Dynamic Behavior and Control in an Industrial Fluidized-Bed Polymerization Reactor Nina P. G. Salau,* ,† Gustavo Alberto Neumann, ‡ Jorge O. Trierweiler, † and Argimiro R. Secchi* ,† Group of Integration, Modeling, Simulation, Control and Optimization of Processes (GIMSCOP), Chemical Engineering Department - Federal UniVersity of Rio Grande do Sul (UFRGS), Rua Sarmento Leite, 288/24 - CEP: 90050-170 - Porto Alegre - RS, Brazil, and Braskem S.A., III Po ´lo Petroquı ´mico, Via Oeste, Lote 5 - CEP: 95853-000 - Triunfo RS, Brazil In an industrial fluidized-bed polymerization reactor, tight temperature control is of utmost importance to ensure that the temperature in the reaction zone is kept above the dew point of reactants, yet below the melt point of the polymer. Even within a narrow temperature range, temperature excursions must be avoided because they can result in low catalyst productivity and significant changes in product properties. Furthermore, if the reactor temperature is under open-loop conditions, these reactors are prone to instability and undesired nonlinear dynamic behaviors. In this work, a first principles model, including the recycle stream and the heat exchange system, is used to describe an industrial fluidized-bed polymerization reactor of the UNIPOL process. A detailed study of the dynamic behavior of this process is carried out, with the location of bifurcation points and system stabilization by PID controller designed via optimization in the frequency domain. Nonetheless, if the manipulated variable (cooling water valve position) saturates, the reactor operates without a feedback temperature controller, leading to oscillatory behavior and limit cycles. For this case, it has been also demonstrated the necessity of using auxiliary manipulated variables to decrease the polymerization heat generation and to help control the reactor temperature. 1. Introduction The multiple steady states and instability in chemical reactors problems are features of great industrial interest, and a great number of models have been proposed to describe the dynamic behavior of fluidized-bed polymerization reactors. Choi and Ray 1 investigated the steady-state multiplicity and the bifurcation phenomenon in fluidized-bed polymerization reactors. For these proposes, they considered both emulsion and bubble phases in reactor modeling, taking the mass and heat transfer in the fluidized bed into account. A review of the dynamic behavior and stability of gas-phase polymerization reactors was provided by McAuley et al. 2 They also demonstrated that the addition of a gas recycle system and a heat exchange system to the gas- phase reactor model enables a detailed study of complex dynamics and the location of bifurcation points that could not be reproduced by the reactor model alone. In addition, they investigated the effects on the stability and multiplicity of the system caused by the size and dynamics of the heat exchanger, the catalyst properties, the gas composition (monomer, comono- mer, and inert), and the addition of a monomer concentration controller to the reactor system. A great variety of polymerization processes for which multiple steady states, sustained oscillations, and other nonlinear phenomena arise routinely in industrial practice were presented, analyzed, and discussed in a series of papers by Ray and co- workers at the University of Wisconsin. In Ray and Villa 3 and references therein, a variety of examples are provided illustrating the nonlinear dynamics found in polymerization processes. A strategy based on bifurcation theory and nonlinear dynam- ics that addresses robust control design of nonlinear systems can be found in Hahn et al. 4 It applies bifurcation analysis to closed-loop nonlinear systems by considering controller param- eters, set points, and system parameters as bifurcation param- eters. In this way, controller settings can be determined that result in stable operation of the closed-loop system for a specified degree of model uncertainty. Mo ¨nnigmann and Mar- quardt proposed an optimization-based strategy 5 that is based on constraints that enforce a minimal backoff from critical manifolds. Critical manifolds are boundaries in the space of system and controller parameters that separate regions with qualitatively different system behaviors, e.g., a region with stable operating points from a region with unstable system behavior. Dadebo et al. 6 demonstrated that fluidized-bed polymerization reactors without a temperature feedback controller are prone to unstable steady states, limit cycles, and temperature excursions toward unacceptable high-temperature steady states. In their work, the ability of the designed controllers to stabilize desired set points of industrial interest was evaluated using a bifurcation approach. They considered the temperature of cooled water entering the heat exchanger as the reactor temperature control manipulated variable. However, the actual manipulated variable of the reactor temperature control in an industrial plant is the cooling water valve position, which is considered for the first time in the current work. Ghasem 7,8 analyzed the effects of polymer particle size, catalyst feed rate, and inlet gas temperature on fluidized-bed polymerization reactors. Furthermore, the dynamic behavior of these reactors under a proportional-integral (PI) controller for the reactor temperature was also analyzed. It was observed that maximum polyethylene production rates can be achieved by operating in unstable steady states, which definitely require a suitable controller to stabilize them. However, Ghasem showed that the presence of the integral action in the reactor temperature controller destroys the multiplicity of steady states that is present in the system using proportional controller alone, but at the expense of larger zones of instability and chaotic behavior. * To whom correspondence should be addressed. E-mail: ninas@ enq.ufrgs.br (N.P.G.S.), arge@enq.ufrgs.br (A.R.S.). Tel.: . Fax: +55- 51-3308-3277. † Federal University of Rio Grande do Sul (UFRGS). ‡ Braskem S.A. Ind. Eng. Chem. Res. 2008, 47, 6058–6069 6058 10.1021/ie0712838 CCC: $40.75  2008 American Chemical Society Published on Web 07/17/2008