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Ind. Eng. Chem. Res. 1998, 37, 528-534
Plantwide Design and Control of Processes with Inerts. 2. Heavy Inerts Paul W. Belanger and William L. Luyben* Chemical Process Modeling and Control Research Center and Department of Chemical Engineering, Lehigh University, Iacocca Hall, 111 Research Drive, Bethlehem, Pennsylvania 18015
This is the second paper of a series that explores the design and control of processes containing inert components. Three strategies for removal of heavy inerts from a process are compared both from the standpoint of steady-state economics as well as from the standpoint of dynamic controllability. These processes are essentially the “inverses” of the processes discussed in the first paper of the series. It is shown that the best structure for the case of heavy inerts is the inverse of the best light inert structure (the reader is referred back to the first paper of the series). A reactor and full column with side draw is used. The heavy inert is removed as the bottoms product, the sidestream is recycled back to the reactor, and the overhead is the plant product. Introduction In the first paper of this series the economic and dynamic properties of processes utilizing various light inert removal strategies were studied. Similar studies are presented in this paper for the case of heavy inerts. The first part of this paper involves the study of how to design a process that has favorable steady-state economics in the face of heavy inert loading. The second part focuses on how the dynamic controllability of each process impacts its overall profitability. All of the assumptions that were made in the first paper are made in this paper (e.g., reaction kinetics, economics, tray hydraulics, etc.). The relative volatilities of the reactant and product are 1.0 and 2.0, respectively (the reactant is heavier than the product to ensure that inert can accumulate in the recycle). The relative volatility of the heavy inert is 0.1 in some case studies and 0.25 in others. Heavy Inert Removal Strategies Three process flow sheets for removing heavy inert from the process are investigated. These processes are essentially the inverses of the processes studied in the previous paper where light inerts were present. The first strategy (system H1, shown in Figure 1) involves designing the separations section to only separate reactant from product. A small amount of the recycle stream is purged from the process in order to prevent the buildup of inert. The concentration of inert must be high in order to prevent excessive raw material losses. The second strategy (system H2, shown in Figure 2) involves designing the separation section to separate both reactant from product and inert from reactant. Since the system is able to produce a purge stream that has less reactant in it, a smaller purge stream is required. This reduces raw material losses. The third strategy (system H3, Figure 3) involves the design of a separation unit to pretreat the fresh feed. * Author to whom correspondence should be addressed. Telephone: (610)758-4256. Fax: (610)758-5297. E-mail: wll0@ lehigh.edu.
The fresh feed is fed to a distillation column where inert is separated from reactant. The reactant is then sent to a reactor/separation system. In the reactor/separation system the reactant reacts to form product, the product is separated from the reactant, and the reactant is recycled back to the reactor. A small portion of the recycle is removed from the reactor/separation system and is fed back to the preseparation column. Analysis of Steady-State Economics The optimal designs of systems H1, H2, and H3 for feed inert levels zI0 ) 0.01 and 0.05 and inert volatilities RI ) 0.1 and 0.25 are summarized in Tables 1-3. Figure 4 illustrates the steady-state profitabilities of these designs. As was the case in the previous paper, the system utilizing the first inert removal strategy (system H1) is the least profitable from a steady-state standpoint of all of the systems considered. The main reason for this is the inability of system H1 to separate inert from reactant. In order to minimize raw material losses, the recycle must be rich in inert and lean in reactant and product. This is especially important in the current case where the purge is the same composition as the recycle stream (in the previous paper the purge was always richer in inert than that in the recycle stream because the purge was drawn off as a vapor). In order to achieve a high concentration of inert in the recycle stream, a large buildup of inert at steady state is required. The large buildup of inert necessitates the use of a larger reactor, which increases the capital cost of the plant. Despite the large buildup of inerts in system H1 at steady state, the raw material losses for system H1 are still substantially higher than for systems H2 or H3. This is due to the inability of system H1 to separate inert from reactant. The system utilizing the third inert removal strategy (system H3) is significantly less profitable from a steadystate standpoint than the system utilizing the second inert removal strategy (system H2). This was not the case for light inerts. The difference can be attributed to the energy costs associated with the pretreatment column. For the case of light inerts, a relatively small
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Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 529
Figure 1. Reactor/column system with recycle and purge (system H1).
vapor boilup rate in the pretreatment column could be used to obtain a purge stream that was rich in inert. This was because the distillate flow rate in the pretreatment column was small. For the case of heavy inerts the purge is drawn from the bottom of the pretreatment column and the distillate flow rate is large. This means that nearly all of the liquid feed to the column must be vaporized in the reboiler. This results in substantially higher energy costs and explains the difference between the profitability of systems H2 and H3. As can be seen in Figure 4 the profitability of each system decreases as the inert volatility increases and as the amount of inert in the fresh feed increases. The amount of inert in the feed stream has a stronger effect on profitability than changes in inert volatility, especially for system H1. Systems H2 and H3, being able to effectively separate inert from reactant, are not affected as strongly for increases in feed inert levels. From the standpoint of steady-state economics it appears that the second inert removal strategy leads to a more profitable system than the first or third removal strategies. This is in contrast to the light inert case where the second and third inert removal strategies led to process designs of comparable steady-state profitability. While the decision of which removal strategy to use is more clear in the heavy inert case, the effects of dynamic performance are yet to be accounted for. The next section focuses on assessing the effects of dynamic performance on the profitability of the systems.
Dynamic Analysis Control Structures. The control structures used in this study are similar to those used in the previous paper and are illustrated in Figures 1-3. In each system the production rate is determined by the fresh feed flow rate F0. The reactor effluent flow rates are manipulated to regulate reactor holdups. Again, a loosely tuned proportional only reactor inventory controller is used (tuned such that a 20 (lb mol)/h change in fresh feed flow rate leads to a 50 (lb mol)/h change in reactor inventory). The pressure of each column is controlled by manipulating the cooling water flow rate. In all systems the liquid inventory in the reflux accumulators are controlled by manipulating the overhead product flow rate of the corresponding column. The base level of the column in system H1 is controlled by manipulating the recycle flow rate. The steam flow rate is used to regulate the liquid level in the base of the column in system H2. The flow rate of the recycle in system H2 is used to regulate the inventory of the side draw accumulator. In system H3 the base level of the pretreatment column is controlled via the steam flow rate while the base level of the product column is controlled via the recycle flow rate. All inventory control loops with the exception of the reactor inventory control loop are assumed “perfect”. It was found that for system H1 the rate of steam to the column must be ratioed to the column feed rate. Without the ratio control the plantwide inventory control system fails (it has a recycle gain greater than 1.0). A ratio controller is also used
530 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998
Figure 2. Reactor/column with side draw recycle and purge (system H2).
in system H3 since it contains system H1 as a subprocess. These ratio controllers also operate under the “perfect control” assumption (the tuning of the controllers is tight enough that their dynamics are negligible). The purge compositions of each system are controlled by manipulating the corresponding purge flow rate. The product compositions of each system are controlled via the reflux flow rates in the product columns. All of the composition loops use tightly tuned PI controllers. A 3 min dead time is associated with each composition measurement. Relay-feedback tests (Astrom, 1984) are used to determine TL settings (Tyreus and Luyben, 1992) for each of these quality control loops. Quantification of Dynamic Properties. With the control structures selected and tuned for each process design, LATV tests were performed to determine the peak closed-loop regulator log moduli from each load disturbance (F0 and zI0) to each output variable of interest (xAD and xIP). The magnitudes of the closedloop log moduli are shown in Figure 5. This figure illustrates some interesting dynamic characteristics of processes utilizing the three different inert removal strategies, many of which are similar to those of the previous paper. Tables 4 and 5 list the recycle gains and reactor inventory control gains for each system for each level of inert loading and each inert volatility considered. As was the case for light inerts, the effects of fresh feed flow rate fluctuations on product quality are higher for system H1 than for systems H2 and H3, especially
for higher levels of inert in the feed. This trend cannot be attributed to differences in recycle gains since the gains for system H1 are substantially lower than those of system H2 for all four cases. Differences in recycle gains do contribute, however, to the differences seen between systems H2 and H3. The primary factor responsible for the poor performance of system H1 is the large buildup of inert in the reactor at steady state. As noted in the first paper in this series, the larger the difference between the reactor composition and the reactor feed composition, the more sensitive the system will be to fluctuations in the reactor feed flow rate. For system H1 the inert levels in the reactor are substantially higher than the inert levels in the feed for all four cases considered. This is not the case for systems H2 and H3. Thus, larger fluctuations in the reactor effluent inert levels can be expected for system H1 than for systems H2 and H3. This tends to affect the separations system and cause larger fluctuations in product quality. Figure 5 also shows that the effects of fresh feed flow rate fluctuations on purge composition are significantly lower for system H2 than for systems H1 and H3. As was stated above, the fluctuations in inert levels in the reactor effluent are smaller for system H2 than for system H1. This causes the differences in performance seen between these two systems. The sensitivity of system H3 in this regard is due to the location of the disturbance. In system H3 the disturbance is introduced directly to the distillation column being used to purify the purge stream whereas in the other two
Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 531
Figure 3. Reactor/column system with pretreatment of fresh feed (system H3).
Figure 4. Steady-state profitability of systems H1, H2, and H3 vs feed inert levels and inert volatility.
Figure 5. Closed-loop regulator log moduli for systems H1 (solid), H2 (dashed), and H3 (dash-dotted).
532 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 Table 1. Economic Impact of Changes in Feed Inert Level and Inert Volatility on System H1 RI zI0
0.1 0.01
0.25 0.01
0.1 0.05
0.25 0.05
NT FT xAF xIF F xAP xIP P xAB xIB B V R VR
15 12 0.251 0.374 775.1 0.359 0.541 4.51 0.359 0.541 531.1 809.3 569.8 2524.0
12 11 0.215 0.421 1145.7 0.269 0.532 4.58 0.269 0.532 901.6 865.3 625.8 2953.4
14 10 0.117 0.514 742.1 0.168 0.758 16.9 0.168 0.758 485.7 689.4 449.9 5646.0
13 10 0.128 0.506 766.0 0.181 0.737 17.4 0.181 0.737 509.0 799.5 560.0 5184.0
Reactor and Stripper Diameters 5.23 5.41 4.83 11.7 12.3 15.3
5.20 14.9
reboiler condenser
Heat Exchanger Areas (ft2) 2023 2163 1723 3372 3605 2872
1999 3331
reactor cost col. cost
Capital Costs ($1000) 989.8 1091.4 1633.3 730.3 726.0 651.0
1548.8 702.5
Dc (ft) Dr (ft)
Utility and Raw Matl. Costs ($1000/yr) energy cost 424.9 454.3 361.9 raw matl. cost 40 993.7 41 005.4 43 075.2
419.7 43 162.6
DCFROR
0.210 14
0.368 17
0.359 05
0.220 20
Table 2. Economic Impact of Changes in Feed Inert Level and Inert Volatility on System H2 RI zI0
0.1 0.01
0.25 0.01
0.1 0.05
0.25 0.05
NT FT DT xAF xIF F xAP xIP P xAB xIB B V R VR
17 14 13 0.355 0.007 833.3 0.027 0.971 2.49 0.496 0.006 591.3 830.8 591.3 1781.5
18 14 13 0.326 0.107 876.8 0.048 0.951 2.54 0.446 0.144 634.7 874.2 634.7 1941.9
16 13 12 0.185 0.036 672.8 0.004 0.995 12.7 0.289 0.027 420.6 660.1 420.6 3576.0
17 13 12 0.185 0.145 731.6 0.025 0.974 13.0 0.277 0.195 479.1 718.6 479.1 3559.2
Reactor and Stripper Diameters 5.30 5.43 4.72 10.4 10.7 13.1
4.93 13.1
reboiler condenser
Heat Exchanger Areas (ft2) 2077 2186 1650 3462 3643 2750
1797 2994
reactor cost col. cost
Capital Costs ($1000) 797.0 1 840.9 1 1229.4 764.3 1 800.0 1 653.4 1
1225.8 698.9
Dc (ft) Dr (ft)
Utility and Raw Matl. Costs ($1000/yr) energy cost 436.2 459.0 346.6 raw matl. cost 40 654.3 40 662.7 42 364.5
377.3 42 413.3
DCFROR
0.26 789
0.40 206
0.39 29
0.27 450
systems the disturbance is fed to a large reactor that serves as a disturbance filter. This not only explains the sensitivity of the purge composition of system H3 to feed flow rate disturbances but also explains the sensitivity of the purge composition of system H3 to feed composition disturbances. These are the same trends that were noted in the case of light inerts.
Table 3. Economic Impact of Changes in Feed Inert Level and Inert Volatility on System H3 RI zI0 NT1 FT1 NT2 FT2 xAF xIF F xAF1 xIF1 F1 xAP xIP P xAP2 xIP2 P2 xAB xIB B V1 R1 V2 R2 VR
0.1 0.01 5 1 16 12 0.418 0.038 770.5 0.875 0.006 269.8 0.014 0.986 2.5 0.601 0.055 30.3 0.601 0.055 500.7 269.8 0.0 772.4 532.9 1515.4
0.25 0.01 5 1 17 12 0.313 0.215 641.8 0.832 0.063 293.4 0.192 0.808 3.0 0.492 0.343 53.9 0.492 0.343 348.5 293.4 0.0 758.0 518.5 2024.3
0.1 0.05 5 1 17 12 0.314 0.050 738.5 0.853 0.014 296.7 0.015 0.985 12.8 0.460 0.074 57.2 0.460 0.074 441.8 296.7 0.0 674.6 435.1 2099.6
0.25 0.05 5 1 17 13 0.173 0.369 702.8 0.699 0.201 373.7 0.065 0.935 13.5 0.257 0.560 134.2 0.257 0.560 329.1 373.7 0.0 650.0 410.5 3817.1
Reactor and Stripper Diameters 3.02 3.15 3.17 5.11 5.06 4.77 9.8 10.9 11.0
3.55 4.69 13.4
reboiler 1 condenser 1 reboiler 2 condenser 2
Heat Exchanger Areas (ft2) 674 733 742 1124 1222 1236 1931 1895 1687 3218 3159 2811
934 1557 1625 2708
reactor cost col. 1 cost col. 2 cost
Capital Costs ($1000) 720.7 862.9 882.7 303.8 320.5 322.6 720.2 722.3 672.2
1280.3 373.4 656.9
Dc1 (ft) Dc2 (ft) Dr (ft)
Utility and Raw Matl. Costs ($1000/yr) energy cost 547.1 552.0 509.9 raw matl. cost 40 647.6 40 740.0 42 386.4
537.5 42 509.0
DCFROR
0.245 23
0.380 12
0.363 31
0.261 27
Table 4. Recycle Gains (kSr) system H1 system H2 system H3
0.527 0.712 -0.398 RI ) 0.1 zI0 ) 0.01
0.625 0.736 -1.233 RI ) 0.25 zI0 ) 0.01
0.144 0.624 -0.764 RI ) 0.1 zI0 ) 0.05
0.166 0.654 -4.220 RI ) 0.25 zI0 ) 0.05
Table 5. Reactor Inventory Controller Tunings (Kc) system H1 system H2 system H3
2.534 1.389 0.859 RI ) 0.1 zI0 ) 0.01
3.195 1.515 0.538 RI ) 0.25 zI0 ) 0.01
1.402 1.064 0.680 RI ) 0.1 zI0 ) 0.05
1.438 1.156 0.230 RI ) 0.25 zI0 ) 0-0.05
It can be seen that in general the effects of fresh feed composition changes on product quality are smaller for systems H2 and H3 than for system H1. System H2 tends to be the best at rejecting the effects of composition changes on product quality for the more severe cases of inert loading (higher levels of inert in the feed and higher inert volatilities); however, for low inert volatility and low levels of inert in the feed system H3 tends to be the most controllable in this regard. Altogether, the information in Figure 5 indicates that system H2 is the most controllable of the three systems; however, this information must be quantified on an economic scale in order to make an informed decision
Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 533 Table 6. Percentage of Offspec Product and Offspec Purge under Worst Case Loading Conditions system H1 system H2 system H3
% product offspec % purge offspec % product offspec % purge offspec % product offspec % purge offspec
17.3
0.5
2.3
8.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
77.4
26.8
39.6
RI ) 0.1 zI0 ) 0.01
RI ) 0.25 zI0 ) 0.01
RI ) 0.1 zI0 ) 0.05
RI ) 0.25 zI0 ) 0-0.05
as to which inert removal strategy is the best strategy from an overall economic standpoint. The capacitybased economic approach is applied to quantify the effects of dynamic controllability on overall profitability. For the application of the capacity-based economic approach the following assumptions are made: 1. Peak fluctuations in F0 are 20 (lb mol)/h for each case study. 2. Peak fluctuations in zI0 are 1.0 mol % for zss I0 ) 0.01 and 5.0 mol % for zss ) 0.05. I0 3. The specification band on product quality is (0.1 mol %. 4. The specification band on purge quality is (1.0 mol %. 5. The revenue of the plant is penalized in proportion to the fraction of the product and purge that is offspec. The fraction of revenue lost is equal to 10% of the fraction of offspec product plus the fraction of offspec purge (it is assumed that offspec product can still be sold back to the plant for reprocessing). Using the assumptions above and the frequencies obtained from LATV tests, worst case load disturbances were constructed for each system for each level of inert loading and each inert volatility. Each process was simulated using its worst case disturbance to determine the percentage of offspec product and offspec purge that is expected for each system under worst case loading conditions. This information is given in Table 6 and was used to find new, more conservative predictions for the return on investment of each process, taking into account both the controllability of product and purge as well as the need to invest in a larger reactor (the reactor must be oversized to be able to handle holdup fluctuations). The new values of return on investment are shown in Figure 6. A comparison of Figures 4 and 6 illustrates the effects that dynamic performance can have on the profitability predicted from steady-state models. System H2, having very favorable dynamic characteristics, has an overall profitability that is very similar to the profitability predicted from steady-state models. The only difference is the added capital associated with the increased reactor size. The overall profitability of system H1 is slightly lower than its predicted steady-state profitability. This is due to the variability that is seen in product quality. The overall profitability of system H3 is drastically reduced for cases where the inert volatility is high or the inert level in the feed is high. This is because of the very large purge composition fluctuations that occur under these conditions. For all cases, system H2 is the most favorable system from the standpoint of overall profitability. Thus, the use of the second inert removal strategy results in plant designs with more
Figure 6. More conservative profitability estimates for systems H1, H2, and H3 vs feed inert level and inert volatility.
favorable economics than the first or third inert removal strategies. The same conclusion that was drawn for the case of light inerts also holds for the case of heavy inerts. Conclusions It was shown in this paper that many of the conclusions drawn in the previous paper concerning the effectiveness of light inert removal strategies hold for the case of heavy inerts as well. The second inert removal strategy (designing the separation section of the plant to be able to purify the purge stream as well as the product stream) is the most favorable from an overall economic standpoint. As was the case with light inerts, it is economically desirable to design the plant in such a way that heavy inert can be removed from the plant while avoiding excessive losses of raw material through the purge stream and large buildups of inert within the recycle loop. This can be accomplished by designing the separation section of the plant to be able to purify the purge stream, provided this alternative is not too expensive (i.e., requires the use of high-pressure steam or high vacuum). The purification of the purge results not only in an improvement in steady-state profitability but an improvement in plantwide controllability as well. Allowing inerts to build up in the reactor increases fluctuations in the composition of the reactor effluent stream for a given feed flow rate fluctuation. This places a larger load on the separation system. It is important from a dynamic standpoint to introduce the fresh feed to a location in the plant that has a high capacitance (the liquid phase CSTR). Introducing the fresh feed directly to a distillation column connected to a product stream results in a high sensitivity of product quality to fluctuations in fresh feed conditions. Nomenclature Ac ) condenser area (ft2) Ar ) reboiler area (ft2) Bj ) bottoms flow rate of column j ((lb mol)/h) CLLM ) closed-loop log modulus (dB) D ) product flow rate ((lb mol)/h) DCFROR ) discounted cash flow rate of return Dc ) column diameter (ft) Dr ) reactor diameter (ft)
534 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 F ) reactor effluent flow rate ((lb mol)/h) Lc ) column height (ft) Lr ) reactor height (ft) P ) purge flow rate ((lb mol)/h) Rj ) reflux flow rate in column j ((lb mol)/h) VR ) reactor holdup (lb mol) Vj ) vapor boilup in column j ((lb mol)/h) xij ) liquid mole fraction of component i in stream j yij ) vapor mole fraction of component i in stream j zij ) total mole fraction of component i in stream j Greek Symbols Rij ) volatility of component i with respect to component j
Literature Cited Astrom, K. J.; Hagglund, T. Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica 1984, 20 (5), 645-651. Tyreus, B. D.; Luyben, W. L. Tuning PI controllers for integrator/ dead time processes. Ind. Eng. Chem. Res. 1992, 31, 2625-2628.
Received for review April 16, 1997 Accepted September 26, 1997X IE9702892
X Abstract published in Advance ACS Abstracts, November 15, 1997.
