Design and Control of Stacked-Column Distillation Systems

Aug 1, 2014 - ... Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States ... the reflux drum and on the pressure drop through th...
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Design and Control of Stacked-Column Distillation Systems William L. Luyben* Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States ABSTRACT: The separation of close-boiling, low-relative volatility components by distillation requires many trays and high reflux ratios (high energy consumption). Temperature-sensitive components often limit temperatures, so vacuum conditions must be used in which pressure drop through trays or packing becomes very important. More trays produce higher base pressures and higher base temperatures for a given pressure in the reflux drum. Therefore, it may be impossible to achieve the desired separation in single column if the maximum temperature limits the number of trays. In this situation, multiple columns must be used to stay within the feasible number of trays per vessel. Each column has its own condenser and reboiler. The bottoms from the upper column is fed to the top of the lower column, and the overhead vapor from the lower column is condensed, pumped to a higher pressure, and fed into the base of the upper column. This stacked column configuration has high energy and capital cost, but it may be the only feasible way to achieve the desired separation and not exceed the maximum temperature limitation. This paper explores the design and control of this complex process.

1. INTRODUCTION Thermal instability of chemical components often limits the allowable temperatures in distillation columns. Pressures must be kept low enough to stay under the maximum temperature limitation for the desired bottoms product composition. The pressure in the base of the column depends on the pressure in the reflux drum and on the pressure drop through the trays. If many trays are required for the separation (low relative volatility), it may not be feasible to achieve the separation in a single vessel because the reflux-drum pressure cannot be lower than a practical limit of about 0.04 atm (30 mmHg). Below this pressure, energy and capital costs become prohibitive for industrial-scale production. A recent paper1 discussed a thermally sensitive system in which low pressure was not the problem. The issue was low reflux-drum temperatures requiring expensive refrigeration. The proposed configuration used two columns in series. In the first, the pressure was set by the use of cooling water in the condenser, and the base temperature was kept at its limit by letting some of the light-key component drop out the bottom. This was fed to a second column that achieved low pressure by using refrigeration. The bottoms product from the second column was the heavy-key component with its specified composition. The maximum temperature limitation was high enough in the system studied that column pressures were greater than 0.04 atm. In addition, the separation was quite easy so few trays were required. In the current paper we explore a system in which the separation is difficult (relative volatility is 1.15) so many trays are required. The effect of the temperature limitation on the required flowsheet is studied. Lower base temperatures require lower base pressures for the same bottoms composition. Lower base pressures require lower reflux-drum pressures or fewer trays. The results illustrate that the configuration must be changed as a function of the temperature limitation. The most extreme example of this situation is the separation of heavy water.2,3 The normal boiling points of water and deuterium differ by only 1.4 K. A stacked-column system with © 2014 American Chemical Society

10 vessels operating at 50 mmHg pressure was used in the early stages of the atomic bomb development in the 1930s. Capital costs and energy consumption were very high, and other more economical methods of separation were developed after the war. No literature references have been found that give other industrial applications of stacked columns.

2. PROCESS STUDIED As an example of a difficult separation, the system of metaxylene (boiling point = 412.1 K) and ortho-xylene (boiling point = 417.4 K) is studied. The desired product purities in the binary system are assumed to be 95 mol % m-xylene in the distillate and 95 mol % o-xylene in the bottoms. Chao-Seader physical properties are used in the Aspen simulations. Three cases are considered. In the first, there is no base temperature limitation, so a single conventional column can be used, which produces a base temperature of 388 K. In the second case, the temperature limitation is 360 K and two stacked columns are required. In the third case, the temperature limitation is 350 K and three stacked columns are required. Tray or packing pressure drop is a critical parameter in these systems. A low pressure drop per theoretical stage of 0.003 atm is assumed. Low weir heights of 0.01 m are assumed to achieve this low pressure drop. 3. NO TEMPERATURE LIMITATION The left part of Figure 1 gives the flowsheet with one large distillation column. A standard Aspen Radf rac model (equilibrium based, Version 8) is used with the specifications of xD = 0.95 and xB = 0.05. Two Aspen Design spec/vary functions are used to achieve these specifications by varying the distillate flow rate and reflux ratio. The feed flow rate is 100 Received: Revised: Accepted: Published: 13139

May 15, 2014 July 20, 2014 August 1, 2014 August 1, 2014 dx.doi.org/10.1021/ie501981f | Ind. Eng. Chem. Res. 2014, 53, 13139−13145

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Figure 1. Flowsheets of stacked columns.

kmol/h with a composition of z = 50 mol % m-xylene. Two condenser pressures are explored (0.1 and 0.041 atm). The total number of trays is varied, and energy and capital costs are calculated. The economic objective function is total annual cost, which considers both energy and capital costs. Table 1 shows that economic optimum flowsheet has 111 stages.

investment in the vessel shell, reflux drum, reboiler, and condenser is $3,854,000. The reboiler energy cost is $1,974,000 per year, using low-pressure steam at 433 K and $7.78 per GJ. The economic basis for the capital and energy costs are taken from Luyben.4 This separation is expensive because many trays and a high reflux ratio are required. These results are for a case in which the condenser pressure is set at 0.1 atm, which gives a reflux-drum temperature of 341.5 K. The reflux-drum temperature could be reduced to 320 K and still use cooling water. At 320 K, the condenser pressure is 0.041 atm with a distillate composition of 95 mol % m-xylene. A 111-stage column designed at 0.041 atm produces a lower base temperature of 383 K since the base pressure is lower (0.377 atm). The reflux ratio is slightly lower (12.18), as is the reboiler duty (7.949 MW) so the energy cost is somewhat lower ($1,950,000 per year). However, the lower pressure gives a larger column diameter (5.877 versus 4.715 m) and a larger condenser (902 versus 286 m2), so the capital cost is significantly higher ($4,968,000). Therefore, the 0.1 atm pressure design is more economical than the 0.041 atm design. The single-column design has a base temperature of 388 K. In the following sections, we consider systems in which the temperature limitation is either 360 or 350 K.

Table 1. Optimum Number of Stages in Single Columna NT

91

111

131

QR (MW) ID (m) TB (K) PR (atm) Energy Cost (106 $/y) Capital Cost (106 $) TAC (106 $/y)

8.785 4.94 383 0.37 2.155 3.540 3.335

8.065 4.72 388 0.43 1.979 3.854 3.263

7.779 4.62 393 0.49 1.909 4.231 3.319

a

PC = 0.1 atm; TC = 342 K. NT = total number of stages; QR = reboiler duty; ID = column diameter; TB = base temperature; PR = base pressure.

Note that the base temperature is 388 K when the condenser pressure is set at 0.1 atm. The 110 trays with a 0.003 atm pressure drop give a base pressure of 0.43 atm. Remember that the bottoms composition is 5 mol % m-xylene. The required reflux ratio is 12.7, and the reboiler duty is 8.065 MW. The column diameter is 4.72 m. This total capital

3. TEMPERATURE LIMITATION AT 360 K If the base temperature must not exceed 360 K, the base pressure can be found from a bubblepoint calculation of the 13140

dx.doi.org/10.1021/ie501981f | Ind. Eng. Chem. Res. 2014, 53, 13139−13145

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bottoms product at a composition of 5 mol % m-xylene and 360 K. This pressure is 0.173 atm. If the condenser pressure is set at 0.041 atm and the tray pressure drop is 0.003 atm, the number of trays that can be used in a single column is NT =

1. An Aspen Design Spec/Vary function is used in the upper column to drive xD1 to 95 mol % by varying distillate flow rate D1. The other design degree of freedom is the reflux ratio (set at its initial value). 2. An Aspen Design Spec/Vary function is used in the lower column to drive xB2 to be equal to 5 mol % by varying reboiler duty QR2 in the lower column. This gives a value for the reboiler duty in the upper column QR1. 3. The second design degree of freedom in the upper column is changed from reflux ratio to reboiler duty. 4. An Aspen Flowsheet Design Spec function is used to make the two reboiler duties equal. The basic assumption in the procedure is that the two reboiler duties should be the same. This may not be the precise optimum, but it is a practical approach since it makes the column diameters essentially equal. In addition, it makes the selection of a simple control structure much easier, as we demonstrate in a later section. 3.3. Results. The total energy consumption in this system is over twice that of the single column system. The energy cost is $4,757,000 per year. The capital investment is $5,917,000, which is 50% higher than that for the single column system. However, the base temperatures do not exceed the 360 K limit. 3.4. Difference between Stacked Columns and a Split Column. A similar two-vessel structure is sometimes used if a column has a very large number of trays and a single tower would be too tall for structural or other reasons. In this situation two vessels are used, one with a reboiler and the other with a condenser. The vapor from the top of the vessel with the reboiler is piped to the base of the vessel with the condenser. The liquid from the base of this vessel is pumped to the top of the other vessel. The pressure in the reboiler is equal to the pressure in the condenser plus the pressure drop through all the trays in the two vessels. This split-column configuration only reduces the height of the unit. It does not reduce base temperatures.

0.173 − 0.041 = 44 0.003

This sets the number of trays that can be used in one vessel with a base temperature of 360 K (bottoms composition 5 mol % m-xylene) and a reflux-drum temperature of 320 K (distillate composition 95 mol % m-xylene). Unfortunately this is below the minimum number of trays predicted by the Fenske Equation for the desired separation under total reflux conditions.

(

log Nmin + 1 =

xDLK xBHK * xDHK xBLK

log αLK / HK

) = log(

0.95 0.05 * 0.05 0.95

log(1.149)

) = 42

A common distillation heuristic is to use twice the minimum number of trays. Therefore, a design with two stacked columns is considered. 3.1. Flowsheet for Two-Column Process. The middle section of Figure 1 gives the flowsheet of the two-stackedcolumn process. Each column has a reboiler and a condenser. The feed is introduced into the bottom of the upper column (or alternatively into the top of the lower column). The liquid from the bottom of the upper column is fed to the top of the lower column. The overhead vapor from the lower column (1001 kmol/h with a composition of 58.9 mol % m-xylene) is condensed, fed to a drum, and pumped into the bottom of the upper column. The reflux ratio in the top column is 11.7. The column diameters are about 5.7 m. In the Aspen simulation, the upper column uses a Radf rac rectifier model, and the lower column uses a Radfrac stripper model. The condenser on the lower column is modeled with a Heater model, and the reflux drum is modeled with a Flash2 model (the vapor flow rate is set at zero). 3.2. Converging the Flowsheet. Setting up the twocolumn process is not completely straightforward since there are recycle streams between the two columns (the bottoms from the upper column B1 goes to the top of the lower column, and the overhead liquid from the lower column D2 is fed to the base of the upper column). The flow rates of the two product streams D1 from the top of the upper column and B2 from the bottom of the lower column are set at their appropriate values as calculated from overall component and molar balances. A larger reflux ratio in the upper column is initially assumed. The D2 stream is “torn” (not connected the lower column). Guesses of the flow rate D2 and composition xD2 of the torn stream are made and the simulation is run, which gives calculated values of flow rate and composition of the overhead from the lower column. The direct substitution convergence method is used to update the guessed values of D2 and xD2 until the differences between the guessed and calculated values are small. Then the torn stream is connected and the file is converged. However, at this point the product compositions are not at their specified values (xD1 = 0.95 and xB2 = 0.05) because an arbitrary reflux ratio has been assumed. The procedure to achieve the desired product compositions is as follows:

4. TEMPERATURE LIMITATION AT 350 K Now we see how an even lower base temperature limitation affects the design. If the maximum base temperature is lowered 10 to 350 K, the base pressure can be found from a bubblepoint calculation of the bottoms product at a composition of 5 mol % m-xylene and 350 K. This pressure is 0.11 atm, which is lower than that in the 360 K maximum temperature design. Therefore, fewer trays can be used. If the condenser pressure is set at 0.041 atm and the tray pressure drop is 0.003 atm, the number of trays that can be used in the column is NT =

0.11 − 0.041 = 23 0.003

This sets the number of trays that can be used in one vessel with a base temperature of 350 K (bottoms composition 5 mol % m-xylene) and a reflux-drum temperature of 320 K (distillate composition 95 mol % m-xylene). 4.1. Three-Column Flowsheet. The minimum number of stages is still 42. Using two vessels would only give 46 trays. Therefore, this design requires at least three stacked columns. Each column has a reboiler and condenser. The overhead vapors from the bottom and middle column are condensed and fed to the base of the next higher column. 13141

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Figure 2. Control structures for stacked columns.

Figure 3. One column; 20% flow rate disturbances.

The total energy consumption in this system is over three times that of the single column system. The energy cost is $7,960,000 per year. The capital investment is $7,583,000, which is over twice that of the single column system. However, the base temperatures do not exceed the 350 K limit. These results clearly demonstrate that the economics are very strongly dependent on the temperature limitation. 4.3. Effect of Product Purity Specifications. The purity level used in this study is 95%. Increasing this specification

The convergence procedure is similar to that used for the two-column process. Now there are two recycle streams to initially guess (D2 and D3). The three reboiler duties are made equal with the D1 and B3 product streams driven to their specified values of xD1 = 0.95 and xB3 = 0.05. 4.2. Results. The right section of Figure 1 shows the flowsheet and the conditions. The reflux ratio in the top column is 15.1. The column diameters range from 6 to 7 m. 13142

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Figure 4. Two column; 20% flow rate disturbances.

deadtime are used. Settings are KC = 0.25 and τI = 69 min with a 0 to 0.1 composition transmitter range and a maximum reboiler duty of twice the design. With this controller on automatic, the xD-to-D loop is tuned using a relay-feedback test with a 3 min deadtime. Settings are KC = 16 and τI = 78 min with a 0.9 to 1 composition transmitter range and the distillate valve half open at design.. Figure 3 gives results for 20% disturbances in feed flow rate, which are effectively rejected in about 8 h in this very large 112stage single column. Note that the base temperature TB increases as throughput increases because tray pressure drops increase with the larger internal vapor and liquid flow rates. 5.2. Two Columns. The composition of the distillate product xD1 from the top of the upper column is controlled by manipulating the distillate flow rate D1. The composition of the bottoms from the lower column xB2 is controlled by manipulating the reboiler duties in both of the two reboilers QR. The output signal from the bottoms composition controller positions both reboiler steam valves. Liquid levels in the base of both columns are controlled by manipulating the flow rate of the liquid leaving. The reflux drum level in the upper column is controlled by manipulating the flow rate of reflux R1. The liquid level in the surge tank at the top of the lower column is controlled by manipulating the liquid fed to the base of the upper column D2. Pressures in both columns are controlled by manipulating condenser heat removals. Proportional-only level controllers are used for all liquid levels, but different gains are used in different locations. The level controller in the base of the lower column has a conventional gain KC = 2. The level controllers in the reflux drum, the base of the upper column, and the overhead surge tank in the lower column all use a gain KC = 5 to speed up the dynamic responses.

would have several effects, all of which would increase the costs and complexity. First, the bubblepoint pressure of the distillate at 320 K would increase, which would increase the condenser pressure. For a given maximum base temperature, a more pure bottoms (lower mol % m-xylene) would decrease the base pressure. The difference between the pressure at the bottom (decreasing) and the pressure at the top (increasing) would get smaller due to both pressures approaching each other. For a given tray pressure drop, the number of trays would get smaller, so more columns would be required. In addition, the minimum number of trays also increases as purities increase, which would further increase the number of columns required.

5. CONTROL Low relative volatility systems require the use of dual composition control since temperature profiles are very flat and both reflux ratios and reflux-to-feed ratios vary significantly with feed composition. Figure 2 gives the control structures used on the three systems, which are basically a “DV” structure (manipulating distillate and vapor boilup to control the two product compositions). 5.1. One Column. The composition of the distillate product is controlled by manipulating the distillate flow rate D. The composition of the bottoms is controlled by manipulating the reboiler duty QR. The column base level is controlled by manipulating the flow rate of the bottoms B (proportional-only controller with KC = 2). The reflux drum level is controlled by manipulating reflux (proportional-only controller with KC = 5 to speed up the DV structure). The reflux-drum pressure is controlled by manipulating condenser heat removal using default pressure controller tuning. The two interacting composition controllers are tuned sequentially. First, the faster xB-to-QR loop is tuned with the xD-to-D loop on manual. A relay-feedback test and Tyreus− Luyben tuning rules with a 3 min composition measurement 13143

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Figure 5. Three column; 20% flow rate disturbances.

Figure 6. Feed composition disturbance: 50 to 60 mol % m-xylene.

additional liquid holdup occurs in the base of the upper column and in the surge tank in the overhead system of the lower column. So the dynamics are slower. Note that the base temperature TB in the lower column increases as throughput increases for the same bottoms composition. This occurs because tray pressure drops increase.

Sequential tuning using relay-feedback tests gives controller settings in the xB2-to-QR loop of KC = 0.44 and τI = 80 min and in the xD1-to-D1 loop of KC = 16 and τI = 83 min. Figure 4 gives results for 20% disturbances in the feed flow rate, which are effectively rejected in about 15 h in this very large two-vessel stacked-column process. There are fewer trays than in the single column process, but diameters are bigger and 13144

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The system must be designed for the worst-case situation so that the temperature limitation is not exceeded. 5.3. Three Columns. The composition of the distillate product xD1 from the top column is controlled by manipulating the distillate flow rate D1. The composition of the bottoms from the bottom column xB3 is controlled by manipulating the reboiler duties in all three reboilers QR. The output signal from the bottoms composition controller positions the three reboiler steam valves. Liquid levels in the base of all columns are controlled by manipulating the flow rate of the liquid leaving. The reflux drum level in the top column is controlled by manipulating the flow rate of reflux R1. The liquid levels in the two surge tanks between the columns are controlled by manipulating the liquid stream fed to the base of the adjacent upper column. All level controllers use a gain of KC = 5 except the base of the bottom column, which uses KC = 2. Pressures in all columns are controlled by manipulating condenser heat removals. Sequential tuning using relay-feedback tests gives controller settings in the xB3-to-QR loop of KC = 0.18 and τI = 71 min and in the xD1-to-D1 loop of KC = 6.8 and τI = 50 min. Figure 5 gives results for 20% disturbances in the feed flow rate, which are effectively rejected in about 15 h in this very large three-vessel stacked-column process. The dynamic responses of the three processes are compared in Figure 6 for a disturbance in feed composition. At time equals 0.5 h, the feed composition is changed from 50 to 60 mol % m-xylene with an appropriate reduction in o-xylene. Note that the flow rate of the distillate product increases to the expected value of 61.1 kmol/h with the bottoms held at 5 mol % and the distillate held at 95 mol %.

(in the vaporizer). Heat input to the vaporizer would have to be used and therefore could not be used for composition control.

7. CONCLUSION The use of sequences of stacked distillation columns can be used to avoid temperature limitations in low-pressure, difficult separation systems, but the energy and capital costs are very high.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 610-758-4256. Fax: 610-758-5057. E-mail: WLL0@ Lehigh.edu. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Masel, R. H.; Smith, D. W.; Luyben, W. L. Use of Two Distillation Columns in Systems with Maximum Temperature Limitations. Ind. Eng. Chem. Res. 2013, 52, 5172−5176. (2) Benedict, M., Pigford, T. H., Levi, H. W. Nuclear Chemical Engineering, 2nd ed.; McGraw-Hill: 1981; p 725. (3) Miller, A. I. Heavy water manufacture guide for the hydrogen century. Canadian Nuclear Society Bulletin 2001, 22, no. 1, February. (4) Luyben, W. L. Distillation Design and Control using Aspen Simulation, 2nd ed.; Wiley: 2013.

6. ALTERNATIVE BASE CONFIGURATION During the review of this paper an interesting suggestion was made to use a different configuration in the base of the upper column. The setup shown in Figure 1 is the common arrangement with a simple base in which liquid from the bottom tray of the upper column flows into the base of the column. The liquid from the condensed overhead vapor from the lower column is also fed into the base. The reboiler (thermosiphon, stab-in or kettle) vaporizes some of the liquid depending on the flow rate of steam fed to it as set by the composition controller. The suggestion was to condense the overhead vapor from the lower column, pump it up to a higher pressure, and completely vaporize it before feeding to the bottom of the upper column below the bottom tray. Such an arrangement should be slightly more efficient, in theory, because it would avoid the mixing of the two liquid streams that are fed into the base of the upper column. The liquid from the bottom tray (57.02 mol % mxylene) is mixed with the liquid coming from the top of the lower column (59.09 mol % m-xylene). The resulting liquid in the base of the upper column has a composition of 56.54 mol % m-xylene after the vapor generated in the partial reboiler is produced. In practice, however, the suggested configuration would have two problems. First, the liquid from the bottom tray of the upper column could not be in contact with the vapor fed into the base of the column below the bottom tray. This would require a special column base to segregate the liquid and vapor streams or an external tank to collect the liquid. The second issue is having an additional liquid level that must be controlled 13145

dx.doi.org/10.1021/ie501981f | Ind. Eng. Chem. Res. 2014, 53, 13139−13145