化工过程稳定性分析研究进展

doi:10.11949/j.issn.0438-1157.20170883

摘要/Abstract

摘要：

化工过程在实际操作过程中时刻面临着扰动，稳定性作为化工过程可操作性的一个重要元素，决定着化工过程在扰动消失之后能否回到原来的操作点，直接关系到产品的质量以及过程的安全性。对于稳定性的研究有助于理解及调控化工过程的非线性行为，例如多稳态现象和持续振荡等，从而保证化工过程在扰动的作用下能够长周期、平稳、安全运行。本文从多稳态现象和多稳态点的稳定性分析、考虑稳定性的化工过程优化方法、化工过程稳定性的调控以及不确定性条件下的稳定性分析4个方面综述了化工过程稳定性分析的研究进展。

关键词: 安全, 多稳态现象, 稳定性, 分岔, 优化, 不确定性

Abstract:

Chemical processes may experience a large number of disturbances. Stability is a key of chemical process operability, related to product quality and process safety directly. It is a criterion to determine whether a process can return to its original operating point when disturbance disappears. The research on stability can help to understand and adjust the nonlinear behaviors in chemical processes, such as multiple steady state and oscillation. Therefore, with the consideration of stability analysis, the chemical processes can be operated smoothly and safely under disturbance for a long time. This review concludes the progress in stability analysis from four aspects:multiple steady state and stability analysis, optimization with guaranteed stability, dynamic behavior adjustment of chemical processes, and stability analysis under uncertainty.

Key words: safety, multiple steady state, stability, bifurcation, optimization, uncertainty

中图分类号:

TQ018

蒋浩, 陈丙珍. 化工过程稳定性分析研究进展[J]. 化工学报, 2018, 69(1): 76-87.

JIANG Hao, CHEN Bingzhen. Research progress of chemical process stability analysis[J]. CIESC Journal, 2018, 69(1): 76-87.

参考文献 99

[1]	BAYBUTT P. Layers of protection analysis for human factors (LOPA-HF)[J]. Process Safety Progress, 2002, 21(2):119-129.
[2]	HENDERSHOT D C. An overview of inherently safer design[J]. Process Safety Progress, 2006, 25(2):98-107.
[3]	王杭州, 陈丙珍, 赵劲松, 等. 面向本质安全化的化工过程设计:多稳态及其稳定性分析[M]. 北京:清华大学出版社, 2017. WANG H Z, CHEN B Z, ZHAO J S, et al. Inherently Safer Design Oriented Analysis of Steady-State Multiplicity and Stability of Chemical Processes[M]. Beijing:Tsinghua University Press, 2017.
[4]	WOLFF E A, SKOGESTAD S, PERKINS J. A procedure for operability analysis[C]//Institution of Chemical Engineers Symposium Series. 1994, 133:95-102.
[5]	SEIDER W D, BRENGEL D D, WIDAGDO S. Nonlinear analysis in process design[J]. AIChE Journal, 1991, 37(1):1-38.
[6]	王杭州, 陈丙珍, 何小荣, 等. 化学反应系统的多稳态分析[J]. 化工学报, 2009, 60(1):127-133. WANG H Z, CHEN B Z, HE X R, et al. Analysis of steady state multiplicity of chemical reaction systems[J]. CIESC Journal, 2009, 60(1):127-133.
[7]	KIVA V N, ALUKHANOVA B M. Multiple steady states of distillation and its realisation[J]. Computers & Chemical Engineering, 1997, 21:S541-S546.
[8]	WANG C, WONG D, CHIEN I, et al. Experimental investigation of multiple steady states and parametric sensitivity in azeotropic distillation[J]. Computers & Chemical Engineering, 1997, 21:S535-S540.
[9]	ELNASHAIE S S, GRACE J R. Complexity, bifurcation and chaos in natural and man-made lumped and distributed systems[J]. Chemical Engineering Science, 2007, 62(13):3295-3325.
[10]	李庆扬, 莫孜中, 祁力群. 非线性方程组的数值解法[M]. 北京:科学出版社, 1987. LI Q Y, MO Z Z, QI L Q. Numerical Methods for Nonlinear Systems of Equations[M]. Beijing:Science Press, 1987.
[11]	WAYBURN T, SEADER J. Homotopy continuation methods for computer-aided process design[J]. Computers & Chemical Engineering, 1987, 11(1):7-25.
[12]	GRITTON K S, SEADER J, LIN W J. Global homotopy continuation procedures for seeking all roots of a nonlinear equation[J]. Computers & Chemical Engineering, 2001, 25(7):1003-1019.
[13]	JALALI F, SEADER J, KHALEGHI S. Global solution approaches in equilibrium and stability analysis using homotopy continuation in the complex domain[J]. Computers & Chemical Engineering, 2008, 32(10):2333-2345.
[14]	陈传淼, 谢资清. 非线性微分方程多解计算的搜索延拓法[M]. 北京:科学出版社, 2005. CHEN C M, XIE Z Q. The Continuation Method for Multi-solution of Nonlinear Differential Equations[M]. Beijing:Science Press, 2005.
[15]	LYAPUNOV A M. The general problem of the stability of motion[J]. International Journal of Control, 1992, 55(3):531-534.
[16]	马知恩, 周义仓. 常微分方程定性与稳定性方法[M]. 北京:科学出版社, 2001. MA Z E, ZHOU Y C. Qualitative Method and Stability of Ordinary Differential Equations[M]. Beijing:Science Press, 2001.
[17]	GHOMMIDH C, VAIJA J, BOLARINWA S, et al. Oscillatory behaviour of Zymomonas in continuous cultures:a simple stochastic model[J]. Biotechnology Letters, 1989, 11(9):659-664.
[18]	尤里·阿·库兹涅佐夫. 应用分支理论基础[M]. 金成桴, 译. 北京:科学出版社, 2010. KUZNETSOV Y A. Fundamental Applied Bifurcation Theory[M]. JIN C F, trans. Beijing:Science Press, 2010.
[19]	张楠. 非线性聚合过程的稳定性与分岔特性调控[D]. 北京:清华大学, 2016. ZHANG N. Bifurcation control and ajustment of nonlinear polymerization processes[D]. Beijing:Tsinghua University, 2016.
[20]	ZHANG N, QIU T, CHEN B. Bifurcation control and eigenstructure assignment in continuous solution polymerization of vinyl acetate[J]. Chinese Journal of Chemical Engineering, 2015, 23(9):1523-1529.
[21]	DOEDEL E J. AUTO:a program for the automatic bifurcation analysis of autonomous systems[J]. Congr. Numer., 1981, 30:265-284.
[22]	BACK A, GUCKENHEIMER J, MYERS M, et al. DsTool:computer assisted exploration of dynamical systems[J]. Notices Amer. Math. Soc., 1992, 39(4):303-309.
[23]	DHOOGE A, GOVAERTS W, KUZNETSOV Y A. MATCONT:a MATLAB package for numerical bifurcation analysis of ODEs[J]. ACM Transactions on Mathematical Software (TOMS), 2003, 29(2):141-164.
[24]	WANG H Z, CHEN B Z, HE X R, et al. Numerical analysis tool for obtaining steady-state solutions and analyzing their stability characteristics for nonlinear dynamic systems[J]. Journal of Chemical Engineering of Japan, 2010, 43(4):394-400.
[25]	VAN HEERDEN C. Autothermic processes[J]. Industrial & Engineering Chemistry, 1953, 45(6):1242-1247.
[26]	BILOUS O, AMUNDSON N R. Chemical reactor stability and sensitivity[J]. AIChE Journal, 1955, 1(4):513-521.
[27]	UPPAL A, RAY W, POORE A. On the dynamic behavior of continuous stirred tank reactors[J]. Chemical Engineering Science, 1974, 29(4):967-985.
[28]	WANG H Z, YUAN Z H, CHEN B Z, et al. Analysis of the stability and controllability of chemical processes[J]. Computers & Chemical Engineering, 2011, 35(6):1101-1109.
[29]	HAMER J, AKRAMOV T, RAY W. The dynamic behavior of continuous polymerization reactors(Ⅱ):Nonisothermal solution homopolymerization and copolymerization in a CSTR[J]. Chemical Engineering Science, 1981, 36(12):1897-1914.
[30]	SCHMIDT A D, RAY W H. The dynamic behavior of continuous polymerization reactors(Ⅰ):Isothermal solution polymerization in a CSTR[J]. Chemical Engineering Science, 1981, 36(8):1401-1410.
[31]	SCHMIDT A, CLINCH A, RAY W. The dynamic behaviour of continuous polymerization reactors(Ⅲ):An experimental study of multiple steady states in solution polymerization[J]. Chemical Engineering Science, 1984, 39(3):419-432.
[32]	TEYMOUR F, RAY W. The dynamic behavior of continuous solution polymerization reactors(Ⅳ):Dynamic stability and bifurcation analysis of an experimental reactor[J]. Chemical Engineering Science, 1989, 44(9):1967-1982.
[33]	TEYMOUR F, RAY W. The dynamic behavior of continuous polymerization reactors(Ⅴ):Experimental investigation of limit-cycle behavior for vinyl acetate polymerization[J]. Chemical Engineering Science, 1992, 47(15/16):4121-4132.
[34]	TEYMOUR F, RAY W. The dynamic behavior of continuous polymerization reactors(Ⅵ):Complex dynamics in full-scale reactors[J]. Chemical Engineering Science, 1992, 47(15):4133-4140.
[35]	PINTO J, RAY W. The dynamic behavior of continuous solution polymerization reactors(Ⅶ):Experimental study of a copolymerization reactor[J]. Chemical Engineering Science, 1995, 50(4):715-736.
[36]	PINTO J, RAY W. The dynamic behavior of continuous solution polymerization reactors(Ⅷ):A full bifurcation analysis of a lab-scale copolymerization reactor[J]. Chemical Engineering Science, 1995, 50(6):1041-1056.
[37]	PINTO J, RAY W H. The dynamic behavior of continuous solution polymerization reactors(IX):Effects of inhibition[J]. Chemical Engineering Science, 1996, 51(1):63-79.
[38]	刘柱彬, 邱彤, 赵劲松. 气相卧式搅拌釜聚丙烯反应器的模拟及多稳态分析[J]. 化工学报, 2014, 65(11):4451-4458. LIU Z B, QIU T, ZHAO J S. Modeling and steady-state multiplicity analysis of gas-phase polypropylene horizontal stirred bed reactor[J]. CIESC Journal, 2014, 65(11):4451-4458.
[39]	YUAN Z, WANG P, YANG C. Steady-state multiplicity analysis of two-stage-riser catalytic pyrolysis processes[J]. Computers & Chemical Engineering, 2015, 73:49-63.
[40]	XIU Z L, ZENG A P, DECKWER W D. Multiplicity and stability analysis of microorganisms in continuous culture:effects of metabolic overflow and growth inhibition[J]. Biotechnology and Bioengineering, 1998, 57(3):251-261.
[41]	MEEL A, SEIDER W D, SOROUSH M. Game theoretic approach to multiobjective designs:focus on inherent safety[J]. AIChE Journal, 2006, 52(1):228-246.
[42]	袁志宏, 王杭州, 陈丙珍, 等. 厌氧型发酵生产丙二醇体系的操作区域分区与分析[C]//中国过程系统工程年会暨中国MES年会, 2009. YUAN Z H, WANG H Z, CHEN B Z, et al. Analysis and operating zone segregation of anaerobic fermentation system[C]//Symposium of Process Systems Engineering and MES. 2009.
[43]	WANG H Z, ZHANG N, QIU T, et al. A process design framework for considering the stability of steady state operating points and Hopf singularity points in chemical processes[J]. Chemical Engineering Science, 2013, 99:252-264.
[44]	KOKOSSIS A, FLOUDAS C. Stability in optimal design:synthesis of complex reactor networks[J]. AIChE Journal, 1994, 40(5):849-861.
[45]	BLANCO A B M, BANDONI J A. Interaction between process design and process operability of chemical processes:an eigenvalue optimization approach[J]. Computers & Chemical Engineering, 2003, 27(8):1291-1301.
[46]	BLANCO A M, BANDONI J A. Design for operability:a singular-value optimization approach within a multiple-objective framework[J]. Industrial & Engineering Chemistry Research, 2003, 42(19):4340-4347.
[47]	BLANCO A M, BANDONI J A. Eigenvalue and singular value optimization[J]. Mecanica Computational, 2003, 22:1258-1272.
[48]	BLANCO A M, BANDONI J A, BIEGLER L. Re-design of the Tennessee Eastman challenge process:an eigenvalue optimization approach[C]//Proceedings of Foundations of Computer Aided Process Design. 2004:517-520.
[49]	BLANCO A M, BANDONI J A. Eigenvalue optimization-based formulations for nonlinear dynamics and control problems[J]. Chemical Engineering and Processing:Process Intensification, 2007, 46(11):1192-1199.
[50]	LEWIS A S, OVERTON M L. Eigenvalue optimization[J]. Acta Numerica, 1996, 5(1):149-190.
[51]	RINGERTZ U T. Eigenvalues in Optimum Structural Design. Large-scale Optimization with Applications[M]. New York:Springer, 1997:135-149.
[52]	HURWITZ A. On the conditions under which an equation has only roots with negative real parts[J]. Selected Papers on Mathematical Trends in Control Theory, 1964, 65:273-284.
[53]	CHANG Y, SAHINIDIS N V. Optimization of metabolic pathways under stability considerations[J]. Computers & Chemical Engineering, 2005, 29(3):467-479.
[54]	XIA Z, ZHAO J S. Steady-state optimization of chemical processes with guaranteed robust stability and controllability under parametric uncertainty and disturbances[J]. Computers & Chemical Engineering, 2015, 77:116-134.
[55]	XIA Z, ZHAO J S. Robust optimization of index-2 differential algebraic equations with guaranteed stability under parametric uncertainty:application to a reactor-separator-recycle process[J]. Industrial & Engineering Chemistry Research, 2015, 54(41):10031-10039.
[56]	WANG H Z, ZHANG N, QIU T, et al. Optimization of a continuous fermentation process producing 1, 3-propane diol with Hopf singularity and unstable operating points as constraints[J]. Chemical Engineering Science, 2014, 116:668-681.
[57]	CHANG H C, CHEN L H. Bifurcation characteristics of nonlinear systems under conventional PID control[J]. Chemical Engineering Science, 1984, 39(7/8):1127-1142.
[58]	LUO L, ZHANG N, XIA Z, et al. Dynamics and stability analysis of gas-phase bulk polymerization of propylene[J]. Chemical Engineering Science, 2016, 143:12-22.
[59]	HASSOUNEH M A, LEE H C, ABED E H, et al. Washout filters in feedback control:benefits, limitations and extensions[C]//Proceedings of the 2004 American Control Conference. 2004:3950-3955.
[60]	LEVINE W S. The Control Handbook[M]. 2nd ed. Boca Raton:CRC Press, 1996.
[61]	ABED E H, FU J H. Local feedback stabilization and bifurcation control(Ⅰ):Hopf bifurcation[J]. Systems & Control Letters, 1986, 7(1):11-17.
[62]	ABED E H, FU J H. Local feedback stabilization and bifurcation control(Ⅱ):Stationary bifurcation[J]. Systems & Control Letters, 1987, 8(5):467-473.
[63]	WANG H Z, ZHANG N, QIU T, et al. Method for regulating oscillatory dynamic behavior in a Zymomonas mobiliz continuous fermentation process[J]. Industrial & Engineering Chemistry Research, 2014, 53(31):12399-12410.
[64]	MÖNNIGMANN M, MARQUARDT W. Bifurcation placement of Hopf points for stabilization of equilibria[C]//Proceedings of the 15th IFAC World. 2002.
[65]	HYNNE F, SORENSEN P G, MOLLER T. Complete optimization of models of the Belousov-Zhabotinsky reaction at a Hopf bifurcation[J]. The Journal of Chemical Physics, 1993, 98(1):219-230.
[66]	BASSO M, EVANGELISTI A, GENESIO R, et al. On bifurcation control in time delay feedback systems[J]. International Journal of Bifurcation and Chaos, 1998, 8(4):713-721.
[67]	YU P, CHEN G. Hopf bifurcation control using nonlinear feedback with polynomial functions[J]. International Journal of Bifurcation and Chaos, 2004, 14(5):1683-1704.
[68]	KANG W. Bifurcation and normal form of nonlinear control systems (Ⅰ)[J]. SIAM Journal on Control and Optimization, 1998, 36(1):193-212.
[69]	KANG W. Bifurcation and normal form of nonlinear control systems. (Ⅱ)[J]. SIAM Journal on Control and Optimization, 1998, 36(1):213-232.
[70]	MOIOLA J, CHEN C. Controlling the multiplicity of limit cycles[C]//Proceedings of the 37th IEEE Conference. 1998:3052-3057.
[71]	LEE H C, ABED E H. Washout filters in the bifurcation control of high alpha flight dynamics[C]//American Control Conference. 1991:206-211.
[72]	LEE H C. Robust control of bifurcating nonlinear systems with applications[D]. College Park:University of Maryland, 1991.
[73]	ABED E H, LEE H C. Nonlinear stabilization of high angle-of-attack flight dynamics using bifurcation control[R]. College Park:University of Maryland, 1990.
[74]	WANG H O, ABED E H. Bifurcation control of a chaotic system[J]. Automatica, 1995, 31(9):1213-1226.
[75]	WANG J, CHEN L, FEI X. Bifurcation control of the Hodgkin-Huxley equations[J]. Chaos, Solitons & Fractals, 2007, 33(1):217-224.
[76]	DING L, HOU C. Stabilizing control of Hopf bifurcation in the Hodgkin-Huxley model via washout filter with linear control term[J]. Nonlinear Dynamics, 2010, 60(1/2):131-139.
[77]	JIANG H, CHEN B Z. Study on dynamic behavior adjustment of nonlinear chemical processes[J]. AIChE Journal, 2016, 62(9):3189-3198.
[78]	ZHANG N, SEIDER W D, CHEN B Z. Bifurcation control of high-dimensional nonlinear chemical processes using an extended washout-filter algorithm[J]. Computers & Chemical Engineering, 2016, 84:458-481.
[79]	WICAKSONO D S, MARQUARDT W. Reformulation strategies for eigenvalue optimization using Sylvester's criterion and Cholesky decomposition[C]//Proceedings of the 23rd European Symposium on Computer Aided Process Engineering. 2013:487-492.
[80]	GOLUB G H, VAN LOAN C F. Matrix Computations[M]. 4th ed. Baltimore:JHU Press, 2012.
[81]	ZHANG Y, CHUFU L, XIAORONG H, et al. Simulation and optimization in the process of toluene liquid-phase catalytic oxidation[J]. Chinese Journal of Chemical Engineering, 2008, 16(1):36-38.
[82]	WANG H Z, ZHANG N, QIU T, et al. Modeling, simulation and analysis of the liquid-phase catalytic oxidation of toluene[J]. Chemical Engineering Journal, 2010, 158(2):220-224.
[83]	GROSSMANN I E, SARGENT R W H. Optimum design of chemical plants with uncertain parameters[J]. AIChE Journal, 1978, 24(6):1021-1028.
[84]	GROSSMANN I E, HALEMANE K P. Decomposition strategy for designing flexible chemical plants[J]. AIChE Journal, 1982, 28(4):686-694.
[85]	GROSSMANN I E, HALEMANE K P, SWANEY R E. Optimization strategies for flexible chemical process[J]. Computers & Chemical Engineering, 1983, 7(4):439-462.
[86]	HALEMANE K P, GROSSMANN I E. Optimal process design under uncertainty[J]. AIChE Journal, 1983, 29(3):425-433.
[87]	SWANEY R E, GROSSMANN I E. An index for operational flexibility in chemical process design(Ⅰ)[J]. AIChE Journal, 1985, 31(4):621-630.
[88]	SWANEY R E, GROSSMANN I E. An index for operational flexibility in chemical process design(Ⅱ)[J]. AIChE Journal, 1985, 31(4):631-641.
[89]	GROSSMANN I E, FLOUDAS C A. Active constraint strategy for flexibility analysis in chemical process[J]. Computers & Chemical Engineering, 1987, 11(6):675-693.
[90]	PISTIKOPOULOS E N, GROSSMANN I E. Optimal retrofit design for improving process flexibility in linear systems[J]. Computers & Chemical Engineering, 1988, 12(7):719-731.
[91]	PISTIKOPOULOS E N, GROSSMANN I E. Optimal retrofit design for improving process flexibility in nonlinear systems(I):Fixed degree of flexibility[J]. Computers & Chemical Engineering, 1989, 13(9):1003-1016.
[92]	PISTIKOPOULOS E N, GROSSMANN I E. Optimal retrofit design for improving process flexibility in nonlinear systems(Ⅱ):Optimal level of flexibility[J]. Computers & Chemical Engineering, 1989, 13(10):1087-1096.
[93]	JIANG H, CHEN B Z, WANG H Z, et al. Novel method for considering process flexibility and stability simultaneously[J]. Industrial & Engineering Chemistry Research, 2014, 53(38):14765-14775.
[94]	MOHIDEEN M, PERKINS J, PISTIKOPOULOS E. Robust stability considerations in optimal design of dynamic systems under uncertainty[J]. Journal of Process Control, 1997, 7(5):371-385.
[95]	MÖNNIGMANN M, MARQUARDT W. Normal vectors on manifolds of critical points for parametric robustness of equilibrium solutions of ODE systems[J]. Journal of Nonlinear Science, 2002, 12(2):85-112.
[96]	MÖNNIGMANN M, MARQUARDT W. Steady-state process optimization with guaranteed robust stability and feasibility[J]. AIChE Journal, 2003, 49(12):3110-3126.
[97]	MONNIGMANN M, MARQUARDT W. Steady-state process optimization with guaranteed robust stability and flexibility:application to HDA reaction section[J]. Industrial & Engineering Chemistry Research, 2005, 44(8):2737-2753.
[98]	CHANG Y, SAHINIDIS N V. Steady-state process optimization with guaranteed robust stability under parametric uncertainty[J]. AIChE Journal, 2011, 57(12):3395-3407.
[99]	TRAINOR M, GIANNAKEAS V, KISS C, et al. Optimal process and control design under uncertainty:a methodology with robust feasibility and stability analyses[J]. Chemical Engineering Science, 2013, 104:1065-1080.