CONTROL STRUCTURE DESIGN FOR PARALLEL PROCESSES
Application to Heat-integrated Distillation
W.-H. TSAI, H.-P. HUANG and C.-C. YU
Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan
P
arallel process units are often encountered in chemical process systems for different considerations, e.g., parallel reactors from reactor network synthesis, parallel columns for heat integration. One notable example is the feed split configuration of heat-integrated distillation columns. In this work, the control of parallel processes is illustrated with the heat-integrated distillation column example. Results show that more consistent control performance can be achieved using the proposed control structure for both feed composition and feed flow disturbances. More importantly, the improvement is obtained using simpler instrumentation and much less engineering effort.Keywords: heat-integration; distillation configuration; parallel process; control structure design.
INTRODUCTION
Parallel process units are often encountered in chemical pro-cess systems for different considerations, e.g., parallel reac-tors from reactor network synthesis, parallel columns for heat integration. On the production plant level, we have seen parallel production lines for the same product. On the unit operation level, one notable example is the feed split configuration of heat-integrated distillation column (King, 1980; Chiang and Luyben, 1983; Andrecovich and Wester-berg, 1985) where the feed is splitted into two streams and are fed separately to two columns which are heat-integrated, theoretically 50% energy can be saved by parallelizing the process. This unique process configuration, in theory, will lead to somewhat different control structure design, because we are interested in the global product quality measure (instead of the local one). In other words, one should take advantage of the process configuration to devise simpler and yet effective control structure.
We have seen extensive literature on the design and control of heat-integrated distillation systems. Tyreus and Luyben (1976) examine the control issue of double-effect distillation and an auxiliary reboiler is suggested for improved control performance. Chiang and Luyben (1988) study the control for three different heat-integration configurations: feed-split, light-split forward (integration), and light-split reverse. They concluded that the light-split reverse is the most controllable scheme. Weitz and Lewin (1996) study the same system using the disturbance cost as a controllability measure and a similar conclusion is
drawn. Wang and Lee (2002) explore nonlinear PI control for binary high-purity heat-integrated columns with light split/reverse configuration. Yang et al. (2000) use a simpli-fied model derived from state space equations to evaluate disturbance propagation for double-effect column under feed-split configuration.
Interaction between design and control for heat-integrated and/or thermally coupled distillation systems are studied by Rix and Gelbe (2000) and Bildea and Dimian (1999) using dynamic RGA as a controllability measure. Lin and Yu (2004) explore the interaction between design and control for heat-integrated columns. However, few of these works take advantage of the parallel character-istic of the processes into account. That is, in control struc-ture design, one should emphasize on the output of the entire system instead of the output of individual (parallel) unit. The objective of this work is to explore the design and control of parallel processes and it is illustrated using heat-integrated distillation columns with feed split (FS) configuration. The remainder of this paper is organized as follows. The Steady-State Design section describes the advantage of the heat-integrated configurations via quantitative analysis. The control structure design and controller design are pre-sented in the Control section followed by rigorous nonlinear simulations for performance comparison. The conclusion is drawn in the final section.
STEADY-STATE DESIGN
Process Configuration and Design Procedure At the steady-state design, a systematic procedure is employed to find the number of trays and feed tray location. For the single column configuration, initially the reflux
Correspondence to: Dr C-C. Yu, Department of Chemical Engineering,
National Taiwan University, Taipei 106-17, Taiwan. E-mail: [email protected]
www.icheme.org/journals Trans IChemE, Part A, February 2005
ratio is set to 1.2 times of the minimum reflux ratio (RRmin),
then the number of trays and feed tray location are found by tray-by-tray calculation until the specification is reached, followed by refining the reflux ratio to meet the exact product specifications. For the heat-integrated systems, three configurations are considered: (1) feed split (FS), (2) light-split reserve (LSR), and light-split forward (LSF). Figure 1 shows these three configurations where one column is pressurized and the high pressure column provides the heat to boilup the vapour in the low pressure column via condensation. Theses three configurations differ in the direction of material flow versus the direction of the heat-integration. Again, the ‘1.2 RRmin’ criterion is
used for the design of the heat-integrated column and 5% heat loss in the high pressure column is assume. That is heat transfer to the low pressure column via the heat exchange is limited to 95% of the heat of condensation in the high pressure column. Fifteen degrees of temperature driving force is assumed for heat transfer in all cases.
Steady-State Economics
Three systems are studied, they are: methanol – water, benzene – toluene, and isobutane – n – butane systems which correspond to high (a¼ 2.45 –7.58), medium (a¼ 2.35 –2.65), and low (a¼ 1.29 – 1.30) relative volati-lities, respectively. Table 1 compares the absolute energy consumption for these three chemical systems with three different feed compositions (of light component). The results show that percent energy saving ranges from 32 – 41% for the feed-split configuration, from 3 – 36% for the light-split forward configuration, and from 14 – 43% for the light-split reverse configuration. The percent of energy saving clearly reveals that the feed split configuration consistently provides economical incentives over the conventional single column configuration. How-ever, the FS configuration show four product streams and, in the context of process control, this implies that we have a system with four controlled variables, quite possibly
a 44 multivariable system. A possible tradeoff between steady-state economics and dynamical controllability may result as compared to the 22 multivariable system in the conventional configuration.
Figure 2 shows that the FS configuration is a typical parallel process where the products come from two parallel units and what we really care is the resultant composition after blending the product streams. That is, from a system perspective, we only need to control two product compo-sitions, as opposed to the 44 control problem from the unit-wide perspective.
CONTROL
Nominal Operating Condition
A methanol – ethanol system is used to illustrate the control of heat-integrated system. The separation process separates 50/50 mixture of methanol and ethanol with top and bottom product specification of 99% methanol and 99% ethanol. All simulations were carried out using
Figure 1. Three different heat-integration configurations.
Table 1. Percentages of energy consumption (compared with the single column case as 100%) of various heat-integration configurations for different chemical systems with different feed compositions.
xF 0.3 0.5 0.8 Methanol – water FS 68% 64% 62% LSF 75% 67% 64% LSR 70% 61% 57% Benzene – toluene FS 66% 64% 61% LSF 97% 81% 66% LSR 86% 71% 59% Isobutane– n – butane FS 60% 59% 59% LSF 80% 75% 67% LSR 77% 70% 60%
ASPEN Plus with the NRTL activity coefficient model to describe liquid phase nonideality. Steady-state economic analysis indicates that, again, the FS structure can save up to 49% as compared to 23% for the LSF and 24% for the LSR configurations (Table 2). Table 3 gives the nominal steady-state design with the low pressure column operated at 1 atm with 21 trays while the high pressure column is held at 3.5 atm with 35 trays. The heat input to the high pressure column is 107.3 kW which corresponds to a
49% energy saving as compared to the single
column configuration which operated at 1 atm (208.1 kW). Figure 3 shows the process flowsheet with four product streams.
Control Structure Design
Two control structures are studied here. One is the conventional control structure for the heat-integrated column, called structure S-1 hereafter, and the other control structure treated the FS configuration is a parallel process which is denoted as structure S-2. As pointed out earlier, for the heat-integrated columns, we have only three control degrees of freedom (as opposed to four control degrees of freedom for two independent columns). For example, if the reflux-vapor boilup (RV) control structure is con-sidered, these three possible manipulated variables are: reflux flows of high and low pressure column (RF,L and
RF,H) and the heat input to the high pressure column
(QB,H). However, we have four controlled variables for
structure S-1 and they are: xD,H, xB,H, xD,L and xB,L as
shown in Figure 3. The additional control degree of free-dom comes from the feed ratio to these two columns (FSv) and, therefore, we have a 44 multivariable control
problem. Once the controlled and manipulated variables are determined, the next step is to pair the input – output variables. One obvious choice is: xB,H– QB,H, xD,H– RF,H,
xD,L– RF,L and xB,L– FSv (Figure 3). Actually, this is the
control structure proposed by Chiang and Luyben (1988) when all four compositions are controlled.
Table 2. Percentages of energy consumption of various heat-integration configurations for methanol–ethanol systems (F ¼ 10 kmol/h and xF¼ 0.5).
Configuration FS LSF LSR
% Energy consumption 51.4 77.3 76.5
Compared to single column case.
Figure 2. Treating the feed-split configuration as parallel units.
Table 3. Nominal steady-state for the methanol – ethanol heat-integrated columns.
Value Unit
Feed flow rate 10 kmol/h
Feed composition 0.5 m.f. of methanol
HP col LP col
Top composition 0.99 0.99 m.f.
Bottoms composition 0.01 0.01 m.f.
Column pressure 1 3.5 atm
Tray pressure drop 0.0085 0.0085 atm
Total no. of trays 36 57
Feed location 21 35
Reboiler duty 107.3 kW
Approximated relative volatility
1.5 1.8 1.5 1.8
Figure 3. Conventional control structure for the FS configuration with control structure S-1.
For the S-2 control structure, we have two controlled variables, the blended compositions of top and bottom products from high and low pressure different columns as shown in Figure 4. Thus, two of these four possible control degrees of freedom needed to be fixed. An obvious choice is to set the feed ratio (FSv) at a constant value. This
may lead to a suboptimal operating point as the feed com-position changes. Figure 5 shows that when the feed composition varies from 0.1 to 0.8, the feed ratio falls between 0.52 and 0.55. Moreover, if one fix the feed ratio at 0.52, the optimality still can be achieved for +20% feed composition changes. That implies little
economic loss will be encounter when one choose to fix the feed ratio (FSv). The second variable to be fixed is
less obvious. The candidates are reflux ratio of the high or low pressure column (RRH or RRL) and the ratio of
these two reflux ratios (RRH/RRL). Fixing the ratio of the
reflux ratios is intuitively appealing because it seem to maintain the relative degree of fractionation in each unit. Once the two control degrees of freedom (FSvand RRH/
RRL) is fixed, we are left with two possible choices:
xB,mix– QB,H, xD,mix– RF,L and xB,mix– QB,H, xD,mix– RF,H.
Here, the subscript mix stands for the mixed product composition. The later (xB,mix– QB,H, xD,mix– RF,H with a
relative gain of 1.81) is selected because it is dynamically more favourable (the effects of manipulated variable propagate from the high pressure column to the low pressure one) (Figure 4).
Controller Design
For the control structure S-1, the 44 process transfer function matrix is obtained from step tests. First order responses were assumed and the process transfer function matrix becomes: xD,L xB,L xD,H xB,H 2 6 6 6 4 3 7 7 7 5 ¼ 2:49e3s 264:8s þ 1 0:44e3s 307:4s þ 1 0:21e3s 834:1s þ 1 3e3s 278:4s þ 1 2:59e3s 284:9s þ 1 0:56e3s 190:8s þ 1 0:16e3s 585:9s þ 1 3:55e3s 294:6s þ 1 0 0:56e 3s 493:8s þ 1 2:61e3s 450:5s þ 1 1:93e3s 311:4s þ 1 0 1:2e 3s 319:5s þ 1 3:27e3s 322:2s þ 1 6:59e3s 390:6s þ 1 2 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 5 RF,L FSV RF,H QB,H 2 6 6 6 4 3 7 7 7 5 (1)
A three minute analyser dead time is added to each transfer function for the composition measurement. Corre-sponding relative gain array is:
RF,L FSV RF,H QB,H L ¼ 6:58 3:23 0:21 2:42 5:85 3:95 0:15 2:75 0 0:60 1:91 0:30 0 0:88 0:85 0:97 2 6 6 6 4 3 7 7 7 5 xD,L xB,L xD,H xB,H (2)
Next, sequential design is taken to find the tuning con-stants of the decentralized PID controllers (Huang et al., 2003; Shen and Yu, 1994). That is an iterative procedure is taken and each controller is designed while rest of the loops are closed. In doing this, the closed-loop interaction Figure 4. Treating the FS heat-integrated column in parallel topology with
control structure S-2.
is taken into account while maintaining the simplicity of single loop design. The controller parameters become:
loop 1 : Kc¼20:601 tI¼74:77 tD¼1:17 loop 2 : Kc¼14:335 tI¼105:58 tD¼2:41 loop 3 : Kc¼32:63 tI¼70:25 tD¼1:15 loop 4 : Kc¼ 4:704 tI¼144:15 tD¼2:07
Because of its high dimensionality, a second set of tuning constants are obtained by reducing Kcto 60% and
increasing reset time (tI) to 130% of their nominal
values. For the control structure S-2, the 22 process transfer function matrix is also identified from step responses. xD,mix xB,mix ¼ 3:06e3s 347:4s þ 1 2:77e3s 302:2s þ 1 2:68e3s 298s þ 1 5:42e3s 366s þ 1 2 6 6 4 3 7 7 5 RF,H QB,H (3)
This pairing gives a relative gain of 1.81. Again the sequen-tial design approach is taken and PID settings become:
loop 1 : Kc¼20:75 tI¼31:36 tD¼1:198 loop 2 : Kc¼ 12:34 tI¼31:48 tD¼1:197
Control Performance and Discussion
Dynamic simulations were performed to compare per-formance of these two control structures. All simulations were carried out in ASPEN Dynamics. The results indicate that for +10% feed composition changes, the simpler S-2 structure gives much better performance and the peak errors is consistently smaller than that of using control struc-ture S-1 (Figure 6). It should be emphasized here that the control performance is actually evaluated according to the consistency in the closed-loop responses. Also note that two sets of tuning constants were evaluated under structure S-1: the tight tuning (S1-1) and loose tuning (S1-2). For +10% feed flow rate changes, the closed-loop responses of S-2 are comparable to that of the control structure S-1 as shown in Figure 7. The results presented here clearly
Figure 6. Responses for +10% methanol feed composition changes using control structures S-1 (tight tuning S1-1 and loose tuning S1-2) and S-2.
Figure 7. Responses for +10% feed flow rate changes using control structures S-1 (tight tuning S1-1 and loose tuning S1-2) and S-2.
show that more consistent control performance can be achieved using simpler control structure by taking the pro-cess topology into account. More importantly, for the heat-integrated columns, the improvement is obtained with virtually no loss in the economic objective (i.e., energy consumption).
The concept of treating the parallel units as a whole seems to offer an attractive alternative to control such processes. The advantages can be more evident if the number of units increases (Figure 8). Consider a process with n parallel unit (e.g., Figure 8). Immediately, this corresponds to a n n multivariable system by keeping the output of n subunits on specification. Because we are
only interested in the composition of the net output (this is especially true for plants making homogeneous pro-ducts), the control system can be reduced to a SISO system (e.g., only one composition loop) with n21 ratio loops. This simplifies the control system design (e.g., from n n to 1 1) while maintaining comparable control performance. Still limitations are also observed for such a control strategy. An obvious one is that the ability to handle wide range of disturbances. Consider the feed split configuration with control structures S-1 and S-2. Based on dynamic simulations, the ranges of feed compo-sition changes can be handled by S-1 and S-2 are 0.1 xF0.9 and 0.2 xF0.8, respectively. The
reason is that the feed ratio is fixed for the structure S-2. A second potential problem is that it may become difficult to use the simple single temperature control for the struc-ture S-2. That is composition control or some type of soft sensor should be used.
CONCLUSION
Parallel processes are often encountered in process industries. In control system design, we can take advantage of this type of process topology. In this work, the control of parallel processes is illustrated with the heat-integrated distillation column example. The feed-split configuration is known to provide significant energy saving over the traditional single column configuration and it provides close to 50% energy saving over the system without heat-integration. However, the energy integration results in a highly interacting multivariable system with higher dimen-sionality and less control degrees of freedom. However, the parallel nature of the system leads to a completely different thinking of the control objective (as opposed to the conven-tional practice): control the global product composition at the end of the production line instead of the quality of each individual unit. This greatly simplifies the design pro-cedure and subsequently results in a much simpler control system. The feed-split heat-integrated distillation example clearly shows that improved control performance can be achieved by taking the process topology into account. More importantly, this is obtained with much simpler hard-ware requirement as well as engineering manpower. The benefit can be much more substantial when the number of parallel units increases.
REFERENCES
Andrecovich, M.J. and Westerberg, A.W., 1985, A simple synthesis method based on utility bounding for heat-integrated distillation sequences, AIChE J, 31: 363.
Bildea, C.S. and Dimian, A.C., 1999, Interaction between design and control of a heat-integrated distillation system with prefractiontor, Trans IChem, Part A, Chem Eng Res Des, 77: 597.
Chiang, T.P. and Luyben, W.L., 1983, Comparison of energy consumption of five heat-integrated distillation configurations, Ind Eng Chem Proc Des Dev, 22: 175.
Chiang, T.P. and Luyben, W.L., 1988, Comparison of the dynamic performance of three heat-integrated distillation configurations, Ind Eng Chem Res, 27: 99.
Huang, H.P., Jeng, J.C., Chiang, C.H. and Pan, W., 2003, A direct method for multi-loop PI/PID controller design J Process Control, 13: 769. King, C.J., Separation Processes, 2nd edition (1980) (McGraw-Hill,
New York, USA). Figure 8. Conventional control structure (a) versus treating the parallel
Lin, S.W. and Yu, C.C., 2004, Interaction between design and control for recycle plants with heat-integrated separators, Chem Eng Sci, 59: 53. Rix, A. and Gelbe, H., 2000, On the impact of mass and heat integration on
design and control of distillation column Systems, Trans IChemE, Part A, Chem Eng Res Des, 78: 542.
Shen, S.H. and Yu, C.C., 1994, Use of relay-feedback test for automatic tuning of multivariable systems, AIChE J, 40: 627.
Tyreus, B.D. and Luyben, W.L., 1976, Dynamics and control of heat-integrated distillation columns, Chem Eng Prog, 72(9): 59.
Wang, S.J. and Lee, E.K., 2002, Nonlinear control of high-purity heat-integrated distillation system, J Chem Eng Jpn, 35(9): 848.
Weitz, O. and Lewin, D.R., 1996, Dynamic controllability and resiliency diagnosis using steady state process flowsheet data, Comput Chem Eng, 20: 325.
Yang, Y.H., Lou, H.H. and Huang, Y.L., 2000, Steady state disturbance propagation modelling of heat integrated distillation processes, Trans IChemE, Part A, Chem Eng Res Des, 78: 245.
ACKNOWLEDGEMENT
This work was supported by the Ministry of Economic Affairs under grant 92-EC-17-A-09-S1-019.
The manuscript was received 24 May 2004 and accepted for publication after revision 15 December 2004.
