/G\i, which is the slope of the operat-ing line either in the rectifying or stripping sections, for thesedi f f icu l t separations will not vary significantly from 1.0.This is the case because the operating line is enclosed withinboundaries created by the equilibrium curve and the diago-,nal.

As a result, X = mG\IL\, or the ratio of the two slopes,__^emains close to 1.0 for such systems. One should not expect

X to be an important variable in the performance efficiencyof distillation towers making difficult separations. Undersuch conditions HETP = (HTU)oo, and HETP is an ap-propriate design tool.

Easy separations, on the other hand, where a > > 1.0,X can have values much less than 1.0 to much greater than1.0. Therefore, X becomes an important variable in the per-formance of a distillation tower making easy separations, es-pecially when making very pure products.

Surface tension effects can be considered using a defini-tion given by Zuiderweg and Harmens.8 They termed distil-lation systems positive or negative on the basis of whetherthe surface tension of the ref lux liquid increases or decreasesas it flows down the column.

Experimental data. Two binary systems that can be charac-terized as easy separations were chosen in order to comparethe performance of two high a systems and, at the sametime, contrast the performance of a system with a positivesurface tension with one having a negative surface tension.

The first system was the methanol-water binary men-tioned earlier in connection with Fig. 1. The a of this systemranged from 2.6 to 8.1 and the m ranged from 0.38 to 8.1, atatmospheric pressure. This is a strongly surface-tension-pos-itive system. The second binary system was a water-di-methylformamide (DMF) system whose a varied from 3.6 to6.8 and m varied from 0.28 to 6.8, at atmospheric pressure.This latter is a strongly surface-tension-negative system.

The data for HETP versus log X for both systems are illus-•,—crated in Fig. 3. The HETP values were calculated using a

modified McCabe-Thiele method taking into account theenthalpy difference between the components.'' Tower opera-tions were held within a narrow range of boil-up rates in or-

2.500

2,000

. 1.500

Methanol-water•*- Water-DMF

'*«,, .,0%

I I I I I I10-' 2 3 4 5 6 7 8910° 2 3 4 5 6 7 8910

Slope ratio X

Fig. 3—Two binary systems compared.

EEQ.-200

10-' 2 3 4 56 810° 2 3 4 5 6 8 10' 2 3 4 56 8102

Slope ratio X

Fig. 4—Literature data for isopropanol-water.10

TABLE 1—Variation of £mm with 0 and X

(30

0.10.30.50.71.03.05.07.09.0oo

X

00

285.9632.8171.7061.00.019540.09360.05830.04120

£min

00.4691.0031.3731.6602.03.2193.8364.2504.560

00

der to eliminate the effect of tower loading on efficiency. Forboth systems, HETP goes through a minimum at a X valueof approximately 1, although boil-up limitations preventedgetting data for the water-DMF system at X values greaterthan 1.0.

Other data for an isopropanol-water system reported byDeed, et al., are shown in Fig. 4.'° They performed atmo-spheric rectification of the binary below azeotropic conditionin a 152-mm-diameter brass column with 1,194 mrn of 13-mm ceramic Raschig Rings. These data also indicate HETPgoes through a minimum.

Based on the observation that (HTU)oo increased rapidlyas X was raised, Deed, et al., concluded that the principalresistance to mass transfer was in the liquid phase. This ex-planation implies that, at large values of X, /? defined by Eq.3 increases.

On the other hand, Norman, et al.,11 conclude that largevariations in HETP are probably the result of poor liquiddistribution over the packing and variations in the wettedarea. This conclusion was based on wetted wall column datadetermined by other researchers in the field who found largevariations in HETP in experiments with packed columns.However, based on recent experience with liquid distributorsproviding a widely varying number of distribution pointsand liquid flowrates, there are no indications that liquid dis-

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fig. 5—Vapor-liquid equilibrium diagram.

tribution was a limiting factor for our test data.Surface tension effects. According to Zuiderweg and Har-mens,8 a binary system is positive if the less volatile compo-nent has the higher surface tension. They demonstratedthat, in apparatus where the interfacial area is mainly of thefilm type, mass transfer rates for positive systems (with stabi-lized film) may be much higher than for negative systems.

This generalization, however, may fail when applied tonegative systems, where the reduction in contact angles mayresult in spray formation. The interfacial surface area insuch formations is not significantly affected by surface ten-sion changes.

Fig. 3 illustrated that for the range of X values for whichcomparison can be made, the HETP for the methanol-water(positive) system is consistently lower than that for the water-DMF (negative) system. Meier, et al.,12 who performed dis-tillation at total reflux on both systems in a structured stain-less steel tower packing, found that the HETP for thewater-DMF system is approximately twice that of the metha-nol-water system.

For these tests, the concentration range of the methanol-water mixture was 10% methanol at the bottom and 98%methanol at the top. The range of the water-DMF systemwas 30% water at the bottom and 99.5% water at the top.The authors attribute the lower HETP for the methanol-wa-ter system to its good wettability. The present study, how-ever, demonstrates that wettability per se does not explainthe widely differing values of HETP obtained for essentiallythe same range of separation at different reflux ratios. Thedata indicate that at X values much larger or smaller than1.0, HETP increases dramatically.Application. The practical importance of our findings canbe illustrated in Fig. 5 and the following:

Case I: X is much less than 1. The circumstances whenthis happens are:

• high purity of the more volatile component, i.e., m —* I/a.

• high reflux ratio, i.e., L_\/G_\i ~*• 1.0.• both foregoing conditions mean X —* I/a.

Case II. X = 1. The following situations will producethis condition:

• very low reflux ratio for high purity rectification, i.e., x-* i .o

• very high reflux ratio for high purity stripping, i.e., x-" 0

• total reflux for a symmetric separation. Note, the term

"symmetric separation" is used here to mean that on aMcCabe-Thiele diagram, the liquid phase compositionsof the overhead product and bottom product are roughlyequidistant from 0.5.

Case III. X is much greater than 1. The circumstanceswhen this occurs are:

• high purity of bottoms products, i.e., x -» 0 and m -• low L/V approaching total reflux, i.e., LIV —*• 1.0• both foregoing conditions mean that X -*• a.

NOMENCLATURE

Cs - capacity factor Vsvpc/(pL ~ PG)> m/sGM - gas flowrate, kg-moles/hHETP - height equivalent to a theoretical plate, mHTU - height of a transfer unit, mLM - liquid rate, kg-moles/hm - slope of the equilibrium lineVs - superficial gas flow velocity based on tower area, m/sx - mole fraction of the more volatile component in the

liquid phasey - mole fraction of the more volatile component in the

vapor phase

Greek symbols

a - relative volatility between components 1 and 2/3 - as defined in Eq. 3X - m GM/LM, ratio of the slopes of equilibrium and

operating lines£ - as defined in Eq. 4p - density, kg/m3

Subscripts

G - gas phaseL - liquid phaseM - moles of gas or liquidOG - overall gas phase

LITERATURE CITED

1 Lewis, W. K., and Whitman, W. G., Industrial and Engineering Chemistry, Vol. 16, p.,1215, 1924.

: Whitman. W. G., Chemical and Metallurgical Engineering, Vol. 29, p. 247, 1923.:i Shulman, H. L., Ullrich, C. F, and Wells, N., AlChE Journal, Vol. 1, p "

1955.4 Shulman, H. L., Ullrich, C. F, Proulx, A. Z. , and Zimmerman, J. O., AlChE

Journal, Vol. 1, p. 259, 1955.~~' Shulman, H. L., Ullrich. C. F., Wells, N., Proulx, A. Z., AlChE Journal, Vol. 1, p.

259, 1955.6 Onda, K., Takeuchi, H., and Okumoto, Y. J., Chemical Engineering Japan, Vol. 1, p.

56, 1968.7 Onda, K., Mem. Fac. Eng., Nagoya Univ., 24 (2), p. 64, 1972.R Zuiderweg, F. J., and Harmens, A., Chemical Engineering Science, Vol. 9, Nos. 2/3,

p. 89, 1958.y Neretnieks, I., Ericson, I., Eriksson, S., British Chemical Engineering, Vol. 14. No.

12, p. 653, 1969.1(1 Deed, D. W., Schutz, P. W., Drew, T. B., Industrial and Engineering Chemistry, Vol.

39, No. 6, p. 766, 1947.11 Norman, W. S., Cakaioz, T., Fresco, A. Z., Sutcliffe, D. H., Transaction of the Insti-

tution of Chemical Engineers, Vol. 41, p. 61, 1963.12 Meier, W., Hunkeler, R., Stocker, D., Institution of Chemical Engineers Symposium Se-

ries No. 56, 3.3, p. 1, 1979.

The authorsT. Dan Koshy is manager, mass transfer devel-opment, Norton Chemical Process Products,Akron, Oft/o, where he manages pilot plant re-search and data correlation. Earlier he was adesign and development engineer (distillation)with Union Carbide Corp., Linde Division. Heholds a BS degree from Nagpur University, In-dia, an MS degree from Wayne State University,Mich., both in chemical engineering, and anAlChE membership.

Frank Rukovena, Jr., is manager, mass transferengineering and development, Norton ChemicalProcess Products, Akron, Ohio, where he man-ages mass transfer development, packed towerapplication and mechanical engineering. Earlierhe was a research development engineer witKoppers Co. and a design and project engine*, .„.with General Tire. Holder of a BS in chemical en-gineering from \bungstown University, he is amember of AlChE.

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