A comparison of conventional and reduction approaches for phase equilibrium calculations

Martín, Pablo; Nichita, Dan Vladimir

doi:10.1016/j.fluid.2014.11.017

Cited by 44 publications

(35 citation statements)

References 41 publications

(117 reference statements)

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“…The variables ln K ik are much better scaled than the mole numbers n ik and the condition number is greatly improved in J as compared to H [32] (the diagonal part of the matrix U spans usually many orders of magnitude). Moreover, unlike n ik , lnK ik are unbounded.…”

Section: The Hessian Matrix H Ismentioning

confidence: 99%

“…Moreover, unlike n ik , lnK ik are unbounded. Newton iterations are more robust for the latter set of variables [6,32].…”

Section: The Hessian Matrix H Ismentioning

confidence: 99%

“…It had been proven (for two-phase flash [32] and for stability testing [29]) that the Newton iterations in the reduction methods using the Lagrange multipliers as independent variables have the same convergence paths as the conventional method with ln K ik variables. Following the same lines, the proof for multiphase flash calculations can be easily established.…”

Section: Constrained Minimization Of the Gibbs Free Energymentioning

confidence: 99%

“…Recently, comparisons of conventional and reduction methods performance for two-phase equilibrium have been carried out by Michelsen et al [8], Haugen and Beckner [30], Gorucu and Johns [31] and Petitfrere and Nichita [32]; the reference reduction method in all these papers was the reduced flash of Nichita and Graciaa [20]. A common conclusion is that the curves corresponding to the CPU time dependence on the numbers of components (linear for reduction methods, quadratic for conventional methods) are crossing each other at a certain value of nc (between 15 , showing that for the stability analysis problem the reduction methods are faster even for mixtures with few components, while for flash calculations the reduction methods are faster only for mixtures with many components (more than 20).…”

Section: Introductionmentioning

confidence: 99%

“…Using a different set of reduction parameters [17], the reduction method has been applied by Okuno et al [33] to threephase equilibria and Mohebbinia et al [34] to four-phase equilibria. It was found that the reduction methods using the independent variables (h) proposed in Nichita and Graciaa [20] lead to more efficient and robust formulations than the ones taking the reduction parameters (Q) as independent variables, for both two-phase flash calculations [24,31,32] and phase stability testing [32].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multiphase equilibrium calculations using a reduction method

Martín

Nichita

2015

Fluid Phase Equilibria

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Section: The Hessian Matrix H Ismentioning

confidence: 99%

“…Moreover, unlike n ik , lnK ik are unbounded. Newton iterations are more robust for the latter set of variables [6,32].…”

Section: The Hessian Matrix H Ismentioning

confidence: 99%

Section: Constrained Minimization Of the Gibbs Free Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiphase equilibrium calculations using a reduction method

Martín

Nichita

2015

Fluid Phase Equilibria

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State function‐based flash specifications for open systems in the absence or presence of chemical reactions

2020

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Diverse engineering fields require flash calculations like isothermal flash, isenthalpic flash, and isentropic flash. They can be cast as minimization of a thermodynamic state function and solved by Michelsen's Q‐function approach. Flash calculations for open systems, that is, systems where chemical potentials are specified instead of the mole numbers for some components, also belong to this scope. By analyzing the construction of Q‐functions through Legendre transforms, we extend this approach to the flash for open systems in the absence or presence of chemical reactions, resulting in general formulations for various specifications. For systems without reactions, the classical framework using mole numbers as independent variables is employed; for those with reactions, the modified‐RAND framework is employed. We present examples for open systems at constant temperature and pressure. Using the Q‐function minimization, we can solve multicomponent nonreactive or reactive systems at a specified chemical potential with quadratic convergence over a wide range of conditions.

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Rapid multi‐component phase‐split calculations using volume functions and reduction methods

Fathi

Hickel

2021

AIChE Journal

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We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This article provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective.

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A comparison of conventional and reduction approaches for phase equilibrium calculations

Cited by 44 publications

References 41 publications

Multiphase equilibrium calculations using a reduction method

Multiphase equilibrium calculations using a reduction method

State function‐based flash specifications for open systems in the absence or presence of chemical reactions

Rapid multi‐component phase‐split calculations using volume functions and reduction methods

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