Design and Control of Distillation Columns with Intermediate Reboilers

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Design and Control of Distillation Columns with Intermediate Reboilers William L. Luyben† Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

Distillation columns in which the components being separated have widely different boiling points feature large temperature differences between the condenser and reboiler. If cooling water is used in the condenser, the base temperature of this type of column is often quite high, requiring the use of expensive high-pressure steam. Energy costs can sometimes be reduced by using two reboilers. One at the base of the column uses high-pressure steam. A second at an intermediate tray in the stripping section can use lower-pressure steam because the column temperature is lower at that location. This paper compares the steady-state design and the dynamic control of a conventional single-reboiler distillation column with a column having both intermediate and base reboilers. Design involves determining the optimum heat removal in the intermediate reboiler, which affects both the column diameter and the rates of consumption of the two types of steam, having different costs. Control involves handling the large temperature difference in the column by the use of “average temperature” control and developing a control scheme to effectively use the additional control degree of freedom. 1. Introduction Despite the predictions of many self-proclaimed visionaries during the last several decades that “distillation is dead”, the unit operation of distillation remains the premiere separation method in the chemical and petroleum industries. Its wide application results in a very large variety of distillation columns. Some operate at high pressure and others at low pressure. Some operate at high temperature and some at low temperature. Some require many trays and others few trays. This variability results in many different types of columns and many different control structures. Many of these are discussed by Luyben.1 When the boiling point temperatures of the components to be separated are close together, the separation is difficult. The resulting column has many trays and operates with a high reflux ratio. The propylenepropane separation is the most important industrial example. The temperature difference between the reflux drum and the reboiler is quite small. Heat integration or vapor recompression can be considered for this type of column because of the relatively small temperature change over the column. When the boiling point temperatures of the components to be separated are far apart, the situation is exactly the reverse. The separation is an easy one, so the resulting column requires few trays and operates with a low reflux ratio. Examples of this situation occur in chemical plants where the effluent from a reactor is a mixture of a light component, typically one of the reactants, and a heavy component, typically a product. This mixture must be separated so that the light reactant can be recovered and recycled. Distillation is often used because of the easy separation. In these easy separation systems, the temperature difference between the reflux drum and the reboiler is very large because of the difference in boiling points. †

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This means that the temperature of the heating source in the reboiler is much higher than the temperature of the heat-removal sink in the condenser. Many distillation columns are designed to have refluxdrum temperatures high enough (minimum of 110 °F) so that cooling water can be used in the condenser. This temperature and the distillate composition fix the column pressure. In these easy separation columns, both products are usually produced at very high purity. The bottoms is typically a final product that requires high purity. The distillate is a recycle stream whose purity is less critical. Because the separation is an easy one, it does not cost much to make high-purity recycle, which helps to reduce recycle rates and the reactor size. This means that the column pressure is essentially the vapor pressure of the lighter component (in a binary system) at 110 °F. The pressure at the base of the column is equal to the pressure in the condenser plus the pressure drop through the trays. The base temperature is essentially the vapor-pressure temperature of the heavier component at this pressure. Thus, the reboiler temperature can be quite high because the heavy component is high boiling, and a high-temperature heat source is required. High temperature means that high-pressure steam must be used, or in cases with temperatures above about 500 °F, a fired reboiler or a hot oil system must be used. High-pressure steam is more expensive than lowpressure steam. For example, Turton et al.2 give prices for steam at several pressure levels: 87 psia of steam is $8.20/106 Btu, 160 psia of steam is $8.67/106 Btu and 609 psia of steam is $10.40/106 Btu. Thus, there is an economic incentive to substitute as much low-pressure steam as possible for high-pressure steam. This substitution can be achieved by designing the column to have two reboilers, one in the base and one up higher in the column. The base reboiler will have to use a high-temperature heat source. However, the

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2. Process Studied

Figure 1. Single-reboiler column.

Figure 2. Intermediate-reboiler column.

intermediate reboiler in the stripping section can use a lower-temperature heat source because the tray temperatures are lower. Figures 1 and 2 compare a standard single-reboiler column with a column having two reboilers. The specific numerical values correspond to the case discussed in the next section. The consumption of high-pressure steam in the standard configuration is 15.3 × 106 Btu/ h. With the intermediate reboiler, the consumption of high-pressure steam is reduced to 5.83 × 106 Btu/h in the base reboiler while the consumption of low-pressure steam is 9.53 × 106 Btu/h. The annual savings in energy cost is about $50 000/year. In addition, as we show later in this paper, the capital cost of the column is reduced because the diameter is smaller. This more than compensates for the slightly higher capital cost of using three heat exchangers instead of two. The net result is a reduction in capital investment. In this paper, a numerical example is used to illustrate the design aspects of columns with intermediate reboilers and to study their dynamic controllability. The commercial simulation software from Aspen Technology is used for both the steady-state design (Aspen Plus) and the dynamic studies (Aspen Dynamics).

The chemical system selected as a numerical example is the binary separation of propylene (C3d) from normal heptane (nC7). The normal boiling points of these two components are -53.8 and +209 °F, respectively. So, there is a large difference between the reflux-drum temperature and the base of the column. So that cooling water can be used in the condenser, the reflux-drum temperature is set at 110 °F. The specified purity of the distillate is 99.99 mol % propylene. This means that the reflux-drum pressure is 250 psia. Assuming a 30-tray column with 0.15 psi of pressure drop per tray, the pressure in the base is 255 psia. This means that the reboiler temperature is 453 °F for a bottoms product that is 99.99 mol % n-heptane. Figure 1 gives the flowsheet of the standard singlereboiler process. A feed flow rate of 1000 lb‚mol/h is used with a feed temperature of 100 °F and a feed composition of 50 mol % propylene and 50 mol % n-heptane. The feed is introduced at stage 15 (using Aspen notation of numbering stages from the condenser down the column). The distillate flow rate is set at 500 lb‚mol/h, and the reflux ratio is found that gives the specified product purities. Because the separation is an easy one, the required reflux ratio is only 0.253. This means that the liquid flow rates in the rectifying section of the column are very much smaller than those below the feed tray, which has implications in the hydraulic design and the control of the column. The reboiler uses 620 psia of steam (490 °F). Figure 2 gives the flowsheet of the process with two reboilers. The intermediate reboiler is located at stage 25 in the stripping section below the feed tray. The tray temperature at this location is 323 °F. A liquid pumparound stream is removed from the column at stage 25, heated to 375 °F using 326 psia of steam (425 °F), and returned to the column at stage 24. Note that the minimum differential temperature is 50 °F at the hot end of the heat exchanger. As discussed in the next section, the flow rate of the pumparound is a design parameter. In the specification of the pumparound in Aspen Plus, it is important to set the “valid phases” of the “destination” as “liquid-vapor” because the pumparound return from the heat exchanger is about 20% vaporized. 3. Steady-State Design Both the standard flowsheet and the intermediatereboiler flowsheet are simulated in Aspen Plus. The Chao-Seader physical property package is used, and the “petroleum wide-boiling” convergence algorithm is selected to solve the column equations. The “design spec/ vary” capability of Aspen Plus is used to find the reflux ratio needed to give a distillate purity of 99.99 mol % propylene. The overall component balance results in a bottoms purity of 99.99 mol % n-heptane with the distillate set at 500 lb‚mol/h. The “tray sizing” calculations of Aspen Plus are used to determine the diameter of the column. The worstcase location depends on the flow rate of the pumparound, as discussed below. Flowsheet conditions are shown in Figures 1 and 2 for the two systems. Details of column designs and the economics are given in Table 1. Note that the intermediate-reboiler process requires three heat exchangers instead of the two required in the standard configura-

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Table 1. Design Parameters for Two Cases standard intermediatesingle-reboiler reboiler column column reflux ratio flows (lb‚mol/h)

compositions (mf C3d) (mf C3d) (mf nC7) pressure (psia) temperatures (°F)

D B F R pumparound z xD xB

0.253 500 500 1000 127

0.253 500 500 1000 127 2000

0.50 0.9999 0.9999 250 110 252

0.50 0.9999 0.9999 250 110 323 375 453 3.38 9.53

reflux drum stage 25 P/A return base heat duty (106 Btu/h) condenser intermediate reboiler reboiler diameter (ft) total stages area (ft2) condenser intermediate reboiler reboiler capital (106 $) column HX energy (106 $/year)

15.3 9.06 32 1129

5.83 6.03 32 1127 1192

3066 0.620 0.438 1.39

1166 0.402 0.459 1.34

TAC (106 $/year)

1.75

1.63

453 3.39 0

Table 2. Basis of Economics Condenser heat-transfer coefficient ) 150 Btu/h‚°F‚ft2 differential temperature ) 20 °F capital cost ) 1557(area)0.65 Base Reboiler heat-transfer coefficient ) 100 Btu/h‚°F‚ft2 differential temperature ) 50 °F capital cost ) 1557(area)0.65 Intermediate Reboiler heat-transfer coefficient ) 100 Btu/h‚°F‚ft2 log-mean differential temperature ∆TLM ) (∆T1 - ∆T2)/ln(∆T1/∆T2) ∆T1 ) 425 - T25 ∆T2 ) 425 - 375 capital cost ) 1557(area)0.65 column vessel capital cost ) 1917D1.066L0.802 energy cost: 620 psia steam ) $10.37/106 Btu 326 psia steam ) $9.74/106 Btu capital cost TAC ) + energy cost payback period payback period ) 3 years

tion. The bases for heat-exchanger sizing and capital and operating costs are given in Table 2. 3.1. Column Profiles. Figure 3 gives temperature, composition, and flow-rate profiles for the two flowsheets. The solid lines are for the intermediate-reboiler column. The dashed lines are for the standard singlereboiler column. Notice that the vapor and liquid flow rates are very different from those expected from the commonly used “equimolal overflow” assumption. This is due to the large temperature differences and the large difference in the molar latent heats of vaporization of the two components: 5700 and 16 000 Btu/lb‚mol for propylene and n-heptane, respectively, at 77 °F. For example, consider the feed tray, stage 15. The feed is 1000 lb‚mol/h of liquid (50 mol % propylene). We

would expect the liquid flow rate to increase by about 1000 lb‚mol/h from the rectifying section to the stripping section. However, it actually increases by about 1400 lb‚mol/h. This occurs because the liquid feed enters at 100 °F, while the feed tray is at 157 °F. Some vapor coming into the feed tray is condensed to provide the sensible heat of this temperature change. Thus, there is more vapor entering the feed tray than leaving it. Because the difference between the liquid and vapor rates in the stripping section is equal to the bottoms flow rate, the increase in vapor means an increase in liquid. Both the liquid and vapor flow rates increase quite significantly from the rectifying section to the stripping section, as shown in Figure 3. There are also large changes in the liquid and vapor flow rates near the bottom of the column. This is due to the large changes in temperature and composition that occur in this region. Note that the maximum vapor rate occurs at the bottom tray (stage 31), so the column diameter is usually set by this worst-case flow. It is significant to compare the vapor rates for the standard single-reboiler column with the vapor rates in the column with the intermediate reboiler. The vapor rate at the base of the intermediate-reboiler column is less than half that of the standard column. The limiting vapor rate now occurs on the trays where the liquid pumparound circulates through the intermediate reboiler. The vapor flow rate increases significantly at this location because of the heat added in the intermediate reboiler. 3.2. Selection of the Pumparound Flow Rate. The presence of the intermediate reboiler provides an additional degree of freedom in the design. When the pumparound flow rate is zero, we have the standard flowsheet. In this situation, the limiting column diameter location is at the base of the column because this is where the vapor flow rate is the highest. As the pumparound rate increases, the vapor rates decrease in the section of the column below it. However, the liquid load at stages 24 and 25 increases, and this impacts the required column diameter. Figure 4 shows how the flow rate of the pumparound affects the column diameter and the reboiler heat duties. The return temperature of the pumparound from the intermediate reboiler is set at 375 °F, which gives a 50 °F temperature difference between the process and 326 psia of steam (425 °F). The temperature of the stream entering the intermediate reboiler is the temperature at stage 25. The steam is about 20% vaporized in the reboiler when the flow rate is 2000 lb‚mol/h. The results in Figure 4 show that as the pumparound flow increases less heat is added in the base reboiler and more in the intermediate reboiler. The diameter is large at low pumparound flow rates because of the high vapor flow rates at the base of the column. The diameter is large at high pumparound flow rates because of the high liquid loads on those trays (stages 24 and 25) where the pumparound flows through the column. The minimum column diameter occurs with a pumparound flow rate of 2000 lb‚mol/h. This is selected as the optimum design condition. 3.3. Economics. The results given in Table 1 show that the intermediate-reboiler process has a 6.6% lower total annual cost (TAC). This economic advantage is primarily the result of the smaller diameter column, which reduces the capital cost of the column shell by

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Figure 3. Column profiles.

Figure 4. Effect of P/A flow rate.

35%. The capital cost of the three reboilers in the intermediate-reboiler column is only 5% higher than the standard single-reboiler process because the total reboiler area is less (because of the larger log-mean temperature difference in the intermediate reboiler). Energy cost is reduced about 4%, which is (somewhat unexpectedly) not as significant as the reduction in the column cost. Of course, this savings depends on the

difference in cost between 620 psia of high-pressure steam and 326 psia of lower-pressure steam. The larger this differential, the larger the economic incentive. The cost figures used in this paper are those given by Turton et al.,2 which predict a differential of only $0.63/106 Btu. In many chemical plants, this differential is often much larger because high-pressure steam can be efficiently used to drive steam turbines.

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4. Dynamics and Control Both of the flowsheets are “explored” from Aspen Plus into Aspen Dynamics as “pressure-driven” simulations after all of the parameters required for dynamic simulation are calculated. Reflux-drum and base liquid holdup sizes are calculated to give 5-min residence times at 50% level. Proportional level controllers are used with gains equal to 2. The Aspen Dynamics default structure of a constant mass flow rate of reflux is used. This is appropriate because of the very small flow rate in the rectifying section of the column. The standard explicit Euler integrator in Aspen Dynamics did not perform well in the simulations, probably because of the large difference in volatilities between the two components. Changing to the Gear algorithm solved this problem. 4.1. Average Temperature Control. There are very large temperature changes from tray to tray in this type of column. If only a single temperature is used, the process gain is very large, which means the controller gain must be small and load response is poor. A common way to overcome the problem3 of very sharp temperature profiles is to measure the temperature on several trays above and below the sharp break and average the temperature signals. The trays selected are stages 26, 28, and 30 in the standard column with temperatures 172, 333, and 446 °F, respectively, giving an average temperature of 317 °F. In the column with the intermediate reboiler, stages 27, 28, and 29 are used with temperatures 345, 393, and 433 °F, respectively, giving an average temperature of 390 °F. These average temperatures are the setpoints of temperature controllers manipulating the base-reboiler heat input. A 1-min deadtime is inserted in the temperature loops, and relay-feedback testing is used to determine the ultimate gains and periods. Temperature transmitter spans are 200-400 °F. TyreusLuyben tuning rules are used, giving values of KC ) 0.6 and τI ) 7.6 min for the conventional column and KC ) 0.42 and τI ) 10.6 min for the intermediate-reboiler column. The average temperature is controlled in both columns by manipulating the heat input to the reboiler in the base of the column. The heat input to the intermediate is not manipulated because it should always be maximized. Therefore, the pumparound rate is fixed at its maximum (2000 lb‚mol/h). We assume that the pumparound return temperature is always 375 °F because of the constant pressure of the steam on the hot side of this heat exchanger. The tray temperature will vary dynamically with time, so the heat-transfer rate is not constant. 4.2. Specifying the Pumparound in Aspen Dynamics. The fixed and free variables in the column simulation must be specified to achieve the desired operation of the pumparound during dynamic operation. We want to keep the pumparound flow rate constant at 2000 lb‚mol/h and the pumparound return temperature constant at 375 °F. These are not the default fixed variables in Aspen Dynamics. As shown in Figure 5, the “All Variables” window in “Forms” for the column is opened, and the following variables are set to be “fixed” variables: (1) pump(1).F (2) PumpAround(1).LiqOut.T 4.3. Dynamic Performance. The two processes are subjected to a series of feed flow-rate disturbances. At

Figure 5. Fixing appropriate pumparound variables.

a time equal to 0.2 h, a 20% step increase in the setpoint of the feed flow controller is made. At a time equal to 2 h, the setpoint is decreased back to normal. Finally, at a time equal to 4 h, the setpoint is reduced 20%. Figure 6 shows that both columns handle these large disturbances well. The two graphs on the left-hand side are for the standard single-reboiler column. The two graphs on the right-hand side are for the column with the intermediate reboiler. The heat inputs for both the base and intermediate reboilers are shown. The former is manipulated by the average temperature controller. The flow rate and return temperature of the pumparound from the intermediate reboiler are held constant. The heat duty changes because of changes in the temperature and composition of the liquid coming from stage 25. Maximum deviations of the average temperature are 35-40 °F for both systems. These large changes result from the very large temperature difference over the column. Figure 7 gives results for feed composition disturbances. At a time equal to 0.2 h, the feed composition is changed from 50 to 60 mol % propylene. Then at a time equal to 4 h, it is changed to 40 mol % propylene. Both processes handle these disturbances well. Figures 6 and 7 show that the intermediate-reboiler case has somewhat slower dynamics. This may be a controller tuning issue, despite the fact that the same tuning procedure was used in both cases. As discussed in section 4.1, the controller gain is smaller and the integral time is larger for the intermediate-reboiler case. The responses of the base case indicate more aggressive tuning (a smaller closed-loop damping coefficient). As shown in Figure 3, the column temperature profiles are different. The trays selected to calculate the average temperature are also different, and this leads to slightly different dynamics. 5. Conclusion The design and control of a distillation column utilizing a partial reboiler have been compared with those of a standard column. Consumption of high-pressure heat can be reduced, and the column diameter is also reduced. The economic effect is a reduction in both energy and capital costs. Dynamic controllability is just as good in the intermediate-reboiler column as it is in the standard column. Average temperature control should be used in both because of the very sharp temperature profile. The energy input in the intermediate reboiler is not used

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Figure 6. Feed-rate disturbances.

Figure 7. Feed composition disturbances.

as a control variable because it should be maximized so that the use of higher-pressure steam is minimized. This paper has considered the use of intermediate reboilers. Of course, a similar situation occurs when intermediate condensers can be used to conserve the use of high-cost cooling in the top condenser. If refrigeration

is needed in the top condenser, an intermediate pumparound/condenser using inexpensive cooling water could be located on a tray down far enough in the rectifying section to have temperatures greater than 110 °F. The design and control issues for this type of system would be very similar to those considered in this work.

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Nomenclature B ) bottoms flow rate (lb‚mol/h) D ) distillate flow rate (lb‚mol/h) D ) diameter of vessel (ft) F ) feed flow rate (lb‚mol/h) HX ) heat exchanger KC ) controller gain L ) length of the vessel (ft) P ) pressure (psia) P/A ) pumparound QC ) condenser heat removal (Btu/h) QInt ) intermediate-reboiler heat input (Btu/h) QR ) base-reboiler heat input (Btu/h) R ) reflux flow rate (lb‚mol/h) RR ) reflux ratio ) R/D TR ) reflux-drum temperature (°F) TAC ) total annual cost (106 $/year) xD ) distillate composition (mol fraction propylene) xB ) bottoms composition (mol fraction n-heptane) z ) feed composition (mol fraction propylene) τI ) controller integral time (min)

∆TLM ) log-mean temperature differential in the intermediate reboiler (°F) ∆T1 ) temperature differential at the cold end of the intermediate reboiler (°F) ∆T2 ) temperature differential at the hot end of the intermediate reboiler (°F)

Literature Cited (1) Luyben, W. L., Ed. Practical Distillation Control; Van Nostrand Reinhold: New York, 1992. (2) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaeiwitz, J. A. Analysis, Synthesis and Design of Chemical Processes, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 2003. (3) Luyben, W. L. Control of distillation columns with sharp temperature profiles. AIChE J. 1971, 17, 713.

Received for review June 16, 2004 Revised manuscript received September 17, 2004 Accepted September 27, 2004 IE040178K