Bifurcation and complex dynamics in fixed-bed catalytic reactors

Wagialla, K.M.; Elnashaie, S.S.E.H.

doi:10.1016/0009-2509(95)00042-4

Cited by 6 publications

(6 citation statements)

References 32 publications

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“…Isothermal sources arise from mass transport at catalyst (diffusion) (Morbidelli et al, 1986;Lee et al, 1987) or reactor scale (convection, dispersion). Thermo-kinetic sources are mainly caused by nonisothermicities, which influence the nonlinear reaction rate coefficients according to the Arrhenius relation (Eigenberger, 1972a;Heinemann and Poore, 1982;Wagialla and Elnashaie, 1995).…”

Section: State-space Multiplicitymentioning

confidence: 99%

“…The dominating opinion is that the ideal PFTR is free of any state-space multiplicity due to the absence of transport in countercurrent direction (feedback). However, some studies opposed that the ideal PFTR is rather characterized by an infinite number of steady states (Liu and Amundson, 1962;Wagialla and Elnashaie, 1995;Nibbelke et al, 1998). These studies refer to the fact that the continuum description of an ideal PFTR corresponds to a series of infinite CSTRs.…”

Section: State-space Multiplicitymentioning

confidence: 99%

“…Id. PFTR Liu and Amundson (1962), Wagialla and Elnashaie (1995), Nibbelke et al (1998) Pseudo-homogeneous models (lumped gas and solid phase) A e , B e , E e tk 1 exp , 2 exp 100 e DM Kalthoff and Vortmeyer (1980 et al (1986), Lee et al (1987 2007A m,e , B e , E e tk 1, 3, 5 0-560 eg , 0-5'600 ec , 0-1'680 mg DM Bostandzhiyan and Shkadinskii 2010Purely experimental studies-comprehensive reviews given by Padberg and Wicke (1967), Wedel and Luss (1984), Harold and Luss (1985), Adaje and Sheintuch (1990) 2 exp (stable) Puszyński and Hlavacek (1984), Adaje and Sheintuch (1990) 4 exp (stable) Harold and Luss (1985) m -mass; e -energy; g -gas; c -catalyst; exp -experimental; k -kinetic; i -isothermal; tk -thermo-kinetic; CM -cell model; DM -dispersion model; MSS -multiple steady states. numerical tool for such analyses.…”

Section: State-space Multiplicitymentioning

confidence: 99%

“…Furthermore, there is no guarantee that this method obtains all solutions. More details on bifurcation theory and numerical continuation techniques can be found in (Heinemann and Poore, 1981;Jensen and Ray, 1982;Kubíček and Marek, 1983;Wagialla and Elnashaie, 1995).…”

Section: Multi-stage Cstr Cascadementioning

confidence: 99%

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Novel Multiplicity and Stability Criteria for Non-Isothermal Fixed-Bed Reactors

Bremer

Sundmacher

2021

Front. Energy Res.

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With the increasing need to utilize carbon dioxide, fixed-bed reactors for catalytic hydrogenation will become a decisive element for modern chemicals and energy carrier production. In this context, the resilience and flexibility to changing operating conditions become major objectives for the design and operation of real industrial-scale reactors. Therefore steady-state multiplicity and stability are essential measures, but so far, their quantification is primarily accessible for ideal reactor concepts with zero or infinite back-mixing. Based on a continuous stirred tank reactor cascade modeling approach, this work derives novel criteria for stability, multiplicity, and uniqueness applicable to real reactors with finite back-mixing. Furthermore, the connection to other reactor features such as runaway and parametric sensitivity is demonstrated and exemplified for CO2 methanation under realistic conditions. The new criteria indicate that thermo-kinetic multiplicities induced by back-mixing remain relevant even for high Bodenstein numbers. In consequence, generally accepted back-mixing criteria (e.g., Mears’ criterion) appear insufficient for real non-isothermal reactors. The criteria derived in this work are applicable to any exothermic reaction and reactors at any scale. Ignoring uniqueness and multiplicity would disregard a broad operating range and thus a substantial potential for reactor resilience and flexibility.

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Section: State-space Multiplicitymentioning

confidence: 99%

Section: State-space Multiplicitymentioning

confidence: 99%

Section: State-space Multiplicitymentioning

confidence: 99%

Section: Multi-stage Cstr Cascadementioning

confidence: 99%

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Novel Multiplicity and Stability Criteria for Non-Isothermal Fixed-Bed Reactors

Bremer

Sundmacher

2021

Front. Energy Res.

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“…In particular, the presence of CO 2 in the EO reactor severely affects plant operation in several ways: catalyst selectivity, ethylene conversion, performance of the coolant temperature control loop, and EO production rate . A closed‐loop stability analysis showed that such a system is sensitive to decreases in CO 2 concentration in the reactor feed because such disturbances favour the complete oxidation of ethylene …”

Section: Introductionmentioning

confidence: 99%

Greenhouse gas removal from industrial effluents: The role of inorganic additives

Gomes

Ahmadi

2018

Can J Chem Eng

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This work is focused on the investigation of the effects of inorganic additives for carbon dioxide absorption in a liquid solvent containing potassium carbonate. Incorporating the kinetics of the main reaction steps, we considered the interactions between the governing transport mechanisms for determining the effects of gas and liquid outlet temperatures and lean carbonate compositions on outlet carbon dioxide concentration. We estimated the mass transfer coefficient using the surface renewal formalism. Based on the rate-determining steps for the reaction and mass transfer, we developed mathematical models comprising sets of nonlinear differential and algebraic equations, which were solved using the software we developed. Plant data from an industrial unit were used for validating the model, which was subsequently employed for evaluating species concentration profiles, flow rates, temperature, and pressure in the absorber. The effects of the types of promoters, pressure, temperature, and concentration profiles of the promoters were estimated to evaluate the performance of the absorber.

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