Chapter 11. Economics and Energy Conservation in Distillation

There are an estimated 40,000 distillation columns in the United States, which have a combined capital value in excess of $8 billion. These columns are estimated to have at least a 30-year life, and they are used in more than 95% of all chemical processes. The total energy use of these columns is approximately 3% of total U.S. energy consumption (Humphrey and Keller, 1987). Thus, estimating and, if possible, reducing capital and operating costs of distillation are important.

1. Estimate the capital and operating costs for a distillation column, including the condenser and reboiler costs

2. Predict the effect of the following variables on column capital and operating costs:

a. Feed rate

b. Column pressure

c. External reflux ratio

3. Estimate the effects that energy cost and the general state of the economy have on capital and operating costs

4. Discuss methods for reducing energy in distillation systems; develop flowsheets with appropriate heat exchange

5. Use heuristics to develop alternative cascades for the distillation of almost ideal multicomponent mixtures

6. Use distillation or residue curves to develop a feasible separation scheme for nonideal multicomponent mixtures

Capital costs for an entire plant can be determined by estimating delivered equipment costs and adding on installation, buildings, land, piping, engineering, contingency, and indirect costs. These latter costs are often estimated as a factor times the sum of the delivered equipment cost for major items of equipment.

where the Lang factor ranges from approximately 3.1 to 4.8. The Lang factor for a plant processing only fluids is 4.74 (Turton et al., 2012). Thus, these extra costs greatly increase the capital costs.

Capital costs of entire plants can often be estimated from a power law formula if the cost of a similar plant of different size is known.

Equation (11-2) is known as the six-tenths rule based on the value of the exponent that best fits the data. Plant capacity is measured in units such as metric tons per year. Since the exponent in Eq. (11-2) is less than 1, as size increases, the cost per unit capacity decreases. This will be translated into a lower cost per kilogram of product. This “economy of scale” is the major reason that large plants have been built in the past. However, there are advantages to smaller, more flexible plants that can change when the economy changes.

Individual equipment purchase costs often follow a very similar equation based on equipment size, but the exponent varies widely. Values of the exponent for a variety of equipment types are available in Woods (2007) (see also Table 11.3).

The appropriate size term depends on the type of equipment. For example, for shell and tube heat exchangers such as condensers, the size used is the area of heat exchanger surface. For shell and tube heat exchangers, the exponent has been reported as 0.41 (Seider et al., 2009), 0.48 (Rudd and Watson, 1968), 0.59 (Turton et al., 2012), 0.65 (Luyben, 2013), and 0.71 (Woods, 2007). Thus

As the area becomes larger, the cost per square meter decreases.

The current cost of plants and equipment can be estimated from older data by updating costs with a cost index.

The Chemical Engineering Plant Cost Index (CEPCI) is usually used. Current values are given in most issues of Chemical Engineering magazine. Values for several years’ cost indices are tabulated in Table 11-1. Costs usually increase from year to year due to inflation, except during recessions when costs often drop.

For individual items of equipment that will be installed in an existing plant we use the module costing technique originally developed by Guthrie (1969) to determine the plant installed or bare module cost of the equipment instead of using Lang factors. The cost estimation procedure follows the following steps (Turton et al., 2012):

1. Estimate the purchased cost of equipment for base case conditions, , at some past time. Base conditions are typically carbon steel (c/s) below 350°C at pressures close to ambient.

2. Determine factors for higher or lower pressure, (F_p), for different materials of construction, (F_M), and for quantity (F_q, used for trays and packing).

3. Estimate the bare module cost, C_BM, for each module.

4. Use the CEPCI, Eq. (11-5), and Table 11-1 to update the bare module cost of each module to the present and then add all the bare module costs.

5. Determine the total annual cost (TAC) or the payback period (see Section 11.3).

Step 1. Purchased equipment costs for base case conditions, , have been collected by different authors. Thse results are displayed either as graphs (e.g., Peters et al., 2003; Seider et al., 2009; Turton et al., 2012) or in equation form (e.g., Luyben, 2013; Turton et al., 2012; Woods, 2007). Previous editions of Separation Process Engineering use graphs, which have the advantage of visually displaying trends. The fourth edition switches to presentation of cost data in equation form because this form is easier to use in calculations, particularly spreadsheets, and it is easy to present the cost equations from different authors.

Turton et al. (2012) fit their data to the general empirical form

where S is the size factor. The values for distillation equipment are listed in Table 11-2.

Woods (2007) uses Eq. (11-3) as his basic cost equation. He gives the cost of the item at a reference size, the exponent for Eq (11-3), the range, and the factors for other materials and extras. Values that are useful in distillation design are shown in Table 11-3.

Step 2. Pressure effects on the costs of process vessels and heat exchangers are included through the pressure factor, F_p. The pressure factor for process vessels is (Turton et al., 2012)

which is valid for a vessel wall thickness > 0.0063 m. In this equation p = gauge pressure in barg and Dia = vessel diameter in meters. If F_p < 1, set F_p = 1.0. For vacuum operation use F_p = 1.25 if p < –0.5 barg. Further limitations on the use of this equation are discussed by Turton et al. (2012). The pressure factor for condensers and kettle-type reboilers can be determined from Eq. (11-6) with F_p replacing (Table 11-3).

Since they do not experience a large differential pressure, sieve and valve trays and packing costs do not depend directly on pressure (F_p = 1); however, they depend indirectly on pressure since column diameter depends on pressure. Sieve tray costs depend on the number of trays ordered through the quantity factor, F_q, which can be calculated from Eq. (11-6) (Table 11-3). Woods (2007) lists N > 40 as a minimum for the lowest tray cost but does not give a factor for smaller orders. Packing costs/m³ also depend slightly on the amount of packing, which is inherently included in the cost equation in Table 11-3.

All types of equipment are affected by increased costs due to expensive materials, and the material factors, F_m, for these increased costs in distillation systems are given in Table 11-4 (Turton et al., 2012; Woods, 2007).

Step 3. For heat exchangers and towers used in distillation systems (Turton et al., 2012)

Vertical towers: B₁ = 2.25 and B₂ = 1.82.

Shell-and-tube heat exchangers and kettle reboilers: B₁ = 1.63 and B₂ = 1.66.

For sieve and valve trays the final bare module cost is determined from

where N = number of trays. For packings the final bare module cost is

The use of these equations is illustrated in Example 11-1. The installed cost of structured packing varies greatly. Seider et al. (2009) suggest $250/ft³ as a rough average installed cost for stainless steel, corrugated-sheet structured packing.

Luyben (2013) takes a somewhat different approach and combines the bare module costs of trays and packings into a single equation for distillation systems operating at a pressure below 6.0 bar with carbon steel equipment.

For condensers and reboilers Luyben’s cost equation is

Use Eqs. (11-6) to (11-10) for operation at pressures greater than 6 bar and for equipment requiring more expensive materials than carbon steel.

Although detailed design of condensers and particularly reboilers is specialized (Ludwig, 2001; McCarthy and Smith, 1995) and beyond the scope of this book, an estimate of the heat transfer area is sufficient for preliminary cost estimates. The sizes of the heat exchangers can be estimated from the heat transfer equation

where U = overall heat transfer coefficient, A = heat transfer areas, and ΔT is the temperature difference between the fluid being heated and the fluid being cooled. Cost depends on area, which is directly proportional to |Q| and thus is directly proportional to F.

Because these fluids are flowing countercurrently to each other, the most accurate form of ΔT is the log mean temperature difference ΔT_lm defined as

The smaller value of (T_hot – T_cold) is known as the approach temperature. A minimum approach temperature of 5°C is often used. Applications of Eqs. (11-13) and (11-14) are explained in detail in books on transport phenomena and heat transfer (e.g., Greenkorn and Kessler, 1972; Kern, 1950; Ludwig, 2001). Approximating ΔT_lm with ΔT calculated from the difference between average hot and cold temperatures is usually sufficiently accurate for preliminary cost estimates of reboilers and condensers.

Steam is the preferred heating medium for reboilers except in small isolated systems in which electricity may be used (Jobson, 2014). Since pure fluids condense at a constant temperature, the steam side is at a constant temperature T_hot, and ΔT_lm is approximately

T_hot is the condensing temperature of steam, and T_cold,avg = (1/2)(T_cold,in + T_cold,out). The cold temperature for a pure bottoms product is constant at the boiling temperature. Since ΔT_lm is undefined, if T_hot and T_cold are both constant, use

For multicomponent mixtures in the bottoms the cold temperature varies in the reboiler from the bubble point to the highest temperature. The highest temperature can be obtained from a flash calculation. For total reboilers all material is vaporized, V/F = 1, and the highest temperature is the dew point. For partial reboilers not all material is vaporized, V/F < 1, and T_{highest, partial reboiler} < T_{highest, total reboiler}. Thus, for multicomponent mixtures partial reboilers can use lower steam temperatures and are preferred. The values of the heat transfer coefficient U depend on the fluids being heated and cooled and the condition of the heat exchangers. Tabulated values and methods of calculating U are given in the references, and Table 11-5 lists approximate ranges. With the steam pressure known in the reboiler, the steam temperature can be found from the steam tables; then, with an average U, the area of the reboiler can be found, and reboiler costs can be determined. One subtle point is that steam pressure, and also temperature, in the reboiler is always less than the pressure of the boiler where the steam is produced (Luyben, 2013). Luyben states the typical differential temperature between the hot and cold streams in a reboiler is 34.8 K. This value can be used to check if steam pressure is adequate.

The preferred cooling medium in condensers is water if it is available and is cold enough. Chilled water (∼5°C) and refrigeration (temperatures < 0°C) are used only when absolutely necessary. In areas with water shortages air-cooled condensers may be employed. If a pure distillate product is produced, the condensation (hot) temperature will be constant, and ΔT_lm is approximately

Equation (11-16a) is valid for both partial and total condensers. If the distillate product is a multicomponent mixture, the condensation temperature will decrease as the fraction of distillate condensed increases. With a total condenser the final temperature is the bubble point, and the inlet temperature is the temperature on the top stage. In this case,

For a partial condenser the final condensation temperature T_final can be determined by a flash calculation, T_final > T_bp. In this case T_cold,avg is still given by Eq. (11-16c), and

Partial condensers are used when a vapor product is desired. Compared to total condensers they have the advantages of a lower value of |Q_c| (since less fluid is condensed), which results in a smaller heat exchanger, and the cooling liquid can be at a higher temperature.

If the column pressure is raised, the condensation temperature in the condenser will be higher. This is desirable, since ΔT in Eq. (11-16) is larger, and the required condenser area is less. In addition, higher pressures often allow the designer to cool with water instead of using refrigeration (e.g., Lab 4 in Appendix A of Chapter 6). Cooling with water can result in a large decrease in cooling costs because refrigeration is expensive. With increased column pressure, the boiling point in the reboiler rises. Since this is the cold temperature in Eq. (11-15), the value of ΔT in Eqs. (11-15) is reduced, and the reboiler area will increase. Building a larger reboiler is almost always preferable to using chilled or refrigerated water in the condenser. An alternative solution is to use a higher-pressure steam so that the steam temperature is increased and a larger reboiler is not required. This approach increases operating costs because higher pressure steam is more expensive.

The height of a staged column is

The column diameter is found using the methods in Chapter 10. Equation (10-16) shows that for higher pressures the diameter is somewhat reduced. Conversely, for vacuum operation the diameter is increased. Increases in tray spacing increase C_{sb, flood}, which also increases u_op, and thus, the diameter decreases while the column height increases.

As L/D → ∞ (total reflux), the number of stages approaches a minimum that minimizes the column height, but the diameter goes to infinity. As L/D → (L/D)_min, the number of stages and the height become infinite, while the diameter becomes a minimum. Both these limits have infinite capital costs. Thus, we expect an optimum L/D to minimize capital costs. Column height is independent of feed flow rate, while diameter is proportional to F^1/2 and (1.0 + L/D)^1/2.

Pressure effects on distillation columns are extremely important and were discussed previously in Section 3.3. At first glance Eq. (10-16) shows that the diameter of staged columns is proportional to (1.0/p)^1/2. However, as p increases, T also increases, and u_flood decreases. Thus, the effect is less than (1.0/p)^1/2. Operating at higher pressures reduces the column diameter, although the height usually increases because relative volatility typically decreases as pressure increases. Near atmospheric pressure the effect of pressure on diameter is often significantly larger than its effect on column height. Based on the cost data in Tables 11-2 and 11-3 and in Eq. (11-11) we would expect the base purchased cost of the column to decrease. Typically the pressure factor F_p = 1.0 below approximately 5.0 barg and then rises modestly for pressures below about 20.0 barg. If the column is made of an expensive material (high F_m), cost factors for pressure increases are accelerated since the bare module factor depends on the product of F_p and F_m, Eq. (11-8). Since sieve tray purchase cost decreases as diameter decreases (Table 11-3), we would expect the purchased cost per tray to drop, although a few more trays may be required. Keller (1987) reports on detailed economic analyses and finds that the net result is that bare module costs of distillation columns (shell and trays) generally decrease up to a pressure of approximately 6.8 atm (100.0 psia). The effect of pressure on purchase costs above 6.8 atm needs to be determined on a case-by-case basis. Jobson (2014), on the other hand, concludes that operation at atmospheric pressure is usually most economical.

Results for atmospheric and higher pressures assume that there is no thermal degradation at these pressures. Compounds that degrade must often be processed under vacuum (at lower pressures the boiling points and hence column temperatures are lower) even though the column diameters become larger, making the columns more expensive. If the chemicals being distilled are flammable, special safety precautions must be taken to prevent air from leaking into vacuum columns (Biegler et al., 1997).

The total operating costs per year can be determined as

For most continuous distillation columns, electricity costs are modest, and labor costs are the same regardless of the values of operating variables. The hours of operation per year for continuous plants is typically 8000 (shut down for approximately 1 month for maintenance, repairs, and new construction) or 8760 (operate 24/7 all year).

The amount of cooling water used in the condenser is determined from an energy balance.

where ΔT_w = T_w,hot – T_w,cold. The cooling water cost per year is

This cost is proportional to (1 + L/D)F if cost per kilogram is constant. The following rules of thumb can be useful in determining the amount of water required:

Assume T_{w, cold} = 90°F and T_{w, hot} = 120°F (Seider et al., 2009).

A water condenser can easily cool to 100°F (O’Brien and Schultz, 2004).

The typical difference between hot and cold temperatures in a condenser is 13.9 K (Luyben, 2013).

In the reboiler the steam is usually condensed from a saturated or superheated vapor to a saturated liquid. Then the steam rate is

In most applications, H_steam = H_{saturated vapor}, and

where λ is the latent heat of vaporization of water at the operating pressure. The steam rate is proportional to F and increases linearly with (1.0 + L/D). The value of λ can be determined from the steam tables. Then the steam cost per year is

At higher pressures, λ decreases, and the cost/kg steam increases. Thus, higher pressures have a modest increase in steam cost.

Costs for utilities may be stated as $/GJ (G = giga, which is 10⁹). In this case,

Because Q_c and Q_R are proportional to feed rate F, doubling F doubles cooling water and steam rates. Q_c is also proportional to (1.0 + L/D). Q_R is linearly dependent on (1.0 + L/D) but is not proportional to (1.0 + L/D).

The total operating cost per year is given in Eq. (11-18). The qualitative effects of various variables on the operating cost are summarized in Table 11-6. The value of the total operating cost per year can be estimated once steam and cooling water or refrigeration costs are known. However, to calculate these costs, we need prices. Determining prices can be difficult since they depend on geographic location and the circumstances of the particular plant. For example, in a highly integrated plant steam is reused at progressively lower pressures until it is condensed at low pressure and then sent back to the high-pressure boiler. (The steam is condensed since it is much cheaper to pump a liquid to a high pressure than compress a gas.) If a distillation column can use this low-pressure steam, the cost in $/GJ may be quite low, zero, or even negative (Smith and Varbanov, 2005). A widely accepted approach is to prepare cost estimates for scenarios with different energy prices. Table 11-7 lists reasonable starting points for energy costs for calculating operating costs.

Energy costs vary over time, but for a given production rate operating costs are usually pretty well known for the short term. Although capital costs are more uncertain than energy costs, we can estimate these costs using the procedures discussed in Section 11.1. The individual equipment costs depend on the condenser area, reboiler area, tower size, and tray diameter. Some of the variable effects on the capital costs are complex. These influences are outlined in Table 11-8.

The total cost per year requires a summation of capital cost per year with the operating cost per year. Since the method used to determine TAC can have a major impact on investment decisions, reported profit, and taxes; a large number of methods have been developed. We use a simple method for determining the TAC based on the desired payback period, which is the number of years required to recover the investment.

A 3-year payback period is fairly common, although payback periods can be varied as desired.

The net results of increasing the external reflux ratio, L/D, of a distillation column on operating cost/year, capital cost/year, and TAC are shown in Figure 11-1; all yearly costs go through minima, and there is an optimum reflux ratio. As operating costs increase (increased energy costs), the optimum shifts closer to the minimum reflux ratio. As capital cost increases due to special materials or very high pressures, the total cost optimum shifts toward the capital cost optimum. The optimum L/D is usually in the range from 1.05(L/D)_min to 1.25(L/D)_min. Since the cost increases quite slowly for reflux ratios above the optimum value, distillation columns are often designed to operate somewhat above the optimum reflux ratio. This conservative design procedure helps ensure the column will operate despite inaccuracies in equilibrium or efficiency data.

The column pressure has complex effects on costs. If two pressures both above 1.0 atm but less than about 6.8 atm are compared and cooling water can be used for both pressures, then total costs can be either higher or lower for the higher pressure. The effect depends on whether tower costs or tray costs dominate. If refrigeration is required for cooling at the lower pressure and cooling water can be used at the higher pressure, then the operating costs and the total costs will almost always be less at the higher pressure (see Tables 11-6 and 11-8).

The effects of other variables are somewhat simpler than the effect of L/D or pressure. For example, when the design feed rate increases, all costs go up; however, the capital cost per kilogram of feed drops. Thus, total costs per kilogram can be significantly cheaper in large plants than in small plants. The effects of other variables are also summarized in Tables 11-6 and 11-8. A useful rule of thumb is the annual operating cost of a distillation system is half operating costs and half capital costs (Keller, 1987).

The kg steam/h, kg water/h, and kW electricity/h are all directly proportional to F. Thus, except for labor costs, the operating cost per kilogram will be constant regardless of the feed rate. Since labor costs are often a small fraction of total costs in automated continuous chemical plants, we can treat the operating cost per kilogram as constant.

Capital cost per kilogram depends on the total amount of feed processed per year. If we calculate the total capital cost of the plant from Eq. (11-1) and introduce

Operation at half the designed feed rate doubles the capital cost per kilogram.

The total cost per kilogram is

The effect of reduced feed rates depends on what percent of the total cost is due to capital and administrative costs.

If the cost per kilogram for the entire plant is greater than the selling price, the plant will lose money. However, if the selling cost is greater than the operating cost plus administrative costs, then the plant is still helping to pay off the capital costs. Since the capital charges are present even if F = 0, it is usually better to keep operating (Seider et al., 2009). Of course, a new plant would not be built under these circumstances.

What can be done to reduce energy consumption in an existing, operating plant? Since the equipment already exists, there is an incentive to make rather modest, inexpensive changes. Retrofits like this are a favorite assignment to give new engineers, since they serve to familiarize the new engineer with the plant, and failure is not critical. The first thing to do is to challenge the operating conditions (Geyer and Kline, 1976). If energy can be saved by changing the operating conditions, the change may not require any capital. When the feed rate to the column changes, is the column still operating at vapor rates that are near those for optimum efficiency? If not, explore the possibility of varying the column pressure to change the vapor flow rate and thus, operate closer to the optimum. This will allow the column to have the equivalent of more equilibrium contacts and allow the operator to reduce the reflux ratio. Reducing the reflux ratio saves energy in the system. Challenge the specifications for the distillate and bottoms products. When products are very pure, rather small changes in product purities can mean significant changes in the reflux ratio. If a product of intermediate composition is required, side withdrawals require less energy than mixing top and bottom products (Allen and Shonnard, 2002).

Second, look at modifications that require small capital investments. Improving the controls and instrumentation can increase the efficiency of the system (Geyer and Kline, 1976; Luyben, 2014; Mix et al., 1978; Shinskey, 1984). Better control allows the operator to operate much closer to the required specifications, which means a lower reflux ratio. Payback on this investment can be as short as 6 months. Distillation column control is an extremely important topic that is beyond the scope of this textbook. Rose (1985) provides a qualitative description of distillation control systems, Shinskey (1984) is more detailed, and Luyben (2014) summarizes important aspects for different distillation situations. Columns with damaged insulation should have the insulation removed and replaced, and damaged trays or packing should be replaced with high-efficiency/high-capacity trays or packing (Kenney, 1988).

If the column has relatively inefficient trays (e.g., bubble caps) or packing (e.g., Raschig rings), putting in new, highly efficient trays (e.g., valve trays) or new high-efficiency packing (e.g., modern rings, saddles, or structured packing) will usually pay off even though it is fairly expensive (Kenney, 1988). Heat exchange and integration of columns may be far from optimum in existing distillation systems. An upgrade of these facilities should be considered to determine whether it is economical.

When designing new facilities, energy conservation approaches can be used that might not be economical in retrofits. Heat exchange between streams and integration of processes should be used extensively to minimize overall energy requirements. These methods have been known for many years (e.g., see Robinson and Gilliland, 1950, or Rudd and Watson, 1968), but they were not economical when energy costs were very low. When energy costs shot up in the 1970s and early 1980s and again after 2004, many energy conservation techniques suddenly became very economical (Doherty and Malone, 2001; Geyer and Kline, 1976; King, 1981; Mix et al., 1978; Seider et al., 2009; Shah and Agrawal, 2014; Shinskey, 1984; and Siirola, 1996). Current concerns over global warming, the existing or pending carbon dioxide cap, and trading legislation in many parts of the world make energy reduction in distillation columns even more important.

The basic idea of heat exchange is to use hot streams that need to be cooled to heat cold streams that need to be heated. The optimum way to do this depends on the configuration of the entire plant, since streams from outside the distillation system can be exchanged. The goal is to use exothermic reactions to supply all or at least as much as possible of the heat energy requirements in the plant. Pinch technology has been developed that allows analysis of optimum heat exchange for very complicated plants (Seider et al., 2009). If only the distillation system is considered, the basic heat exchange procedure is illustrated in Figure 11-2. The cold feed is preheated by heat exchange with the hot distillate; this partially or totally condenses the distillate. The trim condenser is used for any additional cooling that is needed and for improved control of the system. The feed is then further heated with the sensible heat from the bottoms product. The heat exchange is done in this order since the bottoms is hotter than the distillate. Further heating of the feed is done in a trim heater to help control the distillation. The system shown in Figure 11-2 may not be optimum, though, particularly if several columns are integrated.

A technique similar to that of Figure 11-2 is to produce steam in the condenser. If there is a use for this low-pressure steam elsewhere in the plant, this can be a very economical use of the energy available in the overhead vapors. Intermediate condensers (Sections 4.9.4 and 10.4) have hotter vapor that can also be used to produce steam.

Heat exchange integration of columns is an important concept for reducing energy use (Biegler et al., 1997; Doherty and Malone, 2001; King, 1981; Robinson and Gilliland, 1950; Seider et al., 2009; Shah and Agrawal, 2014). The basic idea (Figure 11-3) is to condense the overhead vapor from one column in the reboiler of a second column. (In practice, heat exchanges such as those in Figure 11-2 will also be used, but they have been left off Figure 11-3 to keep the figure simple.) Obviously, the condensation temperature of stream D₁ must be higher than the boiling temperature of stream B₂. When distillation is used for two rather different separations, the system shown in Figure 11-3 can be used without modification. However, in many cases stream D₁ is the feed to the second column, or B₂ is the feed to column 1 as shown in Figure 11-4. The system shown in Figure 11-3 will work if column 1 is at a higher pressure than column 2 so that stream D₁ condenses at a higher temperature than the boiling point of stream B₂.

Many variations of the basic idea shown in Figure 11-3 have been developed. If a solvent is recovered from considerably heavier impurities, some variant of the multieffect system shown in Figure 11-4 is useful (Agrawal, 2000; Doherty and Malone, 2001; King, 1981; Robinson and Gilliland, 1950; Shah and Agrawal, 2014; Siirola, 1996). After preheating, the solvent is first recovered as the distillate product in the low-pressure column. By selecting a pressure that raises the condensation temperature of the overheads from the high-pressure column to be greater than the boiling temperature in the reboiler of the low-pressure column, the low-pressure reboiler and the high-pressure condenser can be combined as a single unit. Thus, the steam used in the reboiler of the high-pressure column serves to heat both columns, which almost doubles steam efficiency. Since separation is easy, not many stages are required, and both distillate products are essentially pure solvent. Multieffect systems can also have feed to the high-pressure column in addition to or instead of feed to the low-pressure column. Liquefied oxygen and nitrogen from air are produced on very large scales in Linde double columns, which are multieffect distillation columns. Multieffect distillation is closely related to multieffect evaporation.

A vapor recompression heat pump (Figure 11-5) allows use of condensing overhead vapor to heat the reboiler of the same column (Humphrey and Keller, 1997; King, 1981; Robinson and Gilliland, 1950; Shah and Agrawal, 2014; Shenvi et al., 2011). The overhead vapors are compressed to a pressure at which they condense at a higher temperature than the bottoms boiling point. Vapor recompression works best for close-boiling distillations, since modest pressure increases are required. If the heat pump is employed with an intermediate reboiler and/or an intermediate condenser, the temperature and hence pressure differences can be kept modest for even wide-boiling distillations (Shenvi et al., 2011). Heat pumps are used when the column is an isolated installation or is operating at temperature extremes. O’Brien and Schultz (2004) report heat pumps are used for the difficult propane-propylene separation.

In how many ways can columns be coupled for multicomponent distillation? Lots! For example, Figure 11-6 illustrates ten ways in which columns can be coupled for a ternary system that does not form azeotropes. With more components the number of possibilities increases geometrically. Figure 11-6A shows the normal sequence, in which the more volatile components are removed in the distillate one at a time. This is probably the most commonly used sequence, particularly in older plants. Scheme B shows an inverted sequence, in which products are removed in the bottoms one at a time. With more components a wide variety of combinations of these two schemes are possible. The scheme in Figure 11-6C is similar to scheme A except that the reboiler has been removed, and a return vapor stream from the second column supplies boilup to the first column. Capital costs will be reduced, but the columns are coupled, which will make control and startup more difficult. Scheme D is similar to B except that a return liquid stream supplies reflux.

The scheme in Figure 11-6E uses a side enricher, while scheme F uses a side stripper to purify the intermediate component B. The stream is withdrawn at the location where component B has a concentration maximum. Side strippers and enrichers are often used in petroleum refineries.

Figure 11-6G illustrates a thermally coupled system (sometimes called Petyluk columns). The first column separates A from C, which is the easiest separation, and the second column then produces three pure products. The system will have relatively low energy requirements when the separation is symmetric, but it is not always the lowest energy system (Shah and Agrawal, 2014). In addition, thermally coupled systems are more difficult to start up and control than a sequence of separate columns. Thermally coupled systems may also require an excessive number of stages if either the A-B or B-C separations are difficult.

Sometimes thermally coupled approaches are practiced in a single, divided-wall column, as shown in Figure 11-6H (Jobson, 2014; Schultz et al., 2002). This four-section column has a vertical wall between two parts of the column in the middle two sections. The feed enters on the left side of the wall, and the two sections on the left side of the wall do the same separation done by the first column in Figure 11-9G. At the top of the wall a mixture of A and B would spill over the wall and go into the rectifying and top intermediate sections. At the bottom of the wall a mixture of B and C would flow under the wall and into the stripping and bottom intermediate sections. Thus, the two intermediate sections on the right side of the wall do the separation done in the middle two sections of the second column in Figure 11-6G. Compared to Figure 11-6G, divided-wall columns have been reported to have savings up to 30% for energy costs and 25% for capital costs (O’Brien and Schultz, 2004). Note that this arrangement appears to be somewhat sensitive to upsets, and control of the vapor split inside the column can be difficult. Despite these difficulties divided-wall columns are used in industry for specialty chemicals, petroleum products, and other applications (Jobson, 2014). Divided-wall columns can also be used for four-component separations (called a Kaibel column) and extractive distillation.

The schemes in Figure 11-6I and J are quite different from the others, since a single column with a sidestream is used (Tedder and Rudd, 1978). The sidestream cannot be completely pure B, although it may be pure enough to meet the product specifications. This or closely related schemes are most likely to be useful when the concentration of C (for 11-6I) or A (for 11-6J) in the feed is quite low. Then at the point of peak B concentration there will not be much C (or A) present. Methods using sidestreams to connect columns (Doherty and Malone, 2001) and for four-component separations (Kim and Wankat, 2004) can also be used.

These sequences are only the start of what can be done. For example, the heat exchange and energy integration schemes discussed in the previous section can be interwoven with the separation scheme. Agrawal (2000) shows multieffect distillation cascades (Figure 11-4) adapted for ternary separations. These schemes are currently the most economical methods to produce oxygen, nitrogen, and argon from air by cryogenic distillation. Obviously, the system becomes quite complex.

The number of possible schemes increases dramatically as the number of components increases (Shah and Agrawal, 2014). For a quaternary separation with no azeotropes in regular columns (not including divided-wall columns shown in Figure 11-6H) they determined that there are 5 sharp and 13 nonsharp configurations without thermal coupling, 116 partially thermally coupled, and 18 completely thermally coupled configurations for a total of 152 configurations. With 5 components the number of regular column configurations increases to 6128, with 6 components to 506,912, with 7 components to 85,216,192, and with 8 components to 29,022,693,888.

Which method is the best to use depends on the separation problem. The ease of the various separations, the required purities, and the feed concentrations all are important in determining the optimum configuration. The optimum configuration may also depend on how best is defined. The engineer in charge of operating the plant may prefer the uncoupled systems, while the engineer charged with minimizing energy consumption may prefer the coupled and integrated systems. The only way to be assured of finding the best method is to model all the systems and try them. Although modeling all systems is difficult to do, Shah and Agrawal (2014) have been successful with a sequential optimization approach for up to five components and believe six is possible. Shortcut methods are often used for the calculations to save computer time and money. Unfortunately, the result may not be optimum. Many studies have ignored some of the arrangements shown in Figure 11-6; thus, they may not have come up with the optimum scheme. Conditions are always changing, and a distillation cascade may become nonoptimum because of changes in plant operating conditions such as feed rates and feed or product concentrations. Changes in economics such as energy costs or interest rates may also alter the optimality of the system. Sometimes it is best to build a nonoptimum system because it is more versatile.

An alternative approach to design is to use heuristics, which are rules of thumb used to exclude many possible systems. The heuristic approach may not result in the optimum separation scheme, but it usually produces a scheme that is reasonably close to optimum. Heuristics have been developed by doing a large number of simulations and then looking for ideas that connect the best schemes. Some of the most common heuristics listed in approximately the order of importance (Biegler et al., 1997; Doherty and Malone, 2001; King, 1981) include:

1. Remove dangerous, corrosive, and reactive components first.

2. Do not use distillation if α_LK-HK < α_min, where α_min ∼ 1.05 to 1.10.

3. Remove components requiring very high or very low temperatures or pressures first.

4. Do the easy splits (large α) first.

5. The next split should remove components in excess.

6. The next split should remove the most volatile component.

7. Do the most difficult separations as binary separations.

8. Favor 50:50 splits.

9. If possible, final product withdrawals should be as distillate products.

Two additional heuristics not listed in order of importance that can be used to force the designer to look at additional sequences are:

10. Consider sidestream withdrawals for sloppy separations.

11. Consider thermally coupled and multieffect columns, particularly if energy is expensive.

There are rational reasons for each of the heuristics. Heuristic 1 minimizes safety concerns, removes unstable compounds, and reduces the need for expensive materials of construction in later columns. Heuristic 2 eliminates the need for excessively tall columns. Since very high and very low temperatures and pressures require expensive columns or operating conditions, heuristic 3 keeps costs down. Since the easiest split requires a shorter column and low reflux ratios, heuristic 4 says to do this when there are a number of components present and feed rates are large. The next heuristic suggests reducing feed rates as quickly as possible. Removing the most volatile component (heuristic 6) removes difficult to condense materials, probably allowing for reductions in column pressures. Heuristic 7 forces the lowest feed rate and hence the smallest diameter for the large column required for the most difficult separation. Heuristic 8 balances columns so that flow rates do not change drastically. Since thermal degradation products are usually relatively nonvolatile, heuristic 9 is likely to result in purer products. The purpose of heuristics 10 and 11 is to force the designer to think outside the usual box and look at schemes that are known to be effective in certain cases.

Each heuristic should be preceded with the words All other things being equal. Unfortunately, all other things usually are not equal, and the heuristics often conflict with each other. For example, the most concentrated component may not be the most volatile. When there are conflicts between the heuristics, the cascade schemes suggested by both of the conflicting heuristics should be generated and then compared with more exact calculations.

Operational Suggestions: General Overview

1. Obtain reliable equilibrium data and/or correlations for the system.

2. Develop residue curves or distillation curves for the system.

3. Classify the system as A) almost ideal; B) nonideal without azeotropes; C) one homogeneous binary azeotrope without a distillation boundary; D) one homogeneous binary azeotrope with a distillation boundary; E) two or more homogeneous binary azeotropes with possibly a ternary azeotrope; or F) heterogeneous azeotrope, which may include several binary and ternary azeotropes. Although solutions for cases D to F are beyond the scope of this introductory treatment, they are discussed briefly.

4. Generate variants including selection of solvents.

5. Screen variants with residue and distillation curves for feasibility.

6. Cautiously use shortcut calculation methods with assumptions such as CMO, constant relative volatilities, minimum reflux (Underwood equations), and general pinch calculations (Köhler et al., 1995) to further screen variants. Caution is required because highly nonideal systems often do not satisfy the assumptions.

7. Do rigorous simulation and economic optimization either by trial and error or with a computerized optimization scheme (Caballero and Grossmann, 2014).

Operational Suggestions: Case by Case

A. Almost ideal. If the system is reasonably close to ideal (Figure 8-7), rejoice and use the heuristics in Section 11.5.

B. Nonideal systems without azeotropes. These systems are often similar to ideal, and a variety of column sequences will probably work. However, it may be easier to do the most difficult separation with a non-key present instead of the binary separation recommended for ideal mixtures. Doherty and Malone (2001) present a detailed example for the acetaldehyde-methanol-water system.

1. Generate the y-x curves for each binary pair. If all separations are relatively easy (reasonable relative volatilities and no inflection points causing tangent pinches for one of the pure components) use the ideal heuristics in Section 11.5.

2. If one of the binary pairs has a small relative volatility or a tangent pinch, determine if this separation is easier in the presence of the third component. This can be done by generating distillation curves or y-x binary equilibrium at different constant concentrations of the third component. If the presence of the third component aids the separation, separate the difficult pair first. The concentration of the third component can be adjusted by recycling it from the column in which it is purified. This approach can be designed as extractive distillation using the third component as solvent for separation of close boiling components (Section 8.6).

C. One homogeneous binary azeotrope, without a distillation boundary. The residue curve maps look like Figure 8-11A or 8-11C.

1. If the binary azeotrope is between the light and intermediate components (Figure 8-11C), the situation is very similar to using extractive distillation to separate a binary azeotrope, and the heavy component can be used as solvent. In general, the flowsheet is similar to Figure 8-13 except the heavy component product is withdrawn where the makeup solvent is added. If there is sufficient heavy component in the feed, a heavy recycle may not be required. The residue curve map will be similar to the extractive distillation residue map, Figure 8-14, but since the feed contains all three components, point F will be inside the triangle.

2. If the binary azeotrope is between the heavy and light components (Figure 8-11A), a separation can be obtained with an intermediate recycle as shown in Figures 11-7A and 11-7B. If there is sufficient intermediate component in the feed, the intermediate recycle may not be required. Separation using the flowchart in Figure 11-7A is illustrated in Example 11-3.

D. One homogeneous binary azeotrope with distillation boundary. There can be either a maximum-boiling azeotrope (Figure 8-8) or a minimum-boiling azeotrope (Figure 8-11B).

1. If the distillation boundary is straight, complete separation of the ternary feed is not possible without addition of a mass-separating agent (Doherty and Malone, 2001).

2. If the distillation boundary is curved, complete separation of the ternary feed may be possible. Distillation boundaries can often be crossed by mixing a feed with a recycle stream. An example of the synthesis of feasible flowsheets is given by Biegler et al. (1997) for the system in Figure 8-8. Detailed solution of this case and the remaining two cases is beyond the scope of this section.

E. Two or more homogeneous binary azeotropes, with possibly a ternary azeotrope. These systems are messy, and there are invariably one or more distillation boundaries. If there is a single curved distillation boundary, it may be possible to develop a scheme to separate the mixture without addition of a mass-separating agent. If there are only two binary azeotropes and no ternary azeotropes, look for a separation method (e.g., extraction) that will remove the component that occurs in both azeotropes.

F. Heterogeneous azeotrope, which may include several binary and ternary azeotropes (Biegler et al., 1997; Doherty and Malone, 2001; Skiborowski et al., 2014). An example is shown in Figure 8-12 for an azeotropic distillation scheme. The residue curve map developed by a process simulator probably will not show the envelope of the two-phase region, and this region will have to be added. Since liquid-liquid separators can cross distillation boundaries, there is a good chance that a separation can be achieved without adding an additional mass-separating agent. Distillation boundaries can be crossed by mixing, decanting, and reaction. If possible, use components already in the feed as an extractive distillation solvent or entrainer for azeotropic distillation. Also explore using components in the feed as extraction solvents. Biegler et al. (1997) discuss a process example.

Allen, D. T., and D. R. Shonnard, Green Engineering: Environmentally Conscious Design of Chemical Processes, Prentice Hall, Upper Saddle River, NJ, 2002.

Biegler, L. T., I. E. Grossmann, and A. W. Westerberg, Systematic Methods of Chemical Process Design, Prentice Hall, Upper Saddle River, NJ, 1997.

Caballero, J. A., and I. E. Grossmann, “Optimization of Distillation Processes,” in A. Gorak and E. Sorenson (Eds.), Distillation: Fundamentals and Principles, Chapter 11, Elsevier, London, UK, 2014.

Doherty, M. F., and M. F. Malone, Conceptual Design of Distillation Systems, McGraw-Hill, New York, 2001.

Doherty, M. F., Z. T. Fidkowski, M. F. Malone, and R. Taylor. “Distillation,” in D. W. Green and R. H. Perry (Eds.), Perry’s Chemical Engineer’s Handbook, 8th ed., McGraw-Hill, New York, Section 13 (2008).

Geyer, G. R., and P. E. Kline, “Energy Conservation Schemes for Distillation Processes,” Chem. Eng. Progress, 72 (5), 49 (May 1976).

Green, D. H, and R. H. Perry (Eds.), Perry’s Chemical Engineers’ Handbook, 8th ed., McGraw-Hill, New York, 2008.

Greenkorn, R. A., and D. P. Kessler, Transfer Operations, McGraw-Hill, New York, 1972.

Guthrie, K. M., “Capital Cost Estimating,” Chemical Engineering, 76 (3), 114 (March 1969).

Humphrey, J. L., and G. E. Keller II, Separation Process Technology, McGraw-Hill, New York, 1997.

Jobson, M., “Energy Considerations in Distillation,” in A. Gorak and E. Sorenson (Eds.), Distillation: Fundamentals and Principles, Chapter 6, Elsevier, London, UK, 2014.

Keller, II, G. E., Separations: New Directions for an Old Field, AIChE Monograph Series, 83 (17) 1987.

Kenney, W. F., “Strategies for Conserving Energy,” Chem. Eng. Progress, 84 (3), 43 (March 1988).

Kern, D. Q., Process Heat Transfer, McGraw-Hill, New York, 1950.

Kim, J. K., and P. C. Wankat, “Quaternary Distillation Systems with Less than N – 1 Columns,” Ind. Eng. Chem. Res., 43, 3838 (2004).

King, C. J., Separation Processes, 2nd ed., McGraw-Hill, New York, 1981.

Köhler, J., P. Pöllmann, and E. Blass, “A Review on Minimum Energy Calculations for Ideal and Nonideal Distillations,” Ind. Eng. Chem. Res. 34, 1003 (1995).

Ludwig, E. E., Applied Process Design, 3rd ed., Vol. 3, Gulf Pub Co., Boston, 2001.

Luyben, W., Distillation Design and Control Using Aspen™ Simulation, Wiley, New York, 2013.

Luyben, W., “Distillation Control,” in A. Gorak and H. Schoenmakers, Distillation: Operation and Applications, Chapter 1, Elsevier, London, UK, 2014.

McCarthy, A. J., and B. R. Smith, “Reboiler System Design: The Tricks of the Trade,” Chem. Eng. Progress, 91 (5), 34 (May 1995).

Mix, T. J., J. S. Dweck, M. Weinberg, and R. C. Armstrong, “Energy Conservation in Distillation,” Chem. Eng. Progress, 74 (4), 49 (April 1978).

O’Brien, D., and M. A. Schultz, “Ask the Experts: Distillation,” Chem. Eng. Progress, 100 (2), 14 (February 2004).

Peters, M. S., K. D. Timmerhaus, and R. E. West, Plant Design and Economics for Chemical Engineers, 5th ed., McGraw-Hill, New York, 2003.

Robinson, C. S., and E. R. Gilliland, Elements of Fractional Distillation, McGraw-Hill, New York, 1950.

Rose, L. M., Distillation Design in Practice, Elsevier, Amsterdam, 1985.

Rudd, D. F., F. J. Powers, and J. J. Siirola, Process Synthesis, Prentice Hall, Upper Saddle River, NJ, 1973.

Rudd, D. F., and C. C. Watson, Strategy of Process Engineering, Wiley, New York, 1968.

Schultz, M. A., D. G. Stewart, J. M. Harris, S. P. Rosenblum, M. S. Shakur, and D. E. O’Brien, “Reduce Costs with Dividing-Wall Columns,” Chem. Eng. Progress, 98 (5), 64 (May 2002).

Seider, W. D., J. D. Seader, D. R. Lewin, and S. Widagdo, Design Process Principles, 3rd ed., Wiley, New York, 2009.

Shah, V. H., and R. Agrawal, “Conceptual Design of Zeotropic Distillation Processes,” in A. Gorak and E. Sorenson (Eds.), Distillation: Fundamentals and Principles, Chapter 7, Elsevier, London, UK, 2014.

Shenvi, A. A., D. M. Herron, and R. Agrawal, “Energy Efficiency Limitations of the Conventional Heat Integrated Distillation Column (HIDiC) Configuration for Binary Distillation,” Ind. Eng. Chem. Res., 50, 119 (2011).

Shinskey, F. G., Distillation Control: For Productivity and Energy Conservation, 2nd ed., McGraw-Hill, New York, 1984.

Siirola, J. J., “Industrial Applications of Chemical Process Synthesis,” Adv. Chem. Engng., 23, 1–62 (1996).

Skiborowski, M., A. Harwardt, and W. Marquardt, “Conceptual Design of Azeotropic Distillation Processes,” in A. Gorak and E. Sorenson (Eds.), Distillation: Fundamentals and Principles, Chapter 8, Elsevier, London, UK, 2014.

Smith, R., and P. Varbanov, “What’s the price of steam?” Chem. Engr. Prog., 29–33 (July 2005).

Tedder, D. W., and D. F. Rudd, “Parametric Studies in Industrial Distillation: Part 1. Design Comparisons,” AIChE J., 24, 303 (1978).

Turton, R., R. C. Bailie, W. B. Whiting, and J. A. Shaeiwitz, Analysis, Synthesis, and Design of Chemical Processes, 4th ed., Prentice Hall, Upper Saddle River, NJ, 2012.

Woods, D. R., Rules of Thumb in Engineering Practice, Wiley-VCH, New York, 2007.

A1. If valve trays cost more than sieve trays, why are valve trays often advertised as a way of decreasing tower costs?

A2. Develop your key relations chart for this chapter.

A3. What is the effect of increasing the feed temperature if L/D = 1.15(L/D)_min? Note that (L/D)_min will change as feed temperature changes. Include effects on Q_R and the number of stages. Use a McCabe-Thiele diagram.

A4. Optimums usually occur because there are two major competing effects. For the optimum L/D these two major effects for capital cost are (select two answers):

a. The number of stages is infinite as L/D goes to infinity and has a minimum value at (L/D)_min.

b. The number of stages is infinite at (L/D)_min and approaches a minimum value as L/D goes to infinity.

c. The column diameter becomes infinite at (L/D)_min and approaches a minimum value as L/D approaches infinity.

d. The column diameter becomes infinite as L/D approaches infinity and has a minimum value at (L/D)_min.

A5. How does the general state of the economy affect:

a. Design of new plants?

b. Operation of existing plants?

A6. Ethanol, i-propanol, and n-propanol are separated in a distillation column with a sidestream. Relative volatilities can be assumed to be constant: α_E-nP = 2.17, α_iP-nP = 1.86, α_nP-nP = 1.0. We want to recover ethanol in distillate, n-propanol in bottoms, and as pure a sidestream of i-propanol as possible. The feed has equal amounts of ethanol and n-propanol. To obtain maximum sidestream purity, the best location and type of sidestream is:

a. A vapor sidestream between the feed and the distillate.

b. A liquid sidestream between the feed and the distillate.

c. A vapor sidestream between the feed and the bottoms.

d. A liquid sidestream between the feed and the bottoms.

Explain your answer.

A7. Why is the dependence on size usually less than linear—in other words, why is the exponent in Eq. (11-3) usually less than 1?

A8. It is common to design columns at reflux ratios slightly above (L/D)_opt. Use a curve of total cost/yr vs. L/D to explain why there is not a large cost penalty if L/D > (L/D)_opt is used.

A9. Discuss the concept of economies of scale. What happens to economies of scale if the feed rate is half the design value?

A10. Sketch a divided-wall column for separation of a four-component mixture.

A11. Referring to Figure 11-3 if D1 is the feed to column 2, explain what conditions are necessary for this system to work.

A12. Sometimes a list of what not to do is as valuable as a list of what to do. For separation of a close to ideal system by distillation, develop a list of heuristics of what not to do.

A13. To estimate future values of the cost indices, one is tempted to assume that the average value for the year occurred at midyear (June 30–July 1) and that the linear fit to the recent data can be extrapolated past the last data point. Based on Table 11-1, for which years would this procedure work fairly well, and for which years will it fail?

A14. The use of components in the feed as solvents for extractive or azeotropic distillation or extraction is recommended even if they are not the best solvents for stand-alone separations. Explain the reasoning behind this recommendation.

A15. Residue and distillation curves have similar shapes but are not identical. Even though the residue curves might be misleading in some cases, they are still useful for screening possible distillation separations. Explain why.

A16. Preheating the feed often increases the number of stages required for the separation (F, z, x_D, x_B, L/D constant). Use a McCabe-Thiele diagram to explain why this happens.

A17. Draw the entirely thermally coupled system (an extension of Figure 11-6G) for Example 11-2.

B. Generation of Alternatives

B1. Sketch possible column arrangements for separation of a four-component system. Do not include sidestream products. Note that there are a large number of possibilities.

B2. We wish to generate additional arrangements for quaternary mixtures (see Problem 11.B1). Sketch possible arrangements that use one or two columns that have sidestreams for one or both of the intermediate component product streams.

B3. Multieffect distillation or column integration can be done with more than two columns. Use the basic ideas in Figures 11-2 and 11-3 to sketch as many ways of thermally connecting three columns as you can.

B4. Separate a feed that is 10.0 mol% benzene, 55.0 mol% toluene, 10.0 mol% xylene, and 25.0 mol% cumene. Use heuristics to generate desirable alternatives. Average relative volatilities are α_BT = 2.5, α_TT = 1.0, α_XT = 0.33, α_CT = 0.21. 98.0% purity of all products is required.

B5. Repeat Problem 11.B4 for an 80.0% purity of the xylene product.

C. Derivations

C1. Show that Eq. (11-1) will plot as a straight line on log-log paper, and show that the exponent can be determined from a slope.

C2. If packing costs are directly proportional to the volume of packing, show that packing costs go through a minimum as L/D increases.

C3. What restrictions on the values of K₁, K₂, and K₃ are necessary for Eq. (11-6) to follow the power law formula of Eq. (11-3)?

D. Problems

*Answers to problems with an asterisk are at the back of the book.

D1.* Repeat Example 11-1 except at 700.0 kPa. F = 1000.0 lb mol/h, L/D = 4.0, distillate is 99.9 mol% n-hexane and bottoms is 0.1 mol% n-hexane. At this pressure E_o = 0.73, D = 9.0 ft. Relative volatility depends on pressure (determined in Problem 10.D1).

a. Find (L/D)_min.

b. Find N_min.

c. Estimate N_equil.

d. Estimate N_actual.

e. Find cost of shells and trays using the bare module cost calculation procedure and the data in Table 11-2. Update costs to 2014.

f. Update cost of shells and trays to current date.

D2.* Estimate the 2014 cost of the condenser and the reboiler (shell and tube, floating head) for Problem 11.D1. Steam is available at 41.0 barg, but due to pressure losses the steam is at 230.0°C when it enters the reboiler. Cooling water is available at 30.0°C and is returned to the cooling tower at 45.0°C. Latent heat of n-hexane and n-heptane can be estimated from (Perry and Green, 2008, 2-152):

λ_C6 (kJ/kmol) = 45,440 (1 – T/T_c)^0.39002, T in K, T_c = critical temp. = 507.6 K,

λ_C7 (kJ/kmol) = 50,014 (1 – T/T_c)^0.38795, T in K, T_c = critical temp. = 540.2 K, and boiling points can be estimated from the DePriester charts.

D3. Determine steam and water operating costs per year and TAC for the distillation system described in Problems 11.D1 and 11.D2. Cost of steam is $9.88/GJ, and cost of cooling water is $0.34/GJ. Use 8000.0 h/year. Payout period is 3 years, and costs are based on 2014 costs. What fraction of the TAC is due to energy costs?

D4. Calculate steam and water operating costs per year for Example 11-1. Cost of steam is $7.78/GJ, and cost of cooling water is $0.34/GJ. Use 8000.0 h/yr. Calculate the TAC for Example 11-1. Payout period is 3 years, and costs are based on 2014 costs. What fraction of the TAC is due to energy costs?

D5.* Calculate the cost of column plus trays, reboiler, and condenser for Example 11-1 using Luyben’s cost data. The answers are in the example. In addition, calculate TAC for the entire system if Luyben’s equipment cost data is used, payback period is 3 years, cooling water is $1.00/GJ, low-pressure steam is $10.00/GJ, and operation is 8000.0 h/yr.

D6. Repeat the residue curve analysis for Example 11-3 but using the flowsheet in Figure 11-7b. Arbitrarily use a recycle flow rate of 100.0 kmol/h.

D7. Repeat the residue curve analysis for Example 11-3 but with no recycle:

a. For the process in Figure 11-7A.

b. For the process in Figure 11-7B.

D8.

a. If feed rate in Example 11-1 is doubled, what is total bare module capital cost (column plus trays and heat exchangers) in 2014? Use Eq. (11-6) and Table 11-2 for cost data.

b. Compare the 2014 total bare module capital cost per kmol of product for the two different feed rates.

D9. Example 10-4 and Problem 10.D17 sized the diameter of a packed column doing the separation in Example 11-1. Suppose a 15.0-ft-diameter column is to be used. The 1.0-in. ceramic Intalox saddles have an HETP of 0.37 m. Estimate the packing and tower costs in 2013. Pressure is 101.3 kPa.

F. Problems Requiring Other Resources

F1. Update Table 11-1 by looking up current cost indices in Chemical Engineering magazine.

G. Computer Simulation Problems

G1. Repeat the computer simulation proof of feasibility for Example 11-3, but use the flowsheet in Figure 11-7B. The input for the simulator should be based on the solution to Problem 11.D6. Try different feed stages in the first column for recycle stream and fresh feed.

G2. Repeat the computer simulation proof of feasibility for Example 11-3 but with no recycle. The input for the simulator should be based on the solution to Problem 11.D7.

a. For the process in Figure 11-7A.

b. For the process in Figure 11-7B.

G3. A distillation column is being designed to process a feed that is 10.0 mol% ethanol and 90.0 mol% water. The feed rate is 100.0 kmol/h, and the feed is a saturated liquid at a pressure of 5.0 atm. The column has a partial reboiler, a total condenser, N = 10 in Aspen notation, D = 10.0, and L/D = 2.0. Do tray sizing for a sieve try with one pass, 0.4572-m tray spacing, 85.0% approach to flood (use Fair’s flooding calculation method), and default values for other design variables.

a. Operate the column at 1.0 atm. Find and report the optimum feed stage (based on maximum separation). For the optimum feed stage, report Q_reboiler, Q_condenser, the distillate and bottoms mole fractions ethanol, and the maximum tray diameter.

b. Operate the column at 3.0 atm. Find and report the optimum feed stage (based on maximum separation). For the optimum feed stage, report Q_reboiler, Q_condenser, the distillate and bottoms mole fractions ethanol, and the maximum tray diameter.

c. Operate the column at 5.0 atm. Find and report the optimum feed stage (based on maximum separation). For the optimum feed stage, report Q_reboiler, Q_condenser, the distillate and bottoms mole fractions ethanol, and the maximum tray diameter.

d. Compare your results.

D1. Which pressure gives the best separation? Why?

D2. Which pressure has the lowest Q_reboiler? Why?

D3. Which pressure has the lowest absolute value of Q_condenser? Why?

D4. Which pressure has the smallest diameter column? Why?

e. When operating and capital costs are considered, the optimum pressure to obtain the same purity is usually between 1.0 and 6.8 atm. Speculate on the reasons for this.

G4. (This problem is extensive.) A plant needs to distil 1000.0 kmol/h of a 5.0 mol% ethanol and 95.0 mol% water feed at 76.0°C. We desire a bottoms that is 0.01 mol% ethanol or slightly less and a distillate that is 75.0 mol% ethanol or slightly more. Use NRTL for equilibrium data.

a. Design (find number of equilibrium stages, optimum feed stage, and column diameter) of a distillation column operating at 1.0 atm. The column has a total condenser and partial reboiler. Operate with a saturated liquid reflux, and L/D = 1.1 × (L/D)_min. Determine (L/D)_min from simulations with 100 stages and feed on stage 50. Operate at 80.0% of flooding (use Fair’s method) with sieve plates and 0.6096-m tray spacing. Report number of trays, optimum feed tray, column diameter, L/D, Q_R, and Q_c.

b. Design a multieffect distillation system to produce two bottoms products that are 0.01 mol% ethanol or slightly less and two distillate products that are 75.0 mol% ethanol or slightly more. Both columns receive fresh feed. The low-pressure column operates at 1.0 atm. The high-pressure column is at 3.0 atm. In the plant the condenser of the high-pressure column is also the reboiler of the low-pressure column; thus, Q_{c,high-pressure column} = –Q_{R,low-pressure column}. In Aspen you can show normal reboiler and condenser and then match heat loads. Use the same optimum feed stage and the total number of stages for the low-pressure column as determined in part a. Add one stage to the high-pressure column, but use the same feed location as in the low-pressure column. Make Q_R in the high-pressure column 0.7555 × Q_R determined in part a (this is arbitrary, but it works). Adjust the feed flow rate in the two columns so that F(low-pressure column) + F(high-pressure column) = F_total = 1000.0 kmol/h.

Operate both columns at 80.0% of flooding (based on Fair’s method) with sieve plates and 0.6096-m spacing between trays. Report F, number of trays, feed tray, column diameter, L/D, Q_R, and Q_c for both columns.

e. Compare the results of parts a and b.

G5. Use Figure 11-6A (methanol product distillate from the first column, ethanol product distillate from second column, and 1-propanol product bottoms of second column) to purify a ternary feed. Feed mole fractions are methanol = 0.2, ethanol = 0.5, and 1-propanol = 0.3. The feed is at 75.0°C, flow rate is 1000.0 kmol/h, and pressure is 1.0 bar. Each product is 99.0 mol% or greater. Operate both columns at a constant pressure of 1.0 bar. Both columns have total condensers and kettle-type reboilers. Each column has only one feed. Column 1 has N (Aspen notation) = 40. Column 2 has reflux ratio = 2.0.

a. Which VLE correlation will you use? Briefly explain why you selected this correlation.

b. First, find any conditions that give methanol, ethanol, and 1-propanol products that are all 99.0 mol% or greater. Report the conditions that worked:

Column 1. Aspen N = 40 (given), Aspen feed location = ____, Operating condition 1 on Setup-Configuration tab ____ (e.g., distillate flow rate) and value ______; Operating condition 2 on Setup-Configuration tab _____ and value ____.

Column 2. Aspen N = ___, Aspen feed location = _____, Operating condition 1 on Setup-Configuration tab ____ (e.g., distillate flow rate) and value _____; reflux ratio = 2.0 (specified).

Results: Methanol mole fraction in methanol product ______, ethanol mole fraction in ethanol product _______, 1-propanol mole fraction in 1-propanol product ________.

c. Second, for column 1, keep all variables except for reflux ratio and feed location constant. Find the optimum feed location for N = 40. Then with N = 40 and the optimum feed stage, find the lowest reflux ratio that gives the methanol mole fraction within range 0.99000 to 0.99004.

Report Column 1. Aspen N = 40 (specified), Aspen optimum feed location = ______, reflux ratio = __________, Methanol mole fraction in methanol product __________.

d. Third, the changes in column 1 may cause column 2 products to no longer meet specifications. If this is the case, find conditions that work, but keep reflux ratio = 2.0, and do not change column 1. If column 2 already meets specifications or once column 2 meets specifications, keep all variables except for N and feed location constant. Find the optimum feed location. Reduce N as much as possible while using optimum feed location and obtaining ethanol and 1-propanol product mole fractions that are greater than or equal to 0.99000.

Report: Column 2. Aspen N = _____, Aspen optimum feed location = ___, Operating condition 1 on Setup-Configuration tab _______ (e.g., distillate flow rate) and value ____; reflux ratio = 2.0. Ethanol mole fraction in ethanol product _______, 1-propanol mole fraction in 1-propanol product _______.

G6. A distillation column with a partial condenser and a partial reboiler is separating 1500.0 kmol/h of a 10.0 mol% ethane, 30.0 mol% n-butane, and 60.0 mol% n-pentane saturated liquid feed at 8.1 atm. The column operates at a constant pressure of 8.0 atm. The distillate is withdrawn as a saturated vapor. In Aspen notation N = 40, and the feed is on stage 25. In an attempt to obtain close to three pure products, a sidestream is withdrawn between the partial condenser and the feed stage. We want a 99.9% recovery of n-pentane in the bottoms (split fraction in bottoms stream > 0.999).

Note: Use Petroleum/Wide-boiling convergence in the Configuration tab for the RadFrac Block. List the VLE correlation used.

a. Set distillate flow rate D = 150.0 kmol/h and side withdrawal flow rate S = 450.0 kmol/h (these are appropriate values if the separation is perfect—although the separation is not and cannot be perfect). Put the side withdrawal on stage 12, and make it a liquid. Increase the reflux ratio until the mole fraction of ethane in the distillate is > 0.98 (remember that distillate is a vapor). Record the reflux ratio.

b. To improve the ethane mole fraction in the distillate to > 0.99, first try increasing the reflux ratio. Find the value necessary, and report this reflux ratio.

c. The reflux ratio required for part b is rather high. Reduce the reflux ratio to 20.0. Now set D = 150.0 – Δ and S = 450.0 + Δ. Find the Δ value that gives ethane mole fraction in the distillate > 0.99. Report D, S, and mole fractions in the three products. The reason reducing D and increasing S works is since the liquid in the sidestream is in equilibrium with the upward-flowing vapor that carries ethane to the distillate, there must be some ethane in the sidestream. Thus, the sidestream is not pure n-butane, but our original values for D and S assumed it was pure. Since there is ethane in the sidestream, the value of D = 150.0 is too large, which forces some n-butane up into the distillate.

d. Keeping everything the same as in part c, except changing the sidestream to a vapor, run the separation again. Report the mole fractions of the three products (remember to use y values for the sidestream). Why is the separation significantly worse than with a liquid sidestream?

e. We could also put the sidestream below the feed stage (in this case the feed stage would be closer to the condenser). However, this configuration will not work as well for this separation. Why not?

G7 to G10. Basic statement of a team design problem: Find the configuration with the lowest TAC for the separation assigned to your team. Do separation calculations with Aspen Plus to find N, diameter, temperatures, Q_R, and Q_c. Cost calculations should be done on a spreadsheet. Use cost data from Table 11-2. Separation problem: Determine the distillation process with the lowest TAC to separate a mixture of normal paraffins that can include n-butane (C4), n-pentane (C5), n-hexane (C6), n-heptane (C7), n-octane (C8), and n-nonane (C9). Feed flow rate is 1000.0 kmol/h, and feed is a liquid at p = 1.0 bar. Use a 0.4572-m (18 in.) tray spacing for sieve trays designed with the Fair flooding correlation at 80.0% of flooding. Design each column for a constant pressure of 1.0 bar or larger, up to a maximum pressure of 7.8 bar (the different columns can be at different pressures). If you have convergence difficulties, try Petroleum/Wide-boiling convergence instead of standard convergence in the RadFrac Block setup. Ignore capital costs for pumps (but include on flowsheet), and ignore electricity costs of pumps. Do not use compressors. Because of time constraints, do not try thermally coupled systems; thus, except for reboilers and condensers, do not use heat exchangers. Cooling water entering at 30.0°C and exiting at the smaller of either 46.7°C or the (average distillate temperature – approach temperature) costs $1.00/GJ. Minimum approach temperature for reboilers and condensers is 5.0°C. Other energy costs are in Table 11-2.

Specific problem statements are in Problems 11.G7 to 11.G10.

11.G7 to 11.G10: Team Report Requirements:

These requirements are very strict for the following reasons:

1. Companies want brief, to the point, but complete reports.

2. Company reports typically put the details in an appendix.

3. There must be enough detail (in the appendix) so that another engineer can check your work—perhaps years later.

4. A strict page count protects students from having to compete with others for the most complete and longest report.

5. A strict page count protects the person who grades from overly long reports.

The report should be five pages: two pages of text, two pages of figures and tables, and an appendix with a table providing the input data for your best design. References can be placed where there is room. The text should have normal margins, 11-point Times New Roman font, multiple-line spacing at 1.15, line space between paragraphs, and no indention. There should be no cover page. The first six lines of the first page should be:

(Skip a line—line is blank)

Summary: After a heading, start your summary—see the following description. Use headings as shown (you can change the exact wording). Note that the paragraphs start on the same line as the headings.

• Summary. The first paragraph should be a summary that briefly describes the problem, mentions the flowsheets tried, briefly describes the suggested best flowsheet, and discusses why it was selected. (Write this paragraph last.)

• Problem Statement. The second paragraph should describe the separation problem. Do not include details such as cost data, heat transfer coefficients, and so forth.

• Flowsheets Analyzed. The next several paragraphs should briefly describe the different flowsheets analyzed, including a short description of the analysis method used (e.g., heuristic, shortcut calculation with economics, RadFrac calculation with economics). You should refer to your tables, figures, and equations.

• Recommended Solution. Refer to a figure that shows the flowsheet for the recommended system and to a table with pertinent data. Compare costs with any other flowsheets for which costs were calculated.

• Figures and Tables. Include figures, tables, equations, and so forth. Give complete information (in kmol/h, mole fraction, m, kW, $/yr) on your recommended flowsheet. Numbers and letters must be 10-point Times New Roman or larger.

• Appendix: Input data table (p. 5) (for final solution). As an appendix, include a table that has all information needed to run a simulation of your final solution.

• Example Reference: Luyben, W., Distillation Design and Control Using Aspen™ Simulation, p. 84, Wiley, New York, 2013.

• Additional pages. Not allowed, and will not be read.

• Grading: Reports will be graded both for technical accuracy (instructor may run a simulation of your final solution using the input data listed in your appendix) and for written communication. Do a spell and grammar check, and carefully proofread before turning in the report.

• Individual Peer Ratings: Each student in a team will turn in a word-processed hard copy (not an attachment to e-mail) of a one-page peer rating of the other members of their team. Give your name and then list each team member (first and last name), the percentage of the group grade the student has earned (between 0.0% and 100.0%), and a brief reason for the allocation. Note: All team members can receive 100.0% if all contributed. If you complain to the instructor or TA about a team member not working on the project, your rating should agree with your complaints. Sign your peer rating sheet. Do not rate students who withdrew from the group and did the project on their own.

G7. See general statement in G7 to G10. Specific conditions are: Feed: C4 0.0%, C5 68.0%, C6 7.0%, C7 0.0%, C8 25.0%, C9 0.0%, T_feed = 45.0°C. Product purities required: C5 99.9% or higher, C6 97.0% or higher, C8 99.0% or higher.

G8. See general statement in G7 to G10. Specific conditions are: Feed: C4 45.0%, C5 27.0%, C6 28.0%, C7 0%, C8 0%, C9 0%, T_feed = 15.0°C. Product purities required: C4 99.8% or higher, C5 99.7% or higher, C6 99.8% or higher.

G9. See general statement in G7 to G10. Specific conditions are: Feed: C4 28.0%, C5 0.0%, C6 6.0%, C7 66.0%, C8 0.0%, C9 0.0%, T_feed = 33.0°C. Product purities required: C4 99.5% or higher, C6 97.5% or higher, C7 99.8% or higher.

G10. See general statement in G7 to G10. Specific conditions are: Feed: C4 45.0%, C5 0.0%, C6 6.0%, C7 0.0%, C8 0.0%, C9 49.0%, T_feed = 26.0°C. Product purities required: C4 99.8% or higher, C6 99.7% or higher, C9 99.8% or higher.