up in the argon product, in the absence of a pasteurization zone at the top of the argon column. In order to achieve the requisite low nitrogen concentration in the argon column feed, bed A was designed to deliver 15 theoretical stages. The design value of fmax for the bed was 0.008. However, on initial start-up, only 11 theoretical stages were achieved with the result that the nitrogen concentration in the argon product was unacceptably high .
The diagnosis was that the shortfall was caused by the combination of the inevitable small amount of liquid maldistribution that existed in bed A together with the very low value of fmax. The remedy was to reduce fmax by shortening the packed beds.The plant was shut down and bed A was replaced by two beds designed to deliver 7 and 8 theoretical stages, respectively. A new collector-redistributor was installed between the beds to mix and redistribute the liquid. On restart, the combination of the two beds achieved the design number of theoretical stages and the nitrogen content of the argon product was within specification. The calculated values of fmax were 0.11 for the upper bed and 0.51 for the lower bed, which were therefore significantly increased over the original value.
The importance of using two packed beds of about equal height in this section of the upper column has been noted previously [2].
ETHYLBENZENE-STYRENE DISTILLATION
Separation of ethylbenzene from styrene is an important vacuum distillation operation that is widely practiced. Table 1 summarizes the key parameters used in the present study. The column was simulated with the commercial process simulator Hysys, using the Wilson property package. The concentration profiles that resulted from the simulation involved the four components indicated in Table 1. They were converted to a pseudo-binary involving only ethylbenzene and styrene by dividing by the sum of the ethylbenzene and styrene mole fractions. The pseudo-binary concentration profiles were then used to calculate fmax from equation (1). Two cases were considered for the rectifying section that contains 26 stages: a single bed and two beds of 13 stages each. Four cases were considered for the stripping section that contains 69 stages: a single bed, two beds, three beds and finally four beds. As far as possible, the theoretical stages were allocated equally between beds.
Table 6.1 Ethylbenzene-styrene distillation
The results are shown in Figure6.5 for the rectifying section. It shows that fmax=0.066 if one single bed of packing is utilized in this section. However, if the section is split into two beds, the value of fmax in each bed jumps to greater than 0.14. A rule of thumb, based on air separation experience (see also Reference 1), is that it is very difficult to achieve the design separation if fmax <0.05. However, if 0.05 < fmax < 0.10 the separation is possible but will be sensitive to maldistribution. For fmax >0.10 the bed will not be particularly sensitive to maldistribution. Based on the above it is evident that the prudent design is to use two beds in the rectifying section. Two beds are in fact used in practice.
Figure 6.5 Ethlbenzene-styrene rectifying section
The results for the rectifying section are shown in Figure 6.6. In Figures 6.5, 6.6, and 7 where
more than one bed is used, the beds are shown in order with the left hand bar representing the top bed and the right hand bar representing the bottom bed. Figure 6.6 shows that not until four beds are used does the value of fmax for the bottom bed increase above the critical value of 0.05. This is in agreement with industrial practice where four beds are indeed usually in this section. It is evident from Figure 6.6 that the use of an equal number of stages in each bed is not optimum. There seems to be an opportunity to use fewer stages in the bottom bed and rather more in the middle bed(s) of the section with the intention of achieving the same value of fmax in each bed.
Figure6.6 ethylbenzene-styrene stripping section Equal dicision of stages between beds
This is explored further in Figure 6.7 where three beds are used in the stripping section.As the number of stages in the bottom bed is progressively decreased from 23 to 14, the value of fmax for that bed increases to an acceptable value of 0.12. Similarly, it also seems preferable to reduce the number of stages in the top bed from 23 to 18. The final design has 18, 37 and 14 stages in each bed rather than the originally assumed equal split of 23, 23 and 23.
Figure6.7 Ethylbenzene-styrene three bed stripping section Unwqual dicision of stages between beds
The explanation for this finding can be found in the McCabe-Thiele diagram for the separation. The top and bottom of the stripping section are both relatively pinched, whereas the middle section is unpinched at both ends. Thus, the middle section is less sensitive to maldistribution and more theoretical stages can be used in that section.
By optimizing the beds in this way, it should be possible to achieve a column design that uses only three packed beds rather than the four beds currently used in practice, with consequent savings in the cost of column internals and column height.
The discussion above resulted in a design with nearly equal values of fmax in each of the three beds that make up the stripping section. Thus, each bed has approximately the same sensitivity to maldistribution. In recommending an optimized theoretical stage allocation between beds based on this, it is implicitly assumed that liquid maldistribution in a bed reaches an equilibrium value and does not progressively continue to increase as it flows down through the bed. Thus it is assumed that the sensitivity of a bed to maldistribution depends only on fmax and does not increase with bed length because of increasing maldistribution. The existence of a natural or equilibrium liquid maldistribution profile has been deduced by Albright [3], by Zuiderweg [4] and by Sun et al. [5], so there is ample justification for this assumption. CONCLUSIONS
It has been demonstrated that for any given packed bed having a design separation, it is possible to calculate the corresponding value of fmax. Using plant data from air separation, it has been shown that the shortfall in separation for beds that failed to meet design could be correlated with fmax. Beds having fmax <0.05 are particularly at risk of failing to achieve the design
separation. It was shown that calculation of fmax for the beds in an ethylbenzene-styrene splitter indicated that two and four beds should be used in the rectifying and stripping sections, respectively. The use of fmax to optimize the theoretical stage split suggests that it may in fact be possible to use only
three beds in the stripping section for future designs. NOMENCLATURE f liquid maldistribution fraction
fmax maximum value of f above which the separation cannot be achieved L liquid flow-rate, kg-mol s-1
N effective number of theoretical stages NA actual number of theoretical stages V vapor flow-rate, kg-mol s-1
x mole fraction of more volatile component in liquid y mole fraction of more volatile component in vapor α relative volatility Subscript
n leaving theoretical stage n Superscripts ′ for column 1 ′′ for column 2 REFERENCES
1. J. F. Billingham and M. J. Lockett (2001), AIChE Annual Meeting, Reno, Nevada, Nov. 8, paper 18a. Also, Trans IChemE, Part A, In press
2. D. P. Bonaquist and M. J. Lockett (1999), U.S. Patent 5,857,357 3. M. A. Albright (1984), Hydrocarbon Processing, September, 173 4. F. J. Zuiderweg (1999), Trans IChemE, 77, Part A, September, 475
5. C. G. Sun, F. H. Yin, A. Afacan, K. Nandakumar and K. T. Chuang (2000), Trans IChemE, 78, Part A, April, 378