단일탑 증류공정의 정상상태 해의 다중성

장광식; 한경택; 이강주; 윤인섭

HWAHAK KONGHAK, Vol.31, No.1, 36-44, February, 1993

Export Citation

단일탑 증류공정의 정상상태 해의 다중성

Multiplity of Steady State Solutions of Single Column Distillation

장광식, 한경택, 이강주, 윤인섭

초록

본 연구에서는 증류공정을 포함한 단 분리공정에 적합한 Continuation 알고리듬을 통하여 단일탑 증류공정에서의 정상상태 해의 다중성을 구현하였다. 다중해는 주로 농도의 설계사양에 대하여 많이 나타났으며 농도의 설계사양은 공정의 조업 유연성을 떨어뜨리는 역할을 하였다. 열역학적 비이상성이 큰 문제의 경우는 주로 내부 유량 변수들에 대하여 다중해를 나타났으며 다중해를 갖는 공정이라 해서 모든 변수에 대하여 정상상태 해의 다중성이 존재하지는 않았다.

This paper presents the steady state multiplicity for single column distillation. A continuation method which is adequate to implement the multiplicity of separation precesses including distillation is em-ployed. Tight design specification, especially concentration specification, causes most of multiplicity of the solutions and this takes a role of deteriorating the flexibility of process operation. In case of having severe nonideality in the thermodynamic properties, the column internal flow rates may have multiple solutions. But, not all the variables have multiplicities.

[References]

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Rheinholdt WC, Numerical Analysis of Parameterized Nonlinear Equations, John Wiley & Sons, Inc., New York (1986)
Seydel R, Hlavacek V, Chem. Eng. Sci., 42(6), 1281 (1987)
DenHeijer C, Rheinboldt WC, SIAM J. Nucl. Anal., 18, 925 (1981)
Rose A, Sweeny RF, Schrodt VN, Ind. Eng. Chem., 50(5), 737 (1958)
Ellis MF, Kosby R, Mijares G, Gomez-Munoz A, Holland CD, Comput. Chem. Eng., 10(5), 433 (1986)
Georg K, Proceedings of NATO Advanced REsearch Institute on Homotopy Methods and Convergence, Plenum Press, New York, 145 (1980)
Davidenko D, Dokl. Akad. Nauk USSR, 88, 601 (1953)
Wayburn TL, Seader JD, "Solution Systems of Interlinked Distillation Columns by Differential Homotopy Continuation Methods," Foundations of Computer-Aided Chemical Process Design (1983)
Rion WL, Brunt VV, Comput. Chem. Eng., 14, 889 (1990)
Wayburn TL, "A Review of Continuation Methods and Their Application to Separation Problems," in CAST Newsletter, Summer (1989)
Seader JD, "Recent Developments in Methods for Finding All Solutions to General Systems of Nonlinear Equations," in Proc. of Conf. on Foundations of Computer Aided Process Design (1989)
Choi SH, Ph.D. Dissertation, Univ. of Missourri-Rolla (1990)
Rheinboldt WC, Burkardt JV, ACM Trans. Math. Soft, 9(2), 215 (1983)
Watson LT, Billup SC, Morgan AP, ACM Trans. Math. Soft, 13, 281 (1987)
Shacham M, "Recent Developments in Solution Techniques for Systems of Nonliear Equations," in Proc.of Conf. on Foundations of Computer Aided Process Design (1984)
Praustniz JM, Anderson TF, Grens EA, Eckert CA, Hsieh R, O'Connell JP, Computer Calculation for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibrium, Prentice-Hall, Inc., New Jersey (1980)
Edmister WC, Lee BI, "Applied Hydrocarbon Thermodynamics," Gulf Publishing (1984)
Naka Y, Araki M, Takamatsu T, Ind. Chem. Eng., 19, 137 (1979)
Block M, Hegner B, AIChE J., 22, 582 (1976)
Han KT, Lee KJ, Yoon ES, Kim HY, HWAHAK KONGHAK, 30(1), 34 (1992)

[1] Allgower E, Georg K, SIAM Rev., 22, 28 (1980)

[2] Rheinholdt WC, Numerical Analysis of Parameterized Nonlinear Equations, John Wiley & Sons, Inc., New York (1986)

[3] Seydel R, Hlavacek V, Chem. Eng. Sci., 42(6), 1281 (1987)

[4] DenHeijer C, Rheinboldt WC, SIAM J. Nucl. Anal., 18, 925 (1981)

[5] Rose A, Sweeny RF, Schrodt VN, Ind. Eng. Chem., 50(5), 737 (1958)

[6] Ellis MF, Kosby R, Mijares G, Gomez-Munoz A, Holland CD, Comput. Chem. Eng., 10(5), 433 (1986)

[7] Georg K, Proceedings of NATO Advanced REsearch Institute on Homotopy Methods and Convergence, Plenum Press, New York, 145 (1980)

[8] Davidenko D, Dokl. Akad. Nauk USSR, 88, 601 (1953)

[9] Wayburn TL, Seader JD, "Solution Systems of Interlinked Distillation Columns by Differential Homotopy Continuation Methods," Foundations of Computer-Aided Chemical Process Design (1983)

[10] Rion WL, Brunt VV, Comput. Chem. Eng., 14, 889 (1990)

[11] Wayburn TL, "A Review of Continuation Methods and Their Application to Separation Problems," in CAST Newsletter, Summer (1989)

[12] Seader JD, "Recent Developments in Methods for Finding All Solutions to General Systems of Nonlinear Equations," in Proc. of Conf. on Foundations of Computer Aided Process Design (1989)

[13] Choi SH, Ph.D. Dissertation, Univ. of Missourri-Rolla (1990)

[14] Rheinboldt WC, Burkardt JV, ACM Trans. Math. Soft, 9(2), 215 (1983)

[15] Watson LT, Billup SC, Morgan AP, ACM Trans. Math. Soft, 13, 281 (1987)

[16] Shacham M, "Recent Developments in Solution Techniques for Systems of Nonliear Equations," in Proc.of Conf. on Foundations of Computer Aided Process Design (1984)

[17] Praustniz JM, Anderson TF, Grens EA, Eckert CA, Hsieh R, O'Connell JP, Computer Calculation for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibrium, Prentice-Hall, Inc., New Jersey (1980)

[18] Edmister WC, Lee BI, "Applied Hydrocarbon Thermodynamics," Gulf Publishing (1984)

[19] Naka Y, Araki M, Takamatsu T, Ind. Chem. Eng., 19, 137 (1979)

[20] Block M, Hegner B, AIChE J., 22, 582 (1976)

[21] Han KT, Lee KJ, Yoon ES, Kim HY, HWAHAK KONGHAK, 30(1), 34 (1992)