Dynamic Simulation of a Multistage Reactor

Copyright @ IFAC Advanced Control of ClIemicaJ Processes, Kyoto, Japan, 1994

DYNAMIC SIMULATION OF A MULTISTAGE REACTOR Yasuaki Yabuki*, Taketoshi Kajihara**, Chiye Kuwada***, Minoru Yoneda* and Masami Mori * • YokJcaichi Plant Engineering Department. Mitsubishi Kasei Corporation, Mie. Japan •• YokJcaichi Plant Research and Development Center. Mitsubishi Kasei Corporation. Mie. Japan ••• Electronics Division. Mitsubishi Heavy Industries Ltd, Hiroshima. Japan Abstnd. Dyuamic simulation of a multistagc reactor with the continuous polymeri7Jltion process for plMtic was desigoed and model validation was carried out to vaify the model. The controllability study against disturbaoce required for desigoiog operation was dooe and safe operation during transient operation was studied by usiug the dynamic simulation. Key wordL Pclymerizalion~ multistage reactor. simulati~ model pn:dictive control~ plant operation

ing the multistage reactor vary during grade and rate cbaoges. and this paper' confIrms the responae of the control system to these variations. The results of dy· namic simulation conflllD that the use of MOC ~es control of the reactor within a I1IDgC that poses DO problems dnring both rate dJanges and steady st.aleS at

1.INfRODUcnON

In recent years. far-reaching advances in computer bardwan: aod softwan: have given rise to environments for static.cl dyDIm1ic simulations of processes. resulting in an era in which gmcraI process and control engioeen can readily make use of these computa' environments. and a manber of reports conc:eming 1bc:ae maUcrs have appeared. However. the majority of tbcIe ..c .m.cd prinwily .. the design of lII8lysis aod CXlIdroIsystans for proceues. aod tbere 1ft few C88CS CODCaDCd with diacuaiona of plant operation (e.g. operation design in ...ment operabons such as startup. shutdown. grade cbaoge. and optimiDtion of

low rate. The daaa employed in verificatioo is all bcnc:h plant data. The simulation software uscs the CPDS (ClJemical Process Dyuamic SimulatOl') developed by Mitsubisbi Heavy Indostries. Ltd 2.0VERVIEW AND MODEl.LING OF THE MULTISTAGE REACrOR EQUIPMENT

rate~).

For the plastic plants Wgetcd by this paper. W.H. Ray et al (1989) have also reported on nUlDCl'OU8 studies :into the modding and process control fOl' tank reacIon. This paper targc:ta the multiatage reactor. and its .priD8y aim is the optimization of operation, includ:ing the conttoIsystem. dnring transient states. In this :reprd. we have developed a dyoamic modd 00 the ·basis of static simulation. In developing this model. we uaed data c:oUec:tcd through the bench plat. The ·:ootrolayatan is not mcrdy a CODvadiooai PID COD1roI aystan. but alao includes a model predictive COD·troI (MPC)(Garaa et al. 1989).

2.1. TarJCt process The target of this simluatioo is the multistage reactor of a plastic plant. This reactor is opented filled with melt that reacbcs the specified convcmou from the upper stream. It uses a design with altemating stirred tank reactors and heat excbanga'S. Eadil!!tirred tank reactor has a cooling medilDD jacket. T(2DperalUre control for the stirred taok reactors is carried out not . by individual cooling medilDD cin:ulatioo loops for eac:h stirred taok n:actor. but by a COIDIIlOO cooling loop for several stirred tank reactors and heat exc:bangcn. Figure la, lb shows the COIlvc:ntiooai feedforward/feedback COIltrolsystan (FF/FB oontrol).1Di

'fhe flow and temperature of the polymel' (melt) ena-

29

7) The wall temperatures of the stirred tank reactor and heat exchanger are constant 8) Because the radical species concentration of the polymer exists at an extremely lew concentration in comparison with other compositions, quasi-steady-state approximation is assmned to have been achieved

1tOCN: _ _ _ !lEX

6-------------~---0---!

: _ _ ......

=.. .

~~·•luu u:ruuQ/-l--ji___r_':__ !

L____ ______

:t

--«COCLANr

I

The material balance for the stirred tank reactor is given by

--~----.---------- - ------ -- ---- ----------;


Vjpj( ~J )=W(Xji_l -xji)+ VjPj~j _

Fig_la fF/FB oootrol system

(I)

The heat balance for the stirred tank reactor is given by (Processing area)

.

HEX

i ROCN--

~.

ROCN : _ _ _

VjPj<;K~Rj)=W(Cpi-l TRi-l-CpjTRj)

HEX : . ' ' ' - -

+ VjppiRpidHr+AJ'jHj(TW-TRj)+Q+Qw

.'

(2)

(Wall area)

--;

-- ._._----

L._~_ ...

VWPwCpw(~)=AJcHc
1tOCN __ _____.._i

~---

(3)

N

I

....

+

L~_ _ _

AJjHj (TRj-TW)

i=1

:t

(Cooling mcdi1Dl1 area)

Fig. I b Model predictive oootrol system

VboPboCpbo ~)=WH(<;aa THm -Cpbo TI-Ic,) dt

+ AJJIc(fW-THo)+~

. (4)

the MPC system. The material balance of the heat exchanger is given by

2.2. Description of the simulation model Based on the assmnpboos stated below, the model is (:omposeci of material balance and heat balance as the basic system.

dxjjc:D ._ dt ~J .

(5)

The heat balance of the heat exchanger is given by (Processing area)

I) The model ccaten on the multistage reactor, and includes the range from reactor enb'y to reactor· exit The model for the cooling mcdi1Dl1 system is considered to be from the cooling medi1Dl1 supply line. 2) The mass flow of the melt and cooling medi1Dl1 are invariable. 3) The interior of the ~ tank reactor is 000side1red to be a model of continuous stirred tank reactors, and the thermal capacity of the agitator and shaft are ignored. 4) The coolant medi1Dl1 in the stirred tank reactor jacket is well mixed 5) The process side of the heat exchanger is a piston flow pipe, and continuous stirring exists within the separation zone. 6) The t.cmpc:rature of the cooling medi1Dl1 within the heat exchanger is constant

ViPir ' ~)=ViPiRpAHr+A1iHj(fW-TF1)' "-p dt

(6)

(Wall area)

(Cooling medi1Dl1 area)

VhPboc;.,~~)=WH(c;..m THm~ THo) ,

(8)

+ATcHIlfW -THo~+Qr where,aU the symbols are given in the appendix .

Models of other areas. For the control area, the iIlgolithm of the distributed control systc:m in the bench plat operation was employed, and tbc model of the MPC system is a control system using a ~tepped-respoose model for execution. Additiooally,

30

Table I Evaluation of model verification

121.. 121.6

te

frequency

amplitude

room 1

-11.4%

14.8%

room 2

-3 .8%

2 . 1%

room 3

13%

18.5%

UI 4 .

... 121.2 Ui

120.' 120.6

o

.~

"

•

6

correspond weU, and the model is suitable.

Est _____ Set

Exp. Fi:;'Jre.

2. Response of the cooling medium a.--=

3. STUDY OF CONTROlLABILITY THROUGH DYNAMIC SIMULATION 3.1. Controllability Ihroup chanres in melt temperature The multistage reactor is composed of sevc..-ral stirred tank reactors and heat exchangers which sh&re a single coolant loop. With FF/FB tanpcl"8ture control only ODe stirred tank reactor in the single coolant loop was a controlled variable, and the other stirred tank reactors were not controlled, which posed probl.ems .

147

146 I~

._._._.*'

.-~

144

143

142

Figure 4 is a simulation of the bebavior of the stirred tank reactor temperature under FF/FB control when the melt tempcl"8ture from the uppez stream is sub.iected to disturbance. In response to the rise in temperature in the melt from the upper stream, the temperature of the controlled stirred reactor tank is in fact oootrolled, but the other reactors are not (XJDtrulled, and control of the subsequent process is adYersely affected.

141 140 0

1

++++

456

xxx

•

9

10

Exp.

Est Fig 3 .ResporuiC of the stirred tank reactor

To resolve this problem, an MPC system was designed. The decision was made to adopt the steppedresponse model as the model used fer MPC on the basis of statistical methods from identification testing, and dynamic simulations were carried out to confum operational safety. Figure 5 shows the simulated temperature behavior of the each stiJred tank reactors 00del MPC in respoose to identical disturbances. With MPC, the temperature of the each stiJred tar.k reactors was referenced. Although an offset to tIk: set value remains in response to rises in the temperawre of the mdt from the previous process, the other reactors are not uncontrolled. Therefore, oontrollability is supe110r to FF/FB oootrol.

deviations between the controlled variables are weighted to COIDpa1S8te for insufficiencies in the mauipulalion variables for the oontrolled variables. For the control valves, 8. model of the flow cbaracta'istics is made from the design oonditions; for the resistance thermometer, respon:te testing was conducted for the resistance thermometer used in the actual jUnl, expressing dead time and fmt-onb systems.

23. Model validation Variations in load were placed on the bench plant to "erify the model. The load fluctuations involved \'arying the cooling medium setting by 0.6 [0C] up or down every 100 minutes. Figures 2 and 3 show COIDJIIlIisons of the actual plant data and caladatOO simulation values for the process and cooling medium ar(as. These results of error rates are arranged by frecluencyand amplitude in Table 1. It can be ooocluded from this table that the model and the bench process

Operational. safety was confumed from dris simulation, and MPC was employed in the bench plant As reference. Figure 6 compares the bench plao1 data and calculated simulation values with the temperature settings for the each reactor raised by the ratio 1:2.5:5 withMPC.

31

I~r-----~------~----~------~-----.

145.S

3.2.Study of cootrol1ability during rate cha~

The beat balance of the stirred reactor tanks in tbf multistage reactor in response to reactioo beat main· tained a virtual balance with sensible beat and beat re· moved by the jacket. AdditiooaUy. COIIlJmisoos of the sensible beat and the amount of beat removed show ihat the ratio of the sensible heat is largcr.

14S I• .S

With a reduced rate. reactioo heat is increa:Jed and tilt sensible heat becomes smaller. With an increased rate. however. the sensible heat becomes larger ancl reaction beat is reduced because the residence time i~ longer. For this reason. operatioo is JDOle difficult with a reduced rate. when coosideratioo is given to tht: rate change.

TIME (IIca-)

- - Di,turbaDce •••••••. ++++

_._.- Each room

Fig. 4 Respoose of the FF/FB control system

Stable tracking of the decline in rate is demanded of this reactor. including the control system. Therefore . the way in which the temperature of each stirred tam: reactor is brought to a steady value corresponding to the rate at this time hinges upon the method of control

I~

147

1* ....... .t . .t .• ..• 14S

1

144

I~I

~

)(

·· ·.t ...... ·. · ~ ·~··:··:. + + +

....

143

"

+.

+ ........... .

• ••••••

x.',

r-

1~0~~--~2""~""~~""-S~~6""~""~a~~9""~IO

.

~Y;:'"

.-;........... ', ) (

... ...

x·

)I

)(

JC )(

.x- •••

'--,-------~---------------

142 I~I

Distutbance ••••••• . ++++

-

I~

_._.- Each room

Fig.5 RcspoDlIe of MPC to disturbance

mIE~)

Eachrooru

++++

I . r -........~........r -........r -........r -........r -....- - ,

Fig.7 Response of FF/FB control during reduced rate

I~

143 142 I~I

142

•.. le ':

.....~::.i· · · · · · ·~:·::::~·~· · · · - · - · - · - · - · - · - · - ·:~:· :

I

~

I~I

I~

+:

ti

.

I-

1~0~....--~........2~........~........~~........S~....~

137

;++++++.++++ • • • • +.++++ •• +++++

•••• ••••••••••••••••• x •••••••

136

...

.... __ .......

US

- - E,t - - _. Exp. _._.- Set

134 0

Fig.6 Respoose of MPC to changes in setbng5

++++

- ...-... . .-._.....-._._.- - -... ,_._.- -.-

........ 2

---- ... ---~------------------. a

10

Each room

Fig. 8 Response of MPC during reduced rate

32

u

(3) Hidalgo. P.M. and C.B. Brosilow. (1990). Nonlincar Model Prcd:i.ctive Cootrol of S tyrene Polymerizati
147

TDIE~1

1•

6.APPENDIX

rate

Table of symbols AJ,AJc,AT ,ATe Cp.Cpw.Cph H,Hc,Hh

for the cooling medimn system.

QA

Disturbance

Each room

Fig.9 P~ eX MPC to disturbance during 10\'\'

AH Qr Figure 7 displays the raults of simulation whereby the rate is:reduced with conventional FF/FB control . Figure 8 depicts a similar simulation with the MPC system. The effectiveness of MFC in time and cootrol until the tempcmture of each n:.:tor reaches 8. steady state is appment here. Furthermore. the response of MFC to tempcmture disturbaDce in the melt from the pt"Cvious process in the steady state of Figure 8 was alao simulated. -.cl its stability was coofumed.

Qw P,pP,pb

R TH.TR.1W V.Vw.Vh W.WH X Other symbols i j

4.CONCLUSION

in

This paper describes the fnnd8JDeutal verification re-. quired for designing the operation of a multistage reactor. The raults that have been achieved include tIK:

o

following. (1) A dynamic model of a multistage reactor was COIlBtructed. validation with data from the bench plant was canied out. aod an appropriate model was achieved. (2) The controllability against disturbance required for designing operation was coofmned using dynamic simulatioos. aod the effective-Def>8 of MPC was coofllDled. In conjunction with this. the modding of other IR&'I is needed for the investigati
5.REFERENCES (1) Ray. W.H. (1989). Computer-aidcd design.. monitoring. aod cootrol of poIymerizati
33

Area Specific heal Heat transfer coefficient Heat of poIymeri711uon Released heal Tube plate heat Heat of agitation Density Reacti
Temperature Volmne

Mass flow Compooent weight fraction Stirred reaction tank and heat exchaoga- separation zone Reaction OOIIlpooeDt Inflow Outflow