Nonsmooth dynamic simulation with linear programming based methods

Gopal, Vipin; Biegler, Lorenz T.

doi:10.1016/s0098-1354(96)00301-8

Cited by 30 publications

(20 citation statements)

References 19 publications

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“…In most cases, a flash with specified values of internal energy, volume and mole numbers (UVN flash) is at the core of the calculations executed at each time step. Müller and Marquardt (1997) and Gopal and Biegler (1997) modeled the liquid phases in their examples using excess Gibbs free energy ( E G ) models, which, from the computational point of view, are much simpler than EOS. Furthermore, Gopal and Biegler (1997) assume perfect pressure control and specify the temperature trajectory in the drum, what results in a much simpler version of the dynamic flash problem.…”

Section: Introductionmentioning

confidence: 99%

“…Müller and Marquardt (1997) and Gopal and Biegler (1997) modeled the liquid phases in their examples using excess Gibbs free energy ( E G ) models, which, from the computational point of view, are much simpler than EOS. Furthermore, Gopal and Biegler (1997) assume perfect pressure control and specify the temperature trajectory in the drum, what results in a much simpler version of the dynamic flash problem. The articles of Saha and Carroll (1997) and Michelsen (1999) are based on UVN flash formulations that use nested-loops since pressure is an iteration variable.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic simulation of flash drums using rigorous physical property calculations

Goncalves

Castier

Araújo

2007

Braz. J. Chem. Eng.

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-The dynamics of flash drums is simulated using a formulation adequate for phase modeling with equations of state (EOS). The energy and mass balances are written as differential equations for the internal energy and the number of moles of each species. The algebraic equations of the model, solved at each time step, are those of a flash with specified internal energy, volume and mole numbers (UVN flash). A new aspect of our dynamic simulations is the use of direct iterations in phase volumes (instead of pressure) for solving the algebraic equations. It was also found that an iterative procedure previously suggested in the literature for UVN flashes becomes unreliable close to phase boundaries and a new alternative is proposed. Another unusual aspect of this work is that the model expressions, including the physical properties and their analytical derivatives, were quickly implemented using computer algebra.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic simulation of flash drums using rigorous physical property calculations

Goncalves

Castier

Araújo

2007

Braz. J. Chem. Eng.

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“…These discontinuities give rise to the so called "state events" which confer a hybrid nature (continuous/discrete) to the model (Bahl and Linnenger, 2000;Gopal and Biegler, 1997;Mao and Petzold, 2002;Pantelides, 1988;Park and Barton, 1996). A state event defines "a change" in the model equations triggered by some state variables reaching a specific condition.…”

Section: Integrated Systemmentioning

confidence: 99%

Optimal drug infusion profiles using a Particle Swarm Optimization algorithm

Montain

Blanco

Bandoni

2015

Computers & Chemical Engineering

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“…Gopal and Biegler (1997) have an alternate but equivalent formulation of this model including the multiphase setting. Ferris and Pang (1997) catalogue a number of other applications both in engineering and economics that can be written in a similar format.…”

Section: Complementarity Problemsmentioning

confidence: 99%

An extended mathematical programming framework

Ferris

Dirkse²,

Jagla

et al. 2009

Computers & Chemical Engineering

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Extended mathematical programs are collections of functions and variables joined together using specific optimization and complementarity primitives. This paper outlines a mechanism to describe such an extended mathematical program by means of annotating the existing relationships within a model to facilitate higher level structure identification. The structures, which often involve constraints on the solution sets of other models or complementarity relationships, can be exploited by modern large scale mathematical programming algorithms for efficient solution. A specific implementation of this framework is outlined that communicates structure from the GAMS modeling system to appropriate solvers in a computationally beneficial manner.Example applications are taken from chemical engineering.

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Nonsmooth dynamic simulation with linear programming based methods

Cited by 30 publications

References 19 publications

Dynamic simulation of flash drums using rigorous physical property calculations

Dynamic simulation of flash drums using rigorous physical property calculations

Optimal drug infusion profiles using a Particle Swarm Optimization algorithm

An extended mathematical programming framework

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