Ind. Eng. Chem. Res. 2001, 40, 3757-3761
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PROCESS DESIGN AND CONTROL Analysis of Control Properties of Conventional and Nonconventional Distillation Sequences Arturo Jime´ nez,*,† Salvador Herna´ ndez,‡ Francisco Arturo Montoy,§ and Martı´n Zavala-Garcı´a‡ Departamento de Ingenierı´a Quı´mica, Instituto Tecnolo´ gico de Celaya, Celaya, Guanajuato 38010, Me´ xico, Facultad de Quı´mica, Universidad de Guanajuato, Guanajuato 36050, Me´ xico, and Departamento de Ingenierı´a Quı´mica y Metalurgı´a, Universidad de Sonora, Hermosillo, Sonora 83000, Me´ xico
In this paper a controllability analysis of seven distillation sequences for the separation of ternary mixtures using singular value decomposition and closed-loop responses under feedback control is presented. The results show that nonconventional distillation sequences such as thermally coupled distillation sequences can have better control properties than nonintegrated schemes, such as the conventional direct and indirect sequences, distillation systems with side streams, and sequences with three conventional distillation columns. 1. Introduction In addition to the conventional direct and indirect sequences for the separation of ternary mixtures (Figure 1), other sequences such as those shown in Figures 2-6 provide choices of interest. These schemes include the use of a single column with a side stream (Figure 2), the use of three conventional columns (Figure 3), and the use of thermally coupled systems (systems with side columns, Figures 4 and 5, and the Petlyuk system, Figure 6). In particular, the economic potential of thermally coupled sequences has already been recognized,1-6 but their control properties have not been studied to the same degree. Recent efforts have contributed to the understanding of the dynamic properties of integrated schemes.7-10 The expectance that the dynamic properties of those coupled systems may cause more operational problems than the conventional sequences is one of the factors that has contributed to their lack of industrial implementation. This conflict is commonly observed in cases where the optimization of an energy-efficient system leads to tight designs, which in turn are more difficult to control. In this work we develop a comparative study of the control properties of the seven distillation sequences shown in Figures 1-6. Of particular interest is the comparison of the controllability properties of integrated schemes with those of more standard sequences with one, two, or three columns with no recycle streams. 2. Dynamic Analysis A dynamic model that includes the total mass balances, component mass balances, equilibrium relation* Corresponding author. Tel. (52-4) 61-17575 ext. 139. Fax (52-4) 61-17744. E-mail:
[email protected]. † Instituto Tecnolo ´ gico de Celaya. ‡ Universidad de Guanajuato. § Universidad de Sonora.
Figure 1. Classical distillation sequences.
Figure 2. Side-stream distillation columns (Design III).
ships, summation constraints, energy balances, and stage hydraulics11,12 provided the basis for the analysis. The dynamic analysis was conducted in two steps. First, a prediction of the control properties for each case was conducted. Then, closed-loop simulations of some alternatives were used to corroborate the predicted dynamic properties. The prediction of control properties was achieved through the application of the singular value decomposition (SVD) technique. After a proper adaptation of the dynamic model for each distillation system was implemented, transfer functions were obtained by performing
10.1021/ie000047t CCC: $20.00 © 2001 American Chemical Society Published on Web 07/24/2001
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Figure 6. Fully TCDS, or Petlyuk system. Figure 3. Distillation sequences with three conventional columns (Design IV).
dynamic properties of the distillation schemes. Such properties were then tested with closed-loop simulations. 3. Case Study
Figure 4. TCDS with a side rectifier (TCDS direct).
Figure 5. TCDS with a side stripper (TCDS indirect).
step changes in the selected manipulated variables (reflux ratios, heat duties, and side-stream flow rates for designs in which the intermediate component is obtained as a side product) and recording their effect on output variables (product compositions). The resulting open-loop transfer function matrix for each scheme was then subject to SVD:
G ) VΣWH where V is the matrix of left singular vectors, W is the matrix of right singular vectors, and Σ is the diagonal matrix of singular values of G. From the application of SVD, the minimum singular value and the condition number (the ratio of the maximum to the minimum singular value) provide two parameters of interest to assess the theoretical dynamic properties of the system. The minimum singular value provides a measure of the invertibility of the system, while the condition number provides a measure of the sensitivity of the system under uncertainties in process parameters and modeling errors. These two parameters were used to compare the
The separation of a ternary mixture of pentane, hexane, and heptane for two feed compositions, an equimolar feed (feed 1) and a feed with a high content of intermediate component, 70% (feed 2), was analyzed. A feed flow rate of the ternary mixture of 45.4 kmol/h, as a saturated liquid at 22.02 psia, was assumed. Residence times of 5 min for liquid holdups were assumed.11 The seven separation sequences were designed for each case, assuming high recoveries of main products. The design of systems with conventional columns was obtained with standard procedures, assuming a reflux ratio equal to 1.3 times its minimum value; for the design of thermally coupled systems, however, a search procedure on the recycle streams ηV and ηL (defined as dimensionless variables) was conducted until the values that minimize energy consumption for the integrated system were detected. The details for this procedure are available in Herna´ndez and Jime´nez.12,13 Table 1 shows the design details obtained for the seven sequences under analysis, for each of the two feed compositions considered. 4. Results 4.1. SVD Parameters. For the separation of an equimolar feed, Figure 7 shows that thermally coupled distillation systems present higher values of the minimum singular value, σ/, for the whole frequency range; therefore, it can be expected that these coupled systems exhibit better control properties than the other sequences under feedback control. The results for the condition number, γ*, are presented in Figure 8. The TCDS direct sequence offers the best values for most of the frequency range; the Petlyuk column shows good conditioning properties at low frequencies, but those properties deteriorate at higher frequencies, where the TCDS indirect sequence provides the second best choice. As a result, it can be expected that thermally coupled distillation systems (TCDS direct and indirect) are better conditioned to the effect of disturbances than the other distillation systems. For equimolar mixtures, SVD results show that thermally coupled distillation systems, particularly systems with side columns, have better control properties than conventional distillation sequences, sequences with side products, and the sequence with three conventional distillation columns. For the case of a feed with a higher content of the intermediate component, Figure 9 shows that at low
Ind. Eng. Chem. Res., Vol. 40, No. 17, 2001 3759 Table 1. Relevant Variables for the Design of the Seven Distillation Sequences sequence design I
design II
design III
design IV
TCDS direct
TCDS indirect
Petlyuk system
feed 1 (0.333/0.333/0.334) feed 2 (0.15/0.7/0.15) NS1 ) 9 NT1 ) 17 R1 ) 42.52 kmol/h QR1 ) 427.26 kW NS2 ) 10 NT2 ) 19 R2 ) 43.00 kmol/h QR2 ) 457.99 kW NS1 ) 10 NT1 ) 20 R1 ) 43.67 kmol/h QR1 ) 594.97 kW NS2 ) 9 NT2 ) 16 R2 ) 33.21 kmol/h QR2 ) 344.92 kW NE ) 22 NS ) 9 NT ) 36 R ) 1380.60 kmol/h LS ) 15.05 kmol/h QR ) 9755.50 kW NS1 ) 9 NT1 ) 16 R1 ) 68.03 kmol/h QR1 ) 706.55 kW NS2 ) 9 NT2 ) 17 R2 ) 18.81 kmol/h QR2 ) 241.79 kW NS3 ) 10 NT3 ) 19 R3 ) 31.35 kmol/h QR3 ) 307.21 kW NS1 ) 9 NE ) 17 NT1 ) 26 NT2 ) 10 R1 ) 25.2 kmol/h R2 ) 19.4 kmol/h QR1 ) 614.9 kW ηV ) 0.5 NS1 ) 18 NE ) 10 NT1 ) 28 NT2 ) 12 R1 ) 61.9 kmol/h QR2 ) 114.2 kW QR1 ) 458.3 kW ηL ) 0.55 NE1 ) 10 NE2 ) 19 NE3 ) 28 NT1 ) 35 NS2 ) 9 NT2)16 R ) 51.63 kmol/h LS ) 15.11 kmol/h QR1 ) 488.35 kW ηV ) 0.53 ηL ) 0.25
NS1 ) 9 NT1 ) 16 R1 ) 67.36 kmol/h QR1 ) 526.70 kW NS2 ) 11 NT2 ) 19 R2 ) 37.48 kmol/h QR2 ) 545.92 kW NS1 ) 11 NT1 ) 20 R1 ) 40.52 kmol/h QR1 ) 629.65 kW NS2 ) 9 NT2 ) 16 R2 ) 44.79 kmol/h QR2 ) 364.60 kW NE ) 22 NS ) 9 NT ) 36 R ) 595.64 kmol/h LS ) 32.27 kmol/h QR ) 4211.65 kW NS1 ) 9 NT1 ) 16 R1 ) 69.00 kmol/h QR1 ) 715.07 kW NS2 ) 9 NT2 ) 17 R2 ) 22.09 kmol/h QR2 ) 205.31 kW NS3 ) 10 NT3 ) 19 R3 ) 25.48 kmol/h QR3 ) 327.43 kW NS1 ) 9 NE ) 17 NT1 ) 26 NT2 ) 10 R1 ) 30.65 kmol/h R2 ) 31.76 kmol/h QR1 ) 766.67 kW ηV ) 0.68 NS1 ) 18 NE ) 10 NT1 ) 28 NT2 ) 12 R1 ) 106.37 kmol/h QR2 ) 102.20 kW QR1 ) 700.57 kW ηL ) 0.48 NE1 ) 10 NE2 ) 19 NE3 ) 28 NT1 ) 35 NS2 ) 9 NT2 ) 16 R ) 67.84 kmol/h LS ) 31.78 kmol/h QR1 ) 524.0 kW ηV ) 0.5 ηL ) 0.17
frequencies the TCDS direct and indirect sequences exhibit higher values of σ/ than the other sequences. At intermediate frequencies, the Petlyuk system shows values of σ/ similar to those of the TCDS direct sequence, but as the frequency increases, the minimum singular values for the Petlyuk system decrease drastically, and the TCDS direct and indirect sequences offer the best values of this parameter. These results indicate that TCDS sequences are expected to show good closedloop responses in contrast to the other distillation systems under analysis. Figure 10 displays the condition number for each separation system; the TCDS direct
Figure 7. Minimum singular values for feed 1.
Figure 8. Condition numbers for feed 1.
sequence shows the lowest values for most of the frequency range, indicating that this choice offers better conditioning properties against model uncertainties and process disturbances than the other schemes. The SVD analysis presented in this section has shown that the dynamic properties of TCDS may offer some advantages over the conventional nonintegrated sequences. This unexpected result merits further treatment. 4.2. Closed-Loop Responses. To analyze the trends provided by SVD, closed-loop responses of some sequences were obtained. The two classical direct and indirect distillation sequences and the two TCDS that showed better SVD properties were chosen to conduct this analysis. Simulations were carried out with Aspen Dynamics 10. Changes in set-point compositions were considered. Controllers were tuned using the CohenCoon technique. The control loops were chosen from operational considerations. The compositions of the distillate products (component A or component B) were controlled with the reflux flow rates, while the compositions of the bottoms products (component B or component C) were adjusted with the heat duties supplied to
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Figure 11. Closed-loop behavior of product composition A for a positive change in the set point.
Figure 9. Minimum singular values for feed 2.
Figure 12. Closed-loop behavior of product composition A for a negative change in the set point.
Figure 10. Condition numbers for feed 2.
the reboilers. Design product compositions of 0.98 were assumed for components A and C, while the composition of the intermediate component was taken as 0.95 to reflect a typical value for which energy savings of the integrated systems have been reported. Figure 11 shows the dynamic behavior under feedback control of the four distillation sequences for a set-point change in the composition of product A from 0.98 to 0.99, with the other product compositions under open loop. It can be noted that TCDS show good responses because they reach the new steady state in about 1 h, while the conventional sequences take 2 h or more. For the case of a negative change in the set point of the composition of product A from 0.98 to 0.97, TCDS also reach the new steady state faster, taking 0.5 h as opposed to 1 h or more for the conventional distillation sequences (Figure 12). Figure 13 shows similar trends when a change in the composition set point of product C from 0.98 to 0.99 (with compositions of products A and B under open loop) was implemented. The dynamic responses of TCDS direct and indirect are close to each other; the direct sequence, a choice of wide industrial use, shows in contrast a very sluggish response. A final test to control
Figure 13. Closed-loop behavior of product composition C for a positive change in the set point.
the composition of the intermediate component for a step change in the set point from 0.95 to 0.96, with the other compositions under closed loop, was conducted. The dynamic behavior of the B composition is shown in Figure 14. The coupled designs stabilize faster after some overshoot, while the nonintegrated schemes offer a rather poor behavior, with inverse responses and extremely high settling times. These results corroborate the predictions obtained through SVD, because they show that thermally coupled distillation schemes are indeed controllable and that they can have even better dynamic properties than conventional distillation sequences. This is an interest-
Ind. Eng. Chem. Res., Vol. 40, No. 17, 2001 3761 V ) matrix of left singular vectors W ) matrix of right singular vectors Greek Symbols ηL ) liquid fraction extracted from the main column and supplied to the top of the prefractionator ηV ) vapor fraction extracted from the main column and supplied to the bottom of the prefractionator σ/ ) minimum singular value γ* ) condition number Σ ) matrix of singular values ω ) frequency
Acknowledgment
Figure 14. Closed-loop behavior of product composition B for a positive change in the set point (three closed control loops).
Financial support from CONACyT, Me´xico, and the Universidad de Guanajuato, Me´xico, is gratefully acknowledged. Literature Cited
ing result, because integrated systems typically achieve better economics at the expense of designs that require higher control efforts, and the designer aims in those situations for a proper design/control tradeoff. While a more general analysis on how these factors influence each other on integrated separation sequences is still open to research, the results show that there exist conditions under which TCDS with side columns provide both economic and dynamic behavior incentives over the traditional direct and indirect distillation sequences. 5. Conclusions Controllability properties of TCDS, an issue of major importance, have been shown to be better than those of the conventional direct and indirect sequences, sequences involving side streams, and sequences containing three conventional distillation columns. Although the results of this study might seem unexpected, they are in agreement with those reported by Alatiqi and Luyben,14 who showed that the TCDS indirect sequence (Figure 5) offered better dynamic behavior under load changes than the conventional direct sequence (Figure 1a). It is apparent that the presence of recycle streams, instead of deteriorating the dynamic behavior of separation sequences, may contribute positively to their dynamic properties, both under set-point tracking and under load changes. Nomenclature ABC ) ternary mixture G ) transfer function matrix LS ) side product NE, NS, NT ) number of stages as indicated in the figures QR1 ) reboiler heat duty supplied to column 1 QR2 ) reboiler heat duty supplied to column 2 QR3 ) reboiler heat duty supplied to column 3 R1 ) reflux flow rate to column 1 R2 ) reflux flow rate to column 2 R3 ) reflux flow rate to column 3
(1) Glinos, K.; Malone, F. Optimality Regions for Complex Column Alternatives in Distillation Systems. Chem. Eng. Res. Des. 1988, 66, 229. (2) Fidkowski, Z.; Krolikowski, L. Thermally Coupled System of Distillation Columns: Optimization Procedure. AIChE J. 1986, 32, 537. (3) Fidkowski, Z.; Krolikowski, L. Minimum Energy Requirements of Thermally Coupled Distillation Systems. AIChE J. 1987, 33, 643. (4) Fidkowski, Z.; Krolikowski, L. Energy Requirements of Nonconventional Distillation Systems. AIChE J. 1990, 36, 1275. (5) Triantafyllou, C.; Smith, R. The Design and Optimisation of Fully Thermally Coupled Distillation Columns. Trans. Inst. Chem. Eng. 1992, 70, 118. (6) Annakou, O.; Mizsey, P. Rigurous Comparative Study of Energy-Integrated Distillation Schemes. Ind. Eng. Chem. Res. 1996, 35, 1877. (7) Wolff, E. A.; Skogestad, S. Operation of Integrated ThreeProduct (Petlyuk) Distillation Columns. Ind. Eng. Chem. Res. 1995, 34, 2094. (8) Abdul Mutalib, M. I.; Smith, R. Operation and Control of Dividing Wall Distillation Columns. Part I: Degrees of Freedom and Dynamic Simulation. Trans. Inst. Chem. Eng. 1998, 76, 308. (9) Abdul Mutalib, M. I.; Zeglam, A. O.; Smith, R. Operation and Control of Dividing Wall Distillation Columns. Part II: Simulation and Pilot Plant Studies Using Temperature Control. Trans. Inst. Chem. Eng. 1998, 76, 319. (10) Herna´ndez, S.; Jime´nez, A. Controllability Analysis of Thermally Coupled Distillation Systems. Ind. Eng. Chem. Res. 1999, 38, 3957. (11) Luyben, W. L. Practical Distillation Control; Van Nostrand Reinhold: New York, 1992. (12) Herna´ndez, S.; Jime´nez, A. Design of Optimal ThermallyCoupled Distillation Systems Using a Dynamic Model. Trans. Inst. Chem. Eng. 1996, 74, 357. (13) Herna´ndez, S.; Jime´nez, A. Design of Energy-Efficient Petlyuk Systems. Comput. Chem. Eng. 1999, 23, 1005. (14) Alatiqi, I. M.; Luyben, W. L. Control of a Complex Sidestream Column/Stripper Distillation Configuration. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 762.
Received for review January 10, 2000 Revised manuscript received September 7, 2000 Accepted May 20, 2001 IE000047T
