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A Simple Method to Assess the Sensitivity of Packed Distillation Columns to Maldistribution
0263–8762/02/$10.00+0.00 # Institution of Chemical Engineers Trans IChemE, Vol 80, Part A, May 2002
A SIMPLE METHOD TO ASSESS THE SENSITIVITY OF PACKED DISTILLATION COLUMNS TO MALDISTRIBUTION1 J. F. BILLINGHAM and M. J. LOCKETT Praxair, Inc., Tonawanda, NY, USA.
T
his paper provides a new tool for those concerned with the design or performance of packed distillation columns. It gives a simple method to assess the sensitivity of a packed bed to maldistribution. Despite extensive prior work on this topic, the concept proposed here appears to have been previously overlooked. A parallel column model is often used to assess the sensitivity of a packed bed in a distillation column to liquid or vapour maldistribution. However, it is well known that the parallel column model is oversimpli ed because it involves an arbitrary number of parallel columns, it neglects lateral mixing, and the actual extent of maldistribution is unknown. For these reasons, the parallel column model can only be used as a way of identifying packed beds that are particularly susceptible to maldistribution, rather than as a predictive design tool. In this paper it is shown that sensitivity to maldistribution can be predicted much more simply using a single parameter fmax, which is the maximum maldistribution that could possibly occur in a parallel column while still being able to achieve the required separation. It is shown that fmax can be determined very simply, for example from the output of a conventional column simulation program, and a parallel column model is not actually needed. Using fmax, the sensitivity to maldistribution of a proposed packed bed can now easily be compared at the design stage to other packed beds that are known to work satisfactorily. If necessary, the design can then be modi ed to reduce the sensitivity to maldistribution. Routine calculation of fmax during design will help to reduce the signi cant number of distillation column problems that presently occur because of maldistribution. Keywords: distillation; packing; maldistribution
INTRODUCTION
One of the important things about maldistribution is that its effects are not constant. The separation performance loss with the same degree of maldistribution differs from system to system and even section to section within the same distillation column. So to model the effect of maldistribution, two separate steps are involved: prediction of the extent of maldistribution and then prediction of its effect on separation. Three types of models have been proposed for the latter: Detailed models, parallel column models, and by-pass models.
Some degree of maldistribution of liquid or vapour, or both, inevitably occurs in packed columns. Maldistribution can be caused by less than perfect initial distribution, or it can develop within the bed because of wall ow or because of the non-randomness of supposedly random packing. The seams between bricks in structured packing can also cause maldistribution1. Although lateral mixing, perpendicular to the column axis, tends to reduce the effect of maldistribution on separation, it can act only over a limited radial distance, and so large diameter columns are more sensitive to maldistribution than small diameter columns. Also, because of limited lateral mixing, large-scale maldistribution is more damaging than small-scale maldistribution. As lateral mixing is more effective for vapour than for liquid, maldistribution of vapour usually has a smaller detrimental effect on column performance. This paper will therefore, for the most part, deal with maldistribution of liquid, although the results can easily be extended to vapour maldistribution if required as indicated at the end of the paper.
Detailed Models Detailed models to predict liquid maldistribution and then its effect on HETP (the height of an equivalent theoretical plate) have been given by Zuiderweg et al.2,3, Olujic4, Higleret al.5, and Yin et al.6. Kouri7 also developed a similar model for absorption involving transfer units. All these models require speci cation of the initial liquid distribution leaving the distributor, and then they predict how the liquid ow pattern develops in the bed taking into account wall effects and liquid mixing. Once the liquid ow pattern has been xed, it is used to predict the increase of HETP (or HTU) over and above the basic HETP (or HTU) that would be obtained in the absence of
1
# 2001 Praxair Technology, Inc. All rights reserved
373
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BILLINGHAM and LOCKETT
maldistribution. What is evident from these papers is that the extent of maldistribution cannot yet be predicted with suf cient con dence, and so none of these studies has so far evolved into a practically useful design method. Indeed, this approach will never be able to predict unforeseen maldistribution arising from manufacturing or installation errors, for example. These models are useful, however, in showing how the effect of maldistribution on HETP varies with parameters such as relativevolatility, bed depth, concentration,re ux ratio and column diameter, etc. We will refer to this as a sensitivity analysis as opposed to a design method. Parallel Column Models The same sensitivity analysis can be performed more simply using a parallel column model, with the exception that the effect of column diameter cannot be included. Many workers have used the parallel column model shown in Figure 1 to model the effect of liquid maldistribution on separation performance. The two columns have the same cross sectional area and equal vapour ow. One column receives an excess liquid ow at the expense of the other column. Lateral mixing is ignored in this model. The different liquid to vapour ratios in the two columns causes them to have different operating lines as shown in Figure 2. One of the columns tends to pinch at the top and the other at the bottom. The net result is to reduce the effective number of theoretical stages of the combined column system below that of each individual column, as is evident by comparing the solid line with the dotted lines stepped off in Figure 2. In the example shown, each of the individual columns has 4 theoretical stages, whereas the combined column only has 3.3 stages. The earliest work involving the application of the parallel column model to distillation is that of Mullin8. Subsequent
Figure 2. McCabe-Thiele diagram for parallel column model.
authors include: Morris9, Changez and Sawistowski10, Huber and Hiltbrunner11, Meier and Huber12, Yuan and Spiegel13, Thorogood14, Stichlmair and Stemmer15, Klemas and Bonilla16, Martin and Sloley17, and Schultes18. The conclusions reached by all these workers are essentially similar, and they show, using examples, how the effect of maldistribution on separation changes as different parameters are altered. Again, the models cannot be used directly for design. By-pass Models By-pass models assume that a small amount of either liquid or vapour passes through the bed without undergoing any mass transfer, which then contaminates the product. This is particularly damaging when a high purity product is required. Wall ow is a potential source of bypassing. Authors who have proposed by-pass models include Manning and Cannon19, Schafer and Lam20, and Hanley21. Ever more sophisticated versions of the three types of models discussed above are regularly put forward. For example, the parallel column model has been incorporated into a column simulation design package17 and models involving three18 to a hundred15 parallel columns have been proposed. Maldistribution of vapour, induced by the assumed liquid maldistribution, has also been included in the parallel column model16. Unfortunately, because of the dif culty of predicting the extent of maldistribution, these models can only be used to assess sensitivity to maldistribution rather than as direct design tools. A further dif culty is that it is not obvious to a column designer how to incorporate the output from a conventional column simulation design program into the models. The purpose of this paper is to show that, if the objective is limited only to assessment of sensitivity to maldistribution, it can be done much more simply. REPRESENTATION OF RESULTS FROM THE PARALLEL COLUMN MODEL
Figure 1. Parallel column model.
In the parallel column model shown in Figures 1 and 2, xed values are assumed for the number of actual theoretical Trans IChemE, Vol 80, Part A, May 2002
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stages in each column NA, the relative volatility a, the mean concentrations at the top of the columns ( yN, xN ‡ 1), and the vapour concentration entering the columns ( yo). The vapour and liquid owrates are assumed constant within each of the columns, implying that the latent heat of vaporization is constant and independent of composition. The liquid owrate in column 1 is: L0 ˆ …1 ‡ f †L
…1†
L00 ˆ …1 ¡ f †L
…2†
and in column 2 the liquid ow rate is:
The extent of liquid maldistribution is represented by the fraction f. The calculation procedure involved in the model is relatively straightforward and will not be elaborated here. A typical representation of the results is shown in Figure 3. Most previous workers who have used the parallel column model have reported their results in a similar way. Figure 3 shows that as the maldistribution increases the separation achieved falls, as represented by the effective number of theoretical stages, N, that are obtained from a xed number of actual theoretical stages in each column, NA. In order to judge whether the loss of separation will be signi cant, an arbitrary value of the maldistribution fraction f has to be assumed. This will depend to some extent on the type of distributor employed and, based on Sulzer experience, Moser and Damiani22 have suggested that f ˆ 0.04 can be used for a high quality distributor. Using f ˆ 0.04 in Figure 3 shows that 30 actual stages will deliver 21 effective stages in this particular example. Figure 4 shows how the simple representation of Figure 3 becomes more complex as additional values of NA are included. This representation of the results deals with the rating problem i.e. given a xed number of stages what separation can be achieved when maldistribution occurs? An alternative representation is in terms of the design problem
Figure 3. Typical representation of results from the parallel column model. NA ˆ 30, a ˆ 1.538, yo ˆ 0.5, yN ˆ 0.95, xN‡1 ˆ 0.95.
Trans IChemE, Vol 80, Part A, May 2002
Figure 4. More complex results from the parallel column model-rating problem. a ˆ 1.538, yo ˆ 0.5, yN ˆ 0.95, xN‡1 ˆ 0.95.
i.e. given a required xed separation, how many theoretical stages must be provided in each column under conditions of maldistribution? Thorogood14 took this approach for modelling maldistribution in plate columns with a parallel column model. Some of the data used to generate Figure 4 are replotted in Figure 5, where, following Thorogood, an ef ciency is de ned as: Eˆ
NA jf ˆ0 NA
…3†
Figure 5. Results form the parallel column design model—design problem using ef ciency (parameters from Figure 4).
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Although Figure 5 bears a super cial resemblance to Figure 3, they are, in fact, quite different representations of the results. We have found that, for the design problem, it is clearer and more instructive to plot NA directly as shown in Figure 6. Here NA is the number of theoretical stages that must be provided in each parallel column to achieve the same separation as is obtained with no maldistribution ( f ˆ 0). Four lines are shown on Figure 6 corresponding to four different values of NA with no maldistribution. Each line represents a xed separation and they show that as maldistribution increases the required number of stages rises rapidly. DEFINITION AND SIGNIFICANCE OF fm a x For each of the lines shown on Figure 6 there is a maximum value of the maldistribution fraction f above which no increase in the number of actual theoretical stages can provide the required separation. We shall call this maximum fmax. A line representing the locus of fmax is also shown on Figure 4. Moving horizontally across Figure 4 shows that for a required number of effective stages there is a maximum value of f above which the separation cannot be achieved, irrespective of how many actual stages are provided. Note that the locus of fmax on Figure 4 turns into a vertical line corresponding to a minimum value of fmax. If f is greater than the minimum value of fmax there is a limit to the number of effective stages that can be achieved, irrespective of the actual number of stages provided. The physical signi cance of fmax is shown in Figure 7. For a xed required separation, as maldistribution increases, eventually a pinch occurs at the top of one column and at the bottom of the other, corresponding to an in nite number of stages in each column. This determines the maximum maldistribution that can be tolerated while still achieving the required separation. Looking back to Figures 3 and 4, consider how diagrams like these have been used to assess the sensitivity to
Figure 7. Location of pinches when f ˆ fmax.
maldistribution. It is evident that whether or not a particular bed appears sensitive to maldistribution depends on how closely the arbitrarily assumed value of f (say 0.04 as suggested above) approaches the value of fmax. For example, in Figure 4, if 40 effective stages are required, the corresponding value of fmax is 0.037. If 40 actual stages are then provided in each column, and if f is assumed to be 0.04, only 24 effective stages will actually be achieved so there will be a severe loss of separation predicted. On the other hand, if only 15 effective stages are required, for which fmax ˆ 0.063, with an assumed value of f ˆ 0.04, and the provision of 15 actual stages in each column, there is only a slight loss of separation indicated down to 14 effective stages. Now since the predicted sensitivity to maldistribution depends primarily on the assumed value of f and on the value of fmax, and in addition f is arbitrary and usually is assumed to be xed, it follows that fmax alone is an adequate indicator for the sensitivity to maldistribution. This is the main idea put forward in this paper. It is recognized that by concentrating only on fmax, information is then unavailable about the predicted number of effective stages at values of f less than fmax. However, it should be evident that this is unimportant when it is recognized that the predicted number of effective stages has very little practical value, because of the arbitrary number of parallel columns assumed and the neglect of lateral mixing. The question then simply becomes how to calculate fmax without having to resort to a full parallel column model. CALCULATION OF fm a x General Equation This section shows how fmax can be calculated without the need for a parallel column model. From Figure 7, at the pinch condition, the vapour leaving column 1 is in equilibrium with the liquid entering. Similarly, the liquid leaving column 2 is in equilibrium with the vapour entering. The required separation is assumed to be xed. With the same vapour ow in each column, the vapour composition leaving column 2 is obtained from a mass balance:
Figure 6. Results from the parallel column model-design problem. a ˆ 1.538, yo ˆ 0.5, yN ˆ 0.95, xN‡1 ˆ 0.95.
y00NA ˆ 2yN ¡ y0NA
…4†
Trans IChemE, Vol 80, Part A, May 2002
PACKED DISTILLATION COLUMNS The slope of the operating line in column 2 is (1 7 fmax) times the slope of the operating line of the combined column in the absence of maldistribution, from equation (2). So that from Figure 7: ³ ´ y00NA ¡ yo yN ¡ yo ˆ …1 ¡ f † …5† max xN ‡1 ¡ x001 xN‡1 ¡ x1 Combining equations (4) and (5) and using the pinch conditions that: y0NA ˆ yN‡1 and x001 ˆ xo
…6†
gives: ³ ´ yN ¡ yo 2yN ¡ yN ‡1 ¡ yo ˆ …1 ¡ fmax † xN ‡1 ¡ xo xN ‡1 ¡ x1 ³
´ … yN ¡ yN‡1 † ‡ … yN ¡ yo † ˆ xN‡1 ¡ xo ³ ´ …xN‡1 ¡ xo † ‡ …xo ¡ x1 † £ yN ¡ yo ³ ´³ ´ yN ¡ yN‡1 y ¡ yN‡1 xo ¡ x1 ‡ N yN ¡ yo yN ¡ yo xN‡1 ¡ xo xo ¡ x1 ‡1‡ xN‡1 ¡ xo
Hence, the required equation for fmax is: y ¡ yN x ¡ xo fmax ˆ N‡1 ‡ 1 yN ¡ yo xN‡1 ¡ xo ³ ´³ ´ yN‡1 ¡ yN x1 ¡ xo ¡ yN ¡ yo xN‡1 ¡ xo
…7†
Equation (7) can be used to calculate fmax directly without the need for a parallel column model. The equation involves the sum and product of two terms that represent the approach to pinch at the top and bottom of the packed bed. The relationship is powerful in understanding the sensitivity to liquid maldistribution. It shows, for example, that a signi cantly greater tolerance to maldistribution is possible when, at the design point, either the top or the bottom of the packed bed is far away from pinch. Calculation of the terms in equation (7) is straightforward. For a required xed separation, yN, xN ‡ 1, yo and x1 are speci ed. The other terms can be calculated from the equilibrium relationships: a xN‡1 yN ‡1 ˆ …8† ‡ x 1 N ‡1 …a ¡ 1† and: xo ˆ
yo yo ‡ a…1 ¡ yo †
…9†
Alternatively, when the required number of stages N is speci ed, the missing concentrations can be determined from Smoker’s equation23 or, at total re ux, from the Fenske equation24. Trans IChemE, Vol 80, Part A, May 2002
(a) Equation (7) is plotted on Figure 4 as the locus of fmax. The minimum value of fmax, corresponding to the vertical line, occurs because in this example the conditions at the top of the bed are xed, so that for a large number of stages, N, a pinch occurs at the bottom i.e. x1 ! xo : Equation (7) then reduces to: y ¡ yN fmax ˆ N ‡1 …10† yN ¡ yo
Equation (10) de nes the vertical line on Figure 4. (b) Another special case for calculation of fmax is for a bed operating at total re ux with top and bottom concentrations symmetrical about 50% molar. yN ˆ xN‡1 ; yo ˆ x1 ; and xo ˆ y¡1
…11†
yo ˆ 1 ¡ yN and y¡1 ˆ 1 ¡ yN ‡1
…12†
For symmetry about 50% molar:
so that: 1 ¡ fmax ˆ
Some Limiting Cases for fm ax
At total re ux:
from which: 1 ¡ fmax
377
Substituting in equation (7): y ¡ yN yN ‡1 ¡ yN fmax ˆ N ‡1 ‡ yN‡1 ‡ yN ¡ 1 2yN ¡ 1 ³ ´³ ´ y ¡ yN yN‡1 ¡ yN ¡ N‡1 yN‡1 ‡ yN ¡ 1 2yN ¡ 1
…13†
Under the same assumptions, Fenske’s equation becomes: £ ¤¡1 yN‡1 ˆ 1 ‡ a¡…N‡2†=2 …14† £ ¤¡1 yN ˆ 1 ‡ a¡N =2
…15†
From equations (13–15), fmax can be determined simply as a function of a and N only. (c) A third special case is when the relative volatility approaches unity, for which Huber and Hiltbrunner11 reported an approximate equation for fmax. Huber and Hiltbrunner provided no derivation for their equation and it apparently came from simply tting an equation to numerical results obtained using a full parallel column model. Their equation can be derived analytically as follows. For relative volatility very close to unity, total re ux can be assumed, the equilibrium line can be considered straight and parallel to the operating line, and furthermore concentration symmetry can be assumed between the top and bottom of the packed bed as shown in Figure 8. Equation (7) then reduces to: fmax ˆ
A A ‡ B‡C A‡B‡C ³ ´³ ´ A A ¡ B‡C A‡B‡C
…16†
where the distances A, B and C are shown on Figure 8. If N is the number of theoretical stages, it follows from Figure 8 that: Nˆ
B‡C A
…17†
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BILLINGHAM and LOCKETT
Figure 8. Special case when a ! 1.
Substituting into equation (16) gives Huber and Hiltbrunner’s equation for this special case: fmax ˆ
2 N ‡1
…18†
ways to do this. One is to lump components together to form a binary mixture of pseudo light and heavy components. Another is to choose the two key components and to normalize their individual mole fractions with respect to their sum. We have also sometimes found it to be convenient to make the approximation that the number of equilibrium stages in the bed is two less than the actual number (one subtracted from each end). This ensures that the equilibrium concentrations that are required in equation (7) are always directly available from the column simulation output. Otherwise, a separate calculation is sometimes needed to determine these values. An example calculation of fmax from a column simulation output is shown in Table 1. The system consists of the three components methanol, ethanol and 2-propanol. The column has a single packed bed above the feed and another single bed below, delivering 11 and 14 theoretical stages, respectively. Two calculations of fmax are shown in the table. In case (a) methanol is taken as the light key and the sum of ethanol and 2-propanol is the heavy key. In this case, fmax is calculated from equation (7) as 0.276 above the feed and 0.089 below. For case (b) methanol is taken as the light key and 2-propanol as the heavy key, giving fmax as 0.211 above the feed and 0.085 below. Both methods indicate that the bed above the feed is insensitive to maldistribution whereas the bed below the feed is more sensitive, although the separation should be attainable. This is discussed more fully below. In general, some care is necessary when representing a multi-component mixture as a binary and the value of fmax can depend somewhat on which method is chosen.
Calculation of fm ax from a Column Simulation Output
USE OF fm a x DURING DESIGN
Strictly, equation (7) we have derived for fmax is applicable only to a binary system. However, it is usually possible to calculate fmax from the vapour and liquid concentrations that are part of the output of a conventional column simulation program involving multi-component mixtures and theoretical stages. As discussed above, it is not necessary to construct a parallel column model. The rst step is to represent the system as a binary mixture. There are several
Having calculated a value for fmax, the designer then needs to know whether it indicates that the bed will be sensitive to maldistribution. Undoubtedly, the best way to do this is to compare fmax with its value for other beds that have worked satisfactorily in the past, because fmax unambiguously ranks one bed against another for sensitivity to maldistribution. If the designer knows of other operating packed beds of similar diameter having the same or a
Table 1. Calculation of fmax from mole fractions obtained from a column simulation output for the system methanol (m), ethanol (e) and 2-propanol (p). Vapour mole fraction Stage no Above feed 25 24 * * 16 15 Below feed 14 13 * * 2 1
Liquid mole fraction
Case a
Case b
ym
ye
yp
xm
xe
xp
Ylk
Xlk
Ylk
Xlk
0.8782 0.8149
0.0564 0.0770
0.0654 0.1081
0.7829 0.6897
0.0874 0.1117
0.1298 0.1986
0.8782 0.8149
0.7829 0.6897
0.9307 0.8829
0.8578 0.7765
0.5832 0.5795
0.1001 0.0975
0.3167 0.3230
0.4211 0.4174
0.1193 0.1158
0.4596 0.4668
0.5832 0.5795
0.4211 0.4174
0.6480 0.6422
0.4781 0.4721
fmax ˆ
0.276
0.211
0.5772 0.5517
0.0952 0.1021
0.3276 0.3462
0.4150 0.3914
0.1128 0.1189
0.4722 0.4897
0.5772 0.5517
0.4150 0.3914
0.6379 0.6144
0.4677 0.4442
0.0841 0.0587
0.1803 0.1727
0.7356 0.7686
0.0489 0.0338
0.1649 0.1560
0.7862 0.8102
0.0841 0.0587
0.0489 0.0338
0.1026 0.0710
0.0585 0.0401
fmax ˆ
0.089
0.085
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smaller value of fmax, then there is a reasonable degree of con dence that the bed being designed will work properly. In the absence of comparative information, the following rules of thumb may be used, based on the authors’ experience with hundreds of operating packed columns in air separation. ° if fmax < 0.05, the packed bed is likely to be extremely sensitive to maldistribution. The required separation will very probably not be achieved; ° if 0.05 < fmax < 0.10 the bed will be sensitive to maldistribution but the separation probably can be achieved; ° if 0.10 < fmax < 0.20 the bed will not be particularly sensitive to maldistribution; ° if fmax > 0.20 the bed will be insensitive to maldistribution. It should be noted that these guidelines refer to columns of industrial diameter. Small diameter columns, less than about 0.5 m, can be more tolerant of maldistribution. Radial mixing can offset the adverse consequences of maldistribution in small diameter columns, providing that wall ow is not excessive. These guidelines also assume that a high quality liquid distributor is used and care is taken during installation of the packing and distributor, so that the extent of maldistribution is minimized. Several methods have been proposed in the literature to assess distributor quality, Moore and Ruckovena25, Billingham et al.26. The guidelines above are not in con ict with Moser and Damiani’s suggestion (referred to above) to assume f ˆ 0.04 in the full parallel column model.
Figure 9. Effect of number of stages and relative volatility on sensitivity to maldistribution. Total re ux, symmetrical concentrations about 50% molar.
FACTORS AFFECTING THE SENSITIVITY TO MALDISTRIBUTION As fmax is an indicator for the sensitivity to maldistribution, the variation of fmax as various parameters are changed shows how the sensitivity to maldistribution is affected by these same parameters. For the special case of total re ux and concentration symmetry about 50% molar, equations (13)–(15) have been used to construct Figure 9. Each of the lines on Figure 9 is for a constant value of fmax. This gure is particularly useful for design. It shows that for a xed value of relative volatility, the sensitivity to maldistribution increases as the number of stages increases. Similarly, for a xed number of stages the sensitivity to maldistribution increases as the relative volatility increases. Figure 9 is a quantitative version of the design rules abounding in the packed bed literature that recommend a maximum number of stages in a bed before redistribution is necessary. For example, Kister27 states that packed beds containing less than ve stages per bed are relatively insensitive to liquid maldistribution, whereas beds with ten or more stages per bed are extremely sensitive. Similar guidelines can be found in packing suppliers’ literature28. However, the concept of fmax and Figure 9, for example, shows that these guidelines in the literature are oversimpli ed. They should take account of relative volatility and other factors that in uence fmax. Some of these factors can be illustrated by extending Figure 9. The in uence of L=V on fmax is shown in Figure 10. It was constructed using Smoker’s equation for a simple single bed, again without the need to use a parallel column model. The parameters were chosen to correspond to those used by Zuiderweg et al.2. Figure 10 shows that sensitivity to Trans IChemE, Vol 80, Part A, May 2002
Figure 10. Effect of L=V on fmax, a ˆ 2.5, N ˆ 8, yN ˆ xN ‡ 1 ˆ 0.85.
maldistribution is at a maximum at total re ux, which was the same conclusion reached by Zuiderweg et al.2 using the much more complex zone-stage model and also by Yuan and Spiegel13 using the complete parallel column model. Figure 11 shows what happens when the restriction of concentration symmetry, used in Figure 9, is relaxed. Here again, only the Fenske equation was needed to construct the graph. It shows that concentration symmetry is the worst case in determining sensitivity to maldistribution. As previously mentioned when discussing equation (7), beds that are designed with a pinch at one end but not the other
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Figure 11. Effect of concentration symmetry of fmax. Symbols de ned on Figure 7, a ˆ 2.5, N ˆ 6, total re ux.
are less sensitive to maldistribution. For clarity, note again that the terminal concentrations at the design point, (denoted by ( yN, xN‡1) and ( yo, x1) on Figure 7) may or may not be close to a pinch at either end. However, at a maldistribution corresponding to fmax, column 1 is pinched at the top and column 2 at the bottom. Hence, fmax is a measure of the extent that the operating lines can be altered by maldistribution before these limiting simultaneous pinches occur. ANALYSIS OF PUBLISHED FRI DATA USING fm ax In a series of papers Fractionation Research Inc. (FRI) has published experimental HETP data from a commercial-scale column (diameter 1.2 m) using a variety of systems at various pressures. Results were given for random and structured packing using both uniform distribution and controlled maldistribution of liquid. It is of interest to calculate fmax for these studies to determine the sensitivity of the results to liquid maldistribution. In the earlier papers dealing with random packing, HETP was reported only as a
ratio rather than as an absolute value so insuf cient information is available to calculate fmax. A comprehensive set of data was provided by Fitz, Kunesh and Shariat29 for Mellapak 250Y structured packing at total re ux with uniform liquid distribution. The results are summarized in Table 2. Equations (13)–(15) have been used to calculate the values of fmax shown in the table. The results show that none of the FRI experiments was critically sensitive to maldistribution (i.e. in no case was fmax < 0.05). Most of the results were obtained where maldistribution would not have had a signi cant effect providing care was taken to ensure uniform liquid distribution. In these experiments, a tubed drip pan distributor was used that did indeed provide very uniform distribution. A different conclusion can be drawn about later tests reported by FRI on the same packing studying the effect of controlled liquid maldistribution (Fitz, King and Kunesh30). For these tests N was reported as 10.5 and that has a signi cant in uence on fmax, which falls to 0.057 as shown in Table 2. It can be concluded that in the later tests the apparent HETP was very sensitive to maldistribution and indeed that was the broad conclusion reached by FRI in their experimental study. The effect of bed depth, and hence number of stages, on the apparent HETP has been studied by FRI although the results have not been published in the open literature. For the system o=p xylene at 0.13 bar operating at total re ux, Figure 12 shows how fmax varies with bed depth. The results show that a short bed, for example of length 1.69 m, is totally insensitive to maldistribution. Only when the bed depth increases to about 4 m and above would we expect maldistribution to have a signi cant effect on HETP. VAPOUR MALDISTRIBUTION Whereas fmax deals with liquid maldistribution, for completeness an equivalent derivation can be made for vapour maldistribution. In the parallel column model of Figure 1, the liquid is now assumed to be uniformly distributed between the two columns and the vapour is maldistributed. The vapour ow rate in column 1 is: V 0 ˆ …1 ¡ g†V
…19†
and the vapour ow rate in column 2 is: V 00 ˆ …1 ‡ g†V
…20†
Table 2. Summary of FRI tests including fmax . System Uniform liquid distribution o-p xylene o-p xylene o-p xylene Cyclohexane=n-heptane Cyclohexane=n-heptane i-butane=n-butane i-butane=n-butane i-butane=n-butane i-butane=n-butane Controlled liquid maldistribution Cyclohexane=n-heptane
Pressure bar
Relative volatility
Bed height m
HETP m
Number of effective stages, N
fmax
0.02 0.13 1.0 0.34 1.65 6.9 11.4 20.7 27.6
1.31 1.237 1.16 1.85 1.57 1.295 1.236 1.15 1.10
3.78 3.78 3.78 3.78 3.78 3.78 3.78 3.78 3.78
0.3 0.3 0.3 0.5 0.4 0.3 0.3 0.3 0.35
12.6 12.6 12.6 7.6 9.5 12.6 12.6 12.6 10.8
0.089 0.106 0.125 0.090 0.087 0.092 0.107 0.127 0.161
1.0
1.65
3.78
0.36
10.5
0.057
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Figure 13. Liquid by-pass model.
Figure 12. Effect of bed depth on sensitivity to maldistribution. o=p xylene, 0.13 bar, total re ux, HETP ˆ 0.3 m, symmetrical concentrations about 50% molar.
Using a similar derivation to that leading to equation (7) gives the maximum vapour maldistribution, gmax , that can be tolerated. y ¡ yN x ¡ xo gmax ˆ N ‡1 ‡ 1 yN ‡1 ¡ yo xN‡1 ¡ x1 ³ ´³ ´ …21† yN ‡1 ¡ yN x1 ¡ xo ¡ yN ‡1 ¡ yo xN‡1 ¡ x1
The parameter gmax can be used to rank packed beds for their sensitivity to vapour maldistribution although, as mentioned above, usually vapour maldistribution quickly corrects itself in a bed so that sensitivity to vapour maldistribution is of less importance than sensitivity to liquid maldistribution. BY-PASS MODEL Figure 13 illustrates another type of model that can be used to investigate sensitivity to maldistribution. A small fraction of liquid (bL) completely by-passes the bed and contaminates the bottom product. This can be considered as the most adverse possible consequence of wall ow, where it originates at the top of the bed and there is no mixing or mass transfer between the bulk liquid and the liquid owing down the wall. For a xed bottom product composition, the maximum fraction of liquid that can by-pass the bed, bL max , is easily determined. It corresponds to equilibrium between the liquid leaving the bed and the entering vapour, Figure 14. From a mass balance on the liquid at the bottom of the bed: …1 ¡ bL max †xo ‡ bL max xN‡1 ˆ x1
so that:
bL max ˆ
x1 ¡ xo xN‡1 ¡ xo
…22† …23†
Note that bL max is identical to the second term in equation (7). Trans IChemE, Vol 80, Part A, May 2002
Figure 14. Calculation of bLmax.
A similar equation can be derived for vapour by-passing. The maximum fraction of the vapour that can by-pass the bed for a xed top composition, bVmax, is: y ¡ yN bV max ˆ N‡1 …24† yN‡1 ¡ yo
Note again that bVmax is identical to the rst term in equation (21). Equations (23) and (24) quantify the obvious observation that only minimal by-passing can be tolerated when high purity products are required. In general, by-pass models are less informative than parallel-column models for assessing sensitivity to maldistribution because the assumptions on which they are based are less realistic. CONCLUSION Calculation of fmax to assess the sensitivity of a packed bed to maldistribution can now easily be done as part of the routine design procedure using equation (7). When such sensitivity appears to be high, the designer can take remedial measures, such as using a redistributor or using more design contingency in the applied value of HETP. The variation of
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fmax to changes in number of stages, relative volatility, L=V, and terminal concentrations follows that found for the effective number of stages in the presence of maldistribution calculated from more detailed models, such as the zonestage model of Zuiderweg2. It follows that calculation of fmax is an adequate substitute for a detailed model to assess sensitivity and certainly is much easier to do. However, the effect of column diameter cannot be accounted for through fmax. A detailed model is needed for that, so the further re nement of the detailed models is a worthwhile activity for sensitivity assessment. Of course, if the detailed models can ever be developed to the point that they can be used as reliable design tools to predict the number of stages that will be achieved in the bed, they will certainly supplant a simpler sensitivity analysis model such as the one described in this paper. NOMENCLATURE A,B,C bL bLmax bvmax E f fmax g gmax HETP HTU L N NA V Xlk x Ylk y
distances on Figure 8, m fraction of liquid bypassing bed maximum value of bL maximum fraction of vapour bypassing bed ef ciency de ned by equation (3) liquid maldistribution fraction maximum value of f above which the separation cannot be achieved vapour maldistribution fraction maximum value of g above which the separation cannot be achieved height of an equivalent theoretical plate, m height of transfer unit, m liquid ow rate, kg-mol s¡1 effective number of theoretical stages actual number of theoretical stages vapour ow rate, kg-mol s¡1 mole fraction of light key in pseudo-binary liquid mixture mole fraction of more volatile component in liquid mole fraction of light key in pseudo-binary vapour mixture mole fraction of more volatile component in vapour
Greek symbols a relative volatility Subscripts m, e, p value for methanol, ethanol and 2-propanolrespectively in Table 1 n leaving theoretical stage n where ¡ 1 µ n µ NA Superscripts b value when by-passing occurs 0 for column 1 00 for column 2
REFERENCES 1. Kister, H. Z. and Larson, K. F., 1997, Packed distillation tower design, Handbook of Separation Techniques for Chemical Engineers, edited by Schweitzer, P. A., 3rd Edn. (McGraw-Hill, New York, USA), pp 1–315. 2. Zuiderweg, F. J., Hoek, P. J. and Lahm, L., 1987, The effect of liquid distribution and redistribution on the separation ef ciency of packed columns, IChemE Symp Ser, N104: A217. 3. Zuiderweg, F. J., Kunesh, J. G. and King, D. W., 1993, A model for the calculation of the effect of maldistribution on the ef ciency of a packed column, Trans IChemE Part A, Chem Eng Res Des, 71(A1): 38. 4. Olujic, Z., 1997, Development of a complete simulation model for predictingthehydraulicandseparationperformanceofdistillationcolumns equipped with structured packings, Chem Biochem Eng Q, 11(1): 31. 5. Higler, A., Krishna, R. and Taylor, R., 1999, Nonequilibrium cell model for packed distillation columns—The in uence of maldistribution, Ind Eng Chem Res, 38: 3988. 6. Yin, F. H., Sun, C. G., Afacan, A., Nandakumar, K. and Chuang, K. T., 2000, CFD modelling of mass-transfer processes in randomly packed distillation columns, Ind Eng Chem Res, 39: 1369.
7. Kouri, R. J., 1985, An extended Colburn equation for the analysis of packed column performance under conditions of liquid and gas maldistribution, EFChE Working Party Meeting on Distillation, Absorption and Extraction (Amsterdam, Netherlands), 6 June. 8. Mullin, J. W., 1957, The effect of maldistribution on the performance of packed columns, The Ind Chem, Aug: 408. 9. Morris, G. A., 1960, The application of absorption tower design methods to packed distillation columns, Int Symp on Distillation (IChemE, Rugby, UK), pp 146. 10. Changez, N. D. and Sawistowski, H., 1963, Effect of maldistribution on the performance of packed columns, The Ind Chem, April: 181. 11. Huber, M. and Hiltbrunner, R., 1966, Fu¨llko¨rperrekti zierkolonnen mit maldistribution, Chem Eng Sci, 21: 819. 12. Meier, W. and Huber, M., 1969, Measurements of the number of theoretical plates in packed columns with arti cial maldistribution, IChemE Symp Ser, N32: 4: 31. 13. Yuan, H. C. and Spiegel, L., 1981, Theoretical and experimental investigation of the in uence of maldistribution on the number of theoretical stages in packed columns at partial re ux, Proc 2nd World Congress of Chem Eng (Montreal, Canada), 4: 274. 14. Thorogood, R. M., 1981, Maldistribution in plate columns, IChemE Symp Ser, N61: 95. 15. Stichlmair, J. and Stemmer, A., 1987, In uence of maldistribution on mass transfer in packed columns, IChemE Symp Ser, N104: B213. 16. Klemas, L. and Bonilla, J. A., 1995, Accurately assess packed-column ef ciency, Chem Eng Prog, July, 27. 17. Martin, G. R. and Sloley, A. W., 1995, Simulation of ow maldistribution and its results on mass transfer, paper 26D (Houston AIChE meeting, USA), 23 March. 18. Schultes, M., 2000, In uence of liquid redistributors on the masstransfer ef ciency of packed columns, Ind Eng Chem Res, 39: 1381. 19. Manning, R. E. and Cannon, M. R., 1957, Distillation improvement by control of phase channeling in packed columns, Ind Eng Chem, 49(3): 347. 20. Schafer, T. A., Lam, S. Y. S. and Vragolic, S., 1992, Organic strippers: Vapour maldistribution problems and solutions (New Orleans AIChE meeting, USA), 29 March. 21. Hanley, B., 1999, The in uence of ow maldistribution on the performance of columns containing random packings: A model study for constant relative volatility and total re ux, Separ Puri c Tech, 16: 7. 22. Moser, F. and Damiani, M., 2001, Styrene monomer puri cation with MellapakPlus, the new generation of structured packing: Some case studies (Joint meeting of VDI-GVC, DECHEMA and EFChE Working Party on Distillation, Absorption and Extraction, Bamberg, Germany), paper THZ20, 4–6 April. 23. Smoker, E. H., 1938, Analytic determination of plates in fractionating columns, Trans AIChE, 34: 165. 24. Fenske, M. R., 1932, Fractionation of straight-run Pennsylvania gasoline, Ind Eng Chem, 24: 482. 25. Moore, D. and Rukovena, F., 1986, Liquid and gas distribution in commercial packed towers, 36th Cana Chem Eng Conf paper 23b (Also published in Chemical Plants and Processing [European edition], 1987, August, pp 11). 26. Billingham, J. F., Bonaquist, D. P. and Lockett, M. J., 1997, Characterization of the performance of packed distillation column liquid distributors, IChemE Symp, N142: 841. 27. Kister, H. Z., 1992, Distillation Design (McGraw-Hill, New York, USA), pp 551. 28. Norton Chemical Process Products Corp, 1996, IMTP High-performance random packing, Bulletin IHPRP-1, pp 11. 29. Fitz, C. W., Kunesh, J. G. and Shariat, A., 1999, Performance of structured packing in a commercial-scale column at pressures of 0.02–27.6 bar, Ind Eng Chem Res, 38: 512. 30. Fitz, C. W., King, D. W. and Kunesh, J. G., 1999, Controlled liquid maldistribution studies on structured packing, Trans IChemE, Part A, Chem Eng Res Des, 77(A6): 482.
ADDRESS Correspondence concerning this paper should be addressed to Dr. M. J. Lockett, Praxair, Inc., PO Box 44, Tonawanda, NY 14151-0044, USA. E-mail: [email protected] The manuscript was received 1 October 2001 and accepted for publication after revision 29 January 2002.
Trans IChemE, Vol 80, Part A, May 2002
A SIMPLE METHOD TO ASSESS THE SENSITIVITY OF PACKED DISTILLATION COLUMNS TO MALDISTRIBUTION1 J. F. BILLINGHAM and M. J. LOCKETT Praxair, Inc., Tonawanda, NY, USA.
T
his paper provides a new tool for those concerned with the design or performance of packed distillation columns. It gives a simple method to assess the sensitivity of a packed bed to maldistribution. Despite extensive prior work on this topic, the concept proposed here appears to have been previously overlooked. A parallel column model is often used to assess the sensitivity of a packed bed in a distillation column to liquid or vapour maldistribution. However, it is well known that the parallel column model is oversimpli ed because it involves an arbitrary number of parallel columns, it neglects lateral mixing, and the actual extent of maldistribution is unknown. For these reasons, the parallel column model can only be used as a way of identifying packed beds that are particularly susceptible to maldistribution, rather than as a predictive design tool. In this paper it is shown that sensitivity to maldistribution can be predicted much more simply using a single parameter fmax, which is the maximum maldistribution that could possibly occur in a parallel column while still being able to achieve the required separation. It is shown that fmax can be determined very simply, for example from the output of a conventional column simulation program, and a parallel column model is not actually needed. Using fmax, the sensitivity to maldistribution of a proposed packed bed can now easily be compared at the design stage to other packed beds that are known to work satisfactorily. If necessary, the design can then be modi ed to reduce the sensitivity to maldistribution. Routine calculation of fmax during design will help to reduce the signi cant number of distillation column problems that presently occur because of maldistribution. Keywords: distillation; packing; maldistribution
INTRODUCTION
One of the important things about maldistribution is that its effects are not constant. The separation performance loss with the same degree of maldistribution differs from system to system and even section to section within the same distillation column. So to model the effect of maldistribution, two separate steps are involved: prediction of the extent of maldistribution and then prediction of its effect on separation. Three types of models have been proposed for the latter: Detailed models, parallel column models, and by-pass models.
Some degree of maldistribution of liquid or vapour, or both, inevitably occurs in packed columns. Maldistribution can be caused by less than perfect initial distribution, or it can develop within the bed because of wall ow or because of the non-randomness of supposedly random packing. The seams between bricks in structured packing can also cause maldistribution1. Although lateral mixing, perpendicular to the column axis, tends to reduce the effect of maldistribution on separation, it can act only over a limited radial distance, and so large diameter columns are more sensitive to maldistribution than small diameter columns. Also, because of limited lateral mixing, large-scale maldistribution is more damaging than small-scale maldistribution. As lateral mixing is more effective for vapour than for liquid, maldistribution of vapour usually has a smaller detrimental effect on column performance. This paper will therefore, for the most part, deal with maldistribution of liquid, although the results can easily be extended to vapour maldistribution if required as indicated at the end of the paper.
Detailed Models Detailed models to predict liquid maldistribution and then its effect on HETP (the height of an equivalent theoretical plate) have been given by Zuiderweg et al.2,3, Olujic4, Higleret al.5, and Yin et al.6. Kouri7 also developed a similar model for absorption involving transfer units. All these models require speci cation of the initial liquid distribution leaving the distributor, and then they predict how the liquid ow pattern develops in the bed taking into account wall effects and liquid mixing. Once the liquid ow pattern has been xed, it is used to predict the increase of HETP (or HTU) over and above the basic HETP (or HTU) that would be obtained in the absence of
1
# 2001 Praxair Technology, Inc. All rights reserved
373
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maldistribution. What is evident from these papers is that the extent of maldistribution cannot yet be predicted with suf cient con dence, and so none of these studies has so far evolved into a practically useful design method. Indeed, this approach will never be able to predict unforeseen maldistribution arising from manufacturing or installation errors, for example. These models are useful, however, in showing how the effect of maldistribution on HETP varies with parameters such as relativevolatility, bed depth, concentration,re ux ratio and column diameter, etc. We will refer to this as a sensitivity analysis as opposed to a design method. Parallel Column Models The same sensitivity analysis can be performed more simply using a parallel column model, with the exception that the effect of column diameter cannot be included. Many workers have used the parallel column model shown in Figure 1 to model the effect of liquid maldistribution on separation performance. The two columns have the same cross sectional area and equal vapour ow. One column receives an excess liquid ow at the expense of the other column. Lateral mixing is ignored in this model. The different liquid to vapour ratios in the two columns causes them to have different operating lines as shown in Figure 2. One of the columns tends to pinch at the top and the other at the bottom. The net result is to reduce the effective number of theoretical stages of the combined column system below that of each individual column, as is evident by comparing the solid line with the dotted lines stepped off in Figure 2. In the example shown, each of the individual columns has 4 theoretical stages, whereas the combined column only has 3.3 stages. The earliest work involving the application of the parallel column model to distillation is that of Mullin8. Subsequent
Figure 2. McCabe-Thiele diagram for parallel column model.
authors include: Morris9, Changez and Sawistowski10, Huber and Hiltbrunner11, Meier and Huber12, Yuan and Spiegel13, Thorogood14, Stichlmair and Stemmer15, Klemas and Bonilla16, Martin and Sloley17, and Schultes18. The conclusions reached by all these workers are essentially similar, and they show, using examples, how the effect of maldistribution on separation changes as different parameters are altered. Again, the models cannot be used directly for design. By-pass Models By-pass models assume that a small amount of either liquid or vapour passes through the bed without undergoing any mass transfer, which then contaminates the product. This is particularly damaging when a high purity product is required. Wall ow is a potential source of bypassing. Authors who have proposed by-pass models include Manning and Cannon19, Schafer and Lam20, and Hanley21. Ever more sophisticated versions of the three types of models discussed above are regularly put forward. For example, the parallel column model has been incorporated into a column simulation design package17 and models involving three18 to a hundred15 parallel columns have been proposed. Maldistribution of vapour, induced by the assumed liquid maldistribution, has also been included in the parallel column model16. Unfortunately, because of the dif culty of predicting the extent of maldistribution, these models can only be used to assess sensitivity to maldistribution rather than as direct design tools. A further dif culty is that it is not obvious to a column designer how to incorporate the output from a conventional column simulation design program into the models. The purpose of this paper is to show that, if the objective is limited only to assessment of sensitivity to maldistribution, it can be done much more simply. REPRESENTATION OF RESULTS FROM THE PARALLEL COLUMN MODEL
Figure 1. Parallel column model.
In the parallel column model shown in Figures 1 and 2, xed values are assumed for the number of actual theoretical Trans IChemE, Vol 80, Part A, May 2002
PACKED DISTILLATION COLUMNS
375
stages in each column NA, the relative volatility a, the mean concentrations at the top of the columns ( yN, xN ‡ 1), and the vapour concentration entering the columns ( yo). The vapour and liquid owrates are assumed constant within each of the columns, implying that the latent heat of vaporization is constant and independent of composition. The liquid owrate in column 1 is: L0 ˆ …1 ‡ f †L
…1†
L00 ˆ …1 ¡ f †L
…2†
and in column 2 the liquid ow rate is:
The extent of liquid maldistribution is represented by the fraction f. The calculation procedure involved in the model is relatively straightforward and will not be elaborated here. A typical representation of the results is shown in Figure 3. Most previous workers who have used the parallel column model have reported their results in a similar way. Figure 3 shows that as the maldistribution increases the separation achieved falls, as represented by the effective number of theoretical stages, N, that are obtained from a xed number of actual theoretical stages in each column, NA. In order to judge whether the loss of separation will be signi cant, an arbitrary value of the maldistribution fraction f has to be assumed. This will depend to some extent on the type of distributor employed and, based on Sulzer experience, Moser and Damiani22 have suggested that f ˆ 0.04 can be used for a high quality distributor. Using f ˆ 0.04 in Figure 3 shows that 30 actual stages will deliver 21 effective stages in this particular example. Figure 4 shows how the simple representation of Figure 3 becomes more complex as additional values of NA are included. This representation of the results deals with the rating problem i.e. given a xed number of stages what separation can be achieved when maldistribution occurs? An alternative representation is in terms of the design problem
Figure 3. Typical representation of results from the parallel column model. NA ˆ 30, a ˆ 1.538, yo ˆ 0.5, yN ˆ 0.95, xN‡1 ˆ 0.95.
Trans IChemE, Vol 80, Part A, May 2002
Figure 4. More complex results from the parallel column model-rating problem. a ˆ 1.538, yo ˆ 0.5, yN ˆ 0.95, xN‡1 ˆ 0.95.
i.e. given a required xed separation, how many theoretical stages must be provided in each column under conditions of maldistribution? Thorogood14 took this approach for modelling maldistribution in plate columns with a parallel column model. Some of the data used to generate Figure 4 are replotted in Figure 5, where, following Thorogood, an ef ciency is de ned as: Eˆ
NA jf ˆ0 NA
…3†
Figure 5. Results form the parallel column design model—design problem using ef ciency (parameters from Figure 4).
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Although Figure 5 bears a super cial resemblance to Figure 3, they are, in fact, quite different representations of the results. We have found that, for the design problem, it is clearer and more instructive to plot NA directly as shown in Figure 6. Here NA is the number of theoretical stages that must be provided in each parallel column to achieve the same separation as is obtained with no maldistribution ( f ˆ 0). Four lines are shown on Figure 6 corresponding to four different values of NA with no maldistribution. Each line represents a xed separation and they show that as maldistribution increases the required number of stages rises rapidly. DEFINITION AND SIGNIFICANCE OF fm a x For each of the lines shown on Figure 6 there is a maximum value of the maldistribution fraction f above which no increase in the number of actual theoretical stages can provide the required separation. We shall call this maximum fmax. A line representing the locus of fmax is also shown on Figure 4. Moving horizontally across Figure 4 shows that for a required number of effective stages there is a maximum value of f above which the separation cannot be achieved, irrespective of how many actual stages are provided. Note that the locus of fmax on Figure 4 turns into a vertical line corresponding to a minimum value of fmax. If f is greater than the minimum value of fmax there is a limit to the number of effective stages that can be achieved, irrespective of the actual number of stages provided. The physical signi cance of fmax is shown in Figure 7. For a xed required separation, as maldistribution increases, eventually a pinch occurs at the top of one column and at the bottom of the other, corresponding to an in nite number of stages in each column. This determines the maximum maldistribution that can be tolerated while still achieving the required separation. Looking back to Figures 3 and 4, consider how diagrams like these have been used to assess the sensitivity to
Figure 7. Location of pinches when f ˆ fmax.
maldistribution. It is evident that whether or not a particular bed appears sensitive to maldistribution depends on how closely the arbitrarily assumed value of f (say 0.04 as suggested above) approaches the value of fmax. For example, in Figure 4, if 40 effective stages are required, the corresponding value of fmax is 0.037. If 40 actual stages are then provided in each column, and if f is assumed to be 0.04, only 24 effective stages will actually be achieved so there will be a severe loss of separation predicted. On the other hand, if only 15 effective stages are required, for which fmax ˆ 0.063, with an assumed value of f ˆ 0.04, and the provision of 15 actual stages in each column, there is only a slight loss of separation indicated down to 14 effective stages. Now since the predicted sensitivity to maldistribution depends primarily on the assumed value of f and on the value of fmax, and in addition f is arbitrary and usually is assumed to be xed, it follows that fmax alone is an adequate indicator for the sensitivity to maldistribution. This is the main idea put forward in this paper. It is recognized that by concentrating only on fmax, information is then unavailable about the predicted number of effective stages at values of f less than fmax. However, it should be evident that this is unimportant when it is recognized that the predicted number of effective stages has very little practical value, because of the arbitrary number of parallel columns assumed and the neglect of lateral mixing. The question then simply becomes how to calculate fmax without having to resort to a full parallel column model. CALCULATION OF fm a x General Equation This section shows how fmax can be calculated without the need for a parallel column model. From Figure 7, at the pinch condition, the vapour leaving column 1 is in equilibrium with the liquid entering. Similarly, the liquid leaving column 2 is in equilibrium with the vapour entering. The required separation is assumed to be xed. With the same vapour ow in each column, the vapour composition leaving column 2 is obtained from a mass balance:
Figure 6. Results from the parallel column model-design problem. a ˆ 1.538, yo ˆ 0.5, yN ˆ 0.95, xN‡1 ˆ 0.95.
y00NA ˆ 2yN ¡ y0NA
…4†
Trans IChemE, Vol 80, Part A, May 2002
PACKED DISTILLATION COLUMNS The slope of the operating line in column 2 is (1 7 fmax) times the slope of the operating line of the combined column in the absence of maldistribution, from equation (2). So that from Figure 7: ³ ´ y00NA ¡ yo yN ¡ yo ˆ …1 ¡ f † …5† max xN ‡1 ¡ x001 xN‡1 ¡ x1 Combining equations (4) and (5) and using the pinch conditions that: y0NA ˆ yN‡1 and x001 ˆ xo
…6†
gives: ³ ´ yN ¡ yo 2yN ¡ yN ‡1 ¡ yo ˆ …1 ¡ fmax † xN ‡1 ¡ xo xN ‡1 ¡ x1 ³
´ … yN ¡ yN‡1 † ‡ … yN ¡ yo † ˆ xN‡1 ¡ xo ³ ´ …xN‡1 ¡ xo † ‡ …xo ¡ x1 † £ yN ¡ yo ³ ´³ ´ yN ¡ yN‡1 y ¡ yN‡1 xo ¡ x1 ‡ N yN ¡ yo yN ¡ yo xN‡1 ¡ xo xo ¡ x1 ‡1‡ xN‡1 ¡ xo
Hence, the required equation for fmax is: y ¡ yN x ¡ xo fmax ˆ N‡1 ‡ 1 yN ¡ yo xN‡1 ¡ xo ³ ´³ ´ yN‡1 ¡ yN x1 ¡ xo ¡ yN ¡ yo xN‡1 ¡ xo
…7†
Equation (7) can be used to calculate fmax directly without the need for a parallel column model. The equation involves the sum and product of two terms that represent the approach to pinch at the top and bottom of the packed bed. The relationship is powerful in understanding the sensitivity to liquid maldistribution. It shows, for example, that a signi cantly greater tolerance to maldistribution is possible when, at the design point, either the top or the bottom of the packed bed is far away from pinch. Calculation of the terms in equation (7) is straightforward. For a required xed separation, yN, xN ‡ 1, yo and x1 are speci ed. The other terms can be calculated from the equilibrium relationships: a xN‡1 yN ‡1 ˆ …8† ‡ x 1 N ‡1 …a ¡ 1† and: xo ˆ
yo yo ‡ a…1 ¡ yo †
…9†
Alternatively, when the required number of stages N is speci ed, the missing concentrations can be determined from Smoker’s equation23 or, at total re ux, from the Fenske equation24. Trans IChemE, Vol 80, Part A, May 2002
(a) Equation (7) is plotted on Figure 4 as the locus of fmax. The minimum value of fmax, corresponding to the vertical line, occurs because in this example the conditions at the top of the bed are xed, so that for a large number of stages, N, a pinch occurs at the bottom i.e. x1 ! xo : Equation (7) then reduces to: y ¡ yN fmax ˆ N ‡1 …10† yN ¡ yo
Equation (10) de nes the vertical line on Figure 4. (b) Another special case for calculation of fmax is for a bed operating at total re ux with top and bottom concentrations symmetrical about 50% molar. yN ˆ xN‡1 ; yo ˆ x1 ; and xo ˆ y¡1
…11†
yo ˆ 1 ¡ yN and y¡1 ˆ 1 ¡ yN ‡1
…12†
For symmetry about 50% molar:
so that: 1 ¡ fmax ˆ
Some Limiting Cases for fm ax
At total re ux:
from which: 1 ¡ fmax
377
Substituting in equation (7): y ¡ yN yN ‡1 ¡ yN fmax ˆ N ‡1 ‡ yN‡1 ‡ yN ¡ 1 2yN ¡ 1 ³ ´³ ´ y ¡ yN yN‡1 ¡ yN ¡ N‡1 yN‡1 ‡ yN ¡ 1 2yN ¡ 1
…13†
Under the same assumptions, Fenske’s equation becomes: £ ¤¡1 yN‡1 ˆ 1 ‡ a¡…N‡2†=2 …14† £ ¤¡1 yN ˆ 1 ‡ a¡N =2
…15†
From equations (13–15), fmax can be determined simply as a function of a and N only. (c) A third special case is when the relative volatility approaches unity, for which Huber and Hiltbrunner11 reported an approximate equation for fmax. Huber and Hiltbrunner provided no derivation for their equation and it apparently came from simply tting an equation to numerical results obtained using a full parallel column model. Their equation can be derived analytically as follows. For relative volatility very close to unity, total re ux can be assumed, the equilibrium line can be considered straight and parallel to the operating line, and furthermore concentration symmetry can be assumed between the top and bottom of the packed bed as shown in Figure 8. Equation (7) then reduces to: fmax ˆ
A A ‡ B‡C A‡B‡C ³ ´³ ´ A A ¡ B‡C A‡B‡C
…16†
where the distances A, B and C are shown on Figure 8. If N is the number of theoretical stages, it follows from Figure 8 that: Nˆ
B‡C A
…17†
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BILLINGHAM and LOCKETT
Figure 8. Special case when a ! 1.
Substituting into equation (16) gives Huber and Hiltbrunner’s equation for this special case: fmax ˆ
2 N ‡1
…18†
ways to do this. One is to lump components together to form a binary mixture of pseudo light and heavy components. Another is to choose the two key components and to normalize their individual mole fractions with respect to their sum. We have also sometimes found it to be convenient to make the approximation that the number of equilibrium stages in the bed is two less than the actual number (one subtracted from each end). This ensures that the equilibrium concentrations that are required in equation (7) are always directly available from the column simulation output. Otherwise, a separate calculation is sometimes needed to determine these values. An example calculation of fmax from a column simulation output is shown in Table 1. The system consists of the three components methanol, ethanol and 2-propanol. The column has a single packed bed above the feed and another single bed below, delivering 11 and 14 theoretical stages, respectively. Two calculations of fmax are shown in the table. In case (a) methanol is taken as the light key and the sum of ethanol and 2-propanol is the heavy key. In this case, fmax is calculated from equation (7) as 0.276 above the feed and 0.089 below. For case (b) methanol is taken as the light key and 2-propanol as the heavy key, giving fmax as 0.211 above the feed and 0.085 below. Both methods indicate that the bed above the feed is insensitive to maldistribution whereas the bed below the feed is more sensitive, although the separation should be attainable. This is discussed more fully below. In general, some care is necessary when representing a multi-component mixture as a binary and the value of fmax can depend somewhat on which method is chosen.
Calculation of fm ax from a Column Simulation Output
USE OF fm a x DURING DESIGN
Strictly, equation (7) we have derived for fmax is applicable only to a binary system. However, it is usually possible to calculate fmax from the vapour and liquid concentrations that are part of the output of a conventional column simulation program involving multi-component mixtures and theoretical stages. As discussed above, it is not necessary to construct a parallel column model. The rst step is to represent the system as a binary mixture. There are several
Having calculated a value for fmax, the designer then needs to know whether it indicates that the bed will be sensitive to maldistribution. Undoubtedly, the best way to do this is to compare fmax with its value for other beds that have worked satisfactorily in the past, because fmax unambiguously ranks one bed against another for sensitivity to maldistribution. If the designer knows of other operating packed beds of similar diameter having the same or a
Table 1. Calculation of fmax from mole fractions obtained from a column simulation output for the system methanol (m), ethanol (e) and 2-propanol (p). Vapour mole fraction Stage no Above feed 25 24 * * 16 15 Below feed 14 13 * * 2 1
Liquid mole fraction
Case a
Case b
ym
ye
yp
xm
xe
xp
Ylk
Xlk
Ylk
Xlk
0.8782 0.8149
0.0564 0.0770
0.0654 0.1081
0.7829 0.6897
0.0874 0.1117
0.1298 0.1986
0.8782 0.8149
0.7829 0.6897
0.9307 0.8829
0.8578 0.7765
0.5832 0.5795
0.1001 0.0975
0.3167 0.3230
0.4211 0.4174
0.1193 0.1158
0.4596 0.4668
0.5832 0.5795
0.4211 0.4174
0.6480 0.6422
0.4781 0.4721
fmax ˆ
0.276
0.211
0.5772 0.5517
0.0952 0.1021
0.3276 0.3462
0.4150 0.3914
0.1128 0.1189
0.4722 0.4897
0.5772 0.5517
0.4150 0.3914
0.6379 0.6144
0.4677 0.4442
0.0841 0.0587
0.1803 0.1727
0.7356 0.7686
0.0489 0.0338
0.1649 0.1560
0.7862 0.8102
0.0841 0.0587
0.0489 0.0338
0.1026 0.0710
0.0585 0.0401
fmax ˆ
0.089
0.085
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smaller value of fmax, then there is a reasonable degree of con dence that the bed being designed will work properly. In the absence of comparative information, the following rules of thumb may be used, based on the authors’ experience with hundreds of operating packed columns in air separation. ° if fmax < 0.05, the packed bed is likely to be extremely sensitive to maldistribution. The required separation will very probably not be achieved; ° if 0.05 < fmax < 0.10 the bed will be sensitive to maldistribution but the separation probably can be achieved; ° if 0.10 < fmax < 0.20 the bed will not be particularly sensitive to maldistribution; ° if fmax > 0.20 the bed will be insensitive to maldistribution. It should be noted that these guidelines refer to columns of industrial diameter. Small diameter columns, less than about 0.5 m, can be more tolerant of maldistribution. Radial mixing can offset the adverse consequences of maldistribution in small diameter columns, providing that wall ow is not excessive. These guidelines also assume that a high quality liquid distributor is used and care is taken during installation of the packing and distributor, so that the extent of maldistribution is minimized. Several methods have been proposed in the literature to assess distributor quality, Moore and Ruckovena25, Billingham et al.26. The guidelines above are not in con ict with Moser and Damiani’s suggestion (referred to above) to assume f ˆ 0.04 in the full parallel column model.
Figure 9. Effect of number of stages and relative volatility on sensitivity to maldistribution. Total re ux, symmetrical concentrations about 50% molar.
FACTORS AFFECTING THE SENSITIVITY TO MALDISTRIBUTION As fmax is an indicator for the sensitivity to maldistribution, the variation of fmax as various parameters are changed shows how the sensitivity to maldistribution is affected by these same parameters. For the special case of total re ux and concentration symmetry about 50% molar, equations (13)–(15) have been used to construct Figure 9. Each of the lines on Figure 9 is for a constant value of fmax. This gure is particularly useful for design. It shows that for a xed value of relative volatility, the sensitivity to maldistribution increases as the number of stages increases. Similarly, for a xed number of stages the sensitivity to maldistribution increases as the relative volatility increases. Figure 9 is a quantitative version of the design rules abounding in the packed bed literature that recommend a maximum number of stages in a bed before redistribution is necessary. For example, Kister27 states that packed beds containing less than ve stages per bed are relatively insensitive to liquid maldistribution, whereas beds with ten or more stages per bed are extremely sensitive. Similar guidelines can be found in packing suppliers’ literature28. However, the concept of fmax and Figure 9, for example, shows that these guidelines in the literature are oversimpli ed. They should take account of relative volatility and other factors that in uence fmax. Some of these factors can be illustrated by extending Figure 9. The in uence of L=V on fmax is shown in Figure 10. It was constructed using Smoker’s equation for a simple single bed, again without the need to use a parallel column model. The parameters were chosen to correspond to those used by Zuiderweg et al.2. Figure 10 shows that sensitivity to Trans IChemE, Vol 80, Part A, May 2002
Figure 10. Effect of L=V on fmax, a ˆ 2.5, N ˆ 8, yN ˆ xN ‡ 1 ˆ 0.85.
maldistribution is at a maximum at total re ux, which was the same conclusion reached by Zuiderweg et al.2 using the much more complex zone-stage model and also by Yuan and Spiegel13 using the complete parallel column model. Figure 11 shows what happens when the restriction of concentration symmetry, used in Figure 9, is relaxed. Here again, only the Fenske equation was needed to construct the graph. It shows that concentration symmetry is the worst case in determining sensitivity to maldistribution. As previously mentioned when discussing equation (7), beds that are designed with a pinch at one end but not the other
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BILLINGHAM and LOCKETT
Figure 11. Effect of concentration symmetry of fmax. Symbols de ned on Figure 7, a ˆ 2.5, N ˆ 6, total re ux.
are less sensitive to maldistribution. For clarity, note again that the terminal concentrations at the design point, (denoted by ( yN, xN‡1) and ( yo, x1) on Figure 7) may or may not be close to a pinch at either end. However, at a maldistribution corresponding to fmax, column 1 is pinched at the top and column 2 at the bottom. Hence, fmax is a measure of the extent that the operating lines can be altered by maldistribution before these limiting simultaneous pinches occur. ANALYSIS OF PUBLISHED FRI DATA USING fm ax In a series of papers Fractionation Research Inc. (FRI) has published experimental HETP data from a commercial-scale column (diameter 1.2 m) using a variety of systems at various pressures. Results were given for random and structured packing using both uniform distribution and controlled maldistribution of liquid. It is of interest to calculate fmax for these studies to determine the sensitivity of the results to liquid maldistribution. In the earlier papers dealing with random packing, HETP was reported only as a
ratio rather than as an absolute value so insuf cient information is available to calculate fmax. A comprehensive set of data was provided by Fitz, Kunesh and Shariat29 for Mellapak 250Y structured packing at total re ux with uniform liquid distribution. The results are summarized in Table 2. Equations (13)–(15) have been used to calculate the values of fmax shown in the table. The results show that none of the FRI experiments was critically sensitive to maldistribution (i.e. in no case was fmax < 0.05). Most of the results were obtained where maldistribution would not have had a signi cant effect providing care was taken to ensure uniform liquid distribution. In these experiments, a tubed drip pan distributor was used that did indeed provide very uniform distribution. A different conclusion can be drawn about later tests reported by FRI on the same packing studying the effect of controlled liquid maldistribution (Fitz, King and Kunesh30). For these tests N was reported as 10.5 and that has a signi cant in uence on fmax, which falls to 0.057 as shown in Table 2. It can be concluded that in the later tests the apparent HETP was very sensitive to maldistribution and indeed that was the broad conclusion reached by FRI in their experimental study. The effect of bed depth, and hence number of stages, on the apparent HETP has been studied by FRI although the results have not been published in the open literature. For the system o=p xylene at 0.13 bar operating at total re ux, Figure 12 shows how fmax varies with bed depth. The results show that a short bed, for example of length 1.69 m, is totally insensitive to maldistribution. Only when the bed depth increases to about 4 m and above would we expect maldistribution to have a signi cant effect on HETP. VAPOUR MALDISTRIBUTION Whereas fmax deals with liquid maldistribution, for completeness an equivalent derivation can be made for vapour maldistribution. In the parallel column model of Figure 1, the liquid is now assumed to be uniformly distributed between the two columns and the vapour is maldistributed. The vapour ow rate in column 1 is: V 0 ˆ …1 ¡ g†V
…19†
and the vapour ow rate in column 2 is: V 00 ˆ …1 ‡ g†V
…20†
Table 2. Summary of FRI tests including fmax . System Uniform liquid distribution o-p xylene o-p xylene o-p xylene Cyclohexane=n-heptane Cyclohexane=n-heptane i-butane=n-butane i-butane=n-butane i-butane=n-butane i-butane=n-butane Controlled liquid maldistribution Cyclohexane=n-heptane
Pressure bar
Relative volatility
Bed height m
HETP m
Number of effective stages, N
fmax
0.02 0.13 1.0 0.34 1.65 6.9 11.4 20.7 27.6
1.31 1.237 1.16 1.85 1.57 1.295 1.236 1.15 1.10
3.78 3.78 3.78 3.78 3.78 3.78 3.78 3.78 3.78
0.3 0.3 0.3 0.5 0.4 0.3 0.3 0.3 0.35
12.6 12.6 12.6 7.6 9.5 12.6 12.6 12.6 10.8
0.089 0.106 0.125 0.090 0.087 0.092 0.107 0.127 0.161
1.0
1.65
3.78
0.36
10.5
0.057
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Figure 13. Liquid by-pass model.
Figure 12. Effect of bed depth on sensitivity to maldistribution. o=p xylene, 0.13 bar, total re ux, HETP ˆ 0.3 m, symmetrical concentrations about 50% molar.
Using a similar derivation to that leading to equation (7) gives the maximum vapour maldistribution, gmax , that can be tolerated. y ¡ yN x ¡ xo gmax ˆ N ‡1 ‡ 1 yN ‡1 ¡ yo xN‡1 ¡ x1 ³ ´³ ´ …21† yN ‡1 ¡ yN x1 ¡ xo ¡ yN ‡1 ¡ yo xN‡1 ¡ x1
The parameter gmax can be used to rank packed beds for their sensitivity to vapour maldistribution although, as mentioned above, usually vapour maldistribution quickly corrects itself in a bed so that sensitivity to vapour maldistribution is of less importance than sensitivity to liquid maldistribution. BY-PASS MODEL Figure 13 illustrates another type of model that can be used to investigate sensitivity to maldistribution. A small fraction of liquid (bL) completely by-passes the bed and contaminates the bottom product. This can be considered as the most adverse possible consequence of wall ow, where it originates at the top of the bed and there is no mixing or mass transfer between the bulk liquid and the liquid owing down the wall. For a xed bottom product composition, the maximum fraction of liquid that can by-pass the bed, bL max , is easily determined. It corresponds to equilibrium between the liquid leaving the bed and the entering vapour, Figure 14. From a mass balance on the liquid at the bottom of the bed: …1 ¡ bL max †xo ‡ bL max xN‡1 ˆ x1
so that:
bL max ˆ
x1 ¡ xo xN‡1 ¡ xo
…22† …23†
Note that bL max is identical to the second term in equation (7). Trans IChemE, Vol 80, Part A, May 2002
Figure 14. Calculation of bLmax.
A similar equation can be derived for vapour by-passing. The maximum fraction of the vapour that can by-pass the bed for a xed top composition, bVmax, is: y ¡ yN bV max ˆ N‡1 …24† yN‡1 ¡ yo
Note again that bVmax is identical to the rst term in equation (21). Equations (23) and (24) quantify the obvious observation that only minimal by-passing can be tolerated when high purity products are required. In general, by-pass models are less informative than parallel-column models for assessing sensitivity to maldistribution because the assumptions on which they are based are less realistic. CONCLUSION Calculation of fmax to assess the sensitivity of a packed bed to maldistribution can now easily be done as part of the routine design procedure using equation (7). When such sensitivity appears to be high, the designer can take remedial measures, such as using a redistributor or using more design contingency in the applied value of HETP. The variation of
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BILLINGHAM and LOCKETT
fmax to changes in number of stages, relative volatility, L=V, and terminal concentrations follows that found for the effective number of stages in the presence of maldistribution calculated from more detailed models, such as the zonestage model of Zuiderweg2. It follows that calculation of fmax is an adequate substitute for a detailed model to assess sensitivity and certainly is much easier to do. However, the effect of column diameter cannot be accounted for through fmax. A detailed model is needed for that, so the further re nement of the detailed models is a worthwhile activity for sensitivity assessment. Of course, if the detailed models can ever be developed to the point that they can be used as reliable design tools to predict the number of stages that will be achieved in the bed, they will certainly supplant a simpler sensitivity analysis model such as the one described in this paper. NOMENCLATURE A,B,C bL bLmax bvmax E f fmax g gmax HETP HTU L N NA V Xlk x Ylk y
distances on Figure 8, m fraction of liquid bypassing bed maximum value of bL maximum fraction of vapour bypassing bed ef ciency de ned by equation (3) liquid maldistribution fraction maximum value of f above which the separation cannot be achieved vapour maldistribution fraction maximum value of g above which the separation cannot be achieved height of an equivalent theoretical plate, m height of transfer unit, m liquid ow rate, kg-mol s¡1 effective number of theoretical stages actual number of theoretical stages vapour ow rate, kg-mol s¡1 mole fraction of light key in pseudo-binary liquid mixture mole fraction of more volatile component in liquid mole fraction of light key in pseudo-binary vapour mixture mole fraction of more volatile component in vapour
Greek symbols a relative volatility Subscripts m, e, p value for methanol, ethanol and 2-propanolrespectively in Table 1 n leaving theoretical stage n where ¡ 1 µ n µ NA Superscripts b value when by-passing occurs 0 for column 1 00 for column 2
REFERENCES 1. Kister, H. Z. and Larson, K. F., 1997, Packed distillation tower design, Handbook of Separation Techniques for Chemical Engineers, edited by Schweitzer, P. A., 3rd Edn. (McGraw-Hill, New York, USA), pp 1–315. 2. Zuiderweg, F. J., Hoek, P. J. and Lahm, L., 1987, The effect of liquid distribution and redistribution on the separation ef ciency of packed columns, IChemE Symp Ser, N104: A217. 3. Zuiderweg, F. J., Kunesh, J. G. and King, D. W., 1993, A model for the calculation of the effect of maldistribution on the ef ciency of a packed column, Trans IChemE Part A, Chem Eng Res Des, 71(A1): 38. 4. Olujic, Z., 1997, Development of a complete simulation model for predictingthehydraulicandseparationperformanceofdistillationcolumns equipped with structured packings, Chem Biochem Eng Q, 11(1): 31. 5. Higler, A., Krishna, R. and Taylor, R., 1999, Nonequilibrium cell model for packed distillation columns—The in uence of maldistribution, Ind Eng Chem Res, 38: 3988. 6. Yin, F. H., Sun, C. G., Afacan, A., Nandakumar, K. and Chuang, K. T., 2000, CFD modelling of mass-transfer processes in randomly packed distillation columns, Ind Eng Chem Res, 39: 1369.
7. Kouri, R. J., 1985, An extended Colburn equation for the analysis of packed column performance under conditions of liquid and gas maldistribution, EFChE Working Party Meeting on Distillation, Absorption and Extraction (Amsterdam, Netherlands), 6 June. 8. Mullin, J. W., 1957, The effect of maldistribution on the performance of packed columns, The Ind Chem, Aug: 408. 9. Morris, G. A., 1960, The application of absorption tower design methods to packed distillation columns, Int Symp on Distillation (IChemE, Rugby, UK), pp 146. 10. Changez, N. D. and Sawistowski, H., 1963, Effect of maldistribution on the performance of packed columns, The Ind Chem, April: 181. 11. Huber, M. and Hiltbrunner, R., 1966, Fu¨llko¨rperrekti zierkolonnen mit maldistribution, Chem Eng Sci, 21: 819. 12. Meier, W. and Huber, M., 1969, Measurements of the number of theoretical plates in packed columns with arti cial maldistribution, IChemE Symp Ser, N32: 4: 31. 13. Yuan, H. C. and Spiegel, L., 1981, Theoretical and experimental investigation of the in uence of maldistribution on the number of theoretical stages in packed columns at partial re ux, Proc 2nd World Congress of Chem Eng (Montreal, Canada), 4: 274. 14. Thorogood, R. M., 1981, Maldistribution in plate columns, IChemE Symp Ser, N61: 95. 15. Stichlmair, J. and Stemmer, A., 1987, In uence of maldistribution on mass transfer in packed columns, IChemE Symp Ser, N104: B213. 16. Klemas, L. and Bonilla, J. A., 1995, Accurately assess packed-column ef ciency, Chem Eng Prog, July, 27. 17. Martin, G. R. and Sloley, A. W., 1995, Simulation of ow maldistribution and its results on mass transfer, paper 26D (Houston AIChE meeting, USA), 23 March. 18. Schultes, M., 2000, In uence of liquid redistributors on the masstransfer ef ciency of packed columns, Ind Eng Chem Res, 39: 1381. 19. Manning, R. E. and Cannon, M. R., 1957, Distillation improvement by control of phase channeling in packed columns, Ind Eng Chem, 49(3): 347. 20. Schafer, T. A., Lam, S. Y. S. and Vragolic, S., 1992, Organic strippers: Vapour maldistribution problems and solutions (New Orleans AIChE meeting, USA), 29 March. 21. Hanley, B., 1999, The in uence of ow maldistribution on the performance of columns containing random packings: A model study for constant relative volatility and total re ux, Separ Puri c Tech, 16: 7. 22. Moser, F. and Damiani, M., 2001, Styrene monomer puri cation with MellapakPlus, the new generation of structured packing: Some case studies (Joint meeting of VDI-GVC, DECHEMA and EFChE Working Party on Distillation, Absorption and Extraction, Bamberg, Germany), paper THZ20, 4–6 April. 23. Smoker, E. H., 1938, Analytic determination of plates in fractionating columns, Trans AIChE, 34: 165. 24. Fenske, M. R., 1932, Fractionation of straight-run Pennsylvania gasoline, Ind Eng Chem, 24: 482. 25. Moore, D. and Rukovena, F., 1986, Liquid and gas distribution in commercial packed towers, 36th Cana Chem Eng Conf paper 23b (Also published in Chemical Plants and Processing [European edition], 1987, August, pp 11). 26. Billingham, J. F., Bonaquist, D. P. and Lockett, M. J., 1997, Characterization of the performance of packed distillation column liquid distributors, IChemE Symp, N142: 841. 27. Kister, H. Z., 1992, Distillation Design (McGraw-Hill, New York, USA), pp 551. 28. Norton Chemical Process Products Corp, 1996, IMTP High-performance random packing, Bulletin IHPRP-1, pp 11. 29. Fitz, C. W., Kunesh, J. G. and Shariat, A., 1999, Performance of structured packing in a commercial-scale column at pressures of 0.02–27.6 bar, Ind Eng Chem Res, 38: 512. 30. Fitz, C. W., King, D. W. and Kunesh, J. G., 1999, Controlled liquid maldistribution studies on structured packing, Trans IChemE, Part A, Chem Eng Res Des, 77(A6): 482.
ADDRESS Correspondence concerning this paper should be addressed to Dr. M. J. Lockett, Praxair, Inc., PO Box 44, Tonawanda, NY 14151-0044, USA. E-mail: [email protected] The manuscript was received 1 October 2001 and accepted for publication after revision 29 January 2002.
Trans IChemE, Vol 80, Part A, May 2002