Topic

# Gibbs–Duhem equation

About: Gibbs–Duhem equation is a(n) research topic. Over the lifetime, 393 publication(s) have been published within this topic receiving 6248 citation(s). The topic is also known as: Gibbs-Duhem equation.

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TL;DR: In this paper, the ability of the mixing rules proposed by Michelsen to predict high-pressure phase equilibrium, when used in combination with the parameter table of modified UNIFAC, was investigated.

Abstract: Recent procedures developed by Heidemann (1990) and by Michelsen (1990a, b) enable us to formally incorporate excess Gibbs energy model parameters into a fully consistent equation of state, cith accurate reproduction of the behavior of the excess Gibbs energy model at atmospheric pressure.
This paper investigates the ability of the mixing rules proposed by Michelsen to predict high-pressure phase equilibrium, when used in combination with the parameter table of modified UNIFAC. Considering that a group contribution method is used for the excess Gibbs energy and that model parameters are extrapolated over a 200 K temperature interval, quite satisfactory results are obtained for the mixtures investigated.

345 citations

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TL;DR: In this paper, a self-consistent method for determining whether a predicted equilibrium state is false is presented, which makes use of the equation of state to calculate the Gibbs energy surface and the tangent plane corresponding to the predicted equilibrium solution.

Abstract: For fluid systems that exhibit multiple phases, an equation of state may predict false phase equilibrium solutions. This paper presents a self-consistent method for determining whether a predicted equilibrium state is false. The method makes use of the equation of state to calculate the Gibbs energy surface and the tangent plane corresponding to the predicted equilibrium solution. If the tangent plane lies above the Gibbs energy surface at any point, the predicted equilibrium solution is false. Conversely, if the plane lies entirely below or tangent to the Gibbs energy surface, the solution does describe the equilibrium state.

342 citations

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TL;DR: In this article, a method that combines the best elements of thermodynamic integration and the Gibbs ensemble technique is proposed for the direct evaluation of phase equilibria by molecular simulation, given the conditions of coexistence at a single state point, simultaneous but independent NPT simulations of each phase are performed in succession along the saturation line.

Abstract: A method that combines the best elements of thermodynamic integration and the Gibbs ensemble technique is proposed for the direct evaluation of phase equilibria by molecular simulation. Given the conditions of coexistence at a single state point, simultaneous but independent NPT simulations of each phase are performed in succession along the saturation line. In each simulation, the pressure is adjusted to satisfy chemical potential equality according to the Gibbs-Duhem equation. Each coexistence point is determined by just one simulation, and particle insertions are never performed or attempted. Vapourliquid coexistence for the Lennard-Jones model is evaluated, and extensions are discussed.

314 citations

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TL;DR: In this paper, a procedure for incorporating information from an excess Gibbs energy model into an equation of state is described, where the gE model is used to define mixing rules for an equation-of-state mixture parameter.

Abstract: A procedure for incorporating information from an excess Gibbs energy model into an equation of state is described. The gE model is used to define mixing rules for an equation of state mixture parameter in such a manner that the equation of state reproduces the vapour—liquid equilibrium predicted by the gE model at low temperatures.
The resulting equation of state is fully consistent, performs reasonably at elevated temperatures and is computationally efficient. Typically, the cost of evaluating fugacity coefficients exceeds that of evaluating activity coefficients from the excess Gibbs energy model by 25–50%.

185 citations

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TL;DR: In this paper, it was shown that the classical Gibbs-Duhem relation can be regarded as expressing the obvious geometric impossibility of finding r + 1 linearly independent vectors in an r •dimensional space.

Abstract: It is shown that the classical Gibbs–Duhem relation can be regarded, in the abstract metric framework proposed recently, as expressing the obvious geometric impossibility of finding r + 1 linearly independent vectors in an r‐dimensional space. Certain connections between generalized Gibbs–Duhem relations and permissible scaling hypotheses for thermodynamic potentials are noted.

174 citations