A Cascade Scheme to Control Composition in a Copolymerization Reactor

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Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA

A CASCADE SCHEME TO CONTROL COMPOSITION IN A COPOLYMERIZATION REACTOR Salvador Padilla1 and Jesus Alvarez

l'niversidad Autonoma Afetropo/i/ana-lztapa/apa, Depto. de Ing. de Procesos e Hidraulica, Apdo. 55534, 09340 Mexico, D. F AfE.\7CO

Abstract: In industrial copolymerization reactors. the quality attributes of the product are achieved by controlling the rates of monomer incorporation. The strong nonlinearities in the polymerization rates and their strong coupling with thermal effects lead to a complex mUltiple-input multiple-output (MIMO) nonlinear control problem. Using nonlinear control and polymerization reactIOn engineering tools, the possibility of solving the control problem with a (possibly conventional-type) cascade input-output control scheme is established in terms of conditions that bear physical meaning. The copolymerization of vinyl-acetate with methyl-methacrylate. using ethyl-acetate as solvent. is considered as an application example. Keywords Process control. nonlinear control. cascade controL chemical variable control, nonlinear systems.

I. INTRODUCTION Mass and solution copolymerization reactors are used to produce commodities and specialties in the plastic industry. The regulation of the individual polymerization rates is one of the main requirements to be fulfilled in the operation of a copolymerization reactor. This is important to ensure product properties, among them are copolymer composition. average molecular weight. glass transition temperature. mechanical properties. etc. In practice. the copolymerization processes and their industrial control scheme are usually designed as an extrapolation of previous laboratory tests by means of scale-up procedures. In particular, these systems have as an extra component the solvent, that has an important role in the design of the control scheme (Padilla et. at. 1995) The solvent can iCentro de Investigacion en Polimeros. Apdo 55885, MEXICO.

simplify or complicate the regulation of selected outputs. especially if the solvent participates, via chain transfer reactions to solvent, in the copolymerization reaction. For further details on the state of the art in industry and in its associated research subject, the reader is referred to Padilla and Alvarez (1995). Congalidis et. al. (1989), Adebekun and Schork (1989a.b), and references therein. In Padilla and Alvarez (1995), 5x5 MIMO configurations for a continuous copolymerization reactor were studied, concluding that, to obtain the fastest settling time of instantaneous copolymer composition and production rate, while using outputs that lead to first order closed-loop output dynamics, the outputs should be temperature, volume. solvent concentration, concentration of the unconverted more reactive monomer. and concentration of the less reactive monomer in polymer form. By doing so. the input-output interaction matrix depended on

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compositions, heat transfer coefficient volume and flows, and not on the copolymerization kinetics (the main responsible of the nonlinear nature), provided the uncontrollable dynamics (determined by the election of the outputs) was stable. In the present work. the following questions are addressed. a) Is it possible to obtain a simpler control scheme in the sense that few closed-loops in a cascade structure are required, leading to a simpler (possibly conventional type) control implementation and a simpler tuning? b) what conditions have to be satisfied in order to ensure stability and adequate speed of the uncontrollable dynamics?, and c) what is the limiting attainable performance under state-feedback?

and further modeling details can be seen in Congalidis et. al. (1989), Padilla et. al. (1995), and references therein. RI, RI and Rz are strictly positive smooth scalar fields that correspond to rates of initiator decomposition. conversion of monomer I and conversion of monomer 2, respectively. p and r are strictly positive smooth scalar fields that correspond to the rates of heat production to heat capacity, and of heat exchange to heat capacity. The gel effect is considered (Hamer et. al. , 1981) in the kinetics, and r depends on viscosity. which in turn depends via a free volume-type functionality. on the fraction of polymeric material (Alvarez et. a1.. 1990).

2.2 A preamble: 5x5 control scheme.

2. STATEMENT OF THE PROBLEM

2.1. The

Copo~vmerizati()n

Reactor.

Let us consider a continuous copolymerization reactor where two monomers, solvent and initiator are fed to the tank, heat being removed by means of a cooling jacket. Addition of solvent maintains a low viscosity and facilitates the heat removal. The perfectly mixed continuous stirred tank reactor (CSTR) is described by the following set of eight equations (Hamer et. a1.. 1981: Congalidis et. aI., 1989) (that account for the effect of density changes with conversion) : Ail

= /; + qlgll + qzgzl + qsg31

.\iz = /~ + qlglZ + qzgzz + qSg32

i = h + qlg13 + qZgB + lfSg31

.5' = j~ + qlg)4 + QZgZ4 + (ISg34 l~

/~ + q)gl~ + Qzg2~ + lfSg35 Pz = /~ + (hgl6 + Qzg2(, + QSg36 i = f7 + qlg)7 + qZg27 + (jsgn + y7~ (' =

=

f8 + (IJ,RI8 + lIzgZ8 + l/sg"g

- q

1, M 1, Ah. PI. P 2 and S are concentrations of initiator. unconverted monomer I. unconverted monomer 2. converted monomer I. converted monomer 2. and solvent. respectively. T is the reactor temperature, and V is the reactor volume. The inputs (not necessarily for control) are: (jl (feed rate of monomer I). lie. (feed rate of monomer 2), ql (feed rate of initiator). lis (feed rate of solvent), 1'j (jacket temperature) and q (exit flow rate). r (temperature) and r' (volume) are two output variables that must be regulated with relative degree one (i.e.. first-order closed-loop dynamics must be obtained under static state-feedback). The main model functionalities are given in the appendix.

The objective of this subsection is twofold: i) to present the nonlinear control tools (lsidori. 1989, Nijmeijer and Van der Schaft. 1990). that underlie our approach to the reactor control problem. and ii) to u!,e the results for the 5x5 control scheme of Padilla et. al. (1995) to identify and motivate the possibility of having a simpler cascade inputoutput control configuration. To have a fast closed-loop response with internal stability (i.e .. without input-multiplicity: Adebekun and Schork (1989a». the following output map (Padilla et. al. 1995) (1)

is selected for the 5x5 MIMO state-feedback control scheme. All is the concentration of the most reactive monomer, P 2 is the concentration of the less reactive monomer in polymer form, S is the solvent concentration, T is reactor temperature and V is the reactor volume. With the following notation

the copolymerization reactor can be written as follows:

x = /(x) + (i(x)u, v = h(x)

x

E

X,u EU,Y

E

Y

(2)

where f(x). G(x) and h(x) are smooth vector fields on the neighborhood X E 9{8 of the nominal design operating point X. that is a critical point of the last system, i.e.

o =fU) + G(X)

1/,

Y

= h(X)

The nominal state x can be asymptotically stable (AS) or unstable. The input u and the output Y take values in the neighborhoods U E 9{m and Y EO 9{m of the nominal input u and output y, respectively. Since the robustness of a geometric nonlinear control scheme degrades with the

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Copyright © 1996lFAC 13th Triennial World Congress. San FrancIsco, USA

QUALITY CONTROL SYSTEM FOR AN INDUSTRIAL HIGH DENSITY POLYETHYLENE PROCESS

Morimasa Ogawa1), Masahiro Ohshima 2 ), Fuminao Watanabel) Koji Morinaga 1) and Iori Hashimot( 3 )

1) Milsuhishi Chemical Corporation, Mizushima Plant, Okayama 712, JAPAN, 2) Dept. of Comp. Sci. and Sys. Eng, Miyazaki Univ., Miyazaki 889-21, JAPAN, 3) Dept. 4Chem. Eng., Kyoto Univ., Kyoto 606-01, JAPAN

ABSTRACT: In polyolefin processes, Melt Index, which is difficult to measure frequently, is one of the key polymer properties to be controlled in order to maintain the product quality at a higher level. An oll-line inferential scheme was proposed for predicting the MI using secondary on-line measurelllenl'>. Then, a quality control system of MI is constructed using a two-degree of freedom cascaded model predictive controller by incorporating the on-line inferential scheme of ML Keywords: Quality control, MI Control, Polymerization reactor control, Internal Model Control

1. INTRODUCTION In recent years, demand for consistency in the quality of products is increasingly strong. In the industrial polyolefin production processes, there are many processes required to produce various kinds of polymer in the same reactor while maintaining the polymer quality at a high level. In order to maintain the quality, it is required to regulate the polymer properties at the specified level. To produce various grades of products, frequent grade changeover operations, which often result in producing a large amount of off-spccification polymer, are required. Therefore. in a grade changeover, it is crucial to change the opcrating conditions as safely and quickly as possible. In order to perform optimal grade changeover operations and at the same time precise regulations, it is important to have a sophisticated control system that can ach ieve superior sctpoint tracking and regulation. However, the most critical variables or polymer quality at the end-uscr's level are not easily measured, while most of the process variables are easily measured. This makes both regulatory control and chnngeover control quite difficult. In this study, a quality control system is devcloped for an industrial polyethylcne polymerization process. In order

that the control system can achieve superior setpoint traeking and regulatory control function, it is constructed in a cascaded form of internal model controllers, where the concentration in the reactor is controlled every 15 minutes by the inner loop and the polymer quality is controlled every 2 hours by the outer loop. Following the introduction, a description of the high density polyethylene production process is given. Then, an on-line quality inferential scheme developed for monitoring the polymer quality as well as filtering the outlier in the measurement of the quality is described. The structure of the developed control system incorporating the inferential scheme is presented. Some application results are also illustrated,

2. PROCESS DESCRIPTION The Mitsubishi Chemical corporation has developed a slurry reactor for high density polyethylene (HDPE) production. The schematic of the production plant is illustrated in Fig. 1. The plant consists of a stirred tank reactor, flash drum, stripper, dryer and an extrudn. The feed to the reactor is comprised of ethylene, co-monomer and hydrogen. The

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