Thermodynamic properties for model compounds of coal-liquids and their mixtures — measurements and calculations

doi:10.1016/S0378-3812(00)00513-6

Fluid Phase Equilibria

Volume 179, Issues 1–2, 25 March 2001, Pages 285-296

https://doi.org/10.1016/S0378-3812(00)00513-6 Get rights and content

Abstract

Thermodynamic properties were calculated with various cubic equations of state for the model compounds of coal liquids and their mixtures. These properties included vapor pressure, molar volume, excess volume, excess enthalpy, and vapor–liquid equilibrium. Liquid densities were also measured in this work for bicyclohexyl and mixtures of quinoline+tetralin to complement the experimental data of importance to coal liquefaction processes. The Patel–Teja equation of state yielded better results for calculations of vapor pressures and liquid molar volumes. The values of binary interaction parameter k_a12 as determined from different types of mixture properties were compared and examined for their reliability. The results showed that excess volumes were capable of serving as a reliable data basis for determination of the binary interaction parameter.

Introduction

Coal-liquefaction is a method to upgrade fuel quality. Thermodynamic properties of coal-liquids are needed in development of coal-liquefaction processes. The representative constituents in coal-liquids are m-xylene, hexadecane, tetralin, diphenylmethane, bicyclohexyl, 1-methylnaphthalene, m-cresol, quinoline, etc. Since the liquefaction processes are usually operated at elevated temperatures and pressures, an equation of state (EOS) is essential to calculate the thermodynamic properties of coal-liquids over such severe operating conditions. For engineering application purposes, it is valuable to investigate systematically the validity of property calculations from EOS for coal-liquids.

The cubic EOS, such as the Soave [1] and the Peng–Robinson [2], have been widely used in the simulation and design of chemical processes due to their simplicity and general applicability. The accuracy of property calculations with EOS often depends on equation forms, mixing rules, and the values of adjustable parameters in the models. The fluid-specific parameters in an EOS, if any, are usually determined from vapor pressure and liquid density data. Meanwhile, the binary interaction parameters in mixing rules may be determined from mixture properties of such as density, excess volume, enthalpy, heat of mixing, or phase equilibrium data. Optimal values of interaction parameters, however, could vary with the types of mixture properties used in the parameter determination. Provided that the parameters are not determined by suitable mixture properties, the EOS will fail to calculate accurately other thermodynamic properties over wide ranges of temperature and pressure. As a consequence, it is practically important to study the applicability of mixture properties that can serve as a reliable data basis for determination of the binary interaction parameters.

Five cubic EOS were tested in the present study, including the Soave (SRK), the Peng–Robinson (PR), the Patel–Teja (PT) [3], the Iwai–Margerum–Lu (IML) [4], and the Jan–Tsai (JT) [5]. These cubic EOS were utilized to calculate not only vapor pressures and liquid molar volumes for the pure model compounds of coal-liquids, but also the excess volumes for 11 related binary systems. The PR and the PT were further used for calculations of excess enthalpies, bubble-pressures, saturated vapor compositions, and K-values with various specified binary interaction parameters. The calculated results are compared and discussed.

Section snippets

Measurement of liquid densities

To supplement literature data, liquid densities were measured in the present study for bicylcohexyl and quinoline+tetralin at temperatures from 333.15 to 413.15 K and pressures up to 30 MPa. Bicyclohexyl (99%) and tetralin (99%) were purchased from Aldrich Chemicals. Quinoline (99%) was supplied by Janssen Chemica. The purity of these chemicals has been confirmed by gas chromatography. All the substances were used without further purification. The method of measurement is similar to that of Chang

P–V–T calculations for pure model compounds

Five representative EOS, including the SRK, the PR, the PT, the IML, and the JT, were selected to calculate the vapor pressures and the liquid molar volumes for the pure model compounds of coal-liquids. Of these EOS, there are two constants (a/b) in the SRK and the PR, three constants (a/b/c or a/b/u) in the PT and the IML, and four constants (a/b/u/w) in the JT. Two versions of the PT were tested in this work. The first one, denoted as PT-1, estimated the equation parameters ζ_c and F from the

Mixing rules

An EOS needs to incorporate with mixing rules for property calculations of mixtures. Conventional mixing rules that have been widely applied contain one adjustable binary interaction parameter, k_a12, as follow: $a_{m} = ∑ i=1 2 ∑ j=1 2 x_{i} x_{j} (1−k_{aij})(a_{i} a_{j})^{0.5}$ and $θ_{m} = ∑ i=1 2 x_{i} θ_{i}$ where θ represents b, c, ub, or wb: $c_{i} =−u_{i} b_{i} (for the IML)$ and $u_{m} = (ub)_{m} b_{m} and w_{m} = (wb)_{m} b_{m} (for the JT)$

Reliability of k_a12

The optimal value of the binary interaction parameter k_a12 is dependent on both the definition of objective function and the data sets that are used in its determination. This study examines the reliability of k_a12, which were specified by different properties: molar volumes, excess volumes, excess enthalpies, or vapor–liquid equilibrium (VLE) data. The PR and the PT-2 were selected as illustrative models. Sufficient literature data of good quality are needed to make a comprehensive comparison.

Conclusion

Several representative cubic EOS were tested with the thermodynamic properties of model compounds of coal-liquids and their mixtures. While the Patel–Teja EOS with the fluid-specific ζ_c and F (the PT-2) correlated well the vapor pressures and the liquid molar volumes for those pure compounds with an exception of 1-methylnaphthalene, the accuracy of the predictive EOS follows the order of PT-1>PR>JT>IML>SRK. It is also suggested that excess volumes are usable for determination of binary

Acknowledgements

The financial support from the National Science Council, ROC, through Grant No. NSC83–0402-E011–07 is gratefully acknowledged.

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¹: Present address: Department of Chemical Engineering, National Taipei University of Technology, Taipei, Taiwan.

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Thermodynamic properties for model compounds of coal-liquids and their mixtures — measurements and calculations

Abstract

Introduction

Section snippets

Measurement of liquid densities

P–V–T calculations for pure model compounds

Mixing rules

Reliability of ka12

Conclusion

Acknowledgements

Chem. Eng. Sci.

Chem. Eng. Sci.

Fluid Phase Equlibria

J. Chem. Thermodyn.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

Ind. Eng. Chem. Fundam.

Can. J. Chem. Eng.

J. Chem. Eng. Data

Reliability of k_a12