McCabe-Thiele Method

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  • 1.C07 10/04/2010 Page 258 Chapter 7 Distillation of Binary Mixtures 7.0 INSTRUCTIONAL OBJECTIVES After completing this chapter, you should be able to:Explain the need in distillation for a condenser to produce reux and a reboiler to produce boilup.Determine the ve construction lines of the McCabeThiele method using material balances and vaporliquid equilibrium relations.Distinguish among ve possible phase conditions of the feed.Apply the McCabeThiele method for determining minimum reux ratio, minimum equilibrium stages, number of stages for a specied reux ratio greater than minimum, and optimal feed-stage location, given the required split between the two feed components.Use a Murphree vapor-stage efciency to determine the number of actual stages (plates) from the number of equi- librium stages.Extend the McCabeThiele method to multiple feeds, sidestreams, and open steam (in place of a reboiler).Estimate overall stage efciency for binary distillation from correlations and laboratory column data.Determine the diameter of a trayed tower and the size of the reux drum.Determine packed height and diameter of a packed column. In distillation (fractionation), a feed mixture of two or more components is separated into two or more products, including, and often limited to, an overhead distillate and a bottoms product, whose compositions differ from that of the feed. Most often, the feed is a liquid or a vaporliquid mixture. The bottoms product is almost always a liquid, but the distillate may be a liquid, a vapor, or both. The separation requires that: (1) a second phase be formed so that both liquid and vapor are present and can make contact while owing countercurrently to each other in a trayed or packed column, (2) components have different volatilities so that they partition between phases to different extents, and (3) the two phases are separable by gravity or mechani- cal means. Distillation differs from absorption and stripping in that the second uid phase is usually created by thermal means (vaporization and condensation) rather than by the introduction of a second phase that may contain an addi- tional component or components not present in the feed mixture. According to Forbes [1], distillation dates back to at least the 1st century A.D. By the 11th century, distillation was used in Italy to produce alcoholic beverages. At that time, distilla- tion was a batch process. The liquid feed was placed into a heated vessel, causing part of the liquid to evaporate. The vapor passed out of the vessel into a water-cooled condenser and dripped into a product receiver. The word distillation is derived from the Latin word destillare, which means drip- ping. By the 16th century, it was known that the extent of separation could be improved by providing multiple vapor liquid contacts (stages) in a so-called Recticatorium. The term rectication is derived from the Latin words recte facere, meaning to improve. Today, almost pure products are obtained by multistage contacting. Multistage distillation is the most widely used industrial method for separating chemical mixtures. However, it is a very energy-intensive technique, especially when the relative volatility, a, (2-21), of the key components being separated is low (1.50). Mix et al. [2] report that the energy consump- tion for distillation in the United States for 1976 totaled 2 1015 Btu (2 quads), which was nearly 3% of the entire national energy consumption. Approximately two-thirds of the distillation energy was consumed by petroleum reneries, where distillation is used to separate crude oil into petroleum fractions, light hydrocarbons (C2s to C5s), and other organic chemicals. Distillation is also widely used in the chemical industry, to recover and purify small biomolecules such as ethanol, acetone, and n-butanol, and solvents (e.g., organic alcohols, acids, and ketones) in the biochemical industry. However, it is scarcely used in bioseparations involving larger biological metabolites, polymers, or products that are thermolabile. 258

2. C07 10/04/2010 Page 259 Industrial Example The fundamentals of distillation are best understood by the study of binary distillation, the separation of a two-component mixture. The more general and mathematically complex case of a multicomponent mixture is covered in Chapters 10 and 11. A representative binary distillation is shown in Figure 7.1 for the separation of 620 lbmol/h of a mixture of 46 mol% benzene (the more volatile component) from 54 mol% toluene. The pur- pose of the 80% efcient, 25-sieve-tray column and the partial reboiler that acts as an additional theoretical stage is to separate the feed into a liquid distillate of 99 mol% benzene and a liquid bottoms product of 98 mol% toluene. The column operates at a reux-drum pressure of 18 psia (124 kPa). For a negligible pressure drop across the condenser and a pressure drop of 0.1 psi/tray (0.69 kPa/tray) for the vapor as it ows up the column, the pressure in the reboiler is 18 0:125 20:5 psia (141 kPa). In this pressure range, benzene and toluene form near- ideal mixtures with a relative volatility, a, (2-21), of from 2.26 at the bottom tray to 2.52 at the top tray, as determined from Raoults law, (2-44). The reux ratio (reux rate to distillate rate) is 2.215. If an innite number of stages were used, the required reux ratio would be 1.708, the minimum value. Thus, the ratio of reux rate to minimum reux rate is 1.297. Most distillation columns are designed for optimal-reux- to-minimum-reux ratios of 1.1 to 1.5. If an innite ratio of reux to minimum reux were used, only 10.7 theoretical stages would be required. Thus, the ratio of theoretical stages to minimum theoretical stages for this example is 21=10:7 1:96. This ratio is often about 2 for operating col- umns. The stage efciency is 20/25 or 80%. This is close to the average efciency of trayed distillation columns. The feed is a saturated (bubble-point) liquid at 55 psia (379 kPa) and 294 F (419 K). When ashed adiabatically across the feed valve to the feed-tray pressure of 19.25 psia (133 kPa), 23.4 mol% of the feed is vaporized, causing the temperature to drop to 220 F (378 K). A total condenser is used to obtain saturated-liquid reux and liquid distillate at a bubble-point temperature of 189 F (360 K) at 18 psia (124 kPa). The heat duty of the condenser is 11,820,000 Btu/h (3.46 MW). At the bottom of the column, a partial reboiler is used to produce vapor boilup and a liquid bottoms product. Assuming that the boilup and bottoms are in physical equilibrium, the partial reboiler functions as an addi- tional theoretical stage, for a total of 21 theoretical stages. The bottoms is a saturated (bubble-point) liquid, at 251 F (395 K) and 20.5 psia (141 kPa). The reboiler duty is 10,030,000 Btu/h (2.94 MW), which is within 15% of the condenser duty. The inside diameter of the column in Figure 7.1 is a con- stant 5 ft (1.53 m). At the top, this corresponds to 84% of ooding, while at the bottom, 81%. The column is provided with three feed locations. For the design conditions, the opti- mal feed entry is between trays 12 and 13. Should the feed composition or product specications change, one of the other feed trays could become optimal. Columns similar to those in Figure 7.1 have been built for diameters up to at least 30 ft (9.14 m). With a 24-inch (0.61-m) tray spacing, the number of trays is usually no greater than 150. For the sharp separation of a binary mixture with an a1.05, distillation can require many hundreds of trays, so a more efcient separation technique should be sought. Even when distillation is the most economical separation technique, its second-law efciency, 2.1, can be less than 10%. In Figure 1.13, distillation is the most mature of all sepa- ration operations. Design and operation procedures are well established (see Kister [3, 4]). Only when vaporliquid equi- librium, azeotrope formation, or other data are uncertain is a laboratory and/or pilot-plant study necessary prior to design of a commercial unit. Table 7.1, taken partially from Mix et al. [2], lists common commercial binary distillations in decreasing order of difculty of separation. Included are aver- age values of a, number of trays, typical column operating pressure, and reux-to-minimum-reux ratio. Although the data in Table 7.1 refer to trayed towers, distillation is also carried out in packed columns. Frequently, additional distilla- tion capacity is achieved with existing trayed towers by replacing trays with random or structured packing. Equipment design and operation, as well as equilibrium and rate-based calculational procedures, are covered in this chapter. Trayed and packed distillation columns are mostly identical to absorption and stripping columns discussed pre- viously. Where appropriate, reference is made to Chapter 6 and only important differences are discussed in this chapter. 7.1 EQUIPMENT AND DESIGN CONSIDERATIONS Types of trays and packings for distillation are identical to those used in absorption and stripping, as shown in Figures 6.2 to 6.7, and compared in Tables 6.2 and 6.3. Feed bubble-point liquid, 55 psia 19.25 psia 620 lbmol/h 46 mol% benzene 54 mol% toluene 5-ft diameter, 24-in.-tray-spacing sieve trays Partial reboiler 10,030,000 Btu/h 98 mol% toluene 251 F 99 mol% benzene 189 F 623 lbmol/h Reflux 20.5 psia 18 psiaReflux drum Distillate 708 lbmol/h Boilup Bottoms Total condenser 11,820,000 Btu/hr 25 16 13 10 1 cw Stm Figure 7.1 Distillation of a binary mixture of benzene and toluene. 7.1 Equipment and Design Considerations 259 3. C07 10/04/2010 Page 260 7.1.1 Design and Analysis Factors Factors that inuence the design or analysis of a binary- distillation operation include: 1. Feed ow rate, composition, temperature, pressure, and phase condition 2. Desired degree of component separation 3. Operating pressure (which must be below the critical pressure of the mixture) 4. Pressure drop, particular