Primal-dual interior-point method for thermodynamic gas-particle partitioning

A mathematical model for the computation of the phase equilibrium and gas-particle partitioning in atmospheric organic aerosols is presented. The thermodynamic equilibrium is determined by the global minimum of the Gibbs free energy under equality and inequality constraints for a system that involve...

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Published in:Computational optimization and applications 2011-04, Vol.48 (3), p.717-745
Main Author: Caboussat, Alexandre
Format: Article
Language:English
Subjects:
Aerosols
Algorithms
Atmospheric aerosols
Atmospherics
Computation
Convex and Discrete Geometry
Decomposition
Energy
Equilibrium
Gibbs free energy
Linear algebra
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Outdoor air quality
Partitioning
Quadratic programming
Statistics
Studies
Thermodynamics
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description A mathematical model for the computation of the phase equilibrium and gas-particle partitioning in atmospheric organic aerosols is presented. The thermodynamic equilibrium is determined by the global minimum of the Gibbs free energy under equality and inequality constraints for a system that involves one gas phase and many liquid phases. A primal-dual interior-point algorithm is presented for the efficient solution of the phase equilibrium problem and the determination of the active constraints. The first order optimality conditions are solved with a Newton iteration. Sequential quadratic programming techniques are incorporated to decouple the different scales of the problem. Decomposition methods that control the inertia of the matrices arising in the resolution of the Newton system are proposed. A least-squares initialization of the algorithm is proposed to favor the convergence to a global minimum of the Gibbs free energy. Numerical results show the efficiency of the approach for the prediction of gas-liquid-liquid equilibrium for atmospheric organic aerosol particles.
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subjects Aerosols
Algorithms
Atmospheric aerosols
Atmospherics
Computation
Convex and Discrete Geometry
Decomposition
Energy
Equilibrium
Gibbs free energy
Linear algebra
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Outdoor air quality
Partitioning
Quadratic programming
Statistics
Studies
Thermodynamics
title Primal-dual interior-point method for thermodynamic gas-particle partitioning
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