column $2 (high negative RGA diagonal elements, a is characterised by a central purification system, high condition number, small Morari Resiliency. Fresh and ...
Computers chem. Engng, Vol. 21, Suppl., pp. $291-$296, 1997
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Effect of Recycle Interactions on Dynamics and Control of Complex Plants A.C. Dimian, A.J. Groenendijk, S.R.A. Kersten, P. D. Iedema University of Amsterdam/Nieuwe Achtergracht 166 1018 WV Amsterdam/The Netherlands Abstract Plantwide inventories of main components and impurities in a complex plant are sharply affected by interactions between recycles which, in general, are not desirable. However, this paper demonstrates how the interactions between some recycle loops may be exploited to create feasible plantwide control structures that are impossible to achieve simultaneously with stand-alone units. Thus, flowsheet architecture, equipment design and control system design must be interrelated. Simultaneous design is necessary for items involved in plantwide control structures. The paper presents a simulation based methodology for evaluating the effect of recycle interactions on dynamics and plantwide control of complex plants. Steady-state and dynamic simulations are combined with controllability analysis, both in steady state and in dynamic mode. A case study handling the removal of impurities in a plant with nested loops illustrates the approach. The controllability of two flowsheet alternatives is evaluated. The steady-state analysis is confirmed at low frequencies. Possible difficulties may occur at higher frequencies, where the period of disturbances and the time constants of the distillation columns are of the same order of magnitude. The relative direction of disturbances plays a significant role. Closed loop simulation validates the main trends of the controllability analysis, showing in the same time the difficulty in managing a perfect multivariable control of the material balance.
Introduction
It may be summarised in the following steps: 1. Problem definition: operation window, plantwide control objectives, control structure. 2. Calibration of a steady-state PlantSimulation-Model: rigorous modelling, detailed material balance (main components and impurities) around an operation point. 3. Steady-state controllability: linear analysis, evaluation of control structures, comparison of flowsheet alternatives, simultaneous design of units involvedinrecycles. 4. Dynamic flowsheeting: development of a reduced model which now incorporates the main design and dynamic features detected by the steady-state analysis. 5. Dynamic controllability: transfer functions, controllability indices versus frequency, evaluation of flowsheet alternatives, improvement in flowsheet and unit design. 6. Closed loop simulation: tuning of controllers, dynamic simulation, evaluation of alternatives and recommended plantwide control strategy.
There is a link between some flowsheeting convergence troubles, the dynamic material balance and the plantwide control problems. This has inspired the authors to seek a deeper understanding of the controllability properties of a flowsheet. It will be shown how steady-state and dynamic simulation combined with controllability tools may be used in a systematic manner to evaluate the effect of recycle interactions on dynamics and control of complex plants. An industrial case study which deals with troubleshooting the effects of impurities illustrates this approach. While a steady-state material balance may be achieved for main components, this is not the case for impurities. They are always in transient because of the difficulty in controlling their dynamic inventory. Actually, the control system must be able to reject not only local disturbances, at the unit level, but also at the plant level. Both the flowsheet structure and the design of individual units must fulfil the requirements of a resilient plantwide control of components' inventory,
Methodology The methodology we applied enables a quantitative evaluation of recycle effects on the dynamics and plantwide control of complex plants. $291
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iL I
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Figure 1 - Flowsheet of a balanced V C M process Case Study
Figure 1 shows a reduced flowsheet of a balanced VCM process. Some elements of the steady-state analysis and the open loop dynamic behaviour h a v e . been already presented at ESCAPE 6 [Dimian and al, 1996]. Here we proceed with the dynamic controllability analysis and the closed loop simulation, where special attention is paid to the recycle effects. The reactions take place in RI (Chlorination), R2 (Cracking), R3 (Oxy-chlorination). Keeping a high quality of the intermediate di-chloro-ethane (DCE) sent to cracking is the control objective. The process is characterised by a central purification system, Fresh and recycled DCE are purified in a big distillation column $2, while 'Lights' and 'Heavies' are removed in the column $4 and $5 respectively, The following specifications on the bottom product of the column $2 have to be controlled: (1) maximum concentration of a light key Ii, (2) idem for a heavy key 12, and (3) optimal concentration of 13, an intermediate in volatility, which has a beneficial role in the cracking reaction. They may be seen as outputs in a multivariable control problem, which can be achieved by acting on some inputs, The manipulated variables may belong only to $2, when a stand-alone approach is used, or to other neighbouring units, when a plantwide approach is adopted. Here The inputs may be chosen among top distillate (D2, D4), reflux (R2, R4), reboiler duty (Q2, Q4), side stream (SS2). Two alternatives will be analysed: (1) the base case flowsheet and (2) an alternative A. In the last case an extra reactor R4 was inserted, where most of Ii and some of Iz are destroyed. Consequently, new connections are possible. Thus, the bottom product of the $4 may be sent to the column $5, whose top distillate goes back to the column $2.
The controllability procedure is similar to that described recently by Skogestad and co-workers [Skogestad and Postlethwaite, 1996, Wollf, 1996]. Steady-state and dynamic simulations were performed with ASPEN PLUS TM and SPEEDUPTM, by using rigorous models both for distillation columns as well as for reactors. Scaling of variables is based on the relative changes around the operating point. Steady-State Analysis The controllability analysis of the stand-alone column $2 (high negative RGA diagonal elements, a high condition number, small Morari Resiliency Index, negative Niederlinski index)shows that the above three specifications cannot be regulated with multi SISO controllers when the manipulated variables are D2, SS2 and R2. However, the analysis of the column $2, this time integrated in the recycle structure, gives a completely different picture! The analysis indicates that a simultaneous control of the specifications may be feasible, both for the base case and the alternative A. Now the specification on I3 can be regulated either with D2 or D4, even though they have an opposite action! Increasing the top distillate of $2 increases the concentration of I3 in the bottom of the same column! This strange behaviour is opposite to a stand-alone operation, but it may be explained by a recycle effect. In fact, a 'substitution' of 13 by DCE takes place in the top distillate of $4, that will return more 13 in the recycle loops. Consequently, more 13 will be present in the bottom of $2. It may be noted that the specification 12 is also affected by recycle effects. The concentration of 12 in the bottom product of $2 increases with the top distillate D2, because only a small amount of I2 is destroyed in R4 (kinetic reasons). The excess returns
PSE '97-ESCAPE-7 Joint Conference in the recycle through the bottom of $4. It should also be mentioned that in this configuration the distillate rate of $4 and the bottom flowrate of $5 become interdependent! The RGA analysis for alternative A indicates that the suppression of the back loop $2-$4-R1-$2 may lead to an almost 'decoupled' behaviour. Thus feasible pairings may be I r R 2 , I2-SS2 and I3-D2 or I3-D4. The 'Condition number' and the 'Niederlinski index' attest an integral controllable problem. The increased lower singular values in the alternative A estimates a better conditioning of the 30 •% : g ao
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3. Throughput control should make use of feed forward. Dynamic Analysis The open loop simulations show that it takes a long time to reach a steady-state after a step change. Typically this is 20 times longer than the transient of the stand-alone distillation column $2. Further observations are: * The reboiler duty of the column $2 has a fast and strong influence on all impurities. • D2 has a significant effect both on It and I3 • D4 has a slower but still significant effect on both Ii and I3, and almost no effect on 12. • Short inverse responses are detected on the dynamics of I2. * The alternative A gives a faster response than •
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the base case. The dynamics of the disturbances exhibits long transients. They have a large influence on I3, a moderate influence on 11 and almost no influence on 12.
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manipulated variables with the specifications. The directional effect of the disturbances was found significant. Here the following disturbances are examined: plant throughput, varied by means of the external DCE stream, and its concentration in I3. They may be normalised around an operation point between (-1,1). Their direction may be characterised by an angle 0 defined with the relation 0=arctan (F/[I3]). Thus the disturbance in flow varies along the Y-axis and is zero at 0=0, while the disturbance in I3 varies along the X-axis and is maximum at 0=0. Figure 2 indicates that the best rejection might be obtained for angles close to 0, x, 2r~, etc., where the Disturbance Condition Number is minimum. This predicts that the rejection of a disturbance in impurity concentration would be easier. Contrary, the rejection of a disturbance in throughput would be more difficult. Probably, the introduction of a feed forward element would be of help. It may be observed that that the alternative A possesses better rejection properties than the base case, being also less sensitive with the direction of disturbances, All these steady-state considerations suggest the following design and plant-wide control strategy: 1. The reflux flowrate in the column $2 should be 'set' at its optimal value, according to the production of impurities Il. 2. The side stream of column $2 and the distillate rate of column $4 seems to be the most appropriate to control the impurities 12 and 13 respectively,
Thus, the general trend lines of the steady-state analysis are confirmed, but they are better understood as time dependent variations. However, the use of the side-draw as a candidate in regulating I2 may be questionable, because of its inverse response. The preferred manipulated variable for controlling I3 may be D2 or D4. A choice between the two structures can not be made at this point. Further, a controllability analysis has been performed with dynamic linear models as functions of frequency by using MATLAB TM. Although possible for simple systems, the generation of a state space description from the dynamic simulation model was found to be unreliable in our case. Therefore, we used a simpler but more trustworthy method, which consisted of the identification with MATHCAD TM of appropriate transfer functions G(s) and Gd(S) from open loop time responses at step variations. In all dynamic simulations the level in the reboilers and in the flash drums was always perfectly controlled. Figures 3 to 5 display some of the main results regarding RGA and SVD analysis. At first sight the steady-state behaviour holds well at low frequencies, roughly up to 1 rad/hr. The alternative A seems to posses better controllability properties than the base case. The more effective control action on the impurity 13 is confirmed as D4 instead of D2. However, higher frequencies, especially around 10 rad/hr, show a significant deterioration in controllability. They may be explained by resonance effects between the distillation columns and the rest of the flowsheet. This is due particularly to the action of the reboiler (pairing involving Q2), as well as to the time constant of the column $2, which is in the order of 6 minutes. As a consequence, it may be
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expected that a control aimed to reject disturbances of high frequencies will introduce in fact more disorder! A damping of disturbances would be desirable. This may be done by introducing a tank reservoir on the line receiving the most harmful impurities, in this case from the reactors R2 and R3. This observation is confirmed by the Disturbances Cost diagram shown in figure 6. This graphical representation [Lewin, 1996] offers the advantage of simultaneous visualisation of resiliency capacity of a plant as function both of frequency and of disturbance direction. The best rejection (low cost) occurs at angles around kr~ radians, for perturbations
in concentration (here Ia), while the worst rejection takes place around (~2+ kn). The graph predicts better resilient properties for the 'alternative A', because of a much larger frequency bandwidth and a lower power (cost) required for the manipulated variables. Despite the fact that each of the above controllability indexes gives only a partial picture of the problem, the entire analysis shows clearly that the structure of the recycles produces the dominant effect. However, the control structure can play a role in performance and resiliency. This behaviour will be confirmed by closed loop simulation.
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Closed Loop Simulations According to the controllability analysis we considered decentralised multi SISO PI control with the pairing Ii-Q2, I2-SS2 and 13 with D2 or D4. These controllers may be implemented physically, but also used 'virtually' for Design and Operation purposes. The controllers were tuned with the Ziegler-Nichols method. Extensive simulation indicated that it was difficult to keep all three loops under perfect control. The reflux flowrate in the column $2 should be set at a sufficiently high value according to the production of impurities I1. As high production implies greater elimination of I1 is required. For the same reason the side stream of $2 may be set at a value according to the production of impurities 12. Only one controller impurity 13 needs to be finally implemented. The manipulated variable may be either D2 or D4. It is interesting to mention some interaction effects observed in closed loop simulation. The rejection of a disturbance in 13 may affect negatively or r.ACE 21:13-K
positively the rejection of other two impurities, Ii and I2, depending on the choice of the control structure. When D2 is manipulated then a rejection of an increase in 13 will create a 'positive feedback' for both 11 and 12, whose accumulation will be stimulated. Contrary, when D4 is manipulated a decreasing effect on all three impurities is recorded. The control with D4 will reject the disturbance on I3, and at the same time will produce a 'negative feedback' effect on both Il and I2 whose variation will be compensated. Therefore the structure involving D4 is more resilient. Figure 7 presents a direct comparison between the base case and the alternative A when the only control loop was on the impurity I3, with the manipulated variables either D2 or D4. A step disturbance 13 in the external DCE feed was introduced. The time tracks indicate clearly that the alternative A gives both a faster response and a better setpoint tracking. The settling times are approximately 2 and 10 hours respectively. This shows indeed a significant advantage for the
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alternative A. The explanation lies mainly in a shorter recycle path. The manipulation of distillate rate D4 gives also a somewhat shorter time than D2. However, the main advantage of this structure consists in better resiliency properties, because the rejection of 13 will enhance the rejection of other two impurities, Ii and Iz. The combined effect of recycle dynamics and control structure is demonstrated, Conclusions 1. This paper presents the integration of Process Design and Plantwide Controllability Analysis of a large plant, where recycle effects are significant. It is demonstrated how connectivity between units and interactions between recycles may be exploited to create flowsheet alternatives with feasible plantwide control structures which are impossible to achieve with stand-alone units, The control structures may imply variables belonging to different units. The controllability properties are determined by the competition between 'positive feedback' effects, typically recycles, with 'negative feedback' effects like exit streams and chemical reactors. Decoupling may be obtained with proper design of the units. 2. A methodology to study the interactions of recycles and their impact on plantwide control structures has been developed. This combines steady-state and dynamic simulation with controllability analysis tools like RGA, SVD, disturbances rejection, directional analysis and disturbances cost, both static and in the frequency domain. This methodology enables more value from simulations to be obtained than with usual sensitivity studies. 3. The case study of a complex plant, the removal of impurities in a VCM process, illustrates both the conceptual ideas and the methodology. The plantwide control problem expresses an interconnected dynamic material balance of some impurities. The following points can be highlighted: • The recycle structure has a stabilising effect on the control of the main distillation column. The specifications of impurities in the bottom product cannot be controlled when the column is analysed as 'stand alone', but it will when 'integrated' in the multi-recycle structure. The steady-state analysis suggests to use among the manipulated variables the top distillate from another distillation column, here the exit of lights. This was confirmed later as the best option by closed loop simulation. • The steady-state analysis suggests the side stream of the main column as a manipulated variable for another impurity. However, the dynamic openloop analysis showed that this gives a nasty inverse response. Simulations with this loop closed were not successful. The recycling of
material from the main column to a reactor, where this impurity is destroyed, does not give a sufficient negative feedback effect. • Another explanation for the difficulties in creating a multiloop control structure is related to the dynamic controllability analysis. At higher frequencies a significant deterioration in the controllability may occur. This is due particularly to the reboiler action, when the time constant of the main column, and the period of disturbances is in the same order of magnitude. Therefore the reboiler should not be used as manipulated variable. • Closed loop simulation showed a significant advantage in time response for the flowsheet alternative with a shorter recycle path. • Interactions effects between recycles may stimulate or damp the rejection of some disturbances. Both shorter recycle path and favourable effects of interactions on resiliency properties enable to justify the choice of the best plantwide control structure. References Dimian, A. C., Groenendijk, A.J., Iedema, P.,(1996) Systems Analysis in Handling Impurities in Complex Plants, presented at ESCAPE 6, Computers Chem. Engng., Vol. 20 Suppl., p S805$810 Lewin, D. R., A Simple Tool for Disturbance Resiliency Diagnosis and Feedforward Control Design, 1996, Computers Chem. Engng., Vol 20 No.l,p 13-25 Skogestad, S., Postlethwaite, I., 1996, Multivariable Feedback Control, Analysis and Design, John Wiley, Wollf, E. A., Skogestad, S., 1992, Controllability of Integrated Plants Applied to Recycle Systems, AIChE Spring Mtg, New Orleans; also PhD thesis (1996), University of Trondheim, Norway Aspen PlusTM release 9.2, 1995, Aspen Technology Inc. SPEEDUP TM, release 5.4D, 1 9 9 5 , Aspen Technology Inc. MATLAB TM, release 4.3, 1994, The MathWorks Inc. MATHCADTM, 1995, Professional edition, release 6.0,, Mathsoft Inc.
