Improved temperature control of a batch reactor with actuation constraints

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Abstract

In some industrial batch reactors the accuracy in tracking desired temperature profiles is significantly influenced by the characteristics of the actuation system that regulates the thermal exchange. In these plants it may not be structurally possible to switch promptly between the heating and the cooling configurations; this implies that, for long time periods, the sign of the actuating signal is constrained to be either positive or negative. This fact, as long as spontaneous evaporation of the coolant, limits the possibility of tracking the desired temperature profile. Under the constraints that the actuation system can only subtract heat from the reactor, a new scheme is proposed to improve the controllability of the reactor temperature. The strategy alternates phases of coolant injection and phases of forced draining of the jacket. The proposed scheme has been worked out on the basis of the numerical analysis of a detailed thermodynamic model of an industrial reactor. The scheme has been extensively tested with remarkable results and is now in use in some industrial reactors of the CIBA Specialty Chemicals at Pontecchio Marconi, Italy.

Introduction

The conduction of chemical reactors often represents a challenging task from a controller design perspective. Difficulties originate from many factors, related to the complex and distributed non-linear dynamic of the reactions, and from the technical difficulty of performing online composition measurement of some reaction variables that could be exploited for feedback control (Friedric & Perne, 1995). For these reasons, in practice, the controlled variable of the process is often the mean reaction temperature (Loulech, Cabassud, & Le Lann, 1999). In fact, it is possible to directly influence the quality of the final product by following a desired temperature profile (Adachi, Kawata, & Masubuchi, 1993). Usually, the reactor temperature is controlled through the heat exchange between the reactor and the fluid that flows in the jacket surrounding it. In most of the industrial applications a heating/cooling system that injects cooling and heating fluids in the jacket according to the need is employed.

Standard industrial PID regulators often perform unsatisfactory on these plants, mainly because of the relevant non-linearities and uncertainty of the process (Huzmezan, Gough, Dumont, & Kovac, 2002). Some improvements in terms of performance and robustness have been achieved by employing PID-self-tuning (Cameron & Seborg, 1983) and gain-scheduled-PID controllers (Cheng & Edgar, 1997). To cope with the variable structure nature that is originated by the switching between the cooling and heating configuration, techniques based on variable structure and sliding mode controllers have been proposed (Su and Tsai, 2001, Sakamoto et al., 1998). Recently, model-based technique as model predictive controllers have also been employed (Katende and Jutan, 2000, Garcia et al., 1991).

Although in some specific industrial applications advanced control techniques are currently in use with remarkable results, in many existing industrial reactors possible improvements of the temperature control scheme are strongly constrained by the structural limitations of the existing actuation system and by the deficiency of measurements to be exploited for feedback control.

In some plants there is a practical difficulty of performing a fast switching between the cooling and the heating configuration; in this case the thermal exchange is governed only by the cooling fluid and heating is not employed for control purposes (mono-fluid heat exchanger); this implies that the control signal remains positive (or negative) for long time periods. To date, the problem of tracking reactor temperature profiles under the constraint of “one sign control” have not received much attention; on the other hand this topic has a great practical relevance (Lute and Van Paassen, 1995, Madár et al., 2004).

The control strategy proposed in this paper was designed to meet specifications expressly formulated by industry (CIBA, Specialty Chemicals at Pontecchio Marconi, Italy):

Improve the existing PD temperature control law in order to track accurately a desired cooling profile using a mono-fluid heat exchanger. The hardware and instrumentation modification should be conservative.

Under these constraints on the actuation system, the design of a control strategy is particularly challenging for the following motivations:

  • due to the limitation on the sign of the actuating signal, there are some operative conditions that cannot be controlled.

  • due to the high-temperature of the reaction, bubbling of the cooling water could occur. This phenomena is highly non-linear and is strongly influenced by the flow velocity of the coolant.

Given these specifications, the selection of the control strategy is particularly difficult to be done a priori. In fact, the proposed strategy was selected only after the analysis based on a detailed numerical model of the thermodynamics of a cooling reactor. The strategy, described in detail in Section 5, opportunely alternates phases of coolant injection and phases of coolant draining. The proposed methodology was experimentally tested in some industrial reactors with remarkable results. In the following sections the system analysis, modelling, control law and experimental results will be described in detail.

Section snippets

Mathematical model of the reactor

A schematic diagram of the reactor is shown in Fig. 1. The reactor volume is about 12 m3 and the jacket volume is about 0.25 m3. The input u1 drives the coolant injection valve V1, while V2 is currently employed to drain the jacket for maintenance; V2 is driven by an on/off command signal u2. Valves V3 and V4 are employed to fill and to empty the reactor, respectively.

A mathematical model of the reactor was worked out to characterize the different thermodynamic phases and transitions; details

Thermodynamic analysis of the reactor

For the system under study, the reaction temperature Tu is always higher than the bubbling temperature of the coolant (water); therefore, a significant part of cooling fluid is subject to evaporation, particularly when the coolant flow is small. The fluid change of phase has a relevant thermodynamic effect and must be taken into account in the design phase of the control system.

To rationalize the analysis, it is convenient to put into evidence the possible working phases (WPs) of the reactor

Limits of the previous control strategy

Up to date, the reactor temperature is controlled by a digital PD regulator that drives the valve V1 in function of the error e(k) between the desired reaction temperature Tdes and the actual one Tu. The control law isuPD(k)=Kpe(k)+KdΔe(k),e(k)=Tdes(k)-Tu(k),Δe(k)=e(k)-e(k-1).Since it is possible to inject in the jacket only cooling fluid, in practice, the following “structural” constraint holds:u1(k)=uPD(k),uPD(k)<0,u1(k)=0,uPD(k)0.This gains of the controller were tuned to give appropriate

New control strategies

The thermodynamic analysis of the reactor put into evidence that two main aspects have to be faced in the design of the new control strategy:

  • 1.

    reduction of the effects of the cooling caused by the uncontrolled bubbling and extension of the region of the phase plane [e(k),Δe(k)] where the control action is active,

  • 2.

    using as much as possible, the instrumentation already available on the plant to limit additional hardware installations.

Experimental results

The proposed control strategy were extensively tested on three industrial reactors of the CIBA Specialty Chemicals at Pontecchio Marconi (Italy). In this particular application, it was found through model-based analysis that the most important phase of the cooling profile is at high temperatures and involves only the system operation in working phases P1–P2 and P3; on the other hand, the accuracy in tracking the final ramp of the cooling profile (P4 and P5) does not have a significant influence

Conclusions

In this work a control strategy has been proposed for the tracking of desired cooling profiles for chemical reactors with constraints on the actuation system. Following a detailed numerical analysis of the heat exchange between the reactor and its cooling jacket, it was proposed as an approach that opportunely alternates coolant injection phases and forced draining phases. The forced draining have the positive effect of limiting the uncontrollable cooling effect caused by the bubbling of the

Appendix

The jacket has been divided in n sections of equal length. The water inside the ith finite element has temperature Th,i. Each element has a unique temperature Tm, while the reagent within the reactor has temperature Tu assumed equal in the whole mass. A scheme of the thermal exchange is reported in Fig. 16. The thermal exchange between vessel, cooling fluid and reaction is governed by the following thermodynamic balance equations (the meaning of the parameters are reported in Table 4):mucuT˙u=H

References (13)

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