Nonlinear polymerization reactor

We have previously mentioned that the nonlinear nature of the polymerization reactor gives rise to a nonlinear immersion and as a consequence, it is impossible to construct its corresponding exponential holder. To avoid this problem, it is necessary to analyze the mathematical structure of wiss, to conclude that the nonlinear term is mainly due to the function that describes the effect gel. A suitable solution is given by finding a simpler mathematical function to satisfactorily describe the gel effect phenomena (we should recall that the most common gel effect functions such as (47), are actually given by empirical correlations). We propose the following function for gt to represent the diffusional limitation of the polymerization reaction... 

H. Seki, M. Ogawa, S. Ooyama, K. Akamatsu, M. Ohshima, and W. Yang. Industrial application of a nonlinear model predictive control to polymerization reactors. Control Engineering... 

Control of industrial polymerization reactors is a challenging task because, in general, control engineers lack rigorous polymerization process knowledge, process model, and rapid online or inline sensors to measure polymer properties. Exothermic polymerization processes often exhibit strongly nonlinear dynamic behaviors (e.g., multiple steady states, autonomous oscillations, limit cycles, parametric sensitivity, and thermal runaway), particularly when continuous stirred tank... 

Jeong, B.G. Yoo, K.Y. Rhee, H.K. Nonlinear model predictive control using a Wiener model of a continuous methyl methacrylate polymerization reactor. Ind. Eng. Chem. Res. 2001, 40 (25), 5968-5977. 

B Maner, FJ Doyle III, B Ogunnaike, and R Pearson. Nonlinear model predictive control of a multivariable polymerization reactor using second-order Volterra series. Automatica, 32 1285-1302, 1996. 

One final point about closed-loop process control. Economic considerations dictate that to derive optimum benefits, processes must invariably be operated in the vicinity of constraints. A good control system must drive the process toward these constraints without actually violating them. In a polymerization reactor, the initiator feed rate may be manipulated to control monomer conversion or MW however, at times when the heat of polymerization exceeds the heat transfer capacity of the kettle, the initiator feed rate must be constrained in the interest of thermal stability. In some instances, there may be constraints on the controlled variables as well. Identification of constraints for optimized operation is an important consideration in control systems design. Operation in the vicinity of constraints poses problems because the process behavior in this region becomes increasingly nonlinear. 

This can be seen in the simulation of the PID control of polymerization reactor temperature by Houston and Schork [34]. Reactor temperature is often controlled by manipulating the temperature or flow rate of coolant in the reactor cooling jacket. This scheme is hindered by the slow dynamics of heat removal and the nonlinear nature of the heat evolution process (especially in... 

The really interesting issues in control of polymerization are not in the control of the operating conditions (flow, temperature, etc.). These loops are controlled in much the same way as would be done in any other chemical process. The real interest is in the control of polymer properties (monomer conversion, MW, particle size, copolymer composition, etc.). The next sections will review a number of control studies, each using a different approach to deal with the control problems specific to polymer property control (lack of sensors, one-sided control, nonlinearities, etc.). This will be followed by a discussion of an alternative approach to polymerization reactor control, statistical process control, and a discussion of the optimization of operating trajectories. 

Most polymerizations are nonlinear. The applicability of nonlinear reference control schemes for solution polymerization reactors has been demon-... 

Adebekun, A. K. and Schork, F. J. (1989b) Continuous solution polymerization reactor control. 2. Estimation and nonlinear reference control during methylmethacrylate polymerization, Ind. Eng. Chem. Res. 28, 1846-61. 

C. O. ScHWANKE, A. R. Gomatam, Nonlinear Model Predictive Control of a polymerization reactor , presented at the Tutorial on Polymerization Reactor Control, AIChE Annual Meeting, November, 2003. 

Ahn SM, Park MJ, Rhee HK. Extended Kalman filter-based nonlinear model predictive control for a continuous RIMA polymerization reactor. Ind Eng Chem Res 1999 38 3942-3949. 

Peterson T, Hernandez E, Arkun Y, Schork FJ. A nonlinear DMC algorithm and its application to a semibatch polymerization reactor. Chem Eng Sci 1992 47 737-753. 

It is also known that continuous polymerization reactors may exhibit highly nonlinear dynamics such as multiple steady states, autonomous oscillations, and strong parametric sensitivity. Thus, it is important to understand the steady state and dynamic behaviors of a reactor in order to maintain reactor stability and to achieve smooth transitions for grade changes. 

J. Alvarez, R. Suarez, and A. Sanchez. Nonlinear decoupling control of free radical polymerization continuous stirred tank reactors. Chem. Enq. Sci., 45 3341-3354, 1990. 

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