Dynamics of a distillation column with distributed and

Dynamics of a distillation column with distributed and conventional approach using multivariable control with adjustment based on multiple errors Cintia Marangoni University of Joinville Region - Univille Process Engineering Master’s Program, Mail Box 246 Joinville – SC – Brazil, ZIP CODE 89219-905 [email protected]

Abstract—In this study, an application of a multivariable conventional control structure of the continuous tray distillation columns is compared to a new distributed proposal. This was done considering the process dynamics, more specifically the transition time when the process is disturbed. As the conventional approach, the top and bottom product temperatures of the distillation column were selected as controlled variables and the reflux ratio and reboiler heat supply as manipulated variables. These loops plus an intermediate temperature column stage controlled using the heat supply of one tray as the manipulated variable comprised the distributed control structure. The regulator problem was considered for the experimental control studies. Feed temperature was chosen as the load variable. It is important to notice that this study focuses on the response process and does not address the development or design of the control structure. The main aim is to compare the time response of the process when subject to an expected disturbance using two different approaches (conventional and distributed). Experiments were carried out with multivariable PI controllers and the multiple errors (desired controller variable and the corresponding measured output) of each controlled variable were used together to computed the control actions (interactions were considered). Better performance in relation to transition time was observed with the distributed approach, indicating that this is an interesting strategy which could be used to minimize the transients in a distillation column. Keywords-distillation; dynamics; multivariable system; transient analysis.

I.

heat

distribution;

INTRODUCTION

Distillation is the most widely used fluid separation process in the industrial sector. Since it is a process with relatively low energy efficiency considerable effort is currently being directed toward improving the operation efficiency of distillation towers [1]. Almost all of the recent developments are based on energysaving column configurations. In this regard, it has been reported that several approaches may be appropriate, including the improvement of separation devices, heat integration, and an energy analysis of the process [2]. These potential solutions are

Joel G. Teleken, Iaçanã G. B. Parisotto, Leandro O. Werle, Ariovaldo Bolzan, Ricardo A. F. Machado* Federal University of Santa Catarina– UFSC Chemical Engineering Department, Mail Box 476 Florianópolis – SC – Brazil, ZIP CODE 88010-970. *[email protected] usually interrelated as, for instance, in the case of proposals to use intermediate heat exchangers in distillation columns. Distillation columns exhibit highly non-linear dynamics and this has a major impact on product quality. The use of a control system is commonly employed to reduce the effect of disturbances and maintain the products within desired specifications. According to [3], in properly designed distillation control, the energy consumption, product variability, operator intervention and equipment must be considered, and this represents a considerable challenge. In fact, producing products with low variability (even for an instance) is often crucial. A reduction in the variation of the products can also be used to increase production rates [4]. As in many other cases, the product quality of a chemical processing plant is determined by distillation control, variations in which have been reduced through minimizing the period of operation outside the specifications (transition time). The current proposals to minimize the transient time of distillation columns use control techniques which consider process dynamics but uses a conventional system to control quality (bottom and top control loops) [5]. Multivariable and predictive control seems to be the most used techniques due to their great flexibility. In this context, it is worth mentioning the studies carried out with model-based controllers: Model Predictive Control (MPC) [6], Dynamic Matrix Control (DMC) [7], and Generalized Predictive Control (GPC) [8]. On the other hand, some studies have been carried out with proportional-integral-derivative (PID) controllers, aiming at a more flexible adjustment considering the distillation characteristics [5]. However, even in these recent studies, the controllers used to obtain the quality profile are implemented with the control action only in the bottom and top column stages. A well designed and adjusted control system is not sufficient to eliminate operation transients of a distillation process. One aspect that contributes to this situation, besides the column operation stage, is the centralization of the control system in the bottom and top column variables. Thus there is the propagation of the corrective control action through the

whole unit, generating a production period outside the desired specifications. The formation of transients in a distillation column occurs when the process is disturbed and its characteristics reduce the control system efficiency or when an external factor induces the modification of the unit operation point. In the first case there are factors such as variable coupling, nonlinearities, dead time, high time constants and process constrains. In the second case there are aspects such as the mixture to be subject to distillation, feed composition changes and operation transitions that are necessary due to changes in the market. The proposal here developed, which is the object of this study, consists of the distribution of the control action throughout the column stages aiming at the minimization of the transient operation. This approach is based on the study of diabatic distillation columns [9], where intermediate heating points are used instead of only one heat input (reboiler) and one heat remover (condenser). These additional points keep a certain desired temperature profile throughout the column. Previous research with the use of classic controllers [10, 11] has demonstrated the feasibility of this distributed control approach (PID). The unit dynamics was evaluated using intermediate stages to control the temperature profile. The results showed a reduction in the operation transition time (around 1.5h) with the distributed proposal when feed disturbances were introduced into the distillation column. Although 90% of industrial processes use classic controllers [12], it is also necessary to evaluate this distributed proposal using of advanced controllers which consider the process dynamics. Thus, aiming at the application of easy implementation strategies, the objective of this study was to evaluate the process dynamics of the distillation column with multivariable control using an adjustment based on the multiple errors (desired controller variable and the corresponding measured output) of each controlled variable to compute the control actions (interactions were considered). In this research, the focus is not the selection of the best pairing of controlled and manipulated variables for a multi-loop control scheme or to propose a new controller, control structure or even a tuning method. It is an evaluation of two different proposals (also referred to herein as strategies) in terms of their dynamics, with an easy multivariable adjustment (based on multiple errors of the control loop interactions) aiming to verify whether there is a difference in the distillation behavior in relation to the time when the distributed approach is applied. Since the multivariable control strategies provide good results for a distillation process, it is necessary to compare the new proposal with conventional control. To this aim, we evaluate the use of a 2 x 2 control system (controllers of the temperature loops of the bottom and distillate trays) and compare its dynamics to that of a new distributed approach (same controllers on the bottom and top and an additional temperature control loop on a tray) considering the system as 3 x 3. II.

A. The pilot unit The unit, illustrated in Fig. 1, represents a tray distillation process. It operates in a continuous way and thus there is a main tank responsible for the feed. The column has 13 equilibrium stages and each module has one point for temperature measurement, one for sample collection and a third for the distributed heating adaptation. The latter was carried out by means of electrical resistances designed with up to 3.5 kW of power each. Temperature sensors (Pt-100) were used to monitor this variable in all equilibrium stages, as well as the main tank and the reflux accumulator. The feed was carried out on the fourth tray, with the reboiler as the zero stage. The control configuration of the distillation column is illustrated in Fig. 2. The following control loops were defined: (1) bottom level control through the bottom product flow rate adjustment; (2) reflux accumulator level control by manipulating the top product flow rate; (3) feed flow rate control as a function of the adjustment of the same stream flow rate; (4) feed temperature control through the fluid flow rate adjustment in the heat exchanger of this stage; (5) last tray (distillate) temperature control by means of the manipulation of the reflux flow rate; (6) reboiler temperature control through the steam flow rate in the heat exchanger of this stage; and (7) temperature control of pre-defined stages of the column through the adjustment of the power dissipated by the electrical resistance of the tray. Fig. 3 shows an illustration of the main differences between the conventional and distributed approaches. TABLE I.

OPERATION CONDITIONS USED IN THE EXPERIMENTS. Variable

Value

Ethanol feed volumetric fraction

0.15

Feed Temperature

90oC

Volumetric feed flow

300 L.h-1

Column top pressure

1.25 bar

Drop pressure

0.25 bar

Reflux ratio (Reflux stream/Distillate)

5

MATERIAL AND METHODS

Experiments were carried out in a pilot unit processing an ethanol-water mixture. The conditions used are summarized in Table I. Composition measurements were carried out during the experiments using a densimeter for alcohol.

Figure 1.

Schematic illustration of the experimental unit’s.

of the manipulated variable for the conventional control and (35) for the distributed approach.

Figure 2.

Control configuration of the distillation unit.

Figure 3. Main differences between conventional and distributed control configurations of a distillation unit.

The first, second and third loops represent the column mass balance (inventory) control. The fifth and sixth loops comprise the quality control – in this case represented by the temperature. The use of these two loops in combination is referred to herein as conventional control. When these two loops are combined with the seventh loop mentioned above, it is considered herein as the distributed strategy. B. The control strategies tested In this study, the experiments were carried out employing two different strategies: (1) conventional 2 x 2 – with multivariable control applied to the reboiler and distillate temperatures; and (2) distributed 3 x 3 – with multivariable control applied to the reboiler, second stage and distillate temperatures. C. Controller tuning PI controllers were used in the two strategies tested, since this kind of controller is the most widely used [12]. Multivariable tuning was applied as the experiments consider both loops (reboiler and distillate temperatures) coupled to control the process. For strategies 1 and 2 a multivariable adjustment technique recommended by [13] was applied, which consists of the adjustment of the control loop interactions using the error generated in each loop. Thus, all loops errors interacting with each other are used to tune the control parameters. Equations (1) and (2) show the calculation

M 1 (t ) = Kc11 ∗ e1 (t ) + Kc12 ∗ e2 (t )

(1)

M 2 (t ) = Kc21 ∗ e1 (t ) + Kc 22 ∗ e2 (t )

(2)

M 1 (t ) = Kc11 ∗ e1 (t ) + Kc12 ∗ e2 (t ) + Kc13 ∗ e3 (t )

(3)

M 2 (t ) = Kc 21 ∗ e1 (t ) + Kc 22 ∗ e2 (t ) + Kc 23 ∗ e3 (t )

(4)

M 3 (t ) = Kc 31 ∗ e1 (t ) + Kc 32 ∗ e2 (t ) + Kc 33 ∗ e3 (t )

(5)

M1 and M2 refer respectively, to the steam flow rate in the heat exchanger of the reboiler and the reflux flow rate (both with valve opening). M3 refer to the electrical resistance power. Subscripts 1, 2 and 3 refer to interaction parameters related to the reboiler, reflux and second stage temperature, respectively. Table II summarizes the PI parameters used. These parameters were calculated using the criterion of the integral absolute error (ITAE) as an initial estimate the PI controller. A fine adjustment was then made to the plant. Detailed description of process identification, process parameters, assumptions and hypothesis associated to the model is cited on [14]. D. Stage Selection To identify the most sensitive stage for the consequent application of the distributed control, three different methods were applied [15]. In the first method, the difference between the temperatures of two successive trays was calculated throughout the column and the most sensitive tray was that which presented the greatest difference in relation to its adjacent tray. In the second method, a temperature profile for a given value of the manipulated variable (in this case, the reflux flow and the reboiler heat) was obtained. The most sensitive tray gives a symmetrical response to positive and negative variations. Finally, the third method analyzes the tray with the highest derivative of the temperature in relation to the stage when the process is disturbed. It is important to emphasize that different methods can produce different responses. The definition was based on this analysis together with the characteristics of the plant. E. Disturbances Changes in the feed temperature were introduced, decreasing this variable by around 5oC (from 90oC to 85oC). This was achieved by controlled cooling of this stream. TABLE II.

CONTROL PARAMETERS. Parameters

Control loop

τi (s-1)

Kc (K/% opening) Reboiler

Reflux

Tray 2

Reboiler

Reflux

Tray 2

Reboiler

0.280

Conventional 0.005 -2.5 10-3

1.6 10-5

--

Reflux

-0.100

-0.700

2.6 10-4

1.9 10-3

--

Reboiler

0.280

0.005

Distributed 0.020 2.5 10-3

1.6.10-5

1.4 10-4

2.7 10

-5

1.1 10

-3

2.9 10-4

1.3 10

-4

2.4 10

-5

2.6 10-3

Reflux Tray 2

-0.010 0.050

-0.070 -0.010

--

-0.350 0.450

This study aimed to adjust the column temperature profile in order to minimize the response time when a disturbance occurs. Thus, it was not tested for set point tracking. III.

RESULTS AND DISCUSSION

The first step of this study was to determine the stage at which distributed heating could be applied. As previously mentioned, this was achieved through a sensitivity analysis employing three different methods. The results obtained with the first method (successive trays) using three feed ethanol composition conditions demonstrated the possibility of using trays 1, 2, 3, 5 and 7. As the fifth and seventh trays are located in the rectifying section, they were discarded. It was assumed, following the diabatic studies upon which this proposal was based, that in this section it is better to remove heat than supply it. In addition, as this is an initial study, it was defined that only one tray be used to test the proposal. To define this stage, since method 1 was not conclusive, the analysis of symmetrical response and maximum derivative (methods 2 and 3) was used. The derivative method again indicated to stages 5 and 7, which were previously discarded, but the symmetrical response method indicated tray 2 as the most appropriate for this study. Fig. 4 shows this analysis, where it can be observed that tray 2 is almost the same distance from steady state when the process is disturbed with positive and negative perturbations in the feed flow. Based on this sensitivity analysis, the distributed action of the proposal was used only in tray 2. The simultaneous action of the trays was not tested because the main objective was to analyze the distributed proposal with a multivariable system, and its behavior, through the coupling of control loops. Experimental tests were carried out, data were evaluated and multivariable control algorithms implemented with and without the proposed approach. It is important to note that the objective is to study the operation dynamics, comparing a conventional and distributed proposal, and not to analyze the controller performance or multivariable strategy.

Figure 5.

Effect of the disturbance on reboiler temperature control loop response in relation to setpoint.

Figure 6. Effect of the disturbance on distillate temperature control loop response in relation to setpoint.

Fig. 5 and 6 show the reboiler and distillate temperature profiles for the strategies applied. Fig. 7 gives the second stage temperature profile, for the intermediate tray where the distributed control was implemented. As mentioned above, in these experiments, the disturbance was applied by decreasing the feed temperature.

Figure 7. Effect of the disturbance on the tray 2 temperature control loop response in relation to the setpoint.

From the reboiler and distillate response it can be observed that both approaches are equally oscillatory but quickly reject the disturbance. Differences that may indicate the better control strategy were not observed, although the distributed approach presented better performance at some points.

Figure 4. Results of sensitivity analysis using symmetrical response method („ negative disturbance, ‹ steady state, ▲ positive disturbance).

In contrast to the reboiler and distillate temperatures, for the second tray the temperature control loop with the distributed strategy shows a marginally better performance, maintaining its value slightly closer to the set point than the conventional

approach. At the instant of the disturbance, the distributed approach has a small overshoot and it rejects the undesired output faster. This result was to be expected since, in this case, there is a control loop implemented at this stage. However, it is important to note that the distillation dynamics is dependent on the internal temperature. If this stage has a fast response when the process is disturbed, the whole unit will have a faster dynamics, as observed in previous research with classic controllers [10]. The use of another stage to control the temperature profile of the distillation column could require a greater amount of heat supply. In this study we did not evaluated the heat distribution through a rigorous energy analysis. However, a simple observation showed, as expected, that there is heat distribution when the distributed control strategy is used. As observed in Fig. 8, which shows the steam valve opening in the reboiler, there is a reduction in the steam valve opening with the distributed action, probably due to the tray heat supply (Fig. 9). It is expected that the overall distillation heat supply is the same and in the distributed case there is heat distribution between the reboiler and tray, this being one of the reasons for a faster dynamics. This distribution has been previously studied and verified in an evaluation of distillation startup [16].

Also, in order to evaluate which strategy demonstrated the best performance, the integral error (IE), the integral timeweighted absolute error (ITAE) and the total variation (TV) were considered and the results are summarized in Table III. The total variation is a criterion in the evaluation of the magnitude of the manipulated input, using the total up and down movement of the control signal. According to [17], TV is a good measure of the smoothness of the controller output. Based on these results is possible to observe that there is a small difference in the reboiler and distillate temperature control loops, the integral time-weighted absolute error, the conventional control being better. However, the other criteria show, even for the controlled (IE) and manipulated (TV) variables, that the distributed control has a better performance. These values should be as low as possible to obtain a good controller performance, but this was not the main objective of this study. As an additional time analysis, the derivative of the temperature control loops was evaluated in relation to the time required for the disturbance rejection. Fig. 10 shows the results for reboiler temperature, Fig. 11 for the distillate and Fig. 12 for the second stage. This is an important analysis since it reveals behavior of the transition time, that is, the period during which the controlled variable lies outside the specified values.

TABLE III.

RESULTS FOR INTEGRAL ERROR AND TOTAL VARIATION CRITERIA FOR THE DISTRIBUTED AND CONVENTIONAL APPROACHS. Temperature Control Loop

Criteria

Reboiler

Distillate

Stage 2

Conva

Distb

Conva

Distb

Conva

Distb

IE

-0.255

0.085

-0.765

0.595

-0.680

0.085

ITAE

0.011

0.012

0.013

0.014

0.004

0.002

TV

11.30

2.10

61.30

26.2

--

15.80

a.

Conv = conventional b.

Figure 8. Effect of the disturbance on the steam valve opening in the reboiler (manipulated variable).

Figure 9. Effect of the disturbance on the electrical resistance power in the second stage (manipulated variable) for the distributed approach.

Figure 10. Derivative of the reboiler temperature.

Dist = Distributed

slowest. The next steps will consist of rigorous evaluation of the heat supply and its distribution (which was verified in a preliminary analysis) in order to achieve better control parameters. ACKNOWLEDGMENT The authors are grateful for the financial support of ANP (National Agency of the Petroleum) and the Brazilian Government Funding Agency FINEP through ANP’s Human Resources for the Petroleum and Gas Sector Program - PRH34-ANP/MCT and to the CNPq (Brazilian Government National Research Council). REFERENCES Figure 11. Derivative of the distillate temperature.

Figure 12. Derivative of the second stage temperature.

In all cases is possible to note a lower degree of oscillation in the distributed case, this being more evident for the reboiler and second stage. This behavior indicates that with this strategy was possible to maintain the controlled variable closer to the set point, generating minor deviations from the desired value. This behavior leads to a faster response when the process is disturbed. IV.

CONCLUSIONS

The evaluation of the conventional and distributed approach, for a feed temperature disturbance, allowed a reduction in the oscillations of the controlled variable when the strategy with control at stage 2 was used. As observed in previous research with classic controllers, the introduction of an intermediate action in the distillation leads to good results. Considering the objective of verifying the response analysis process and not the control proposition, we conclude that the insertion of a new temperature control loop contributes to better dynamics of the overall unit with classical and multivariable controllers. The main contribution of this work is with respect to a proposal of a new strategy to operate and control distillation columns. The distribution of control action in reboiler heat supply through this stage and trays demonstrated a faster dynamics with classic and advanced controllers. It is important to note that these results were obtained with a disturbance in the temperature feed. However, it is well known that the feed composition is one of the principal disturbances that occur in a distillation column, and also the

[1]

Z. Olujic, M. Jödecke, A. Shilkin, G. Schuch and B. Kaibel, “Equipment improvement trends in distillation”, Chemical Engineering Processing: Process Intensification, vol. 48, pp. 1089-1104, 2009. [2] M. Kaeser and C. L. Pritchard, “Heat transfer at the surface of sieve trays”, Chemical Engineering Research and Design, vol. 83, pp. 10381043, 2005. [3] I. Chawla, and G. P. Rangaiah, “Evaluation of control configurations for a depropaniser”, Chemical Engineering Research and Design, vol. 86, pp.977-988, 2008. [4] S. Enagandula and J. B.Riggs, “Distillation control configuration selection based on product variability prediction”, Control Engineering Practice, vol. 14, pp. 743-755, 2006. [5] Y. Zhu and X. G. Liu, “Dynamics and control of high purity heat integrated distillation columns” Industrial & Engineering Chemical Research, vol. 44, pp.8806-8814, 2005. [6] F. Bezzo, F. Micheletti, R. Muradore and M. Barolo, “Using MPC to control middle-vessel continuous distillation columns”, Journal of Process Control, vol.15, pp. 925-930, 2005. [7] A. K. Jana, A. N. Samantha and S. Ganguly, “Globally linearized control system design of a constrained multivariable distillation column”, Journal of Process Control, vol. 15, pp., 169-181, 2005. [8] S. Karacan, “Application of a non-linear long range predictive control to a packed distillation column”, Chemical Engineering and Processing, vol. 42, pp. 943-953, 2003. [9] G. Koeijer, A. Røsjorde and S. Kjelstrup, “Distribution of heat exchange in optimum diabatic distillation columns”, Energy. vol. 29, pp. 24252440, 2005. [10] C. Marangoni and R. A. F. Machado, “Distillation tower with distributed control strategy: Feed temperature loads”, Chemical Engineering an. Technoly, vol. 30, pp. 1292-1297, 2007. [11] L.O.Werle, C. Marangoni, J.G. Teleken, C. Sayer, M. B. Quadri and R. A. F. Machado, “Fluid dynamic model and control of distillation column with distributed heating” 8th World Congress of Chemical Engineering WCCE 2009, Montreal – Quebec, Canada, 2009. [12] K. J. Astrom and T. Hägglund, “The future of PID control.” Control Engineering Practice, vol. 9, pp. 1163-1175, 2001. [13] P. B. Desphande, Distillation Dynamics and Control. Edward Arnold, New York, 1985. [14] C. Marangoni, “Implementação de uma estratégia de controle com ação distribuída em uma coluna de destilação”. PhD Thesis. Federal University of Santa Catarina – UFSC, Florianópolis, Brazil, 2005. [15] Luyben, “Evaluation of criteria for selecting temperature control trays in distillation columns”, Journal of Process Control vol. 16, pp. 115-134, 2006. [16] L. O. Werle, C. Marangoni, F. R. Steinmacher, P. H. H. Araújo, C. Sayer and R. A. F. Machado, “Application of a new startup procedure using distributed heating along distillation column”, Chemical Engineering and Processing, vol. 48, pp. 1487–1494, 2009. [17] T. N. L. Vu and M. Lee, “Multi-loop PI controller design based on the direct systesis for interaction multi-time delay processes”, ISA Transactions, vol. 49, pp. 79-86, 2010.