Computation and modeling of tricritical phenomena in ternary and quaternary mixtures using the Perturbed Chain—Statistical Associating Fluid Theory equation of state

Arce, Pedro F.; Aznar, Martı́n

doi:10.1016/j.supflu.2009.01.010

Cited by 5 publications

(17 citation statements)

References 43 publications

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“…19 Finally, in addition, we showed an unprecedented prediction for the ternary mixture comprising methane, n-pentane, and noctane, and the no prediction of the tricritical point of the polar mixture CO 2 /C 2 H 5 OH/H 2 O, whose prediction was considered to be possible by Kohse and Heidemann. 18 Thus, these facts allow us also to conclude that same failures observed in the previous results of Kohse and Heidemann 17,18 are not (necessarily) consequences of possible nonphysical predictions by the Peng−Robinson equation of state.…”

Section: Discussionmentioning

confidence: 78%

“…The same happens with the tricritical temperature and tricritical pressure calculated from the PC-SAFT equation. 19 In this example, the objective function used here reached the order of 10 −7 .…”

Section: Resultsmentioning

confidence: 99%

“…This problem is not new. In fact, in order to avoid such difficulties, Arce and Aznar, 19 for example, used a FORTRAN program with a numerical precision of 32 digits, in the implementation of the finite-difference formulas relating to higher-order partial derivatives of molar Gibbs free energy of mixtures, which were used as mathematical criteria for tricritical points.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of Tricritical Points in Ternary Mixtures by Global Optimization

Henderson

Rodrigues

Sacco

2014

Ind. Eng. Chem. Res.

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Tricritical points of mixtures are characterized by thermodynamic coordinates where three coexisting phases become identical. Here, we formulate and solve for the first time the tricritical-point calculation as a global optimization problem. Using finite-difference formulas and the ordinary criticality criteria, we develop novel numerical approximations for tricriticality conditions associated with the derivatives of the fourth and fifth orders with respect to the compositions, obtained from the Gibbs tangent plane criterion for phase stability. Such approximations simplified the numerical implementations of these two conditions, avoiding propagation errors related to floating-point arithmetic without requiring a code with excessive numerical precision, which usually leads to high computational costs. This paper deals only with ternary mixtures. Thus, the present formulation is described as a minimization problem with strict inequality constraints, having four variables (two independent mole fractions, temperature, and pressure). Using the Peng−Robinson equation of state together with the classical one-fluid van der Waals mixing rule, we observe that the novel procedure is able to determine the tricritical coordinates in a set of ternary mixtures formed by alkanes or alkanes and light gases, which were previously studied by other authors and generally have complex multiphase behavior. The proposed method is compared to previous ones, and the results presented here compare favorably with the experimental values, which are available in the literature. In addition, we present an unprecedented prediction using the Peng−Robinson equation. We also show an example which leads to a no prediction of the tricritical point of a polar mixture, whose prediction (with this equation of state) was considered possible in a previous work.

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Section: Discussionmentioning

confidence: 78%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Prediction of Tricritical Points in Ternary Mixtures by Global Optimization

Henderson

Rodrigues

Sacco

2014

Ind. Eng. Chem. Res.

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“…In eq , n is the mole number, P is the pressure, T is the temperature, V is the molar volume, and Z is the compressibility factor. In this work, the fugacity coefficient was calculated numerically by using finite difference and numerical integration methods. , …”

Section: Methodsmentioning

confidence: 99%

“…In this work, the fugacity coefficient was calculated numerically by using finite difference and numerical integration methods. 21,25 2.1.5. Thermodynamic Consistency.…”

Section: ̂= Fmentioning

confidence: 99%

Thermodynamic Modeling and Simulation of Biodiesel Systems at Supercritical Conditions

Arce

Vieira

Igarashi

2018

Ind. Eng. Chem. Res.

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Biodiesel is becoming a promising fuel in many markets in the world for being a renewable energy source and for not requiring significant adaptation in existing diesel engines. It is biodegradable and its polluting gas emissions are less harmful to the environment. Transesterification is used for the biodiesel synthesis at supercritical conditions using triacylglycerols and solvents in a heterogeneous reaction. The Peng−Robinson (PR), the volume-translated Peng−Robinson (VT-PR), and the perturbed chain statistical associating fluid theory (PC-SAFT) equations of state were using to predict the fluid phase behavior of systems containing solvents and components present in the synthesis of biodiesel at supercritical conditions. Two pure component parameters for the VT-PR equation, N and k 3 , and the five pure component parameters for the PC-SAFT equation, m, σ, and ε as well as the associating parameters κ A i B j and ε A i B j , were predicted based on the vapor pressures and the saturated liquid volumes. Results were compared with experimental data presented in the literature, considered thermodynamically consistent, and it was confirmed that noncubic equations of state are more accurate than cubic equations of state. Thermodynamic modeling was also compared with the thermodynamic simulation using artificial neural networks (ANN) and molecular descriptors at different architectures. Results, in terms of deviations of bubble pressures of and vapor phase composition, predicted by the optimum ANN model are slightly more efficient than the ones obtained by the thermodynamic models, mainly the PC-SAFT equation of state.

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