Plantwide Design and Control of Processes with Inerts. 3. Intermediate

Ind. Eng. Chem. Res. 1998, 37, 535-546

535

Plantwide Design and Control of Processes with Inerts. 3. Intermediate 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

In this final paper of a series that explores the design and control of processes containing inert components we study five strategies for the removal of intermediate inerts. It is shown that the best structure for the case of intermediate inerts uses a direct distillation sequence where the reactant is separated first (and recycled) and then the inert is separated from the product. Introduction In the first and second papers of this series the economic and dynamic properties of processes utilizing various light and heavy inert removal strategies were studied. Similar studies are presented in this paper for the case of intermediate 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 intermediate inert loading. The second part focuses on how the dynamic controllability of each process impacts its overall profitability. The relative volatilities of the reactant and product are 2.0 and 1.0, respectively. The relative volatility of inerts is 1.33 in some case studies and 1.66 in others. Intermediate Inert Removal Strategies Five different flow sheets are investigated. These processes are quite different from the strategies investigated in the previous two papers since the analogies that were drawn between light and heavy inerts are generally not applicable to the case of intermediate inerts. In the discussion that follows many alternative structures are presented. For purposes of clarity, a simplified overview of the structures is given in Figure 1. A system utilizing the first inert removal strategy (system I1) is illustrated in Figure 2. This is a direct distillation sequence where the overhead of the first column (which contains most of the unreacted reactant) is recycled back to the CSTR and the bottoms product is fed to a second distillation column where the inert is separated from the product. System I2 (illustrated in Figure 3) uses a single column to carry out the desired separations. The reactor effluent is fed to a distillation column with a side draw. The overhead product of the column is recycled back to the reactor. The side draw is used to remove the inert from the system. The bottoms product of this column is the plant product. The third strategy (system I3) is illustrated in Figure 4. The major difference between this system and system I1 is the order of separation. Here the reactor effluent is fed to the first distillation column whose bottoms product is the plant product stream. The overhead of the first column is fed to a second distillation column. * To whom correspondence should be addressed. Phone: (610)758-4256. Fax: (610)758-5297. E-mail: [email protected].

Figure 1. Overview of structures.

The inert is withdrawn as the bottoms product of this column. The overhead product is recycled back to the reactor for further processing. System I4 (illustrated in Figure 5) differs from system I2 by the addition of a side rectifier. The fifth intermediate inert removal strategy is illustrated in Figure 5. This system is a modified version of system I2 in which the reactor effluent stream is fed to a prefractionator. The overhead and bottoms products of the prefractionator contain roughly half of the inert in the reactor effluent stream. The overhead product is rich in component A and lean in component B. The bottoms product is rich in component B and lean in component A. These streams are fed to the main column at tray locations above and below the side draw. The differences in feed compositions and volatilities

S0888-5885(97)00290-X CCC: $15.00 © 1998 American Chemical Society Published on Web 02/02/1998

536 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998

Figure 2. System I1.

cause the inert component to concentrate in the region between the two feed trays. This reduces the amounts of raw material and product that are lost in the side stream purge. Analysis of Steady-State Economics The two main factors that affect the choice of purging strategy and the selection of design parameters are the relative volatility of the inert component and the amount of inert that is introduced to the process. Tables 1-5 list the optimal designs of the five systems described above for inert volatilities RI ) 1.33 and RI ) 1.66 and feed inert levels zI0 ) 0.01 and zI0 ) 0.05. A plot of the steady-state profitability of each system is given in Figure 7. The profitability of system I3 is omitted from this plot for reasons that are given later in this section. The first observation that can be made from the tables is that for low levels of inert loading (zI0 ) 0.01) systems I1-I5 all converge to the same optimal designs (one design for each inert volatility). The optimal designs

are simply reactor/stripper systems where all of the inert is removed through the product stream. This is easy to justify. The specified impurity level in the product is 1.05 mol %. This impurity must be either component A, component I, or a mixture of both. If a significant amount of A is present in the bottoms product of a distillation column, then most of the I that is present in the column feed will also exit the column through the bottoms stream. For the case where zI0 ) 0.01 most of the inert will exit in the product stream. A natural conclusion that can be drawn from the argument above is that for an intermediate inert in a ternary system it is desirable to drive as much of the inert out through the product stream as possible without violating end product purity specifications. This is, of course, provided that the presence of inert in the product does not affect the value of the product. For the cases where zI0 ) 0.01 it is possible to allow all of the inert to leave the process through the product stream without violating the 98.95 mol % purity specification. For system I1 this means that the second distillation column

Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 537


is not necessary. Also, since the reaction is irreversible and since energy costs tend to have a stronger impact on profitability than the reactor cost, it is not necessary for the recycle stream to be pure. This means that the rectifying section on the first column is not necessary. Thus the optimal design for system I1 reduces to a simple reactor/stripper system. This may not be the case if the reaction is reversible or if the capital cost associated with building a larger reactor is high. This would lead to a situation where it would be desirable to purify the recycle stream. For system I2, it is not necessary to have a side draw since all of the inert can be removed from the process through the product stream. The elimination of the side draw stream reduces raw material costs. As was the case for system I1, it is not necessary to purify the recycle stream. For these reasons the low inert in the feed case is degenerate and all of the alternative flow sheets reduce to the reactor/stripper system and have the same profitability. The interesting differences in profitability occur at higher inert loading levels (zI0 ) 0.05). A purge is required under the conditions of higher inert loadings since it is impossible to remove all of the inert through the product stream without violating product purity specifications. Figure 7 shows that systems I1 and I4 are the most desirable from the standpoint of steadystate economics for higher inert loading levels. System I3 has been omitted from this figure because it reduces to the same optimal structure as system I2 as is shown in Tables 2 and 3. This is because the optimal design has a significant amount of component B in the recycle. The second column in system I3 is unable to separate inert from the recycle without a significant loss of plant

product. For this reason, the second distillation column in system I3 is undesirable. The main cause of the differences in profitability of the four remaining systems for higher levels of inert loading stems from their abilities to purify the purge stream. The second column of system I1 is dedicated to separating inert from product. Since very little reactant is allowed to leave the reactor/column subsystem, the second column of system I1 can be used to obtain two relatively pure product streams. In system I4, there is very little reactant present in the bottom of the main column. Therefore, by introducing a draw from the bottom of the main column to a side rectifier, a fairly pure purge stream can be obtained. The limitations of simple distillation columns with respect to ternary separations prevent the side draw of system I2 from having a high purity. System I5, while able to overcome some of the limitations of the simple column in system I2 through the use of a prefractionator, is still unable to purify the purge stream to the same extent as systems I1 and I4 without incurring excessive energy and capital costs (extra energy must be expended in order to separate the inert from the reactant). For these reasons systems I1 and I4 are more profitable from a steady-state standpoint than systems I2 and I5. There are other factors besides raw material costs that contribute to the differences in profitability between the designs utilizing different inert removal strategies; however, all of these factors can be traced back to each system’s ability to purify the purge stream. For example, the cost of the reactors for systems I2 and I5 are much higher than that for for systems I1 and I4.



Larger reactors are required in systems I2 and I5 because of large buildups of inert at steady state. As is shown in Figure 7, the profitability of each system increases as the relative volatility of the inert increases. This is due primarily to differences in energy costs. As the relative volatility of the inert component increases, it becomes easier to separate the inert from the product. Although it becomes more difficult to separate the inert from the reactant, this does not become an issue for systems I1-I4 since the separation of the inert from the reactant is not of critical importance in these systems (at least not for the current cases where energy costs are more dominant than the capital costs associated with the reactor). System I5 is affected the most by the change in volatility since its separation system must be capable of producing three product streams of reasonable purity. It is shown in Figure 7 that system I5 actually becomes less profitable for higher inert volatilities than system I2. This is probably due to the presence of a strong local minimum around this optimal design (system I5 can be reduced to the

same structure as system I2 through the removal of the prefractionator). From the standpoint of steady-state economics it appears that the most cost effective inert removal strategies are those used by systems I1 and I4. The profitabilities of systems I2 and I5 are a few percent lower; however, this is not enough of a difference to completely disregard these designs. The decision of which design to use must again incorporate dynamic controllability. While the dynamic characteristics of these designs cannot be determined precisely a priori, there are some characteristics of each design that determine each systems’ controllability. Systems I1 and I4 are better able to separate the inert from the product. This means that smaller amounts of inert are built up at steady state in systems I1 and I4 than that in systems I2 and I5. It has been shown in the previous two papers that this tends to have a detrimental effect on controllability. If the mole fraction of inert in the reactor at steady state is very different from the mole fraction of inert in the fresh feed stream,




540 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 Table 1. Economic Impact of Changes in Inert Volatility and Feed Inert Level on the Optimal Design of System I1

Table 2. Economic Impact of Changes in Inert Volatility and Feed Inert Level on the Optimal Design of System I2

RI zI0

1.33 0.01

1.66 0.01

1.33 0.05

1.66 0.05

RI zI0

1.33 0.01

1.66 0.01

1.33 0.05

1.66 0.05

NT1 FT1 NT2 FT2 xAF xIF F xAD xID D xAB1 xIB1 B1 xAP xIP P xAB2 xIB2 B2 V1 R1 V2 R2 VR

18 1

18 1

NT FT DT xAF xIF F xAD xID D xAB xIB B xAP xIP P V R VR

18 1

0.153 0.152 845.6 0.213 0.208 606.1 0.0005 0.0100 239.5

25 5 30 22 0.142 0.212 558.8 0.255 0.344 308.8 0.002 0.050 250.0 0.040 0.952 10.5 0.0001 0.0104 239.5 558.0 249.2 371.1 360.5 4667.2

18 1

0.390 0.018 986.9 0.515 0.021 747.4 0.0005 0.0100 239.5

20 4 35 25 0.210 0.088 473.6 0.445 0.130 223.5 0.001 0.050 250.1 0.012 0.946 10.6 0.0000 0.0105 239.5 657.6 434.1 995.2 984.6 3145.5

0.390 0.018 986.9 0.515 0.021 747.4 0.0005 0.0100 239.5

0.153 0.152 845.6 0.213 0.208 606.1 0.0005 0.0100 239.5

747.4 0.0 1623.6

606.1 0.0 4141.1

45 11 0 0.068 0.366 578.4 0.116 0.617 322.2 0.0000 0.0105 239.5 0.116 0.617 16.7 1494.8 1155.9 9869.5

30 16 0 0.073 0.324 399.9 0.183 0.792 147.6 0.0001 0.0104 239.5 0.183 0.792 12.8 874.1 713.7 9018.5

747.4 0.0

606.1 0.0

1623.6

4141.1

Reactor and Column Diameters 5.02 4.53 4.71 5.80 10.1 13.8 12.6

4.34 3.54 14.3

reboiler 1 condenser 1 reboiler 2 condenser 2

Heat Exchanger Areas (ft2) 1868 1515 1644 3114 2526 2740 2488 4147

1395 2325 928 1546

reactor cost col. 1 cost col. 2 cost

Capital Costs ($1000) 752.3 1346.8 1135.1 726.3 638.4 690.1 1056.1

1450.9 665.8 551.9

DC1 (ft) DC2 (ft) DR (ft)

Utility and Raw Matl. Costs ($1000/yr) energy cost 392.4 318.2 867.7 raw matl. cost 40236.0 40236.0 42011.7

487.7 42003.4

DCFROR

0.271 36

0.439 99

0.397 61

0.249 38

then the product quality will be sensitive to changes in the fresh feed flow rate. This is because the changes in fresh feed flow rate cause large changes in the composition of the reactor effluent stream. Another effect of having a high level of inerts at steady state is that it necessitates the use of a large reactor. The reactors used in the optimal designs of systems I2 and I5 are substantially larger than those used in the optimal designs of systems I1 and I4. While this tends to increase the capital costs of systems I2 and I5, it also tends to improve their controllability (a large liquid phase CSTR is a better disturbance filter than a small one). In addition to the reactor sizes of systems I2 and I5 being larger than those of systems I1 and I4, the vapor boilup rates in systems I2 and I5 are substantially higher. This increases the energy costs associated with systems I2 and I5; however, like the increased reactor sizes, this also improves their ability to reject the effects of load disturbances (the high internal flow rates in the column tend to “wash out” the effects of feed disturbances). System I4 tends to have higher recycle flow rates than the other systems. This will reduce the sensitivity of system I4 to both fresh feed flow rate and composition

Reactor and Column Diameters 5.02 4.53 7.11 10.1 13.8 18.4

5.43 17.9

reboiler condenser

Heat Exchanger Areas (ft2) 1868 1515 3737 3114 2526 6228

2185 3642

reactor cost col. cost

Capital Costs ($1000) 752.3 1346.8 2311.7 726.3 638.4 1479.3

2185.6 926.7

DC (ft) DR (ft)

Utility and Raw Matl. Costs ($1000/yr) energy cost 392.4 318.2 784.8 raw matl. cost 40 236.0 40 236.0 43 045.3

458.9 42 383.8

DCFROR

0.249 19

0.439 99

0.397 61

0.205 38

disturbances. Disturbances will essentially be washed out by the large recycle stream. The opposite is true for system I5, which has a small recycle flow rate. All of the effects mentioned above will affect the dynamic controllability of the systems and hence their desirability from an overall economic standpoint. Since it is unclear to what extent each variable will affect the dynamic properties of each design, it is necessary to perform experiments in order to quantify the dynamic characteristics of each design on an economic scale. This is the focus of the next section. Dynamic Analysis Control Structures. Control structures for the processes in this paper were selected in the same manner as in the previous papers. Other control structures were investigated, but only the best (“best” meaning the structures that minimized the peak regulator log moduli) among them are presented here (we would like to focus on plant properties rather than control system properties). It is assumed that compositions are measured directly. The dead time associated with a composition measurement is assumed to be 3 min. Reactor inventories are controlled with loosely tuned proportional only controllers (tuned such that a 20 (lb mol)/h change in fresh feed flow rate results in a 50 lb mol change in reactor inventory). This has the benefit of providing smooth flow rate transitions to the separation system. The offset in reactor inventory also helps balance the effects of load disturbances between the separation system and the reactor. The control of all other inventories (column base levels, reflux accumulator levels, and column pressures) is assumed

Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 541 Table 3. Economic Impact of Changes in Inert Volatility and Feed Inert Level on the Optimal Design of System I3

Table 4. Economic Impact of Changes in Inert Volatility and Feed Inert Level on the Optimal Design of System I4

RI zI0

1.33 0.01

1.66 0.01

1.33 0.05

1.66 0.05

RI zI0

1.33 0.01

1.66 0.01

1.33 0.05

NT1 FT1 NT2 FT2 xAF xIF F xAD1 xID1 D1 xAD2 xID2 D2 xAP xIP P xAB1 xIB1 B1 V1 R1 V2 R2 VR

18 1

18 1

45 11

30 16

18 1

18 1

0.390 0.018 986.9 0.515 0.021 747.4 0.515 0.021 747.4

0.153 0.152 845.6 0.213 0.208 606.1 0.213 0.208 606.1

0.073 0.324 399.9 0.183 0.792 160.4 0.183 0.792 147.6 0.183 0.792 12.8 0.0001 0.0104 239.5 874.1 713.7

0.390 0.018 986.9

0.153 0.152 845.6

0.515 0.021 747.4

0.213 0.208 606.1

9018.5

NT FT DT NTR xAF xIF F yADR yIDR DR xABR xIBR BR xAD xID D yAP yIP P xAB xIB B V R RR VR

0.0005 0.0100 239.5 747.4 0.0

0.0005 0.0100 239.5 606.1 0.0

1623.6

4141.1

28 1 18 20 0.253 0.097 960.7 0.001 0.086 658.9 0.000 0.072 647.5 0.343 0.114 709.8 0.023 0.883 11.4 0.0000 0.0105 239.5 1368.7 0.0 647.5 2617.3

DC1 (ft) DC2 (ft) DR (ft)

0.0005 0.0100 239.5 747.4 0.0

0.0005 0.0100 239.5 606.1 0.0

0.068 0.366 578.4 0.116 0.617 338.9 0.116 0.617 322.2 0.116 0.617 16.7 0.0000 0.0105 239.5 1494.8 1155.9

1623.6

4141.1

9869.5

Reactor and Column Diameters 5.02 4.53 7.11 10.1

13.8

18.4

5.43 17.9

(ft2)

reboiler 1 condenser 1 reboiler 2 condenser 2 reactor cost col. 1 cost col. 2 cost

Heat Exchanger Areas 1868 1515 3737 3114 2526 6228

Capital Costs ($1000) 752.3 1346.8 2311.7 726.3 638.4 1479.3

2185 3642

2185.6 926.7

1.66 0.05 23 1 14 10 0.201 0.337 1181.9 0.019 0.297 123.7 0.012 0.237 112.1 0.254 0.415 930.8 0.088 0.871 11.6 0.0001 0.0104 239.5 1054.5 0.0 112.1 3286.8


5.97 2.04 12.8

Heat Exchanger Areas (ft2) reboiler 1868 1515 3422 cond (main column) 3114 2526 5703 cond (rectifyer) 2745

2636 4394 515

DC (ft) DRect (ft) DR (ft)

reactor cost col. + rect. cost

Capital Costs ($1000) 752.3 1346.8 1012.4 726.3 638.4 1689.9

1166.5 1102.2


458.9 42 383.8


553.6 42 180.0

DCFROR

0.249 19

DCFROR

0.264 91

0.439 99

0.397 61

0.205 38

“perfect”. All quality control loops use tightly tuned PI controllers. The flow rate of the fresh feed stream is considered to be a load variable. The control scheme for system I1 is given in Figure 2. In this structure the flow rates of the bottoms stream of each column are used to regulate base levels. A controller is used to adjust the recycle flow rate in order to maintain a constant ratio between the recycle flow rate and the reflux rate in the first column. The accumulator inventories of both columns are controlled by manipulating reflux flow rates. Column pressures are maintained through the manipulation of cooling water flows. Since the main function of the first column is to prevent the reactant from leaving the CSTR/column subsystem, the flow rate of steam to the first column reboiler is used to control the mole fraction of A in the bottoms of the first column (xAB1). The flow rate of steam to the second column reboiler is used to control the purity of the bottoms product stream (xBB2). The purge flow rate is used to regulate the mole fraction of I in the purge (xIP). The control structure for system I2 is illustrated in Figure 3. The reactor effluent stream is used to control reactor inventory. The column base level is controlled via the product flow rate. The reflux flow rate is used to regulate the inventory of the reflux accumulator.

0.439 99

0.397 61

0.251 76

Pressure in the column is regulated by the flow rate of cooling water to the condenser. A controller is used to adjust the recycle flow rate in order to maintain a constant ratio between recycle and reflux flow rates. Two variables remain that can be used for quality control. The flow rate of the purge is used to control the mole fraction of inert in the purge stream. Product quality (xBB) is regulated through the manipulation of the steam flow rate to the column. No control structures have been designed for system I3. This is because it has been shown in the previous section that the optimal designs for this system all converge to the same designs as for system I2. System I3 is omitted from dynamic studies. Figure 5 illustrates the control structure for system I4. The recycle flow rate is used to regulate the inventory in the accumulator of the main column, and the bottoms product flow rate is used to control its base level. The reflux flow rate on the side rectifier is used to control the level in the side rectifier reflux accumulator. The base level in the side rectifier is controlled through the manipulation of the return flow rate. The cooling water flow rate to the side rectifier is used to control the pressure in this column, which must be lower than the pressure in the main column. For the control of product purity (xIB), the flow rate of steam to the main


Figure 7. Steady-state profitability of systems using different inert removal strategies vs feed inert levels and inert volatility. Table 5. Economic Impact of Changes in Inert Volatility and Feed Inert Level on the Optimal Design of System I5 RI zI0

1.33 0.01

1.66 0.01

1.33 0.05

1.66 0.05

NT FT1 FT2 DT NTP FTP xAF xIF F xAF1 xIF1 F1 xAF2 xIF2 F2 xAD xID D xAP xIP P V R VP RP VR

18 1

18 1

0.390 0.018 986.9 0.390 0.018 986.9

0.153 0.152 845.6 0.153 0.152 845.6

0.515 0.021 747.4

0.213 0.208 606.1

747.4 0.0

606.1 0.0

1623.6

4141.1

40 6 30 15 20 10 0.070 0.057 275.4 0.526 0.152 33.2 0.008 0.044 242.2 0.858 0.141 22.4 0.013 0.751 13.5 1399.0 1376.6 299.7 266.5 9504.6

33 5 24 10 13 7 0.069 0.086 281.5 0.461 0.383 36.3 0.011 0.042 245.2 0.590 0.408 28.5 0.196 0.754 13.5 458.7 430.2 391.8 355.5 9545.0


3.94 3.64 18.2

Heat Exchanger Areas (ft2) reboiler (main column) 1868 1515 3498 cond (main column) 3114 2526 5829 reboiler (prefrac) 749 cond (prefrac) 1249

1147 1911 980 1633

DC (ft) DPrefrac (ft) DR (ft)

reactor cost col. + prefrac. cost

Capital Costs ($1000) 752.3 1346.8 726.3 638.4

2258.2 1786.9

2264.2 1099.5

Utility and Raw Matl. Costs ($1000/yr) energy cost 392.4 318.2 891.8 raw matl. cost 0.43999 0.39761 42507.9

446.5 42508.0

DCFROR

0.24254

0.43999

0.39761

0.22305

column is used. The purge flow rate is used to control the mole fraction of inert in the purge. The control structure for system I5 is illustrated in Figure 6. The pressure of each column is regulated via the flow rate of cooling water to the condensers. Bot-

Figure 8. System I5 main column composition profile (zI0 ) 0.05 and RI ) 1.33).

toms flow rates are used to control base levels. Refluxes are used to control accumulator inventories. The main objective of the quality control system is the regulation of product purity. The flow rate of steam to the main column is used for this task. Of major importance, although not the primary function of the quality control system, is the maintenance of the peak in inert composition near the purge location of the main column. This is illustrated for the case of zI0 ) 0.05 and RI ) 1.33 in Figure 8. This peak helps to reduce the amount of raw material and product lost through the purge stream. Several variables must be controlled in order to maintain the peak in inert composition in the main column. The first two are the amount of component B in the overhead product and the amount of component A in the bottoms product of the prefractionator. If the amount of product in the prefractionator distillate increases, then the amount of product in the purge stream increases. Likewise, if the amount of reactant in the prefractionator bottoms stream increases, then the amount of reactant in the purge stream will increase. The amount of reactant in the bottoms stream is fairly insensitive to changes in prefractionator feed conditions. It is, therefore, more important to control the amount of product in the overhead prefractionator product. The flow rate of this stream is used to accomplish this task. Another factor that influences the presence of the peak is the amount of inert recycled to the reactor. If too much inert is recycled to the reactor, then inert will not accumulate around the purge location in the main column. This makes it necessary to control the mole fraction of inert in the recycle stream. The inert levels in the recycle stream are controlled via the recycle flow rate. The final factor that affects the existence and location of the peak in inert concentration is the flow rate of the purge stream. The higher the purge flow rate, the more inert will be removed from the column. This reduces the height of the peak. It is natural, therefore, to use the flow rate of the purge to control purge composition. This not only regulates the quality of one of the plant products but also acts to stabilize the column profile. This control structure has two main weaknesses. The first is that it requires four composition analyzers. This increases the cost of instrumentation as well as the chance of instrumentation failure. This problem can be

Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 543 Table 6. Recycle Gains and Unscaled Reactor Inventory Control Gains (zI0 ) 0.05, rI ) 1.33) system I1 system I2 system I4 system I5

ksr

Kc

0.0029 0.4932 0.8049 0.0816

0.4012 0.7893 2.0503 0.4355

Table 7. LATV Test Results for Each SystemsFresh Feed Flow Rate Disturbance (zI0 ) 0.05, rI ) 1.33) LATV test results system I1 system I2 system I4 system I5

ωmax

Lmax

ωmax

Lmax

2.141 3.103 0.717 1.491

-108.42 -102.23 -109.09 -102.46

8.617 7.129 1.919 7.949

-123.66 -95.55 -91.47 -100.34

xAB

xIP

Table 8. LATV Test Results for Each SystemsFresh Feed Composition Disturbance (zI0 ) 0.05, rI ) 1.33) LATV test results system I1 system I2 system I4 system I5

ωmax

Lmax

ωmax

Lmax

4.384 0.506 2.477 5.283

-72.61 -61.26 -93.80 86.28

0.479 0.506 1.015 0. 771

-46.40 -61.26 -44.19 51.12

xAB

xIP

avoided, of course, if other measurements are used to infer the compositions in the plant. It will be assumed here that direct composition measurements are available. The other weakness of this system is the level of loop interaction that is associated with the main column. Three product composition controls on a distillation column will be highly interacting; however, it is not necessarily the case that loop interaction will degrade performance to the point where this system will be beyond consideration. For this reason, the dynamic qualities of this system with its associated control structure will be investigated. Quantification of Dynamic Properties. The following dynamic analysis is for the case where zI0 ) 0.05 and RI ) 1.33. Lower levels of inert loading are not considered since the optimal economic designs all reduce to the same system. 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 (xIB and xIP). The magnitudes and frequencies of the worst case disturbances are given in Tables 7 and 8. Four main factors affect each system’s ability to reject the effects of fresh feed flow rate disturbances: the recycle gain, the difference in inert mole fraction between the reactor and the fresh feed, the magnitude of the recycle flow rate, and the flow rates internal to the distillation columns. Low values of the recycle gain are desirable because they reduce the magnitude of flow rate recycling and allow a small reactor inventory control gain to be used. Differences between the mole fractions of inert in the reactor and fresh feed tend to amplify the effects of fresh feed flow rate disturbances on the reactor effluent composition. Thus, smaller levels of inert in the reactor are desirable. Larger recycle flow rates are desirable because they tend to wash out the effects of fresh feed flow rate disturbances. For the same reason large internal flow rates are desirable in

the distillation columns. Each system has strengths and weaknesses in rejecting the effects of flow rate disturbances. These strengths and weaknesses can be related to the four factors above. The recycle gains and reactor inventory control gains for each system are listed in Table 6. Systems I1 and I5 have the smallest recycle gains. This tends to improve their abilities to reject the effects of flow rate disturbances. System I4 has the largest steady-state recycle flow rate (709.8 (lb mol)/h). This contributes to its ability to reject the effects of feed flow rate disturbances. On the other hand, system I5 has the smallest recycle flow rate (22.4 (lb mol)/h). This increases its sensitivity to this type of disturbance. Systems I1 and I2 have recycle flow rates that are in between these two extremes. The difference between the inert mole fractions in the feed and in the reactor is the largest for system I2 (0.316) and smallest for system I5 (0.007). The differences for systems I1 and I4 (0.038 and 0.047, respectively) are small. For these reasons the reactor effluent composition of system I2 is much more sensitive to feed flow rate fluctuations than the reactor effluent composition of systems I1, I4, and I5. The sensitivity of the reactor effluent composition to flow rate disturbances is similar for systems I1, I4, and I5; however, it is the smallest for system I5. The internal flow rates (characterized by the vapor rates and liquid rates) of the main columns in each system are similar. The auxiliary columns of systems I4 and I5, however, have relatively small internal flows. Thus, the side rectifier of system I4 and the prefractionator of system I5 will be sensitive to flow rate fluctuations. The prefractionator of system I5, however, will experience larger fluctuations in its feed stream when disturbances in the fresh feed flow rate are present. It will therefore be more sensitive to fluctuations in the fresh feed flow rate. It has been demonstrated in the previous papers that the mole fraction of inert in the reactor has a large influence over the sensitivity of a system to feed flow rate fluctuations. This leads to the hypothesis that system I2 will not be the best system for rejecting the effects of flow rate disturbances. This is, in fact, the case and is shown in Table 7. Of the remaining systems, systems I1 and I4 tend to reject the effects of flow rate disturbances on product composition the best while systems I1 and I5 are the best at rejecting the effects of flow rate disturbances on purge composition. System I1, therefore, would seem to be the best at rejecting the effects of flow rate disturbances. This is probably because system I4 has a large recycle gain while system I5 has a small recycle flow rate. Each of these factors tend to deteriorate the dynamic performance of the closed loop process. Three main factors influence a system’s ability to reject the effects of feed composition disturbances. These are the size of the reactor, the recycle flow rate, and the internal flow rates in the distillation columns. The larger the reactor in a system, the more filtering it will provide and the less sensitive the system will be to composition fluctuations. Again, larger recycle flow rates tend to wash out the effects of disturbances as do large internal flow rates in distillation columns. Systems I2 and I5 have larger reactors (9870 and 9505 lb mol, respectively) than systems I1 and I4 (3146 and 2617 lb mol, respectively). Systems I2 and I5 also


Figure 9. Deviations in product and purge quality under worst case loading conditions.

have large internal flow rates in the distillation columns. Thus, it is natural to assume that systems I2 and I5 are the best at rejecting the effects of composition disturbances. As Table 8 shows this is the case for the control of purge composition; however, it is not the case for product composition control. System I4 is the best at rejecting the effects of composition disturbances on product quality. This is probably due to the fact that system I4 uses two control loops to control the amount of inert in the bottom of the main column. The product composition loop controls it directly while the purge composition control controls it indirectly. System I5 is the second best at rejecting the effects of composition changes on product quality. This is what would be expected. What is not expected is that system I2 appears to be the worst in this respect. From Table 8 it can be seen that the weakness of system I2 is at low frequency. This means that the distillation column of system I2 is simply not capable of rejecting the effects of composition disturbances at low frequencies. From the standpoint of overall dynamic performance, it is difficult to choose the best system from the information discussed above. If flow rate changes are the main disturbance, then system I1 would be the best choice. If composition changes are the main disturbance, then system I4 would probably provide the best dynamic performance (tight control of purge composition is not as important as tight control of product composition). In general both disturbances will be present to some extent. It is therefore necessary to simulate each system with a constructed worst case disturbance consisting of both feed flow rate and composition disturbances to determine which system is the best from a dynamic standpoint. This will also show whether or

Figure 10. Response of system I1 to a 50 (lb mol)/h step increase in fresh feed flow rate.

not the dynamic performance of these plants will have an impact on their overall profitability. Each system was simulated with its worst case load disturbance. Expected bounds on the fluctuations in the loads were 100 (lb mol)/h for the fresh feed flow rate and 5 mol % for the inert level in the feed. Note that a larger fluctuation in fresh feed flow rate was assumed in this paper than those in the first two papers. The main reason for this is that the product compositions of the systems in this paper are much less sensitive to flow rate fluctuations than those in papers 1 and 2. This is because the impurity in the product stream in this chapter is the inert rather than the product. Since only 5 mol % of the feed is inert, it takes larger fluctuations in the fresh feed to result in large fluctuations in product quality. Figure 9 gives a comparison of the product and purge composition deviations for each of the four systems subjected to their worst case load disturbances for the first 100 h. None of the product or purge compositions vary to an extent where it would be reasonable to penalize process economics for poor dynamic performance. None of the product compositions deviate more than 0.1 mol %. The purge compositions are always within 1%. Of course, there are situations where deviations of this magnitude in compositions would be unacceptable (a medical grade gas production facility for example), but for the purposes of this study it is assumed that these deviations are small. It is obvious, however, that the dynamic performance of system I1 is better than that of systems I2 or I4. If purge composition control is not of major importance, then the performance of system I4 is also better than those of systems I2 and I4. The designs with the highest steady-


Figure 11. Response of system I4 to a 50 (lb mol)/h step increase in fresh feed flow rate.

state profitability are also the designs with the most favorable dynamic characteristics. The problem that remains is which design, system I1 or system I4, is the best overall design. Both designs have nearly identical steady-state profitabilities. From Figure 9 it can be seen that the purge composition control of system I1 is superior to that of system I4. In the long term the composition control of system I4 is better than that of system I1. Neither process produces offspec product when forced with their worst case load disturbances, so there is no way to use the capacitybased economic approach to quantitively compare these two designs. There is an important dynamic factor, however, that has not yet been incorporated into the analysis that can be used to compare these two alternative processes. This factor is the possibility of valve saturation. Regardless of what the results of linear analysis predict, if the control valves of one process saturate, then the dynamic performance of that process will be degraded. Thus, the responses of these processes to sustained load disturbances should be considered in order to assess the possibility of valve saturation in each design. Figures 10 and 11 show the responses of systems I1 and I4 to a 50 (lb mol)/h step increase in fresh feed flow rate. Neither the purge composition nor the product composition of either design is very sensitive to changes in flow rate, as is predicted from the magnitudes of the peak load log moduli. What is apparent, however, is that system I4 takes a significantly longer period of time to reach steady state than does system I1. In addition, the flow rates in system I4 change more than those of system I1 in reaching the new steady state. This can be seen by observing the time profiles of the recycle flow rates. The recycle flow rate of system I1 increases by

Figure 12. Response of system I1 to a 2 mol % step increase in fresh feed inert level.

56.5 lb mol (a 25.3% change) whereas the recycle flow rate of system I4 increases by 470.2 lb mol (a 66.2% change). This makes sense since the recycle gain of system I4 (0.8049) is considerably higher than the recycle gain of system I1 (0.0029). It can be concluded that for feed flow rate disturbances the chance of valve saturation is higher in system I4 than in system I1. Figures 12 and 13 show the responses of systems I1 and I4 to a 2 mol % increase in fresh feed inert levels. Again, it appears that system I4 requires a much longer time to reach steady state and that the flow rates in system I4 must change more than those of system I1 in order to reach the new steady state. The recycle flow rate of system I1 increases by 9.5 lb mol whereas the recycle flow rate of system I4 increases by 490.2 lb mol. There is more than a factor of 50 difference between the required changes in recycle flow rate. Since system I4 requires much larger changes in flow rates for both flow rate and composition disturbances, it can be concluded that the chance of valve saturation is much higher in system I4. For this reason, the inert removal strategy used by system I1 is superior to those of the other designs. This leads to the conclusion that whenever linear analysis predicts that two processes will be of comparable controllability, the process with the smallest recycle gain will be the most favorable overall. Conclusions In this paper five different process flow sheets for the removal of intermediate inerts from a ternary system were studied. It was shown that the indirect separation sequence with product removed first was not a profitable alternative from the standpoint of steady-state econom-


characteristics. This can be directly related to the abilities of these flow sheets to produce pure purge streams without the need of a large buildup of inert in the system at steady state. Neither the purge compositions nor the product compositions of systems I1 and I4 were sensitive to changes in fresh feed flow rate or composition. It was necessary, therefore, to use a different criterion to judge the relative dynamic merits of the two strategies. It was determined that the possibility of valve saturation is much higher for system I4 than for I1. For this reason, it was concluded that system I1 is dynamically superior to the other processes. Nomenclature

Figure 13. Response of system I4 to a 2 mol % step increase in fresh feed inert level.

ics. It was also shown that the direct separation sequence with the reactant separated first and the full column with a side rectifier are the most profitable from the standpoint of steady-state economics. As was the case in the previous papers, the reason for the superior steady-state economics can be traced directly to each system’s ability to inexpensively purify the inert component. It was also shown through the use of linear dynamic analysis that systems I1 and I4 have better dynamic

Ac ) condenser area Ar ) reboiler area B ) recycle flow rate CLLM ) closed loop log modulus DCFROR ) discounted cash flow rate of return Dc ) column diameter Dj ) distillate flow rate of column j Dr ) reactor diameter F ) reactor effluent flow rate Lc ) column height Lr ) flow rate of liquid in the rectifying section Lr ) reactor height P ) purge flow rate Rj ) reflux flow rate in column j VR ) reactor holdup Vj ) vapor boilup in column j 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 Received for review April 16, 1997 Revised manuscript received September 26, 1997X IE9702901 X Abstract published in Advance ACS Abstracts, November 15, 1997.

Plantwide Design and Control of Processes with Inerts. 3. Intermediate

Recommend Documents