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# Sieve Tray Stability Factor Based on Efficiency Data

By Dan Summers |

**Using a vast collection of experimental distillation-column data, sieve tray stability, and its influence on efficiency, are explored in terms of several physical and mechanical properties**

For trayed distillation columns, the concept of tray stability was introduced by the author back in 2010 [*1*]. The data used to determine this modified Froude number term were based on simulator data, and the tray hydraulic parameter examined was weeping. This work serves to validate this stability factor concept by demonstrating when tray efficiency data “falls off” as one turns down the capacity of a trayed distillation tower. That information is readily available for sieve trays from the publicly disclosed data that have been collected by Fractionation Research Inc. (FRI; Stillwater, Okla.; www.fri.org) over the past 70 years [*2*]. Table 1 shows a small selection of these data sets, which were used to generate some of the charts in this article.

The FRI data sets are also used in this article to demonstrate that there is a relationship between tray stability and tray efficiency, and determine which physical properties and mechanical design features most impact that relationship. An equation is presented that defines the minimum tray stability factor value for sieve trays. The applicability of this equation covers a wide range of physical and mechanical parameters, using FRI data to expand upon the author’s 2010 work, which was totally based on air-water and air-Isopar simulator data.

## Stability, ∆P and hydrostatic head

Tray stability (ƞ) is defined as the square root of the dry-tray pressure drop over the hydrostatic head on a distillation tray, as shown in Equation (1).

ƞ = [∆*P*_{Dry} ρ_{W} / (ρ_{L}*HS*)] ^{0.5 }(**1**)

Note that ƞ is basically a Froude number (a dimensionless number used to determine the resistance of movement through a fluid). This hydraulic parameter was introduced to the public in 2010 [*2*]. The dry-tray pressure-drop correlation for sieve trays was introduced in 2009 [ *3*] and updated in 2017 [ *4*], and the hydrostatic head of sieve trays was introduced by Charlie Colwell in 1981 [*5*]*. *The updated 2017 equations expressing dry-tray pressure drop of sieve trays are shown in Equations (2), (3) and (4), and Colwell’s hydrostatic head correlation is given in Equation (5).

∆*P*_{Dry} = 12 ρ_{V}( *V*_{H} / *C*_{V})^{2} / (2*g*_{C}ρ_{W})^{ }(**2**)

*C*_{V} = *K* (*D*_{p} / *Pitch*) ^{0.10 } (**3**)

*K* = 0.997 – {0.34 / [1 + (4.925*TT*/*D*_{p})^{3.582}]} (**4**)

*HS* = (α *How*) + *K*_{0} [(α^{0.5} / *Cd* (*GPM*/*Bw*)]^{2/3 }(**5**)

## Discussion

The public domain FRI sieve tray data were examined to see if they substantiate the stability work performed by the author back in 2010. Keep in mind that the author had already looked at the public-domain FRI tray data in 2018 [*6*] to find a relationship between stability and tray efficiency for bubble-cap type trays. For the current article, however, the data examined were established by FRI in Alhambra, Calif. between the years 1957 and 1980. The data were taken in two industrial-size towers (48 in. and 96 in. diameter) at total reflux and show the tray efficiency versus vapor load. There were more than 100 data sets taken during this time period, with numerous compounds and pressures, operating from deep vacuum to 500 psia. Figure 1 shows an example of one such data set with cyclohexane/ *n*-heptane operating at 24 psia pressure. One can see that the tray efficiency drops from about 80% to less than 50% as the vapor load *C*_{B} falls below 0.1 ft/s. This could be interpreted as an indication of minimum efficient operation.

Through the 1,543 pages of available FRI data, the author looked for turndown data, such as what is shown in Figure 1. The black diamonds in this figure represent tray efficiency and the blue circles represent tray pressure drop. The author also looked for data that showed no signs of weeping. The data sets from FRI included an indication, in the data text, if weeping was observed from below the trays. Recent work at FRI has shown that even minor wall weeping/leakage can cause a significant loss of tray efficiency at low vapor rates. Therefore, the author decided to avoid any data that contained observations of weeping in the data. The author also avoided all two-pass tray data because two-pass trays can exhibit their own instabilities, as discussed in the 2010 paper. In addition, only data with the perforation punched downwards were employed in this study.

The non-weeping data sets were then analyzed with the above stability equations and a plot of tray stability was added to each set. This resulted in a number of plots that look like the example shown in Figure 2 below. Since the calculated stability line appears to have a linear relationship with the vapor load *C*_{B}, it was then concluded that tray efficiency can easily be plotted against the calculated stability factor with no degradation in the shape of the curve, as seen in Figure 3. Now, one can visually determine the tray stability factor at turndown where tray efficiency starts to fall, and the minimum stability factor can be determined where good tray efficiency can be maintained. The author was able to identify a total of 91 data sets (Appendix A) that exhibited sufficient credible evidence of efficiency reduction at turndown. **Click here to download Appendix A in an Excel Spreadsheet.**

Tables 1 and 2 show the specific calculations and parameters entailed for the stability determination shown in Figure 2. It is important to note that the Colwell clear liquid height calculation (*HS*) is nearly constant at about 1.6 in. of liquid for the total reflux data runs 14,115 to 14,119 in Table 1.

For each of these data sets, a determination had to be made as to what exactly was the minimum stability factor. This can be very subjective since the difference between a “good” tray efficiency point and a “bad” tray efficiency point can have a large variation in stability factor value. The data sets taken by FRI back in the 1950s and 1960s were primarily focused on maximum capacity determination and were not as focused on finding exactly where tray efficiency drops off at turndown. The data set in the example given in Figure 3 shows good efficiency at a stability factor of 0.35 and much poorer efficiency at a stability factor of roughly 0.2. It is important to note that between stability factor values of 0.35 and 0.9, the tray efficiency in this chart is fairly constant between 95 and 110%. It is very difficult to determine exactly from Figure 3 at what low stability factor the tray efficiency would have started to fall significantly below approximately 90%. Therefore, the data in Appendix A contains the best “subjective” guess as to what the minimum stability factor should be and a range where that minimum stability factor will be found. This was performed for all 91 data sets.

Appendix A shows the data from FRI with the subjective stability factor determinations. This appendix also contains a number of key mechanical, as well as physical property, parameters for each analyzed set. The mechanical parameters include: outlet weir height, outlet weir length, tray spacing, sieve hole diameter, hole area, tray thickness and downcomer type. The physical property variations are: type system, operating pressure, surface tension, weir loading, vapor density and liquid density.

## Physical property impact

One of the first things noticed by the author when analyzing the data in Appendix A was that there is a strong influence of physical properties on the minimum stability factor.

The data for½-in. diameter holes, 2-in. tall outlet weirs, 24-in. tray spacings (TS), 16-gauge tray decks, 33- to 37-in. weir lengths and 8.3 to 8.6% open area, are shown in Figure 4. This curve uses surface tension, σ, as the correlating parameter. The data shown in Figure 4 result in a well-defined curve. The best-fit equation for the curve through these data points is shown in Figure 4.

Other physical properties, such as liquid density and vapor density, can be used as potential correlating parameters as well. The best least-squares fit for the data shown in Figure 4 was found by using vapor density, as seen in Figure 5. Using vapor density, in the author’s opinion, made the most sense because it clearly is indicative of operating pressure, but it is also one of the key physical properties in determining the stability calculation itself.

## Mechanical property influences

After establishing that vapor density has the best fit and that it has a significant influence on tray stability, several mechanical features, and their effect, were examined next. The data sets in Appendix A include quite an assortment of tray mechanical design features that may need to be included into the equation shown in Figure 5. The mechanical features that were examined are outlet weir height, percentage of open area, weir loading, hole diameter and tray spacing.

Outlet weir height’s effect on stability was examined first. It appears to be a small (but significant) effect when observing Figure 6, for example, at 165 psia. The outlet weir height effect should have been accounted for already in the Colwell correlation above; see Equation (5). However, in the author’s opinion, some residual weir height influence appears to be present. There was no data set with perfectly identical tray geometries for the wide range of outlet weir heights examined in Appendix A (from 0.0 to 4.0 in.), but Figure 6 shows that the effect is there regardless. The data show a slight reduction in the minimum stability factor at taller outlet weirs. The adjustment was added to the equation shown in Figure 5 and is shown as Equation (6).

ƞ_{min} = [0.5664 + {0.4794 (1 – e ^{0.27615Ln(ρv))}}] • {1.1 – (0.05*How*)} (**6**)

Open area was examined next. The open-area effect in Figure 7 is shown as *fp*, which represents fraction perforation or percent open area divided by 100. It is clear that open area has an effect on minimum tray stability factor. The Appendix A data were grouped into three major open area categories. One can see that lower open areas require higher minimum stability factors and higher open areas reduce the minimum stability factor.

The adjustment (multiplier) for the open area effect was added to Equation (6) and is expressed as Equation (7).

ƞ_{min} = [0.5664 + {0.4794(1 – e^{(0.27615(Ln(ρv)))})}] • {1.1 – (0.05*How*)} (0.083/*fp*)^{0.33} (**7**)

There also appears to be a small hole diameter effect, as can be seen in Figure 8. This plot was generated at constant open area, weir height and operating pressure. The hole diameter affect appears to be linear and significant. The adjustment (multiplier) needed to capture the hole diameter effect into Equation (7) was added and is now shown as Equation (8). The minimum stability factor equation is now getting quite lengthy.

ƞ_{min} = [0.5664 + {0.4794(1 – e^{0.27615Ln(ρv)})}] • {1.1 – (0.05*How*)} (0.083/*fp*)^{0.33} • [0.858 + 0.142(*D*_{p}/0.5)] (**8**)

Tray spacing was examined next, as seen in Figure 9. The effect appears to be negligible as, theoretically, it should be. Finally, for completeness, weir loading was examined, which should already have been incorporated into the Colwell correlation, as shown in Equation (5). The data appear to have no residual weir-loading effects, as shown in Figure 10, since the data points are too scattered. In the author’s opinion, there is no adjustment needed to Equation (8) with regards to weir loading.

Therefore, Equation (8) is the definitive equation for the minimum stability of sieve trays based on FRI public-domain data. A parity plot for this equation was generated, shown in Figure 11, to see how well Equation (8) compares to all the data in Appendix A.

## Observations

Equation (8) shows us that the 2010 work by the author was limited in scope, since the data evaluated were based only on air-water and air-Isopar simulator weeping observations. The conclusion in 2010 was that a fixed value of 0.6 was appropriate as a minimum guideline for the stability factor. With the current work here, which now includes real column efficiency data, the author now concludes that the minimum stability factor is heavily influenced by the operating pressure and, to a limited extent, by hole size, percentage open area and weir height. Figure 11 shows that Equation (8) does a reasonably good job of representing the data. However, because of the subjectivity of determining exactly where the tray efficiency “drops off” in the data sets examined, there is a significant amount of scatter built into the data shown in Appendix A. A narrower error band than 25% in the Figure 11 parity plot would have been preferable.

It is the author’s opinion that Equation (8) will provide users with another way to look at sieve tray turndown, as compared to applying traditional weeping predictive methods that have led to poor results. It is also the author’s opinion that, similar to the sieve tray results shown here, fixed opening devices should also have a minimum stability curve similar to Equation (8).

In this article, an equation has been generated that defines the minimum tray stability factor value for sieve trays. The applicability of this equation covers a wide range of physical and mechanical parameters, as shown in Table 3. The equation has been set up to be extrapolatable outside of the experience bounds established in Table 3. This equation expands on the 2010 work by the author, which was totally based on air-water and air-Isopar simulator data.

In comparison to the author’s 2010 work, the new minimum stability factor can now have values less than the 0.6 fixed value (as given in 2010) when column operating pressures are high. However, when operating pressures are low, stability factor values will more than likely need to be higher than the original 0.6 value.

## Alternative equation

An alternative equation based on surface tension for the minimum stability factor can be used, as expressed in Equation (9).

ƞ_{min} = 0.273σ^{0.372} {1.1 – (0.05*How*)}(0.083/*fp*)^{0.33 }•[0.858 + 0.142(*D*_{p}/0.5)] (**9**)

The parity plot for this equation, Figure 12, is really no different than the parity plot for Equation (8). Therefore, for those people who think that the controlling physical property to best represent the pressure effect is surface tension, then Equation (9) is a satisfactory alternative.

*Edited by Mary Page Bailey*

## Acknowledgement

The author would like to acknowledge the help he received years ago from Zane King of Sulzer. As an intern, he was able to take the public domain data from FRI and plot it into a usable and visual form for the author so that (after he retired from Sulzer) his work was made so much easier. Also, the author would like to acknowledge FRI for 70 years of industrial distillation data. FRI is a not-for-profit worldwide consortium of approximately 85 companies involved with distillation design ranging from equipment manufacturers to engineering companies to operating companies. FRI offers important deliverables to the distillation industry, including: industrial-scale column operating data; design and rating correlations for both packings and trays; and design practices handbooks.

## References

1. Summers, D. R., Spiegel, L., and Kolesnikov, E., Tray Stability at Low Vapor Load, Conference Proceedings of Distillation and Absorption 2010, p. 611, Eindhoven, The Netherlands, September 12–15, 2010.

2. FRI Sieve Tray Database – Public Domain files, Oklahoma State University Special Collections and University Archives.

3. Summers, D. R., Dry Tray Pressure Drop of Sieve Trays,

Chem. Eng., June 2009, pp 36¬39.

4. Summers, D. R., Cai, T. J., Dry Tray Pressure Drop of Sieve Trays Revisited,

Chem. Eng., August 2017, pp 38–41.

5. C. J. Colwell, Clear Liquid Height and Froth Density on Sieve Trays, Ind. Eng. Process Design and Development, Vol. 20, pp 298–307, April 1981.

6. Summers, D. R., Bubble-Cap Tray Vapor Turndown,

Chem. Eng., February 2018, pp 38–41.

## Author

Dan Summers was (until 2021) the Tray Technology manager for Sulzer Chemtech. After graduating from SUNY at Buffalo in 1977, he started his career with Union Carbide’s Separations Design group in West Virginia. He has also worked for Union Carbide Linde Division (now Linde plc), UOP, Stone & Webster (now Technip Energies), and Nutter Engineering. His entire career has been focused exclusively on distillation. He is the author of over 70 papers on distillation and is a listed inventor on three U.S. patents. At present, Summers is a consultant for FRI’s Design Practices Committee, and served as the chair of that committee for 12 years. He is also a director and the awards co-chair of AIChE’s Separations Division. He is a registered professional engineer in both New York and Oklahoma, and is a Fellow of AIChE. He is also a recipient of the Gerhold Award for outstanding work in the Application of Chemical Separations Technology.

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