관형 촉매반응기 시스템의 동적최적화

오민; 문제권

HWAHAK KONGHAK, Vol.36, No.5, 764-771, October, 1998

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관형 촉매반응기 시스템의 동적최적화

Dynamic Optimisation of a Catalytic Tubular Reactor System

오민, 문제권

초록

o-xylene로부터 PA를 생산하는 관형 촉매반응기의 수학적 모델을 수립하고 이를바탕으로 한 동적최적화를 수행하였다. 촉매반응기시스템의 수학적 모델은 IPDAEs로 표현되며 MOL방법을 사용하여 시간에 대하여 변화하는 DAEs으로 변환하였다. 바꿔어진 DAEs에 포함된 제어변수를 CVP 방법을 통하여 간단한 다항식으로 표현하여 유한차원의 NLP문제로 바꾸었다. 이러한 과정을 통하여 최종적으로 나타난 동적최적화 문제는 NLP와 시간적분의 외부 loop와 내부 loop를 반복적으로 계산하는 과정을 통하여 수치해를 구하였다. 여러 다른 제어전략에 대하여 동적최적화를 수행하고 결과를 비교하였다. 목적함수는 전체 시간영역을 4단계로 나눈 경우에 최대치를 얻을 수 있었으며 동적최적화를 통하지 않은 다른 여러 경우와 비교하여 목적함수가 약 3.6-235% 가량 향상됨을 알 수 있었다.

A mathematical model of a catalytic reactor system, which produces phthalic anhydride from o-xylene, is constucted. Based on the mathematical model, dynamic optimisation of the system is carried out. The mathematical statement of the system is IPDAEs and they are converted into DAEs using MOL. Within the framework of CVP, control variables can be described in terms of a weighted combination of simple polynomials, and this leads an infinite dimensional dynamic optimisation problem to a finite dimensional NLP problem. The reformulated dynamic optimization prob]em using CVP can be solved with repeated calculation of the NLP outer loop and the time integration inner loop. Dynamic optimization is carried out for various control strategies, and the results are compared. The maximum objective function is obtained for the 4 step strategy and we compare its results with intuitively chosen control cases. From the comparison, we noted that the objective function of the optimal case is improved about 3.6-235%.

Keywords:Dynamic Optimisation;CVP;Catalytic Tubular Reactor System;IPDAEs;SQP

[References]

Edgar TF, Himmelblau DM, "Optimization of Chemical Processes," McGraw Hill (1988)
Anderson BDO, Moore JB, "Optimal Control," Prentice-Hall International, New Jersey (1989)
Luns R, Int. J. Control, 51(5), 995 (1990)
Luns R, Rosen O, Ind. Eng. Chem. Res., 30(7), 1525 (1991)
Cuthrell JE, Biegler LT, AIChE J., 33(8), 1257 (1987)
Logsdon JS, Biegler LT, Chem. Eng. Sci., 47(4), 851 (1992)
Vassiliadis VS, Sargent RW, Pantelides CC, Ind. Eng. Chem. Res., 33(9), 2111 (1994)
Vassiliadis VS, Sargent RW, Pantelides CC, Ind. Eng. Chem. Res., 33(9), 2123 (1994)
Ames WF, "Numerical Methods for Partial Differential Equations," Academic Press, New York (1992)
Finlayson BA, "Nonlinear Analysis in Chemical Engineering," McGraw-Hill, New York (1980)
Logsdon JS, Biegler LT, Ind. Eng. Chem. Res., 32, 692 (1993)
Fletcher R, "Practical Methods of Optimization," John Wiley & Sons (1991)
Luenberger DG, "Introduction to Dynamic Systems," Wiley (1979)
Oh M, Jang EJ, Moon JK, HWAHAK KONGHAK, 36(1), 109 (1998)
Carver MB, Hinds HW, Simulation, Aug., 59 (1978)
Schiesser WE, "The Numerical Method of Lines," Academic Press, New York (1993)
Zienkiewicz OC, Morgan K, "Finite Elements and Approximation," John Wiley & Sons, New York (1983)
Finlayson BA, Chem. Eng. Sci., 26, 1081 (1971)
Ferguson NB, Finlayson BA, Chem. Eng. J., 1, 327 (1970)
Oh M, Ph.D. Dissertation, Imperial College, UK (1995)
Froment GF, Bischoff KB, "Chemical Reactor Analysis and Design," John Wiley & Sons, New York (1990)
Chen CL, Macchieto S, Technical Report, Centre for Process Systems Engineering, College, London (1989)
Jarvis RB, Pantelides CC, Technical Report, Centre for Process Systems Engineering, Imperial College, London (1992)

[Referenced By]

[1] Edgar TF, Himmelblau DM, "Optimization of Chemical Processes," McGraw Hill (1988)

[2] Anderson BDO, Moore JB, "Optimal Control," Prentice-Hall International, New Jersey (1989)

[3] Luns R, Int. J. Control, 51(5), 995 (1990)

[4] Luns R, Rosen O, Ind. Eng. Chem. Res., 30(7), 1525 (1991)

[5] Cuthrell JE, Biegler LT, AIChE J., 33(8), 1257 (1987)

[6] Logsdon JS, Biegler LT, Chem. Eng. Sci., 47(4), 851 (1992)

[7] Vassiliadis VS, Sargent RW, Pantelides CC, Ind. Eng. Chem. Res., 33(9), 2111 (1994)

[8] Vassiliadis VS, Sargent RW, Pantelides CC, Ind. Eng. Chem. Res., 33(9), 2123 (1994)

[9] Ames WF, "Numerical Methods for Partial Differential Equations," Academic Press, New York (1992)

[10] Finlayson BA, "Nonlinear Analysis in Chemical Engineering," McGraw-Hill, New York (1980)

[11] Logsdon JS, Biegler LT, Ind. Eng. Chem. Res., 32, 692 (1993)

[12] Fletcher R, "Practical Methods of Optimization," John Wiley & Sons (1991)

[13] Luenberger DG, "Introduction to Dynamic Systems," Wiley (1979)

[14] Oh M, Jang EJ, Moon JK, HWAHAK KONGHAK, 36(1), 109 (1998)

[15] Carver MB, Hinds HW, Simulation, Aug., 59 (1978)

[16] Schiesser WE, "The Numerical Method of Lines," Academic Press, New York (1993)

[17] Zienkiewicz OC, Morgan K, "Finite Elements and Approximation," John Wiley & Sons, New York (1983)

[18] Finlayson BA, Chem. Eng. Sci., 26, 1081 (1971)

[19] Ferguson NB, Finlayson BA, Chem. Eng. J., 1, 327 (1970)

[20] Oh M, Ph.D. Dissertation, Imperial College, UK (1995)

[21] Froment GF, Bischoff KB, "Chemical Reactor Analysis and Design," John Wiley & Sons, New York (1990)

[22] Chen CL, Macchieto S, Technical Report, Centre for Process Systems Engineering, College, London (1989)

[23] Jarvis RB, Pantelides CC, Technical Report, Centre for Process Systems Engineering, Imperial College, London (1992)