Limit Cycles in Homogeneous Azeotropic Distillation

Lee, Moonyong; Dorn, Cornelius; Meski, George A.; Morari, Manfred

doi:10.1021/ie980093h

Cited by 20 publications

(22 citation statements)

References 16 publications

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“…Bifurcations, or changes in the number of steady-state solutions, have been previously observed in multistage distillation column simulation with smooth models − and also confirmed experimentally. , Most cases analyzed involve homogeneous azeotropic distillation systems with at least three components, − although bifurcations have also been observed in binary distillation and Petlyuk columns . In the majority of cases, the curve of steady-state solutions contains two turning points forming a hysteresis curve, and therefore a total number of three steady states exist for parameter values in between the turning points.…”

Section: Introductionsupporting

confidence: 55%

“…In addition, hysteresis behavior is often responsible for the more familiar occurrence of multiple steady states in exothermic chemical reactors. On the other hand, a Hopf bifurcation, with the corresponding appearance of a limit cycle, has also been observed in association with a hysteresis curve for a ternary azeotropic column . However, the occurrence of multiple steady states in distillation simulation might depend, in some instances, on the thermodynamic model used. , …”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, a Hopf bifurcation, with the corresponding appearance of a limit cycle, has also been observed in association with a hysteresis curve for a ternary azeotropic column. 22 simulation might depend, in some instances, on the thermodynamic model used. 20,28 Interestingly, Bekiaris et al 21 presented the theoretical possibility of infinitely many steady states for homogeneous azeotropic distillation with a simplified analysis, which considered infinite reflux, infinitely many trays, and constant molar overflow.…”

Section: ■ Introductionmentioning

confidence: 99%

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Multiple Steady States and Nonsmooth Bifurcations in Dry and Vaporless Distillation Columns

Cavalcanti

Barton

2020

Ind. Eng. Chem. Res.

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Many process systems, such as distillation columns and other equipment with phase change, exhibit multiple modes of physical behavior that can be described by non-differentiable (i.e., nonsmooth) models. In this paper, we introduce a nonsmooth model for steady-state multistage distillation that can describe columns with dry and/or vaporless stages reliably. The model consists of a system of nonsmooth MESH and specification equations, without inequality or complementarity constraints, that can be directly solved with the semismooth Newton method using automatically computed generalized derivatives. With a modified version of pseudo-arclength continuation, we have been able to observe several novel types of bifurcations in dry and/or vaporless distillation columns. Many of the bifurcations exhibit degenerate behavior with an infinite number of steady states for certain critical input specifications, and occur in general multistage distillation systems regardless of the mixture components or thermodynamic models chosen. We present case studies drawn from the literature and analyze the occurrence and behavior of the bifurcations with respect to several types of column configurations, involving ideal stages, stage efficiencies, pressure gradients, tray heat transfer, multiple feeds, and side products. The associated bifurcation curves are inherently nonsmooth and can be described mathematically by the concept of piecewise-smooth manifolds introduced in this paper.

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Section: Introductionsupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

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Multiple Steady States and Nonsmooth Bifurcations in Dry and Vaporless Distillation Columns

Cavalcanti

Barton

2020

Ind. Eng. Chem. Res.

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“…28,29 Further, it was the first mixture for which simulations were published showing the existence of limit cycles in open-loop models of homogeneous azeotropic distillation columns. 6 The binary minimumboiling azeotrope between methanol and toluene is located at 88 mol % methanol (x LH Az ) 7.33). To study the influence of x LI F , a bifurcation diagram (shown in Figure 17-I) is computed for x LI F ) 10, x LH F ) 6, and L′ ) 48 (corresponding to region IIa in Figure 16).…”

Section: Case Studiesmentioning

confidence: 99%

Qualitative Analysis for Homogeneous Azeotropic Distillation. 2. Bifurcation Analysis

Dorn

Morari

2002

Ind. Eng. Chem. Res.

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Studying global mass balances and how they interact with the shape of column profiles, Morari, M. Ind. Eng. Chem. Res. 2002, 41, XXXX) developed a graphical method for a qualitative stability analysis of steady-state profiles in homogeneous azeotropic distillation columns. Based on the qualitative stability analysis, here it is shown how bifurcation diagrams can be constructed containing information on the stability of the equilibria. Fold, Hopf, and homoclinic bifurcations as well as more complex bifurcations can be predicted. The existence of limit cycles is explained and their approximate shape determined. It is explained how the feed composition and the reflux flow rate influence the bifurcation behavior of the column. The results are compiled in two-parameter bifurcation diagrams as well as in projections of a threeparameter bifurcation diagram. The method is applied to predict several new phenomena in distillation, e.g., operating conditions for which the only steady state of the column is unstable and surrounded by a stable limit cycle. All predicted phenomena are confirmed by steady-state and dynamic simulations.

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“…Besides, Dorn et al (1998) verifi ed the existence of a third unstable steady state and studied the transient behavior of that azeotropic column. Also, Lee et al (1999) found periodic oscillations and a limit cycle (sustained oscillations) while analysing the dynamic behaviour of the open-loop column. Bossen et al (1993) found four steady states for the dehydration of ethanol with benzene by dynamic simulation.…”

mentioning

confidence: 96%

Strategies for Starting Up Azeotropic Distillation Columns with Multiple Steady States

Benz¹,

Francesconi²,

Scenna³

2004

Can J Chem Eng

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T here are several works analysing multiple solutions in ideal, azeotropic and/or reactive distillation columns. Jacobsen and Skogestadt (1991), Cairns and Furzer (1990), Bekiaris et al., (1993Bekiaris et al., ( , 1996, Gani and Jørgensen (1994), Hauan et al. (1995), Kienle and Marquardt (1991), Scenna (1997), andMohl et al. (1999), among others, have considered their origins, the hysteresis curve behaviour or the infl uence of different variables upon them. Jacobsen and Skogestad (1995) analysed the operability and instability of binary distillation column with multiple steady state output during continuous operation. They stated that hysteresis may be experienced during the actual operation. Furthermore, Kienle et al. (1995) and Koggersbøl et al. (1996) confi rmed the existence of multiple steady states in an experimental way when separating a binary mixture.As regard to azeotropic distillation operations, Güttinger et al. (1997) found two stable steady states caused by the vapour-liquid equilibrium for the ternary homogeneous methanol-methyl butyratetoluene system in an industrial pilot column. Besides, Dorn et al. (1998) verifi ed the existence of a third unstable steady state and studied the transient behavior of that azeotropic column. Also, Lee et al. (1999) found periodic oscillations and a limit cycle (sustained oscillations) while analysing the dynamic behaviour of the open-loop column. Bossen et al. (1993) found four steady states for the dehydration of ethanol with benzene by dynamic simulation. Moreover, by means of a dynamic experiment, Müller and Marquardt (1997) verifi ed both the existence of multiple steady states in a heterogeneous azeotropic distillation (ethanol dehydration with cyclohexane as entrainer) and the hysteresis behaviour due to multiple steady states. On the other hand, Chien et al. (1999) analysed the dynamic behaviour of another heterogeneous azeotropic column (isopropyl alcohol-cyclohexane-water). They found three branches of steady states. The lowest and highest solutions were stable and the intermediate one was unstable. Besides, a bifurcation analysis showed that different operating regions could be placed in an operating variable diagram (heat duty vs. refl ux). These operating zones of the column (and different steady states) were characterised by the ratios of entrainment to other components and their potential azeotropes. Chien et al. (1999) suggested a particular desirable start-up strategy, but they did not develop it. Later, Chien et al. (2000) developed a suitable operating procedure for reaching the desirable high-purity steady state. Gani and Jorgensen (1994) proposed that the displacement of the internal composition front could be the cause of the possible connection between multiplicity and operability. Here we will show that * Author to whom correspondence may be addressed. E-mail address: sbenz@frro.utn.edu.ar The operability of azeotropic distillation columns with multiplicity is analysed during start-up by dynamic simulation. Different steady states can...

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Limit Cycles in Homogeneous Azeotropic Distillation

Cited by 20 publications

References 16 publications

Multiple Steady States and Nonsmooth Bifurcations in Dry and Vaporless Distillation Columns

Multiple Steady States and Nonsmooth Bifurcations in Dry and Vaporless Distillation Columns

Qualitative Analysis for Homogeneous Azeotropic Distillation. 2. Bifurcation Analysis

Strategies for Starting Up Azeotropic Distillation Columns with Multiple Steady States

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