Systematic construction of dynamic models for phase equilibrium processes

Ponton, J.W.; Gawthrop, P.J.

doi:10.1016/0098-1354(91)80026-r

Cited by 47 publications

(18 citation statements)

References 4 publications

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“…A typical class of applications is given by problems involving reaction equilibrium. The idea which is in line with the exposition in [51] for phase equilibrium systems is illustrated with the following example. The index of this model is two since one of the reaction rates needs to be calculated from a differential equation.…”

Section: Index Reductionmentioning

confidence: 96%

“…[56]) but to problems associated with consistent initialization. Further, it should be noted that the term "index problem" as used for example in [51] does not necessarily relate to models with Vd > 1 but also to some index-one problems where initialization requires differentiation.…”

Section: )mentioning

confidence: 99%

“…Instead, structural arguments have been used for index analysis prior to model implementation by various authors (e.g. [34], [38], [42], [47], [51], [54], [55]). The nature of these methods is considered in more detail in the next section.…”

Section: )mentioning

confidence: 99%

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Numerical Methods for the Simulation of Differential-Algebraic Process Models

Marquardt

1995

Methods of Model Based Process Control

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Abstract. Dynamic simulation of rigorous chemical process models is one of the control engineering tools routinely applied during process analysis, control system evaluation and tuning. These simulations are either done by means of packaged process simulators or by special purpose simulation programs. The development of these programs or even the use of commercial simulators requires a profound knowledge of the mathematical properties of the differential-algebraic process models and the numerical algorithm for their analysis. This survey intends to provide an introduction to the analysis of differential-algebraic process models, on the current state of the art as well as on some future trends.

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Section: Index Reductionmentioning

confidence: 96%

Section: )mentioning

confidence: 99%

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Numerical Methods for the Simulation of Differential-Algebraic Process Models

Marquardt

1995

Methods of Model Based Process Control

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“…This dynamical formulation of mass and enthalpy balances allows the modelling of the system in various states and phase transitions, including full and partial (also known as flash) evaporation and condensation [19].…”

Section: Mathematical Modelmentioning

confidence: 99%

A mathematical model of the defence mechanism of a bombardier beetle

James

Morison

Todd

2013

J. R. Soc. Interface.

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Previous studies of bombardier beetles have shown that some species have a continuous discharge while others exhibit a pulsed discharge. Here, a mathematical model of the defence mechanism of the bombardier beetle is developed and the hypothesis that almost all bombardiers' defences have some sort of cyclic behaviour at frequencies much higher than previously thought is put forward. The observation of pulses arises from secondary lower frequency cycles that appear for some parameter values. For realistic parameter values, the model can exhibit all the characteristics seen in the various species of bombardier. The possibility that all bombardiers have the same underlying defence mechanism gives weight to the theory that all bombardiers' explosive secretory mechanisms have diversified from a common ancestral mechanism.

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“…In order to manipulate the underlying equations accordingly, an algorithm must interpret the PTD and TRAV and locate possible equilibrium assumptions. Such an algorithm is described in Drengstig et al (1996), and its functionality follows the argumentation given in Ponton and Gawthrop (1991) for manipulating high index models into low index models. The benefits of representing assumptions on the TRAV is that we keep the original decomposition of the process and, at the same time, enrich the information about the model.…”

Section: Modeling Assumptionsmentioning

confidence: 99%

A formal graphical based process modeling methodology

Drengstig¹

1997

Computers &Amp; Chemical Engineering

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-In this paper we present a representation scheme for chemical unit processes. The representation is based on a topological and a phenomenological abstraction of the process. The topological abstraction decomposes the process into control volumes and boundaries. The phenomenological abstraction represents the phenomena in the process using three general process characteristics, i.e. transport, reaction/generation and accumulation of mass and energy. For these entities we define a consistent set of graphical symbols that will be connected together in a network according to the modelers understanding of the process, giving a representation of the process. We further suggest to employ this representation in the development of a modeling methodology, where the symbols are related to differential and algebraic equations in order to represent a complete and consistent mathematical model. The methodology is successfully applied to two industrial processes, a ferromanganese furnace and an aluminum electrolysis cell. The latter will be used as an example. Simulations of the aluminum cell focusing on AlF 3 dynamics are included.

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Systematic construction of dynamic models for phase equilibrium processes

Cited by 47 publications

References 4 publications

Numerical Methods for the Simulation of Differential-Algebraic Process Models

Numerical Methods for the Simulation of Differential-Algebraic Process Models

A mathematical model of the defence mechanism of a bombardier beetle

A formal graphical based process modeling methodology

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