Chapter 10: Staged and Packed Column Design
In previous chapters we saw how to determine the number of equilibrium stages and the separation in distillation columns. In the first part of this chapter we will discuss the details of staged column design such as tray geometry, determination of column efficiency, calculation of column diameter, downcomer sizing, and tray layout. We will start with a qualitative description of column internals and then proceed to a quantitative description of efficiency prediction, determination of column diameter, sieve tray design, and valve tray design. In the second part (sections 10.6 to 10.10) we will discuss packed column design including the selection of packed materials and determination of the length and diameter of the column. New engineers are expected to be able to do these calculations. The internals of distillation columns are usually designed under the supervision of experts with many years of experience.
This chapter is not a shortcut to becoming an expert. However, upon completion of this chapter you should be able to finish a preliminary design of the column internals for both staged and packed columns, and you should be able to discuss distillation designs intelligently with the experts.
10.1 STAGED COLUMN EQUIPMENT DESCRIPTION
A very basic picture of staged column equipment was presented in Chapter 3. In this section, a much more detailed qualitative picture will be presented. Much of the material included here is from the series of articles and books by Kister (1980, 1981, 1992, 2003), the book by Ludwig (1997), and the chapter by Larson and Kister (1997). These sources should be consulted for more details.
Sieve trays, which were illustrated in Figure 3-7, are easy to manufacture and are inexpensive. The holes are punched or drilled (a more expensive process) in the metal plate. Considerable design information is available, and since the designs are not proprietary, anyone can build a sieve tray column. The efficiency is good at design conditions. However, turndown (the performance when operating below the designed flow rate) is relatively poor. This means that operation at significantly lower rates than the design condition will result in low efficiencies. For sieve plates, efficiency drops markedly for gas flow rates that are less than about 60% of the design value. Thus, these trays are not extremely flexible. Sieve trays are very good in fouling applications or when there are solids present, because they are easy to clean. Sieve trays are a standard item in industry, but new columns are more likely to have valve trays (Kister, 1992).
Valve trays are designed to have better turndown properties than sieve trays, and thus, they are more flexible when the feed rate varies. There are many different proprietary valve tray designs, of which one type is illustrated in Figure 10-1. The valve tray is similar to a sieve tray in that it is has a deck with holes in it for gas flow and downcomers for liquid flow. The difference is that the holes, which are quite large, are fitted with “valves,” covers that can move up and down as the pressures of the vapor and the liquid change. Each valve has feet or a cage that restrict its upward movement. Round valves with feet are most popular but wearing of the feet can be a problem (Kister, 1990). At high vapor velocities, the valve will be fully open, providing a maximum slot for gas flow (see Figure 10-1). When the gas velocity drops, the valve will drop. This keeps the gas velocity through the slot close to constant, which keeps efficiency close to constant and prevents weeping. An individual valve is stable only in the fully closed or fully opened position. At intermediate velocities some of the valves on the tray will be open and some will be closed. Usually, the valves alternate between the open and closed positions. The Venturi valve has the lip of the hole facing upwards to produce a Venturi opening, which will minimize the pressure drop.
Figure 10-1 A) Valve assembly for Glitsch A-1 valve, and B) small Gitsch A-1 ballast tray; courtesy of Glitsch, Inc., Dallas, Texas
At the design vapor rate, valve trays have about the same efficiency as sieve trays. However, their turndown characteristics are generally better, and the efficiency remains high as the gas rate drops. They can also be designed to have a lower pressure drop than sieve trays, although the standard valve tray will have a higher pressure drop. The disadvantages of valve trays are they are about 20% more expensive than sieve trays (Glitsch, 1985) and they are more likely to foul or plug if dirty solutions are distilled.
Bubble-cap trays are illustrated in Figure 10-2. In a bubble-cap there is a riser, or weir, around each hole in the tray. A cap with slots or holes is placed over this riser, and the vapor bubbles through these holes. This design is quite flexible and will operate satisfactorily at very high and very low liquid flow rates. However, entrainment is about three times that of a sieve tray, and there is usually a significant liquid gradient across the tray. The net result is that tray spacing must be significantly greater than for sieve trays. Average tray spacing in small columns is about 18 inches, while 24 to 36 inches is used for vacuum distillations. Efficiencies are usually the same or less than for sieve trays, and turndown characteristics are often worse. The bubble-cap has problems with coking, polymer formation, or high fouling mixtures. Bubble-cap trays are approximately four times as expensive as valve trays (Glitsch, 1985). Very few new bubble-cap columns are being built. However, new engineers are likely to see older bubble-cap columns still operating. Lots of data are available for the design of bubble-cap trays. Since excellent discussions on the design of bubble-cap columns are available (Bolles, 1963; Ludwig, 1997), details will not be given here.
Figure 10-2 Different bubble-cap designs made by Glitsch, Inc., courtesy of Glitsch, Inc., Dallas, Texas
Perforated plates without downcomers look like sieve plates but with significantly larger holes. The plate is designed so that liquid weeps through the holes at the same time that vapor is passing through the center of the hole. The advantage of this design is that the cost and space associated with downcomers are eliminated. Its major disadvantage is that it is not robust. That is, if something goes wrong the column may not work at all instead of operating at a lower efficiency. These columns are usually designed by the company selling the system. Some design details are presented by Ludwig (1997).
10.1.1 Trays, Downcomers, and Weirs
In addition to choosing the type of tray, the designer must select the flow pattern on the trays and design the weirs and downcomers. This section will continue to be mainly qualitative.
The most common flow pattern on a tray is the cross-flow pattern shown in Figure 3-7 and repeated in Figure 10-3A. This pattern works well for average flow rates and can be designed to handle suspended solids in the feed. Cross-flow trays can be designed by the user on the basis of information in the open literature (Bolles, 1963; Fair, 1963, 1984, 1985; Kister, 1980, 1981, 1992; Ludwig, 1997), from information in company design manuals (Glitsch, 1974; Koch, 1982), or from any of the manufacturers of staged distillation columns. Design details for cross-flow trays are discussed later.
Figure 10-3 Flow patterns on trays; A) cross-flow, B) double-pass
Multiple-pass trays are used in large-diameter columns with high liquid flow rates. Double-pass trays (Figure 10-3B) are common (Pilling, 2005). The liquid flow is divided into two sections (or passes) to reduce the liquid gradient on the tray and to reduce the downcomer loading. With even larger liquid loadings, four-pass trays are used (Pilling, 2005). This type of tray is usually designed by experts, although preliminary designs can be obtained by following the design manuals published by some of the equipment manufacturers (Glitsch, 1974; Koch, 1982).
Which flow pattern is appropriate for a given problem? As the gas and liquid rates increase, the tower diameter increases. However, the ability to handle liquid flow increases with weir length, while the gas flow capacity increases with the square of the tower diameter. Thus, eventually multiple-pass trays are required. A selection guide is given in Figure 10-4 (Huang and Hodson, 1958), but it is only approximate, particularly near the lines separating different types of trays.
Figure 10-4 Selection guide for sieve trays, reprinted with permission from Huang and Hodson, Petroleum Refiner, 37 (2), 104 (1958), copyright 1958, Gulf Pub. Co.
Downcomers and weirs are very important for the proper operation of staged columns, since they control the liquid distribution and flow. A variety of designs are used, four are shown in Figure 10-5 (Kister, 1980e, 1992). In small columns and pilot plants the circular pipe shown in Figure 10-5A is commonly used. The pipe may stick out above the tray floor to serve as the weir, or a separate weir may be used. In the Oldershaw design commonly used in pilot plants, the pipe is in the center of the sieve plate and is surrounded by holes. The most common design in commercial columns is the segmented vertical downcomer shown in Figure 10-5B. This type is inexpensive to build, easy to install, almost impossible to install incorrectly, and can be designed for a wide variety of liquid flow rates. If liquid-vapor disengagement is difficult, one of the sloped segmental designs shown in Figure 10-5C can be useful. These designs help retain the active area of the tray below. Unfortunately, they are more expensive and are easy to install backwards. For very low liquid flow rates, the envelope design shown in Figure 10-5D is occasionally used.
Figure 10-5 Downcomer and weir designs; A) circular pipe, B) straight segmental, C) sloped downcomers, D) envelope
The simplest weir design is the straight horizontal weir from 2 to 4 inches high (Figures 3-7 and 10-5). This type is the cheapest but does not have the best turndown properties. The adjustable weir shown in Figure 10-6A is a very seductive design, since it appears to solve the problem of turndown. Unfortunately, if maladjusted, this weir can cause lots of problems such as excessive weeping or trays running dry, so it should be avoided. When flexibility in liquid rates is desired, one of the notched (or picket-fence) weirs shown in Figure 10-6B will work well (Pilling, 2005); they are not much more expensive than a straight weir. Notched weirs are particularly useful with low liquid flow rates.
Figure 10-6 Weir designs A) adjustable, and B) notched
Trays, weirs, and downcomers need to be mechanically supported. This is illustrated in Figure 10-7 (Zenz, 1997). The trick is to adequately support the weight of the tray plus the highest possible liquid loading it can have without excessively blocking either the vapor flow area or the active area on the tray. As the column diameter increases, tray support becomes more critical. See Ludwig (1997), or Kister (1980d, 1990, 1992) for more details.
Figure 10-7 Mechanical supports for sieve trays from Zenz (1997). Reprinted with permission from Schweitzer, Handbook of Separation Techniques for Chemical Engineers, third ed., copyright 1997, McGraw-Hill, New York
10.1.2 Inlets and Outlets
Inlet and outlet ports must be carefully designed to prevent problems (Kister, 1980a, b, 1990, 1992, 2005; Glitsch, 1985; Ludwig, 1997). Inlets should be designed to avoid both excessive weeping and entrainment when a high-velocity stream is added. Several acceptable designs for a feed or reflux to the top tray are shown in Figure 10-8. The baffle plate or pipe elbow prevents high-velocity fluid from shooting across the tray. The designs shown in Figures 10-8D and E can be used if there is likely to be vapor in the feed. These two designs will not allow excessive entrainment. Intermediate feed introduction is somewhat similar, and several common designs are shown in Figure 10-9. Low-velocity liquid feeds can be input through the side of the column as shown in Figure 10-9A. Higher velocity feeds and feed containing vapor require baffles as shown in Figures 10-9B and C. The vapor is directed sideways or downward to prevent excessive entrainment. When there is a large quantity of vapor in the feed, the feed tray should have extra space for disengagement of liquid and vapor. For large diameter columns some type of distributor such as the one shown in Figure 10-9D is often used.
Figure 10-8 Inlets for reflux or feed to top tray
Figure 10-9 Intermediate feed systems; A) side inlet, B) and C) baffles, D) distributor
The vapor return at the bottom of the column should be at least 12 inches above the liquid surge level. The vapor inlet should be parallel to the seal pan and parallel to the liquid surface as shown in Figure 10-10A. The purpose of the seal pan is to keep liquid in the downcomer. The vapor inlet should not el-down to impinge on the liquid as shown in Figure 10-10B. When a thermosiphon reboiler (a common type of total reboiler) is used, the split drawoff shown in Figure 10-10C is useful.
Figure 10-10 Bottom vapor inlet and liquid drawoffs; A) correct—inlet vapor parallel to seal pan, B) incorrect—inlet vapor el-down onto liquid, C) bottom draw-off with thermosiphon reboiler
Intermediate liquid drawoffs require some method for disengaging the liquid and vapor. The cheapest way to do this is with a downcomer tapout as shown in Figure 10-11A. A more expensive but surer method is to use a chimney tray (Figure 10-11B). The chimney tray provides enough liquid volume to fill lines and start pumps. There are no holes or valves in the deck of this tray; thus, it doesn’t provide for mass transfer and should not be counted as an equilibrium stage. Chimney trays must often support quite a bit of liquid; therefore, mechanical design is important (Kister, 1990). An alternative to the chimney tray is to use a downcomer tapout with an external surge drum.
Figure 10-11 Intermediate liquid draw-off; A) downcomer sump, B) chimney tray (downcomer to next tray not shown)
The design of vapor outlets is relatively easy and is less likely to cause problems than liquid outlets (Kister, 1990). The main consideration is that the line must be of large enough diameter to have a modest pressure drop. At the top of the column a demister may be used to prevent liquid entrainment. An alternative is to put a knockout drum in the line before any compressors.
10.2 TRAY EFFICIENCIES
Tray efficiencies were introduced in Chapter 4. In this section they will be discussed in more detail, and methods for estimating the value of the efficiency will be explored. The effect of mass transfer rates on the stage efficiency is discussed in Chapter 15.
The overall efficiency, EO, is
(10-1 )
The determination of the number of equilibrium stages required for the given separation should not include a partial reboiler or a partial condenser. The overall efficiency is extremely easy to measure and use; thus, it is the most commonly used efficiency value in the plant. However, it is difficult to relate overall efficiency to the fundamental heat and mass transfer processes occurring on the tray, so it is not generally used in fundamental studies.
The Murphree vapor and liquid efficiencies were also introduced in Chapter 4. The Murphree vapor efficiency is defined as
(10-2)
while the Murphree liquid efficiency is
(10-3)
The physical model used for both of these efficiencies is shown in Figure 10-12. The gas streams and the downcomer liquids are assumed to be perfectly mixed. Murphree also assumed that the liquid on the tray is perfectly mixed, which means x = xout. The term y*out is the vapor mole fraction that would be in equilibrium with the actual liquid mole fraction leaving the tray, xout. In the liquid efficiency, x*out is in equilibrium with the actual leaving vapor mole fraction, yout. The Murphree efficiencies are popular because they are relatively easy to measure and they are very easy to use in calculations (see Figure 4-27B). Unfortunately, there are some difficulties with their definitions. In large columns the liquid on the tray is not well mixed; instead there will be a cross-flow pattern. If the flow path is long, the more volatile component will be preferentially removed as liquid flows across the tray. Thus, in Figure 10-12,
xout < x4 < x3 < x2 < x1
Figure 10-12 Murphree efficiency model
Note that xout and hence y*out are based on the lowest concentration on the tray. Thus, it is possible to have y*out < yout, because yout is an average across the tray. Then the numerator in Eq. (10-2a) will be greater than the denominator and EMV > 1. This is often observed in large-diameter columns. Although not absolutely necessary, it is desirable to have efficiencies defined so that they range between zero and 1. A second and more serious problem with Murphree efficiencies is that the efficiencies of different components must be different for multicomponent systems. Fortunately, for binary systems the Murphree efficiencies are the same for the two components. In multicomponent systems not only are the efficiencies different, on some trays they may be negative. This is both disconcerting and extremely difficult to predict. Despite these problems, Murphree efficiencies remain popular. The overall efficiency and the Murphree vapor efficiency are related by the following equation, which is derived in Problem 12.C6.
(10-4)
The point efficiency is defined in a fashion very similar to the Murphree efficiency,
(10-5)
where the prime indicates that all the concentrations are determined at a specific point on the tray. The Murphree efficiency can be determined by integrating all of the point efficiencies (which will vary from location to location) on the tray. Typically, the point and Murphree efficiencies are not equal. The point efficiency is difficult to measure in a commercial column, but it can often be predicted from heat and mass transfer calculations. Thus, it is used for prediction and for scale-up.
In general, the efficiency of a tray depends on the vapor velocity, which is illustrated schematically in Figure 10-13. The trays are designed to give a maximum efficiency at the design condition. At higher vapor velocities, entrainment increases. When entrainment becomes excessive, the efficiency plummets. At vapor velocities less than the design rate the mass transfer is less efficient. At very low velocities the tray starts to weep and efficiency again plummets. Trays with good turndown characteristics have a wide maximum, so there is little loss in efficiency when vapor velocity decreases.
Figure 10-13 Efficiency as a function of vapor velocity
The best way to determine efficiency is to have data for the chemical system in the same type of column of the same size at the same vapor velocity. If velocity varies, then the efficiency will follow Figure 10-13. The Fractionation Research Institute (FRI) has reams of efficiency data, but they are available to members only. Most large chemical and oil companies belong to FRI. The second best approach is to have efficiency data for the same chemical system but with a different type of tray. Much of the data available in the literature are for bubble-cap or sieve trays. Usually, the efficiency of valve trays is equal to or better than sieve tray efficiency, which is equal to or better than bubble-cap tray efficiency. Thus, if bubble-cap efficiencies are used for a valve tray column, the design will be conservative. The third best approach is to use efficiency data for a similar chemical system.
If data are not available, a detailed calculation of the efficiency can be made on the basis of fundamental mass and heat transfer calculations. With this method, you first calculate point efficiencies from heat and mass transfer calculations and then determine Murphree and overall efficiencies from flow patterns on the tray. Unfortunately, the results are often not extremely accurate. A simple application of this method is developed in Chapter 15.
The simplest approach is to use a correlation to determine the efficiency. The most widely used is the O’Connell correlation shown in Figure 10-14 (O’Connell, 1946), which gives an estimate of the overall efficiency as a function of the relative volatility of the key components times the liquid viscosity at the feed composition. Both α and µ are determined at the average temperature and pressure of the column. Efficiency drops as viscosity increases, since mass transfer rates are lower. Efficiency drops as relative volatility increases, since the mass that must be transferred to obtain equilibrium increases. The scatter in the 38 data points is evident in the figure. O’Connell was probably studying bubble-cap columns; thus, the results are conservative for sieve and valve trays (Walas, 1988). Walas (1988) surveys a large number of tray efficiencies for a variety of tray types. O’Brien and Schultz (2004) recently reported that many petrochemical towers are designed with stage efficiencies in the 75 to 80% range. Although these columns are probably valve trays, the efficiency range agrees with O’Connell’s correlation. Vacuum systems, which are not included in Figure 10-14, will typically have efficiencies of 15 to 20% (O’Brien and Schultz, 2004).
Figure 10-14 O’Connell correlation for overall efficiency of distillation columns from O’Connell (1946). Reprinted from Transactions Amer. Inst. Chem. Eng., 42, 741 (1946), copyright 1946, American Institute of Chemical Engineers
For computer and calculator use it is convenient to fit the data points to an equation. When this was done using a nonlinear least squares routine, the result (Kessler and Wankat, 1987) was
(10-6)
Viscosity is in centipoise (cP) in Eq. (10-6) and in Figure 10-14. This equation is not an exact fit to O’Connell’s curve, since O’Connell apparently used an eyeball fit. Ludwig (1997) discusses other efficiency correlations.
Efficiencies can be scaled up from laboratory data taken with an Oldershaw column (a laboratory-scale sieve-tray column) (Fair et al., 1983; Kister, 1990). The overall efficiency measured in the Oldershaw column is often very close to the point efficiency measured in the large commercial column. This is illustrated in Figure 10-15, where the vapor velocity has been normalized with respect to the fraction of flooding (Fair et al., 1983). The point efficiency can be converted to Murphree and overall efficiencies once a model for the flow pattern on the tray has been adopted (see section 15.7).
Figure 10-15 Overall efficiency of 1-inch-diameter Oldershaw column compared to point efficiency of 4-foot-diameter FRI column. System is cyclohexane/n-heptane from Fair et al. (1983). Reprinted with permission from Ind. Eng. Chem. Process Des. Develop., 22, 53 (1983), copyright 1983, American Chemical Society
For very complex mixtures, the entire distillation design can be done using the Oldershaw column by changing the number of trays and the reflux rate until a combination that does the job is found. Since the commercial column will have an overall efficiency equal to or greater than that of the Oldershaw column, this combination will also work in the commercial column. This approach eliminates the need to determine vapor-liquid equilibrium (VLE) data (which may be quite costly), and it also eliminates the need for complex calculations. The Oldershaw column also allows one to observe foaming problems (Kister, 1990).
EXAMPLE 10.1 Overall efficiency estimation
A sieve-plate distillation column is separating a feed that is 50 mole % n-hexane and 50 mole % n-heptane. Feed is a saturated liquid. Plate spacing is 24 in. Average column pressure is 1 atm. Distillate composition is xD = 0.999 (mole fraction n-hexane) and xB = 0.001. Feed rate is 1000 lb moles/hr. Internal reflux ratio L/V = 0.8. The column has a total reboiler and a total condenser. Estimate the overall efficiency.
Solution
To use the O’Connell correlation we need to estimate α and µ at the average temperature and pressure of the column. The column temperature can be estimated from equilibrium (the DePriester chart). The following values are easily generated from Figure 2-12.
Relative volatility is α = (y/x)/[(1−y)/(1−x)]. The average temperature can be estimated several ways:
Arithmetic average T = (98.4 + 69)/2 = 83.7, α = 2.36
Average at x = 0.5, T = 80, α = 2.33
Not much difference. Use α = 2.35 corresponding to approximately 82.5°C.
The liquid viscosity of the feed can be estimated (Reid et al., 1977, p. 462) from
(10-7a)
The pure component viscosities can be estimated from
(10-7b)
where µ is in cP and T is in kelvins (Reid et al., 1977, App. A)
nC6: A = 362.79, B = 207.08
nC7: A = 436.73, B = 232.53
These equations give µC6 = 0.186, µC7 = 0.224, and µmix = 0.204. Then αµmix = 0.480. From Eq. (10-06), EO = 0.62, while from Figure 10-14, EO = 0.59. To be conservative, the lower value would probably be used.
Note that once Tavg, αavg, and µfeed have been estimated, calculating EO is easy.
In many respects the most difficult part of determining design conditions for staged and packed columns is determining the physical properties. For hand calculations good sources are Perry and Green (1997), Reid et al. (1977), Poling et al. (2001), Smith and Srivastra (1986), Stephan and Hildwein (1987), Woods (1995), and Yaws (1999). Commercial simulators have physical property packages to do this grunt work.
10.3 COLUMN DIAMETER CALCULATIONS
To design a sieve tray column we need to calculate the column diameter that prevents flooding, design the tray layout, and design the downcomers. Several procedures for designing column diameters have been published in the open literature (Fair, 1963, 1984, 1985; Kister, 1992; Ludwig, 1997; McCabe et al., 2005). In addition, each equipment manufacturer has its own procedure. We will follow Fair’s procedure, since it is widely known and is an option in the Aspen Plus simulator (see Chapter 6 Appendix). This procedure first estimates the vapor velocity that will cause flooding due to excessive entrainment, then uses a rule of thumb to determine the operating velocity, and from this calculates the column diameter. Column diameter is very important in controlling costs and has to be estimated even for preliminary designs. The method is applicable to sieve, valve, and bubble-cap trays.
The flooding velocity based on net area for vapor flow is determined from
(10-8)
Where σ is the surface tension in dynes/cm and Csb,f is the capacity factor. This is similar to Eq. (02-59), which was used to size vertical flash drums. Csb,f is a function of the flow parameter
(10-9)
where WL and Wv are the mass flow rates of liquid and vapor and densities are mass densities. The correlation for Csb,f is shown in Figure 10-16 (Fair and Matthews, 1958). For computer use it is convenient to fit the curves in Figure 10-16 to equations. The results of a nonlinear least squares regression analysis (Kessler and Wankat, 1987) for 6-in tray spacing are
(10-10a)
for 9-in tray spacing
(10-10b)
Figure 10-16 Capacity factor for flooding of sieve trays from Fair and Matthews (1958). Reprinted with permission from Petroleum Refiner, 37 (4), 153 (1958), copyright 1958, Gulf Pub. Co.
for 12-inch tray spacing
(10-10c)
for 18-inch tray spacing
(10-10d)
for 24-in tray spacing
(10-10e)
and for 36-in tray spacing
(10-10f)
The same flooding correlation but in metric units is available in graphical form (Fair, 1985).
The flooding correlation assumes that β, the ratio of the area of the holes, Ahole, to the active area of the tray, Aactive, is equal to or greater than 0.1. If β < 0.1, then the flooding velocity calculated from Eq. (10-08) should be multiplied by a correction factor (Fair, 1984). If β = 0.08, the correction factor is 0.9; while if β = 0.06, the correction factor is 0.8. Note that this is a linear correction and can easily be interpolated. The resulting value for the flooding velocity will be conservative.
Tray spacing, which is required for the flooding correlation, is selected according to maintenance requirements. Sieve trays are spaced 6 to 36 inches apart with 12 to 16 inches a common range for smaller (less than 5 feet) towers. Tray spacing is usually greater in large-diameter columns. A minimum of 18 inches, with 24 in typical, is used if it is desirable to have a worker crawl through the column for inspection.
The operating vapor velocity is determined as
(10-11)
where the fraction can range from 0.65 to 0.9. Jones and Mellbom (1982) suggest using a value of 0.75 for the fraction for all cases. Higher fractions of flooding do not greatly affect the overall system cost, but they do restrict flexibility. The operating velocity uop can be related to the molar vapor flow rate,
(10-12)
where the 3600 converts from hours (in V) to seconds (in uop). The net area for vapor flow is
(10-13)
where η is the fraction of the column cross-sectional area that is available for vapor flow above the tray. Then 1 − η is the fraction of the column area taken up by one downcomer. Typically η lies between 0.85 and 0.95; its value can be determined exactly once the tray layout is finalized. Equations (10-12) and (10-13) can be solved for the diameter of the column.
(10-14)
If the ideal gas law holds,
(10-15)
and Eq. (10-14) becomes
(10-16)
Note that these equations are dimensional, since Csb is dimensional.
The terms in Eqs. (10-08) to (10-16) vary from stage to stage in the column. If the calculation is done at different locations, different diameters will be calculated. The largest diameter should be used and rounded off to the next highest ½-foot increment. (For example, a 9.18-foot column is rounded off to 9.5 feet). Ludwig (1997) and Kister (1990) suggest using a minimum column diameter of 2.5 feet; that is, if the calculated diameter is 2.0 feet, use 2.5 feet instead, since it is usually no more expensive. These small columns typically use cartridge trays that are prefabricated outside the column (Ludwig, 1997). Columns with diameters less than 2.5 feet are usually constructed as packed columns. If diameter calculations are done at the top and bottom of the column and above and below the feed, one of these locations will be very close to the maximum diameter, and the design based on the largest calculated diameter will be satisfactory. For columns operating at or above atmospheric pressure, the pressure is essentially constant in the column. If we substitute Eqs. (10-08) and (10-15) into Eq. (10-16), calculate the conditions at both the top and bottom of the column, take the ratio of these two equations and simplify, the result is:
(10-17)
The last two terms on the right-hand side are usually close to 1.0 although when water and organics are separated the surface tension term could be approximately 1.1 (water is bottom product) or 0.9 (water is distillate product). The ratio of temperatures is always < 1 with a range for binary separations typically from 0.9 to 0.99 although it can be lower for distillation at low temperatures. For a saturated vapor feed the vapor velocity term is > 1.0 and can range from approximately 1.1 to 2. For a saturated liquid feed this term is very close to 1.0. The molecular weight and liquid density terms can be greater than or less than one. For distillation of homologous series, the molecular weight term is < 1 while the liquid density term is probably > 1. Since one would not expect large differences, the product of these terms is probably ~ 1. For distillation of water and an organic if water is the bottom product, the molecular weight term is < 1 while the density term > 1 and the product of the two terms is probably close to one. If water is the distillate product these two terms flip, and the product of the two terms probably remains close to one.
As a rule of thumb, if feed is a saturated liquid and a homologous series is being distilled, the ratio of diameters is probably less than one and the diameter calculated at the bottom is probably larger. This is also true with a saturated liquid feed if the distillation is water from organics, and water is the distillate product, but if water is the bottoms product (more common), either top or bottom diameter can be larger. If feed is a saturated vapor feed the ratio of diameters is probably greater than one and one should design at the top; however, when water and an organic are distilling with water as the distillate product and for cryogenic distillation the ratio of diameters could be greater than or less than one.
If there is a very large change in the vapor velocity in the column, the calculated diameters can be quite different. Occasionally, columns are built in two sections of different diameter to take advantage of this situation, but this solution is economical only for large changes in diameter. If a column with a single diameter is constructed, the efficiencies in different parts of the column may vary considerably (see Figure 10-13). This variation in efficiency has to be included in the design calculations.
The design procedure sizes the column to prevent flooding caused by excessive entrainment. Flooding can also occur in the downcomers, and this case is discussed later. Excessive entrainment can also cause a large drop in stage efficiency because liquid that has not been separated is mixed with vapor. The effect of entrainment on the Murphree vapor efficiency can be estimated from
(10-18a)
where EMV is the Murphree efficiency without entrainment and ψ is the fractional entrainment defined as
where e is the moles/hr of entrained liquid. The relative entrainment ψ for sieve trays can be estimated from Figure 10-17 (Fair, 1963). Once the corrected value of EMV is known, the overall efficiency can be determined from Eq. (10-7). Usually, entrainment is not a problem until fractional entrainment is above 0.1, which occurs when operation is in the range of 85 to 100% of flood (Ludwig, 1997). Thus, a 75% of flood value should have a negligible correction for entrainment. This can be checked during the design procedure (see Example 10-3).
Figure 10-17 Entrainment correlation from Fair (1963). Reprinted with permission from Smith, B.D., Design of Equilibrium Stage Processes, copyright 1963, McGraw-Hill, New York
EXAMPLE 10.2 Diameter calculation for tray column
Determine the required diameter at the top of the column for the distillation column in Example 10-1.
We can use Eq. (10-16) with 75% of flooding. Since the distillate is almost pure n-hexane, we can approximate properties as pure n-hexane at 69°C. Physical properties are from Perry and Green (1984). T = 69°C = 342 K; liquid sp grav. = 0.659 (at 20°); viscosity = 0.22 cP; MW = 86.17.
ρL = (0.659)(62.4) = 41.12 lb/ft3 (will vary, but not a lot)
Surface tension σ = 13.2 dynes/cm (Reid et al., 1977, p. 610) Flow parameter,
Ordinate from Figure 10-16 for 24 inch tray spacing, Csb = 0.36 while Csb = 0.38 from Eq. (10-10e). Then
K = 0.35 if Eq. (10-10e) is used. The lower value is used for a conservative design. From Eq. (10-08),
We will estimate η as 0.90. The vapor flow rate V = L + D. From external mass balances, D = 500. Since L = V (L/V),
The diameter Eq. (10-16) becomes
Since this procedure is conservative, an 11-foot diameter column would probably be used. If η = 0.95, Dia = 10.74 feet; thus, the value of η is not extremely important. Note that this is a large-diameter column for this feed rate. The reflux rate is quite high, and thus, V is high, which leads to a larger diameter. The effect of location on the diameter calculation can be explored by doing Problem 10-D2. Since the result obtained in that problem is a 12-foot diameter, the column would be designed at the bottom. This result agrees with the rule of thumb given after Eq. (10-17) (hexane and heptane are part of the homologous series of alkanes). The value of η = 0.9 will be checked in Example 10-3. The effect of column pressure is explored in Problem 10-C1.
10.4 SIEVE TRAY LAYOUT AND TRAY HYDRAULICS
Tray layout is an art with its own rules. This section follows the presentations of Ludwig (1997), Bolles (1963), Fair (1963, 1984, 1985), Kister (1990, 1992), and Lockett (1986), and more details are available in those sources. The holes on a sieve plate are not scattered randomly on the plate. Instead, a detailed pattern is used to ensure even flow of vapor and liquid on the tray. The punched holes in the tray usually range in diameter from 1/8- to 1/2-inch. The 1/8-inch holes with the holes punched from the bottom up are often used in vacuum operation to reduce entrainment and minimize pressure drop. In normal operation, holes are punched from the bottom down since this is much safer for maintenance personnel. In fouling applications, holes are 1/2 inch or larger. For clean service, 3/16 inch is a reasonable first guess for hole diameter.
A common tray layout is the equilateral triangular pitch shown in Figure 10-18. The use of standard punching patterns will be cheaper than use of a non-standard pattern. The holes are spaced from 2.5do to 5do apart, with 3.8do a reasonable average. The region containing holes should have a minimum 2- to 3-inches clearance from the column shell and from the inlet downcomer. A 3- to 5-inch minimum clearance is used before the downcomer weir because it is important to allow for disengagement of liquid and vapor. Since flow on the tray is very turbulent, the vapor does not go straight up from the holes. The active hole area is considered to be 2- to 3-inches from the peripheral holes; thus, the area up to the column shell is active. The fraction of the column that is taken up by holes depends upon the hole size, the pitch, the hole spacing, the clearances, and the size of the downcomers. Typically, 4% to 15% of the entire tower area is hole area. This corresponds to a value of β = Ahole/Aactive of 6% to 25%. The average value of β is between 7% and 16%, with 10% a reasonable first guess.
Figure 10-18 Tray geometry; A) equilateral triangular pitch, B) downcomer area geometry
The value of β is selected so that the vapor velocity through the holes, vo, lies between the weep point and the maximum velocity. The exact design point should be selected to give maximum flexibility in operation. Thus, if a reduction in feed rate is much more likely than an increase in feed rate, the design vapor velocity will be close to the maximum. The vapor velocity through the holes, vo, in feet per second (ft/sec) can be calculated from
(10-19)
where V is the lb moles/hr of vapor, ρv is the vapor density in lb/ft3, and Ahole is the total hole area on the tray in ft2. Obviously, Ahole can be determined from the tray layout.
(10-20a)
or
(10-20b)
The active area can be estimated as
(10-20c)
since there are two downcomers. Obviously,
(10-20d)
The downcomer geometry is shown in Figure 10-18B. From this and geometric relationships, the downcomer area Ad can be determined from
(10-21)
where θ is in radians. The downcomer area can also be calculated from
(10-22)
Combining Eqs. (10-20d), (10-21), and (10-22), we can solve for angle θ and the length of the weir. We obtain the results given in Table 10-1. Typically the ratio of lweir/Dia falls in the range of 0.6 to 0.75.
Table 10-1. Geometric relationship between η and lweir/diameter
If the liquid is unable to flow down the downcomer fast enough, the liquid level will increase, and if it keeps increasing until it reaches the top of the weir of the tray above, the tower will flood. This downcomer flooding must be prevented. Downcomers are designed on the basis of pressure drop and liquid residence time, and their cost is relatively small. Thus, downcomer design is done only in the final equipment sizing.
The tray and downcomer are drawn schematically in Figure 10-19, which shows the pressure heads caused by various hydrodynamic effects. The head of clear liquid in the downcomer, hdc, can be determined from the sum of heads that must be overcome.
(10-23)
Figure 10-19 Pressure heads on sieve trays
The head of liquid required to overcome the pressure drop of gas on a dry tray, hΔp,dry, can be measured experimentally or estimated (Ludwig, 1995) from
(10-24)
where vo is the vapor velocity through the holes in ft/sec from Eq. (10-19). The orifice coefficient, Co, can be determined from the correlation of Hughmark and O’Connell (1957). This correlation can be fit by the following equation (Kessler and Wankat, 1987):
(10-25)
where ttray is the tray thickness. The minimum value for do/ttray is 1.0. Equation (10-24) gives hΔp,dry in inches.
The weir height, hweir, is the actual height of the weir. The minimum weir height is 0.5 inch with 2 to 4 inches more common. The weir must be high enough that the opposite downcomer remains sealed and always retains liquid. The height of the liquid crest over the weir, hcrest, can be calculated from the Francis weir equation.
where hcrest is in inches. In this equation, Lg is the liquid flow rate in gal/min that is due to both L and e. The entrainment e can be determined from Figure 10-17. lweir is the length of the straight weir in feet. The factor Fweir is a modification factor to take into account the curvature of the column wall in the downcomer (Bolles, 1946, 1963; Ludwig, 1997). This is shown in Figure 10-20 (Bolles, 1946). An equation for this figure is available (Bolles, 1963). For large columns where lweir is large, Fweir approaches 1.0. On sieve trays, the liquid gradient hgrad, across the tray is often very small and is usually ignored.
Figure 10-20 Weir correction factor, Fweir, for segmental weirs from Bolles (1946). Reprinted with permission of Petroleum Processing
There is a frictional loss due to flow in the downcomer and under the downcomer onto the tray. This term, hdu, can be estimated from the empirical equation (Ludwig, 1997; Bolles, 1963).
(10-27)
where hdu is in inches and Adu is the flow area under the downcomer apron in ft2. The downcomer apron typically has a 1-in gap above the tray.
(10-28)
The value of hdc calculated from Eq. (10-23) is the head of clear liquid in inches. In an operating distillation column the liquid in the downcomer is aerated. The density of this aerated liquid will be less than that of clear liquid, and thus, the height of aerated liquid in the downcomer will be greater than hdc. The expected height of the aerated liquid in the downcomer, hdc,aerated, can be estimated (Fair, 1984) from the equation
(10-29)
where φdc is the relative froth density. For normal operation, a value of φdc = 0.5 is satisfactory, while 0.2 to 0.3 should be used in difficult cases (Fair, 1984). To avoid downcomer flooding, the tray spacing must be greater than hdc,aerated. Thus, in normal operation the tray spacing must be greater than 2hdc.
The downcomer is designed to give a liquid residence time of three to seven seconds. Minimum residence times are listed in Table 10-2 (Kister, 1980e, 1990; Ludwig, 1997). The residence time in a straight segmental downcomer is
(10-30)
where the 3600 converts hours to seconds (from L + e) and the 12 converts hdc in inches to feet. Density is the density of clear liquid, and hdc is the height of clear liquid. Equation (10-30) is used to make sure there is enough time to disengage liquid and vapor in the downcomers. Kister (1990) recommends a minimum downcomer area of 5% of the column area. With saturated liquid feeds downcomers should be designed for the stripping section where liquid flow rate is largest.
Table 10-2. Minimum residence times in downcomers
Source: Kister (1980e, 1990) and Ludwig (1997)
Figure 10-13 showed that the two limits to acceptable tray operation are excessive entrainment and excessive weeping. Weep and dump points are difficult to determine exactly. An approximate analysis can be used to ensure that operation is above the weep point. Liquid will not drain through the holes as long as the sum of heads due to surface tension, hσ, and gas flow, hΔp,dry, are greater than a function depending on the liquid head. This condition for avoiding excessive weeping can be determined from Fair’s (1963) graphical correlation or estimated (Kessler and Wankat, 1987) as
(10-31)
where x = hweir + hcrest + hgrad. Equation (10-31) is valid for β ranging from 0.06 to 0.14. The dry tray pressure drop is determined from Eqs. (10-24) and (10-25). The surface tension head hσ can be estimated (Fair, 1963) from
(10-32)
where σ is in dynes/cm, ρL in lb/ft3, d0 in inches, and hσ in inches of liquid. Equation (10-31) is conservative.
EXAMPLE 10.3 Tray layout and hydraulics
Determine the tray layout and pressure drops for the distillation column in Examples 10-1 and 10-2. Determine if entrainment or weeping is a problem. Determine if the downcomers will work properly. Do these calculations only at the top of the column.
Solution
This is a straightforward application of the equations in this section. We can start by determining the entrainment. In Example 10-2 we obtained Flv = 0.0546. Then Figure 10-17 at 75% of flooding gives ψ = 0.045. Solving for e,
(10-33)
Since L = (L/V)V = 2000 lb moles/hr,
and L + e = 2094.24 lb moles/hr. This amount of entrainment is quite reasonable.
The geometry calculations proceed as follows for a 11.0-foot diameter column:
Eq. (10-20d), Atotal = (π)(11.0)2/4 = 95.03 ft2
Eq. (10-22), Ad = (1 − 0.9)(95.03) = 9.50 ft2
Table 10-1 gives lweir/Dia = 0.726 or lweir = 8.0 feet.
Eq. (10-20c), Aactive = (95.03)(1 − 0.2) = 76 ft2
Eq. (10-20b), Ahole = (0.1)(76) = 7.6 ft2
We will use 14 gauge standard tray material (ttray = 0.078 in) with 3/16-in holes. Thus, do/ttray = 2.4.
From Eq. (10-19)
where ρv is from Example 10-2. This hole velocity is reasonable.
The individual pressure drop terms can now be calculated. The orifice coefficient Co is from Eq. (10-25),
Co = 0.85032 − 0.04231 (2.4) + 0.0017954 (2.4)2 = 0.759
From Eq. (10-24),
In this equation ρw at 69°C was found from Perry and Green (1984, p 3-75). A weir height of hweir = 2 inch will be selected.
The correlation factor Fweir can be found from Figure 10-20. Lg in the abscissa is the liquid flow rate including entrainment in gallons per minute.
From Eq. (10-26),
We will assume hgrad = 0. The area under the downcomer is determined with an 1-in gap.
From Eq. (10-28), Adu = (1/12)(8) = 2/3 ft2.
From Eq. (10-27),
Total head from Eq. (10-23),
hdc = 2.472 + 2 + 1.577 + 0 + 1.871 = 7.92
This is inches of clear liquid. For the aerated system,
Since this is much less than the 24-in tray spacing, there should be no problem. The residence time is, from Eq. (10-30),
This is greater than the minimum residence time of 3 s.
Weeping can be checked. From Eq. (10-32),
Then the left-hand side of Eq. (10-31) is
hΔp,dry + hσ = 2.472 + 0.068 = 2.54
The function x = 2 + 1.577 + 0 = 3.577, and the right-hand side of Eq. (10-31) is 0.725. The inequality is obviously satisfied. Weeping should not be a problem.
Note that the design should be checked at other locations in the column. Since Problem 10-D2 calculated a 12-foot diameter is needed in the stripping section, calculations need to be repeated for the stripping section (see Problem 10-D3). Problem 10-D3 shows that backup of liquid in the downcomers might be a problem in the bottom of the column even with a 12-foot diameter. This occurs because L = L + F = 3000 lb moles/hr, which is significantly greater than the liquid flow in the top of the column. This problem can be handled by an increase in the gap between the downcomer and the tray.
10.5 VALVE TRAY DESIGN
Valve trays, which were illustrated in Figure 10-1, are proprietary devices, and the final design would normally be done by the supplier. However, the supplier will not do the optimization studies that the buyer would like without receiving compensation for the additional work. In addition, it is always a good idea to know as much as possible about equipment before making a major purchase. Thus, the nonproprietary valve tray design procedure of Bolles (1976) is very useful for estimating performance. Ludwig (1997) discusses design of proprietary value trays.
Bolles’s (1976) design procedure uses the sieve tray design procedure as a basis and modifies it as necessary. One major difference between valve and sieve trays is in their pressure drop characteristics. The dry tray pressure drop in a valve tray is shown in Figure 10-21 (Bolles, 1976). As the gas velocity increases, Δp first increases and then levels off at a plateau level. In the first range of increasing Δp, all valves are closed. At the closed balance point, some of the valves open. Additional valves open in the plateau region until all valves are open at the open balance point. With all valves open, Δp increases as the gas velocity increases further. The head loss in inches of liquid for both closed and open valves can be expressed in terms of the kinetic energy.
(10-34a)
where vo is the velocity of vapor through the holes in the deck in ft/sec, g = 32.2 ft/sec2, and Kv is different for closed and open valves. For the data shown in Figure 10-21,
(10-34b)
Note that Eq. (10-34a) has the same dependence on v2oρv/ρL as hΔp,dry for sieve trays in Eq. (10-24).
The closed balance point can be determined by noting that the pressure must support the weight of the valve, Wvalve, in pounds. Pressure is then Wvalve/Av, where Av is the valve area in square feet. The pressure drops in terms of feet of liquid density ρL is then
(10-35)
where the valve coefficient Cv is introduced to include turbulence losses. For the data in Figure 10-21, Cv = 1.25. Setting Eqs. (10-33) and (10-35) equal allows solution of both the closed and open balance points.
(10-36)
where vo,bal is the closed balance point velocity if Kv,closed is used. The values of Kv,closed, Kv,open, and Cv depend upon the thickness of the deck and, to a small extent, on the type of valve (Bolles, 1976).
Figure 10-21 Dry tray pressure drop for valve tray from Bolles (1976). Reprinted from Chemical Engineering Progress, Sept. 1976, copyright 1976, American Institute of Chemical Engineers
Much of the remainder of the preliminary design of valve trays is the same or slightly modified from the sieve tray design (Kister, 1990, 1992; Lockett, 1986; Larson and Kister, 1997). Flooding and diameter calculations are the same except that the correction factor for Ahole/Aa < 0.1 is replaced by a correction factor for Aslot/Aa < 0.1. The same values for the correction factors are used. The slot area Aslot is the vertical area between the tray deck and the top of the valve through which the vapor passes in a horizontal direction. In the region between the balance points the slot area is variable and can be determined from the fraction of valves that are open. The pressure drop Eq. (10-23) is the same, while Eq. (10-24) for hΔp,dry is replaced by Eq. (10-33) or (10-35). Equations (10-26) to (10-30) are unchanged. The gradient across the valve tray, hgrad, is probably larger than on a sieve tray but is usually ignored. Valve trays usually operate with higher weirs. An hweir of 3 inches is normal. There are typically 12 to 16 valves per ft2 of active area (Kister, 1990).
The efficiency of valve tray depends upon the vapor velocity, the valve design, and the chemical system being distilled. Except at vapor flow rates near flooding, the efficiencies of valve trays are equal to or higher than sieve tray efficiencies, which are equal to or higher than bubble-cap tray efficiencies. Thus, the use of the efficiency correlations discussed earlier will result in a conservative design.
10.6 INTRODUCTION TO PACKED COLUMN DESIGN
Instead of staged columns we often use packed columns for distillation, absorption, stripping, and occasionally extraction. Packed columns are used for smaller diameter columns since it is expensive to build a staged column that will operate properly in small diameters. Packed columns are definitely more economical for columns less than 2.5 feet in diameter. In larger packed columns the liquid may tend to channel, and without careful design randomly packed towers may not operate very well; in many cases large-diameter staged columns are cheaper. Packed towers have the advantage of a smaller pressure drop and are therefore useful in vacuum fractionation.
In designing a packed tower, the choice of packing material is based on economic considerations. A wide variety of packings including random and structured are available. Once the packing has been chosen it is necessary to know the column diameter and the height of packing needed. The column diameter is sized on the basis of either the approach to flooding or the acceptable pressure drop. Packing height can be found either from an equilibrium stage analysis or from mass transfer considerations. The equilibrium stage analysis using the height equivalent to a theoretical plate (HETP) procedure will be considered here; the mass transfer design method is discussed in Chapter 15.
10.7 PACKED COLUMN INTERNALS
In a packed column used for vapor-liquid contact, the liquid flows over the surface of the packing and the vapor flows in the void space inside the packing and between pieces of packing. The purpose of the packing is to provide for intimate contact between vapor and liquid with a very large surface area for mass transfer. At the same time, the packing should provide for easy liquid drainage and have a low pressure drop for gas flow. Since packings are often randomly dumped into the column, they also have to be designed so that one piece of packing will not cover up and mask the surface area of another piece.
Packings are available in a large variety of styles, some of which are shown in Figure 10-22. The simpler styles such as Raschig rings are usually cheaper on a volumetric basis but will often be more expensive on a performance basis, since some of the proprietary packings are much more efficient. The individual rings and saddles are dumped into the column and are distributed in a random fashion. The structured or arranged packings (e.g., Glitsch grid, Goodloe, and Koch Sulzer) are placed carefully into the column. The structured packings usually have lower pressure drops and are more efficient than dumped packings, but they are often more expensive. Packings are available in a variety of materials including plastics, metals, ceramics, and glass. One of the advantages of packed columns is they can be used in extremely corrosive service.
Figure 10-22 Types of column packing; A) ceramic Intalox saddle, B) plastic super Intalox saddle, C) Pall ring, D) GEMPAK cartridge, E) Glitsch EF-25A grid. Figures A, B, and C courtesy of Norton Chemical Process Products, Akron, Ohio. Figures D and E courtesy of Glitsch, Inc., Dallas, Texas
The packing must be properly held in the column to fully utilize its separating power. A schematic diagram of a packed distillation column is shown in Figure 10-23. In addition to the packed sections where separation occurs, sections are needed for distribution of the reflux, feed, and boilup and for disengagement between liquid and vapor. The liquid distributors are very important for proper operation of the column. Small random and structured packings need better liquid and vapor distribution (Kister, 1990, 2005). If (column diameter)/(packing diameter) > ~40 maldistribution of liquid and vapor is more probable. Maldistribution also reduces the turndown capability of the packing and causes a large increase in HETP with low liquid rates. Liquid distributors typically have a manifold with a number of drip points. Bonilla (1993) recommends six (ten for high purity fractionation) drip points per square foot for large packings (random packings ≥2.5 inches or structured packings with crimps > ½ inch). For small packings (random packings ≤1 inch or structured packings with crimps ≤¼ inch) he recommends eight (12 for high purity) drip points per square foot at high liquid loads and ten (14 for high purity) drip points per square foot at low liquid loads. Requirements for medium size packings are between the small and large recommendations. Low liquid loads need more drip points because the liquid tends to spread less. The effects of liquid maldistribution are explored in Problem 10.D10. Scale-up of distributors is done by keeping the number of drip points per square foot constant. Redistribution systems may be required on large columns. The packing is supported by a support plate, which may be a grid or series of bars. A hold-down plate is often employed to prevent packing movement when surges in the gas rate occur. Since liquid and vapor are flowing countercurrently throughout the column, there are no downcomers. The packed tower internals must be carefully designed to obtain good operation (see Fair, 1985; Kister, 1990, 2005; Ludwig, 1997; Perry and Green, 1997; and Strigle, 1994). Additional details are given in the manufacturers’ literature. The internals of a packed column for absorption or stripping would be similar to the distillation column shown in Figure 10-23 but without the center feed, reboiler, or condenser.
Figure 10-23 Packed distillation column
10.8 HEIGHT OF PACKING: HETP METHOD
Even though a packed tower has continuous instead of discontinuous contact of liquid and vapor, it can be analyzed like a staged tower. We assume that the packed portion of the column can be divided into a number of segments of equal height. Each segment acts as an equilibrium stage, and liquid and vapor leaving the segment are in equilibrium. It is important to note that this staged model is not an accurate picture of what is happening physically in the column, but the model can be used for design. The staged model for designing packed columns was first used by Peters (1922).
We calculate the number of stages from either a McCabe-Thiele or Lewis analysis and then calculate the height as
(10-37a)
The HETP, which is measured experimentally, is the height of packing needed to obtain the change in composition obtained with one theoretical equilibrium contact. HETPs can vary from ½-inch (very low gas flow rates in self-wetting packings) to several feet (large Raschig rings). In normal industrial equipment the HETP varies between 1 and 4 feet. The smaller the HETP, the shorter the column and the more efficient the packing.
To measure the HETP, determine the top and bottom compositions at total reflux and then calculate the number of equilibrium stages.
Then
(10-37b)
A partial reboiler is usually used but should not be included in the calculation of HETP.
The HETP determined at total reflux is then used at the actual reflux ratio. Ellis and Brooks (1971) found that there is an increase in the HETP for internal reflux ratios below 1.0, but the increase is usually quite small until L/V approaches 1/2. Thus, the usual measurement procedure can be used for most design situations.
The HETP varies with the packing type and size, chemicals being separated, and gas flow rate. Some typical HETP curves are shown in Figure 10-24. The HETP values for several types of packing are listed in the manufacturers’ bulletins and have been compared by Perry (1950, p. 620), Ellis and Brooks (1971), Kister and Larson (1997), Kister et al. (1994), Ludwig (1997), and Walas (1988). Mass transfer results are compared by Furter and Newstead (1973), Ludwig (1997), Perry and Green (1997), and Strigle (1994). Correlations to determine HETP values were developed by Murch (1953) and Whitt (1959), but these do not include modern packings (see Ludwig, 1995). An improved mass transfer model for packings and HETP data for a variety of packings are presented by Bolles and Fair (1982) and discussed in Chapter 15. The HETPs are different for different chemical systems and are higher for larger size packing. Most packings of the same size will have approximately the same HETP. Note from Figure 10-24 that the HETP for a given system and packing size is roughly constant over a wide range of gas flow rates. Then as flooding is approached the efficiency of the contact decreases, and the HETP increases. Also, at very low gas flow rates the HETP often increases. This occurs because the packing is not completely wet. For self-wetting packings, where capillary action keeps the packing wet, the HETP usually drops at very low gas flow rates.
Figure 10-24 HETP vs. vapor rate for metal pall rings; A) Iso-Octane-Toluene, B) acetone-water. Reprinted with permission from “Pall Rings in Mass Transfer Operations,” 1968 courtesy of Norton Chemical Process Products, Akron, Ohio
HETP values are most accurate if determined from data. If no data are available, generalized mass transfer correlations are used (see Chapter 15). If no information is available, Ludwig (1997) suggests using an average of 1.5 to 2.0 feet for dumped packings. If the column diameter is greater than 1 foot, an HETP greater than 1 foot should be used. Another approximate approach is to set HETP equal to column diameter (Ludwig, 1997). Eckert (1979) notes that HETP values for 1, 1½ and 2-inch Pall rings are 1, 1½ and 2 feet, respectively. These HETP values are almost independent of the system distilled. Approximate values of HETP for structured packings can be obtained from the following approximate equation (Geankoplis, 2003; Kister, 1992)
(10-38)
where HETP is in meters and ap, the surface area per volume, is in m2/m3. This result is restricted to low viscosity fluids at moderate or low pressures. Typical HETP values range from 0.3 to 0.6 m. Systems with high surface tensions will have higher HETP values. For example, for systems (amines, glycols) with σ ~ 40 dynes/cm multiply HETP from Eq. (10-38) by 1.5 and for aqueous systems with σ ~ 70 dynes/cm multiply HETP from Eq. (10-38) by 2 (Anon., 2005). A number of other shortcut HETP relationships are summarized by Wang et al. (2005). If liquid distribution is not excellent, a 30 to 50% safety factor is suggested.
Although packed columns operate with a continuous change in vapor and liquid concentrations, the staged model is still a useful design method. Since the HETP is often almost constant throughout the usual design range for gas flow rates, concentrations, and reflux ratios, a single HETP value can usually be used in comparing many different designs. This greatly facilitates design. In certain cases HETP can vary significantly within the column because of changes in composition; it can then be estimated for each stage from the mass transfer coefficient (see Sherwood et al., 1965, pp. 521-523 for an example). Alternatively, a mass transfer design approach can be used and is preferred (see Chapter 15).
10.9 PACKED COLUMN FLOODING AND DIAMETER CALCULATION
The column diameter is sized to operate at 65% to 90% of flooding or to have a given pressure drop per foot of packing. Flooding can be more easily measured in a packed column than in a plate column and is usually signaled by a break in the curve of pressure drop vs. gas flow rate.
The generalized flooding correlation developed by Sherwood et al. (1938) as modified by Eckert (1970, 1979) is shown in Figure 10-25. Note that the ordinate of Figure 10-25 has units and these units need to be used in the calculation. A graph of the same data with an arithmetic scale for the ordinate is available (Geankoplis, 2003; Strigle, 1994). The packing factor, F, depends on the type and size of the packing. The higher the value of F, the larger the pressure drop per foot of packing. F values for several types of dumped packing are given in Table 10-3 (Eckert, 1970, 1979; Ludwig, 1997), and F values for structured packings are in Table 10-4 (Fair, 1985; Geankoplis, 2003). As the packing size increases, the F value decreases, and thus, pressure drop per foot will decrease. More extensive lists of F values are available in Perry’s Handbook (Perry and Green, 1997) and in Strigle (1994). The effect of packing size on the packing factor can be fit reasonably well with the equation (Bennett, 2000),
(10-39a)
where the packing size factor Cp,size is given in Table 10-5 and δp is the characteristic dimension of the packing in inches. For random packing δp = the nominal size or diameter of the packing and for structured packing δp = the height of the corrugation. Ceramic packings have thicker walls than plastic, and the plastic have thicker walls than metal; ceramic packings thus, have the lowest free space, highest pressure drops, and highest F values. Generally, the lower the F value the smaller the column diameter. Figure 10-25 is not a perfect fit of all the data. Better results can be obtained using pressure drop curves measured for a given packing. Specifically, predicted pressure drop for non-aqueous systems at high flow parameter values is too low (Kister and Gill, 1991).
Figure 10-25 Generalized flooding and pressure drop correlation for packed columns. Reprinted with permission from Eckert, Chem.Eng.Prog., 66(3), 39(1970), copyright 1970 AIChE. Reproduced by permission of the American Institute of Chemical Engineers
Table 10-3. Parameters for dumped packings (F is 1/ft)
Source: Eckert (1970), Ludwig (1997), Coker (1991), Geankoplis (2003)
Table 10-4. F values (1/ft) for structured packings (Fair, 1985; Geankoplis, 2003)
The Flooding curve can be fit by the equation (Kessler and Wankat, 1988)
(10-39a)
where µ is the liquid viscosity in cP, ψ = ρwater/ρL, gc = 32.2, and Flv is the abscissa of Figure 10-25 and is given in Eq. (10-09), densities are mass densities and L and G or WL and Wv are mass flow rates.
In the region below the flooding curves, the pressure drop can be correlated with an equation of the form
(10-39b)
where Δp is the pressure drop in inches of water per foot of packing. L′ and G′ are fluxes in lb/s-ft2. Constants α and β are also given in Table 10-3 for dumped packings (Ludwig, 1997). Alternative flooding and pressure drop correlations are given by Kister and Larson (1997), Ludwig (1997), and Strigle (1994).
The generalized correlation in Figure 10-25 for Eqs. (10-39) are used as follows. The designer first picks a point in the column and determines gas and liquid densities (ρG and ρL), viscosity (µ), value of ψ, and packing factor for the packing of interest. The ratio of liquid to vapor fluxes, L′/G′, is equal to the internal reflux ratio, L/V, if the liquid and vapor are of the same composition, because the area terms divide out and molecular weights cancel. If liquid and vapor mole fractions are significantly different at this point, then
(10-40)
In the first design method the designer chooses the pressure drop per unit length of packing. This number ranges from 0.1 to 0.4 inches of water per foot for vacuum columns, from 0.25 to 0.4 inches of water per foot for absorbers and strippers, and from 0.4 to 0.8 inches of water per foot for atmospheric and high-pressure columns (Coker, 1991). With the value of the abscissa and the parameter known, the ordinate can be determined. G′ is the only unknown in the ordinate. Once G′ is known, the area is
(10-41)
In the second design method, the flooding curve in Figure 10-25 or Eq. (10-39a) is used. Then G′flood is calculated from the ordinate. The actual operating vapor flux will be some percent of G′flood. The usual range is 65% to 90% of flooding with 70 to 80% being most common. The area is then determined from Eq. (10-41). The flooding correlation is not perfect. To have 95% confidence a safety factor of 1.32 should be used for the calculated cross-sectional area (Bolles and Fair, 1982).
The diameter is easily calculated once the area is known. Since the liquid and vapor properties and gas and liquid flow rates all vary, the designer must calculate the diameter at several locations and use the largest value. Usually, variations in vapor flow rate dominate diameter calculations.
EXAMPLE 10.4 Packed column diameter calculation
A distillation column is separating n-hexane from n-heptane using 1-inch ceramic Intalox saddles. The allowable pressure drop in the column is 0.5 inches of water per foot. Average column pressure is 1 atm. Separation in the column is essentially complete, so the distillate is almost pure hexane and the bottoms is almost pure heptane. Feed is a 50-50 mixture and is a saturated liquid. In the top, L/V = 0.8. If F = 1000 lb moles/hr and D = 500 lb moles/hr, estimate the column diameter required at the top.
Solution
A. Define. Find the diameter that gives p = 0.5 for top of column.
B. Explore. Need physical properties, most of which are in Examples 10-1 to 10-3: n-Hexane: MW 86.17, bp 69°C = 342 K, sp grav = 0.659, viscosity (at 69°) = 0.22 cP
n-Heptane: MW 100.2, bp 98.4°C = 371.4 K, sp grav = 0.684, viscosity (at 98.4°) = 0.205 cP
The ideal gas law can be used to estimate vapor densities,
Table 10-5. Size factors for Eq. (10-39) (Bennett, 2000), copyright 2000, AIChE. Reproduced by permission of the American Institute of Chemical Engineers.
Water density at 69°C = 0.9783 g/ml. We can use Figure 10-25 with F from Table 10-3 or Eq. (10-39b) with α and β from Table 10-3. We will use both methods.
C. Plan. Figure 10-25 and Eq. (10-39b) can both be used to determine the required diameter.
D. Do it. The top is essentially pure n-hexane. Then,
Abscissa for Figure 10-25 is
From Figure 10-25 at (Δp = 0.5), 
(Obtaining the same value for ordinate and abscissa is an accident!) Then
From Table 10-3, F = 98. Thus
Calculate V from V = L + D = (L/D + 1) D, where
This gives
Alternative: Use Eq. (10-39b). First we must rearrange the equation. Since L′/G′ = L/V, have L′ =(L/V)G′. Then Eq. (10-39b) becomes
(10-42)
From Table 10-3, α = 0.52 and β = 0.16. Then the equation is
This is an equation with one unknown, G′, so it can be solved for G′. Rearranging the equation,
Using our previous answer, G′ = 0.360, as the first guess and using direct substitution, we obtain G′ = 0.404 as the answer in two trials.
Then,
Note that there is a 6% difference between this answer and the one we obtained graphically. Since α and β in Eqs. (10-39b) and (10-42) are specific for this packing and are not based on generalized curves, the lower value is probably more accurate and a 14-foot diameter would be used. If we wanted to be conservative (safe), a 14.5-foot diameter would be used. Additional safety factors (see Fair, 1985) might be employed if the pressure drop is critical.
E. Check. Solving the problem two different ways is a good, but incomplete, check. The check is incomplete because the same values for several variables (e.g., ρG, V, and MW) were used in both solutions. Errors in these variables will not be evident in the comparison of the two solutions.
F. Generalize. Either Figure 10-25 or Eq. (10-39b) can be used for pressure drop calculations in packed beds. The use of both is a good check procedure the first time you calculate a diameter (or Δp). Remember, the required diameters should also be estimated at other locations in the column. It is interesting to compare this design with a design at 75% of flooding. The 75% of flooding design requires a diameter of 12.4 feet and has pressure drop of approximately 1.5 inches of water per foot of packing. It is also interesting to compare this example with Example 10-2, which is a sieve-tray column for the same distillation problem. At 75% of flooding the sieve tray was 11.03 feet in diameter. The packed column is a larger diameter because a small packing was used. If a larger diameter packing were used, the packed column would be smaller (see Problem 10-D16). The effect of location on the calculated column diameter is explored in Problem 10-D17. If pressure drop is absolutely critical, the column area should be multiplied by a safety factor of 2.2 (Bolles and Fair, 1982).
There are three alternatives that can overcome the flooding limitations of counter-current packed columns. The rotating packed bed or Higee process (Ramshaw, 1983; Lin et al., 2003) puts the packing inside an annular-flow column that is rotated at high rpm. This device achieves high rates of mass transfer, and because of the effective increase in gravity floods at much higher velocities. The column size is considerably smaller than for normal distillation or absorption systems, but the device is more complicated. A few commercial units have been built. The second approach is to do absorption, stripping, or extraction in counter-current flow with hollow fiber membrane phase contactors (Humphrey and Keller, 1997; Reed et al., 1995). One phase flows inside the hollow fibers and the other flows counter-current to it in the shell. High flow rates are observed because flooding is unlikely, and relatively low HETP values have been reported because of the very large surface area of hollow fibers. This process has been commercialized by Celanese as Liqui-Cel. The third approach is to avoid counter-current operation altogether and operate in co-current flow where there is no flooding (see Section 12.8).
10.10 ECONOMIC TRADE-OFFS
In the design of a packed column the designer has many trade-offs that are ultimately reflected in the operating and capital costs. After deciding that a packed column will be used instead of a staged column, the designer must choose the packing type. There is no single packing that is most economical for all separations. For most distillation systems the more efficient packings (low HETP and low F) are most expensive per volume but may be cheaper overall. The designer must then pick the material of construction. Since random commercial packings of the same size will all have an HETP in the range of 1 to 2 feet, the major difference between them is the packing factor, F. Perusal of Table 10-3 shows that there is a very large effect of packing size and a lesser but still up to fourfold effect of packing type on F value. The material of construction can also change F by a factor that can be as high as 3. From Figure 10-25,
(10-43)
A fourfold increase in F would cause a halving of G′ and a doubling of the required area [(Eq. (10-41)]. The diameter can then be calculated,
(10-44)
Note that F is the packing factor, not the feed rate! Thus, the major advantage of more efficient packings, structured packings, and the larger size packings is that they can be used with a smaller diameter column, which is not only less expensive but will also require less packing.
At this point, the designer can pick the packing size and determine both the HETP and packing factor. Larger size packing will have a larger HETP (require a larger height), but a smaller F factor and hence a smaller diameter. Thus, there is a trade-off between packing sizes. The larger size packings are cheaper per cubic foot but can’t be used in very small diameter columns. As a rule of thumb,
(10-45)
depending on whose thumb you are using. The purpose of this rule is to prevent excessive channeling in the column. Structured packings are purchased for the desired diameter column and are not restrained by Eq. (10-45). In small-diameter columns (say, less than 6 inches), structured packings allow low F factors and hence low Δp without violating Eq. (10-45).
The designer can also select the pressure drop per foot. Operating costs in absorbers and strippers will increase as Δp/ft increases, but the diameter decreases and hence capital costs for the column decrease. Operation should be in the range of 20% to 90% of flood and is usually in the range of 65% to 90% of flooding. Since columns are often made in standard diameters, the pressure drop per foot is usually adjusted to give a standard size column.
The reflux ratio is a critical variable for packed columns as it is for staged columns. An L/D between 1.05 (L/D)min and 1.25 (L/D)min would be an appropriate value for the reflux ratio. The exact optimum point depends upon the economics of the particular case.
You’re a young engineer asked to design a distillation column. Do you use trays, random packing, or structured packing? In many applications packed columns appear to be the wave of the future. Columns packed with structured packings have a combination of low pressure drop and high efficiency that often makes them less expensive than either randomly packed columns or staged columns. Random packings can be made in a wide variety of materials so that practically any chemicals can be processed. Many of the flow distribution problems that limited the size of packed columns appear to have been solved.
Kister et al. (1994) considered which column to use in considerable detail. They concluded that in vacuum columns, particularly high vacuum, the lower pressure drop of packing is a major advantage and packed columns will have higher capacities and lower reflux ratios than tray columns. For atmospheric and pressure columns pressure drop is usually unimportant, and one needs to compare optimally designed tray columns to optimal packed columns. An optimally designed tray column balances tray and downcomer areas so that both restrict capacity simultaneously. An optimally designed packed column has good liquid and vapor distribution and capacity restrictions are due to the inherent qualities of the packing not due to supports or distributors.
Kister et al. (1994) compared a large amount of data generated by the FRI in a 4-foot diameter column and for the structured packing at p < 90 psia by the Separation Research Program (SRP) at the University of Texas-Austin in a 17-inch diameter column. Nutter rings were chosen to represent state-of the-art random packings. The only structured packing measured at high pressures was Norton’s Intalox 2T, which was chosen to represent structured packing. Test data was available on both sieve and valve trays with 24-inch tray spacing. All comparisons were at total reflux. For efficiency they compared practical HETP values that include height consumed by distribution and redistribution equipment.
(10-46)
where m > 1. For 2 in. random packing m = 1.1 while for structured packing (Intalox 2T) m = 1.2. For trays
(10-47)
where S is the tray spacing in inches and Eo is the fractional overall efficiency. For capacity they compared the capacity factor at flooding,
(10-48)
where Ug is the gas velocity in ft/sec and the densities are mass densities. Both efficiency and capacity results were plotted against the flow parameter FP given in Eq. (10-09) and repeated here.
(10-49)
Since the valve trays were superior to the sieve trays (higher Cs,flood and lower HETP), valve trays were compared to the packings. The overall comparison of tray and packing efficiencies (as measured by the adjusted HETP) is shown in Figure 10-26. The adjusted HETP for the structured packing is lower over most of the range of FP while the HETPs for trays and random packings are almost identical. At high FP values, which are at high pressures, the random packing had the lowest HETP and the structured packing the highest. Capacities, as measured by Cs,flood values, are compared in Figure 10-27. At low FP (low pressures) the structured packing has a 30% to 40% advantage in capacity. At FP values around 0.2 all devices have similar capacities. At high pressures (high FP values) the trays clearly had higher capacities.
Figure 10-26 Overall Comparison of Efficiency of Trays, Random Packing, and Structured Packing (Kister et al., 1994). Reprinted with permission from Chemical Engineering Progress, copyright AICHE 1994
Figure 10-27 Overall Comparison of Capacity of Trays, Random Packing, and Structured Packing (Kister et al, 1994). Reprinted with permission from Chemical Engineering Progress, copyright AICHE 1994.
Since engineers are responsible for safety, they need to be aware that many fires are related to distillation and absorption columns. The most dangerous periods are during abnormal operation—upsets, shutdowns, maintenance, total reflux operation, and startups. Structured packing has been implicated in a number of fires, mainly occurring during shutdown and maintenance of units (Ender and Laird, 2003). Several different mechanisms were identified. 1) Hydrocarbons may coat the packing with a thin film that is very difficult to remove. If the packing is at an elevated temperature when it is exposed to air, the hydrocarbons may self-ignite. 2) Coke or polymers may form on the packing during normal operation. Although coking or polymerization will eventually be signaled by increased pressure drop, a large fraction of the bed will contain coke or polymer by time this is noticed. Cooling the interior of the coke or polymer is very difficult because the thermal conductivity is low. Thus, the interior of the coke or polymer may be much hotter than the vapor, which is where the temperature measuring device is located. When the column is opened to air, the coke or polymer may catch fire. 3) If sulfur is present in the feed, corrosion of carbon steel components up or down stream of the column can form iron sulfide (FeS) that can settle on the packing. This iron sulfide is difficult to remove and will autoignite at ambient temperature when exposed to air. 4) Packing usually arrives from the factory coated with lubricating oil. This oil can catch fire if hot work (e.g., welding) is conducted on the column. 5) If the hydrocarbons, coke, or FeS on the packing catches fire, the very thin metal packing can burn. This is more likely with reactive metals such as aluminum, titanium, and zirconium. The danger of metal fires is because they burn at very high temperatures (up to 1500°C), they can be very destructive.
Standard operating procedures should be designed to prevent these fires (Ender and Laird, 2003).
1. Cool the column to ambient before opening the column. Continuously monitor the temperature.
2. Wash the column extensively to remove residues and deposits.
3. If sulfur is present in the feed assume FeS formed and wash the column with permanganate or percarbonate.
4. Purge with inert gas (nitrogen, carbon dioxide, or steam), and be sure personnel are equipped with respirators before opening the column.
5. Minimize the number of open manways to reduce air entry and allow for rapid closure of the column if there is a fire. Do not force air circulation into the column. This may sound counterintuitive since air circulation will help cool the column if there is no fire; however, fires can be prevented or stopped by starving them of oxygen.
Ultimately, the decision of which column design to use is often economic. Currently, unless there are exceptional circumstances, it appears that structured packings are most economical in low-pressure operation and valve trays are most economical in high-pressure operation. At atmospheric and slightly elevated pressures structured packings have an efficiency but not a capacity advantage; however, structured packings are often considerably more expensive than valve trays (Humphrey and Keller, 1997). The slight added safety risk of structured packing with flammable materials also needs to be considered. Thus, random packings (small-diameter columns) and valve trays will often be preferred for atmospheric and slightly elevated pressures. Exceptional circumstances include the need to use exotic materials such as ceramics, which favors random packings and the need for high holdup for reactive systems, which favors trays. Packed columns are dynamically more stable than staged columns. They are less likely to fail during start-up, shutdown, or other upsets in operation. This is particularly true of absorption and stripping columns (Gunaseelan and Wankat, 2002), and should be considered if the column will be used for processing vent gases in emergencies. Note that tray columns still retain advantages in addition to cost for a number of applications such as very large column diameters, columns with multiple drawoffs, varying feed compositions, highly fouling systems, and systems with solids (Anon., 2005).
10.11 SUMMARY—OBJECTIVES
In this chapter both qualitative and quantitative aspects of column design are discussed. At the end of this chapter you should be able to satisfy the following objectives:
1. Describe the equipment used for staged distillation columns
2. Define different definitions of efficiency, predict the overall efficiency, and scale-up the efficiency from laboratory data
3. Determine the diameter of sieve and valve tray columns
4. Determine tray pressure drop terms for sieve and valve trays and design downcomers
5. Lay out a tray that will work
6. Describe the parts of a packed column and explain the purpose of each part
7. Use the HETP method to design a packed column. Determine the HETP from data
8. Calculate the required diameter of a packed column
9. Determine an appropriate range of operating conditions for a packed column
10. Select the appropriate design (valve tray, random packing, or structured packing) for a separation problem
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HOMEWORK
A. Discussion Problems
A1. What effect does increasing the spacing between trays have on
a. Column efficiency?
b. K and column diameter?
c. Column height?
A2. Several different column areas are used in this chapter. Define and contrast: total cross-sectional area, net area, downcomer area, active area, and hole area.
A3. Relate the head of clear liquid to a pressure drop in psig.
A4. Explain why the notched weirs in Figure 10-6B have better turndown characteristics than straight weirs.
A5. Explain Figure 10-21. What would the pressure drop curve for a sieve tray look like [see Eq. (10-24)]?
A6. Valve trays are often constructed with two different weight valves. What would this do to Figure 12-21? What are the probable advantages of this design?
A7. The basic design method for determining column diameter determines uflood from Eq. (10-08). Is this a vapor or a liquid velocity? How is the flow rate of the other phase (liquid or vapor) included in the design procedure?
A8. Intermediate feeds should not be introduced into a downcomer. Explain why not.
A9. What are the characteristics of a good packing? Why are marbles a poor packing material?
A10. Develop your key relations chart for this chapter.
A11. If HETP varies significantly with the gas rate, how would you design a packed column?
A12. Explain why pressure drop can be detrimental when you are operating a vacuum column.
A13. What effect will an increase in viscosity have on
a. Pressure drop in a packed column?
b. HETP (consider mass transfer effects)?
A14. Refer to Table 10-3.
a. Which is more desirable, a high or low packing factor, F?
b. As packing size increases, does F increase or decrease? What is the functional form of this change (linear, quadratic, cubic, etc.)?
c. Why do ceramic packings have higher F factors than plastic or metal packings of the same type and size? When would you choose a ceramic packing?
A15. Why can’t large-size packings be used in small-diameter columns? What is the reason for the rule of thumb given in Eq. (10-45)?
A16. We have designed a sieve tray distillation column for p = 3 atm. We decide to look at the design for p = 1 atm. Assume feed flow rate, mole fractions in the feed, and L/D are the same for both designs. Feed is a saturated liquid for both designs. We want same recoveries of light and heavy key for both designs. Both designs have a total condenser and a partial reboiler. Compared to the original design at 3 atm., the design at 1 atm. will:
1. |
Have |
a. |
fewer stages |
b. |
more stages |
||
c. |
same number of stages |
||
2. |
Require |
a. |
smaller diameter column |
b. |
larger diameter column |
||
c. |
same diameter column |
||
3. |
Have |
a. |
lower reboiler temperature |
b. |
higher reboiler temperature |
||
c. |
same reboiler temperature |
B. Generation of Alternatives
B1. One type of valve is shown in Figure 10-1. Brainstorm alternative ways in which valves could be designed.
B2. What other ways of contacting in packed columns can you think of?
B3. a. A farmer friend of yours is going to build his own distillation system to purify ethanol made by fermentation. He wants to make his own packing. Suggest 30 different things he could make or buy cheaply to use as packing (set up a brainstorming group to do this—make no judgments as you list ideas).
b. Look at your list in part a. Which idea is the craziest? Use this idea as a trigger to come up with 20 more ideas (some of which may be reasonable).
c. Go through your two lists from parts a and b. Which ideas are technically feasible? Which ideas are also cheap and durable? List about 10 ideas that look like the best for further exploration.
C. Derivations
C1. You need to temporarily increase the feed rate to an existing column without flooding. Since the column is now operating at about 90% of flooding, you must vary some operating parameter. The column has 18-inch tray spacing, is operating at 1 atm, and has a flow parameter
The column is rated for a total pressure of 10 atm. L/D = constant. The relative volatility for this system does not depend on pressure. The condenser and reboiler can easily handle operation at a higher pressure. Downcomers are large enough for larger flow rates. Will increasing the column pressure increase the feed rate that can be processed? It is likely that:
(10-49)
Determine the value of the exponent for this situation. Use the ideal gas law.
C2. Show that staged column diameter is proportional to (feed rate)1/2 and to (1 + L/D)1/2.
C3. Convert the typical pressure drop per length of packing numbers [given after Eq. (13-03)] to Pa/m.
C4. If the packing factor were unknown, you could measure Δp at a series of gas flow rates. How would you determine F from this data?
D. Problems
*Answers to problems with an asterisk are at the back of the book.
D1. *Repeat Example 10-1 for an average column pressure of 700 kPa.
D2. *Repeat Example 10-2, except calculate the diameter at the bottom of the column. For n-heptane: MW = 100.2, bp 98.4°C, sp gravity = 0.684, viscosity (98.4° C) = 0.205 cP, δ (98.4° C) = 12.5 dynes/cm.
D3. The calculations in Example 10-3 were done for conditions at the top of the column. Physical properties will vary throughout the column, but columns are normally constructed with identical trays, downcomers, weirs, etc., on every stage (this is simpler and cheaper). For a 12-foot diameter column, calculate entrainment, pressure drops, downcomer residence time, and weeping at the bottom of the column. The results of Problem 10-D2 are required. If the column will not operate, will it work if the gap between the tray and downcomer apron is increased to 1.5 inches?
D4. *We wish to repeat the distillation in Examples 10-2 and 10-3 except that valve trays will be used. The valves have a 2-inch diameter head. For the top of the column, estimate the pressure drop vs. hole velocity curve. Assume that Kv and Cv values are the same as in Figure 10-21. Each valve weighs approximately 0.08 pound.
D5. *We are testing a new type of packing. A methanol-water mixture is distilled at total reflux and a pressure of 101.3 kPa. The packed section is 1 meter long. We measure a concentration of 96 mole % methanol in the liquid leaving the condenser and a composition of 4 mole % methanol in the reboiler liquid. What is the HETP of this packing at this gas flow rate? Equilibrium data are in Table 2-7.
D6. *We are testing a new packing for separation of benzene and toluene. The column is packed with 3.5 meters of packing and has a total condenser and a partial reboiler. Operation is at 760 mmHg, where α varies from 2.61 for pure benzene to 2.315 for pure toluene (Perry et al., 1963, p. 13-3). At total reflux we measure a benzene mole fraction of 0.987 in the condenser and 0.008 in the reboiler liquid. Find HETP:
a. Using α = 2.315
b. Using α = 2.61
c. Using a geometric average α.
Use either the Fenske equation or a McCabe-Thiele diagram.
D7. You have designed a sieve tray column with 12-inch tray spacing to operate at a pressure of 1.0 atm. The value of the flow parameter is Flv = 0.090 and the flooding velocity was calculated as Unf = 6.0 ft/sec. Unfortunately, your boss dislikes your design. She thinks that 12-inch tray spacing is not enough and that your reflux ratio is too low. You must redesign for a 24-inch tray spacing and increase L/V by 11%. Estimate the new flooding velocity in ft/sec.
Assumptions: Ideal gas, σ, ρL, and ρG are unchanged.
D8. You have designed a sieve tray column with 18-inch tray spacing to operate at a pressure of 2.0 atm. The value of the flow parameter is Flv = 0.5, and the flooding velocity was calculated as Unf = 6.0 ft/sec. Unfortunately, the latest lab results show that the distillation temperature is too high and unacceptable thermal degradation occurs. To reduce the operating temperature, you plan to reduce the column pressure to 0.5 atm. Estimate the new flooding velocity in ft/sec.
Assumptions: Ideal gas, σ and ρL are unchanged, ρL > ρV (thus, ρL − ρV = ρL). Ignore the effect of temperature change in calculation of ρV.
D9. We are distilling methanol and water in a sieve plate column operating at 75% of flooding velocity. The distillate composition is 0.999 mole fraction methanol. The bottoms composition is 0.01 mole fraction methanol. The column operates at 1.0 atmosphere pressure. Use L/V = 0.6. The flow rate of the feed is 1000.0 kg moles/hr. The feed is a saturated vapor that is 60 mole % methanol. Use an 18-inch tray spacing and η = 0.90. Density of pure liquid methanol is 0.79 g/ml. Data are available in Table 2-7. Assume an ideal gas. The surface tension of pure methanol can be estimated as σ = 24.0 – 0.0773 T with T in°C (Dean, 1985, p. 10–110). Calculate the diameter based on the conditions at the top of the column.
D10. The effect of liquid maldistribution in packed columns can be explored with a McCabe-Thiele diagram. Assume that a packed distillation column is separating a saturated liquid binary feed that is 40.0 mole % MVC. A distillate product, D = 100.0 kmoles/hr, that is 90% MVC is desired. Relative volatility = 3.0 and is constant. We operate at an L/D = 2(L/D)min. If there is liquid maldistribution, the actual L/V represents an average for the entire column. Assume that vapor is equally distributed throughout the column, but there is more liquid on one side than the other. The slope of the operating line on the low liquid side will be Llow/V not (L/V)avg. If the low liquid flow rate is small enough, the operating line on the low side will be pinched at the feed point, and the desired separation will not be obtained. What fraction of the average liquid flow rate must the low liquid flow rate be to just pinch at the feed concentration? Then generalize your result for L/D = M(L/D)min, where M > 1.
D11. *We wish to distill an ethanol-water mixture to produce 2250 lb of distillate product per day. The distillate product is 80 mole % ethanol and 20 mole % water. An L/D of 2.0 is to be used. The column operates at 1 atm. A packed column will use 5/8-inch plastic Pall rings. Calculate the diameter at the top of the column.
Physical properties: MWE = 46, MWW = 18, assume ideal gas, µL = 0.52 cP at 176° F, µL = 0.82 g/ml.
a. Operation is at 75% of flooding. What diameter is required?
b. Operation is at a pressure drop of 0.25 inches of water per foot of packing. What diameter is required?
c. Repeat part a but for a feed that is 22,500 lb of distillate product per day. Note: It is not necessary to redo the entire calculation, since D and hence V and hence diameter are related to the feed rate.
D12. *A distillation system is a packed column with 5.0 feet of packing. A saturated vapor feed is added to the column (which is only an enriching section). Feed is 23.5 mole % water with the remainder nitromethane. F=10 kg moles/hr. An L/V of 0.8 is required. xD = xβ = 0.914. Find HETP and water mole fraction in bottoms. Water-nitromethane data are given in Problem 8.E1.
D13. Repeat Problem 10.D9, but use 2-inch plastic Pall rings. Operate at 75% of flooding.
D14. a. We are distilling methanol and water in a column packed with 1-inch ceramic Berl saddles. The bottoms composition is 0.0001 mole fraction methanol. The column operates at 1 atm pressure. The feed to the column is a saturated liquid at 1000.0 kg moles/day and is 40 mole % methanol. An L/D = 2.0 will be used. The distillate product is 0.998 mole fraction methanol. If we will operate at a vapor flow rate that is 80 % of flooding, calculate the diameter based on conditions at the bottom of the column. Data are available in Tables 2-7 and 10-3. You may assume the vapors are an ideal gas. Viscosity of water at 100°C is 0.26 cP.
b. Suppose we wanted to use 1-inch plastic Intalox saddles. What diameter is required?
Note: Part b can be done in one line once part a is finished.
D15. Repeat Problem 10.D14a except determine the diameter of a sieve plate column operating at 80% of flooding velocity. Use a 12-inch tray spacing and η = 0.85. The liquid surface tension of pure water is δ = 58.9 dynes/cm at 100°C.
D16. *Repeat Example 10-4, except use 3-inch Intalox saddles.
D17. *Repeat Example 10-4, except calculate the diameter at the bottom of the column.
D18. You have designed a packed column at 1.0 atm. The flow parameter Flv has a value of 0.2. The calculated gas flux at flooding is 0.50 lbm/[(sec)(ft2)]. Your boss now wants to increase the column pressure to 4.0 atm. Assume that the vapor in the column follows the ideal gas law. What is the new gas flux at flooding?
D19. Determine the diameter and height of a packed distillation column separating a feed that is 50.0 mole % n-hexane and 50.0 mole % n-heptane. Feed is a saturated liquid. Column is at 1.0 atmosphere pressure. The distillate is 0.999 mole fraction n-hexane and the bottoms is 0.001 mole fraction n-hexane. Feed rate is 1000.0 lb moles/hr. L/V = 0.8. The column is designed in Examples 10-4 (for 1-inch saddles) and 11-1. You can adapt these results and do not need to resolve the entire problem. The column has a partial reboiler and a total condenser. The column is now packed with 2-inch stainless steel Pall rings, and has an acceptable pressure drop of 0.4 inches of water/foot. Assume HETP = 2 feet.
D20. Do after studying Chapter 12. If the column uses sieve plates, what column diameter is required for the absorber in Problem 12.D14? Operate at 75% of flood. Use a 24-inch tray spacing. Assume η = 0.85. The density of liquid ammonia is approximately 0.61 gm/ml. Assume that nitrogen is an ideal gas. Note that you will have to extrapolate the graph or the equation for 24-inch tray spacing to find Csb. Since surface tension data is not reported, assume that δ = 20 dynes/cm. Watch your units!
E. More Complex Problems
E1. You need a solution to Problem 9.D23 (batch distillation) for this problem. Since many of the calculations in parts a and b are identical, save effort by transferring values back and forth.
a. The batch distillation column in Problem 9.D23 is a 6-inch diameter packed column that is packed with 5/8-inch metal Pall rings. Operate at a vapor flux that is 70% of flooding. Design for conditions at the end of the batch calculated at the bottom of the column. Estimate the viscosity as that of pure water at 100°C (0.26 cP). Find the operating time for the batch distillation with the packed column.
b. The batch distillation column in Problem 9.D23 is a 12-inch diameter sieve tray column that has a 6-inch tray spacing. Operate at an operating vapor velocity that is 70% of the flooding vapor velocity. Design for conditions at the end of the batch calculated at the bottom of the column. Estimate η = 0.85 and δ = 58.5 dynes/cm. Find the operating time for the batch distillation with the tray column. Watch your units.
F. Problems Requiring Other Resources
F1. Calculate the expected overall efficiency for the column in Problem 10.D9. Viscosities are available in Perry’s Chemical Engineers Handbook (7th edition, p. 2-322 and 2-323). Note that O’Connell’s correlation uses the liquid viscosity of the same composition as the feed at the average temperature of the column. Estimation of the viscosity of a mixture is shown in Eq. (10-7).
F2. Estimate the overall plate efficiency for Problem 10.D15. See Problem 10.F1 for hints.
F3. *We are separating an ethanol-water mixture in a column operating at atmospheric pressure with a total condenser and a partial reboiler. Constant molal overflow (CMO) can be assumed, and the reflux is a saturated liquid. The feed rate is 100 lb moles/hr of a 30 mole % ethanol mixture. The feed is a subcooled liquid, and 3 moles of feed will condense 1 mole of vapor at the feed plate. We desire an xD = 0.8, xB = 0.01 and use L/D = 2.0. Use a plate spacing of 18 inches. What diameter is necessary if we will operate at 75% of flooding? How many real stages are required, and how tall is the column?
The downcomers can be assumed to occupy 10% of the column cross-sectional area. Surface tension data are available in Dean (1985) and in the Handbook of Chemistry and Physics. The surface tension may be extrapolated as a linear function of temperature. Liquid densities are given in Perry’s. Vapor densities can be found from the perfect gas law. The overall efficiency can be estimated from the O’Connell correlation. Note that the diameter calculated at different locations in the column will vary. The largest diameter calculated should be used. Thus, you must either calculate a diameter at several locations in the column or justify why a given location will give the largest diameter.
F4. *Repeat Problem 10-F3, except design a packed column using 1-inch metal pall rings. Approximate HETP for ethanol-water is 1.2 feet.