Multiple steady states in ideal two‐product distillation

Jacobsen, Elling W.; Skogestad, Sigurd

doi:10.1002/aic.690370404

Cited by 108 publications

(111 citation statements)

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“…In fact, multiple solutions have been obtained for similar problems (e.g., Jacobsen and Skogestad, 1991). One thing that these results suggest is that the mathematical criterion used to select the variables to be bisected may be inadequate for process simulation problems.…”

Section: Sequential Resultsmentioning

confidence: 93%

Robust process simulation using interval methods

Schnepper

Stadtherr

1996

Computers & Chemical Engineering

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Ideally, for the needs of robust process simulation, one would like a nonlinear equation solving technique that can find any and all roots to a problem, and do so with mathematical certainty. In general, currently used techniques do not provide such rigorous guarantees. One approach to providing such assurances can be found in the use of interval analysis, in particular the use of interval Newton methods combined with generalized bisection. However, these methods have generally been regarded as extremely inefficient. Motivated by recent progress in interval analysis, as well as continuing advances in computer speed and the availability of parallel computing, we consider here the feasibility of using an interval Newton/generalized bisection algorithm on process simulation problems. An algorithm designed for parallel computing on an MIMD machine is described, and results of tests on several problems are reported. Experiments indicate that the interval Newton/generalized bisection method works quite well on relatively small problems, providing a powerful method for finding all solutions to a problem. For larger problems, the method performs inconsistently with regard to efficiency, at least when reasonable initial bounds are not provided.

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Section: Sequential Resultsmentioning

confidence: 93%

Robust process simulation using interval methods

Schnepper

Stadtherr

1996

Computers & Chemical Engineering

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“…

Jacobsen and Skogestad (1991) Jacobsen and Skogestad (1991) and Bekiaris and Morari (1993)

conditions of perfect fiactionation (infinite number of stages and infinite reflux ratio). Commercial process simulators (Pro/IP and Speedup-) were used to investigate multiple steady states in reactive distillation via the construction of bifirrcation diagrams (the locus of solutions obtained by varying a single continuation parameter).

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mentioning

confidence: 99%

Reaction Hysteresis: A New Cause of Output Multiplicity in Reactive Distillation

Sneesby

Tadé

Smith

1999

Dev. Chem. Eng. Mineral Process.

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Jacobsen and Skogestad (1991) Jacobsen and Skogestad (1991) and Bekiaris and Morari (1993) conditions of perfect fiactionation (infinite number of stages and infinite reflux ratio). Commercial process simulators (Pro/IP and Speedup-) were used to investigate multiple steady states in reactive distillation via the construction of bifirrcation diagrams (the locus of solutions obtained by varying a single continuation parameter). These results indicate that the mechanisms described by

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“…Recently, Jacobsen and Skogestad (1990) observed that valves and pumps control mass or volumetric flow rates (not molar flow rates). Using these process inputs, they demonstrated conditions under which the relationship between the molar and mass flow rates is sufficiently nonlinear to account for multiple steady states in the operation of all distillation …”

mentioning

confidence: 99%