Development of a bifurcation analysis approach based on gPROMS platform

doi:10.1016/j.cjche.2016.05.025

›› 2016, Vol. 24 ›› Issue (12): 1742-1749.DOI: 10.1016/j.cjche.2016.05.025

• Process Systems Engineering and Process Safety • Previous Articles Next Articles

Development of a bifurcation analysis approach based on gPROMS platform

Xueqing Kang, Hongye Cheng, Liwei Tong, Lifang Chen, Zhiwen Qi

Max Planck Partner Group at the State Key Laboratory of Chemical Engineering, School of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China

Received:2015-09-20 Revised:2016-03-07 Online:2017-01-04 Published:2016-12-28
Supported by:
Supported by the National Natural Science Foundation of China (21576081), Major State Basic Research Development Program of China (2012CB720502), and 111 Project (B08021).

Development of a bifurcation analysis approach based on gPROMS platform

Xueqing Kang, Hongye Cheng, Liwei Tong, Lifang Chen, Zhiwen Qi

Max Planck Partner Group at the State Key Laboratory of Chemical Engineering, School of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China

通讯作者: Zhiwen Qi,E-mail address:zwqi@ecust.edu.cn
基金资助:
Supported by the National Natural Science Foundation of China (21576081), Major State Basic Research Development Program of China (2012CB720502), and 111 Project (B08021).

Abstract

Abstract: A bifurcation analysis approach is developed based on the process simulator gPROMS platform, which can automatically trace a solution path, detect and pass the bifurcation points and check the stability of solutions. The arclength continuation algorithm is incorporated as a process entity in gPROMS to overcome the limit of turning points and get multiple solutions with respect to a user-defined parameter. The bifurcation points are detected through a bifurcation test function τ which is written in C++ routine as a foreign object connected with gPROMS through Foreign Process Interface. The stability analysis is realized by evaluating eigenvalues of the Jacobian matrix of each steady state solution. Two reference cases of an adiabatic CSTR and a homogenous azeotropic distillation from literature are studied, which successfully validate the reliability of the proposed approach. Besides the multiple steady states and Hopf bifurcation points, a more complex homoclinic bifurcation behavior is found for the distillation case compared to literature.

Key words: Multiple steady states, Bifurcation analysis, Continuation algorithm, gPROMS

摘要： A bifurcation analysis approach is developed based on the process simulator gPROMS platform, which can automatically trace a solution path, detect and pass the bifurcation points and check the stability of solutions. The arclength continuation algorithm is incorporated as a process entity in gPROMS to overcome the limit of turning points and get multiple solutions with respect to a user-defined parameter. The bifurcation points are detected through a bifurcation test function τ which is written in C++ routine as a foreign object connected with gPROMS through Foreign Process Interface. The stability analysis is realized by evaluating eigenvalues of the Jacobian matrix of each steady state solution. Two reference cases of an adiabatic CSTR and a homogenous azeotropic distillation from literature are studied, which successfully validate the reliability of the proposed approach. Besides the multiple steady states and Hopf bifurcation points, a more complex homoclinic bifurcation behavior is found for the distillation case compared to literature.

关键词: Multiple steady states, Bifurcation analysis, Continuation algorithm, gPROMS

Xueqing Kang, Hongye Cheng, Liwei Tong, Lifang Chen, Zhiwen Qi. Development of a bifurcation analysis approach based on gPROMS platform[J]. , 2016, 24(12): 1742-1749.

References

[1] B.P. Patil, E. Maia, L.A. Ricardez-Sandoval, Integration of scheduling, design, and control of multiproduct chemical processes under uncertainty, AIChE J. 61(2015) 2456-2470.
[2] Nan Zhang, Tong Qiu, Bingzhen Chen, Bifurcation control and eigenstructure assignment in continuous solution polymerization of vinyl acetate, Chin. J. Chem. Eng. 23(2015) 1523-1529.
[3] H.Z. Wang, Z.H. Yuan, B.Z. Chen, X.R. He, J.S. Zhao, T. Qiu, Analysis of the stability and controllability of chemical processes, Comput. Chem. Eng. 35(2011) 1101-1109.
[4] R. Gani, J.B. Jørgensen, Multiplicity in numerical solution of non-linear models:Separation processes, Comput. Chem. Eng. 18(1994) S55-S61.
[5] J.W. Kovach, W.D. Seider, Heterogeneous azeotropic:Experimental and simulation results, AIChE J. 33(1987) 1300-1314.
[6] H.Z. Wang, N. Zhang, T. Qiu, J.S. Zhao, X.R. He, B.Z. Chen, Analysis of Hopf points for a Zymomonas mobilis continuous fermentation process producing ethanol, Ind. Eng. Chem. Res. 52(2012) 1645-1655.
[7] H.Z. Wang, N. Zhang, T. Qiu, J.S. Zhao, X.R. He, B.Z. Chen, A process design framework for considering the stability of steady state operating points and Hopf singularity points in chemical processes, Chem. Eng. Sci. 99(2013) 252-264.
[8] Z.G. Lei, B.H. Chen, Z.W. Ding, Special Distillation Processes, Elsevier, Amsterdam, 2005.
[9] Z.G. Lei, J.F. Yang, J.J. Gao, B.H. Chen, C.Y. Li, Gas-liquid and gas-liquid-solid reactors for the alkylation of benzene with propylene, Chem. Eng. Sci. 62(2007) 7320-7326.
[10] Z.G. Lei, C.N. Dai, J.Q. Zhu, B.H. Chen, Extractive distillation with ionic liquids:a review, AIChE J. 60(2014) 3312-3329.
[11] Z.G. Lei, C.Y. Li, B.H. Chen, Extractive distillation:A review, Sep. Purif. Rev. 32(2003) 121-213.
[12] B. Yang, J. Wu, G. Zhao, H. Wang, S. Lu, Multiplicity analysis in reactive distillation column using ASPEN PLUS, Chin. J. Chem. Eng. 14(2006) 301-308.
[13] S. Li, D. Huang, Simulation and analysis on multiple steady states of an industrial acetic acid dehydration system, Chin. J. Chem. Eng. 19(2011) 983-989.
[14] A. Vadapalli, J.D. Seader, A generalized framework for computing bifurcation diagrams using process simulation programs, Comput. Chem. Eng. 25(2001) 445-464.
[15] J.B. Restrepo, G. Olivar, C.A. Cardona, Bifurcation analysis of dynamic process models using aspen dynamics and aspen custom modeler, Comput. Chem. Eng. 62(2014) 10-20.
[16] L.W. Tong, W.G. Wu, Y.M. Ye, G. Wozny, Z.W. Qi, Simulation study on a reactive distillation process of methyl acetate hydrolysis intensified by reaction of methanol dehydration, Chem. Eng. Process. 67(2012) 111-119.
[17] L.W. Tong, L.F. Chen, Y.M. Ye, Z.W. Qi, Analysis of intensification mechanism of auxiliary reaction on reactive distillation:methyl acetate hydrolysis process as example, Chem. Eng. Sci. 106(2014) 190-197.
[18] gPROMS Foreign Objects and Foreign Processes 3.5.0, Process Systems Enterprise Ltd., London, U.K., 201123-32.
[19] R. Seydel, V. Hlavacek, Review article number 24:role of continuation in engineering analysis, Chem. Eng. Sci. 42(1987) 1281-1295.
[20] H.B. Keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in:P. Rabinowitz (Ed.), Applications of Bifurcation Theory, Academic Press, New York 1977, pp. 359-384.
[21] A.G. Salinger, N.M. Bou-Rabee, E.A. Burroughs, R.B. Lehoucq, R.P. Pawlowski, L.A. Romero, E.D. Wilkes, LOCA 1.0:"theory and implementation manual.", Sandia National Laboratories Technical Report, SAND 2002-0396, Sandia National Laboratories, Albuquerque, NM, 2002, http://www.cs.sandia.gov/LOCA.
[22] J.N. Shadid, Experimental and Computational Study of the Stability of Natural Convection Flow in an Inclined EnclosurePh.D. Thesis University of Minnesota, Minneapolis, Minnesota, 1987.
[23] R. Seydel, Practical Bifurcation and Stability Analysis, Vol. 5, Springer, 2010288-290.
[24] R. Seydel, Numerical computation of branch points in nonlinear equations, Numer. Math. 33(1979) 339-352.
[25] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, Lapack Users' Guide:Release 3.0, International Society for Industrial and Applied Mathematics, 1999 http://www.netlib.org/lapack/lug/.
[26] M. Lee, C. Dorn, G.A. Meski, M. Morari, Limit cycles in homogeneous azeotropic distillation, Ind. Eng. Chem. Res. 38(1999) 2021-2027.
[27] T.E. Güttinger, C. Dorn, M. Morari, Experimental study of multiple steady states in homogeneous azeotropic distillation, Ind. Eng. Chem. Res. 36(1997) 794-802.
[28] C. Dorn, M. Lee, M. Morari, Stability and transient behavior of homogeneous azeotropic distillation, Comput. Chem. Eng. 23(1999) S191-S194.

Development of a bifurcation analysis approach based on gPROMS platform

Development of a bifurcation analysis approach based on gPROMS platform

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 3

Recommended Articles

Metrics

Comments

[1]	Erwei Song, Zengxi Li, Erqiang Wang. A novel kind of multiple steady states characteristics in the dividing wall column [J]. Chinese Journal of Chemical Engineering, 2019, 27(4): 869-876.
[2]	Edgar N. Tec-Caamal, Refugio Rodríguez-Vázquez, Luis G. Torres-Bustillos, Ricardo Aguilar-López. Kinetic analysis via mathematical modeling for ferrous iron oxidation in a class of SBR-type system [J]. Chinese Journal of Chemical Engineering, 2019, 27(10): 2472-2480.
[3]	LI Shaojun, HUANG Dingwei. Simulation and Analysis on Multiple Steady States of an Industrial Acetic Acid Dehydration System [J]. , 2011, 19(6): 983-989.