BibTex RIS Cite

Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term

Year 2013, Volume: 16 Issue: 1, 20 - 27, 12.11.2012

Abstract

Studies related to the development of equations of state (EOS) to represent thermophysical properties of pure compounds are considered as important tools for engineers to design and optimize industrial equipment and processes. Furthermore, these tools also contribute to amplify the researchers’ knowledge related to molecular interaction types, in attempting to predict and correlate both energetic and volumetric effects existing in the compounds. From several equations of state existing, the cubic plus association (CPA) EOS are employed in the calculations of thermophysical properties of compounds, in which the molecular interactions occurring are the association type. In spite of good representation of these properties, it is possible to improve the predictive and correlative capability of the CPA EOS by substitution of terms whose physical meaning can be better. In this way, modifications of the cubic plus association equation of state are proposed: the original repulsive term is replaced by the Carnahan-Starling repulsion term; the attractive term is changed to an attraction term similar to the Peng-Robinson EOS. Furthermore, both attraction and repulsion terms are taken to be temperature dependent when alpha and beta functions are employed in calculations. All implementations make the equation of state non-cubic in relation to volume. Vapor pressure and liquid molar volumes of 1-alkanols (C1 to C10) and water were correlated to experimental data using this non-CPA–EOS format, and good agreement is observed.

References

  • Abbot, M. M. (1989). Thirteen Ways of Looking at the van der Waals Equation, Chemical Engineering Progress, (2), 25-37.
  • Beaton, C. F., Ambrose, D., Brunner, E., Chase, M. W., Downey, J. R., Hobson G., Humphreys, A. E., Jamieson, D. T., Knight, S. R., Schoenberg, M., Walton, J., (1989). Ortobaric densities and molar volumes of liquids, Alcohols, Engineering Sciences Data Unit – ESDU, Eng. Sci. Data Item Nr. 89037.
  • Beaton, C. F., Ambrose, D., Foxcroft, H. J., Hobson, G., Jamieson, D. T., Knight, S. R., Rowell, G. M., Schoenberg, M., White, Jr., H. J., (1989). Vapor pressures and critical points of liquids, Alcohols, Engineering Sciences Data Unit – ESDU, Eng. Sci. Data Item Nr. 89028 Vapor Pressure Data.
  • Carnahan, N. F., Starling, K. E., (1969). Equation of State for Nonattracting Rigid Spheres. The Journal of Chemical Physics, 51, 635-636.
  • Carnahan, N. F., Starling, K. E., (1972). Intermolecular Repulsions and the Equation of State for Fluids. AIChE. J., 18, 1184-1189.
  • Coquelet, C., Chapoy, A. Richon, D., (2004). Development of a New Alpha Function for the Peng-Robinson Equation of State: Comparative Study of Alpha Function Models for Pure Gases (Natural Gas Components) and Water-Gas Systems. Int. J. Thermophys. 25, 133-158.
  • De Santis, R., Gironi, F., Marrelli, L., (1976). Vapor-Liquid Equilibrium from a Hard-Sphere Equation of State. Ind. Eng. Chem. Fundam., 15, 183-189.
  • Fuller, G.G., (1976). A Modified Redlich-Kwong-Soave Equation of State Capable of Representing the Liquid State. Ind. Eng. Chem. Fundam., 15, 254-257.
  • Haghtalab, A., Mahmoodi, P., Mazloumi, S. H., (2011). A modified Peng-Robinson equation of state for phase equilibrium calculation of liquefied, synthetic natural gas, and gas condensate mixtures. Can. J. of Chem. Eng., 89, 1376-1387.
  • Hamam, S. E. M., Chung, W. K., Elshayal, I. M, Lu, B. CY., (1977). Generalized
  • Temperature-Dependent Parameters of the Redlich-Kwong Equation of State for Vapor-Liquid Equilibrium Calculations. Ind. Eng. Chem. Process Des. Dev., 16, 51-59. Huang, S. H., Radosz, M., (1990). Equation of State for
  • Small, Large, Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res., 29, 2284-2294.
  • Koh, C. A., Tanaka, H., Walsh, J. M., Cubbins, K. E., Zollweg, J. A., (1993). Thermodynamic and structural properties of methanol-water mixtures: experiment, theory and molecular simulation. Fluid Phase Equilibria, 83, 51-58.
  • Kontogeorgis, G. M., Michelsen, M. L., Folas, G. K., Derawi, S., von Solms, N., Stenby, E. H., (2006). Ten
  • Years with the CPA (Cubic-Plus-Association) Equation of State. Part 1. Pure Compounds and Self-Associating Systems. Ind. Eng. Chem. Res., 45, 4855-4868.
  • Kontogeorgis, G. M., Voutsas, E. C., Yakoumis, I. V., Tassios, D. P., (1996). An Equation of State for
  • Associating Fluids, Ind. Eng. Chem. Res., 35, 431043
  • Kontogeorgis, G. M., Yakoumis, I. V., Meijer, H., Hendriks, E. M., Moorwood, T., (1999).
  • Multicomponent phase equilibrium calculations for water-methanol-alkane mixtures. Fluid Phase Equilibria, 158, 201-209. Kuester, J. L., Mize, J. H., (1973). Optimization
  • Techniques, McGraw-Hill, USA. Kutney, M.C., Dodd, V.S., Smith, K.A., Herzog, H.J., Tester, J.W., (1997). A hard-sphere volume translated van der Waals equation of state for supercritical process modeling 1. Pure components. Fluid Phase Equilibria, 128, 149-171.
  • Mathias, P. M., Copeman, T. W., (1983). Extension of the Peng-Robinson Equations of State to Complex
  • Mixtures: Evaluation of the Various Forms of the Local Composition Concept. Fluid Phase Equilibria, 13, 91 Nasrifar, K., Moshfeghian, M., (2001). A new cubic equation of state for simple fluids: pure and mixture.
  • Fluid Phase Equilibria, 190, 73-88. Nath, A., Bender, E., (1981). On the thermodynamics of associated solutions. I. An analytical method for determining the enyhalpy and entropy of association and equilibrium constant for pure liquid substances.
  • Fluid Phase Equilibria, 7, 275-287. Sassi, P., Paolantoni, M., Morresi, A., Cataliotti, R. S., (2006). Comparison of Hydrogen Bonding in 1-Octanol and 2-Octanol as Probed by Spectroscopic Techniques. J. Phys. Chem. B, 110, 18017-18025.
  • Peng, D-Y, Robinson, D.B., (1976). A New Two-Constant
  • Equation of State. Ind. Eng. Chem. Fundam., 15, 59-64. Perakis, C. A., Voutsas, E. C., Magoulas, K. G., Tassios, D. P., (2007). Thermodynamic Modeling of the Water +
  • Acetic Acid + CO 2 System: The Importance of the Number of Association Sites of Water and of the Nonassociation Contribution for the CPA and SAFTType Models. Ind. Eng. Chem. Res., 46, 932-938. Queimada, A. J., Miqueu, C., Marrucho, I. M., Kontogeorgis, G. M., Coutinho, J. A. P., (2005). Modeling vapor-liquid interfaces with the gradient theory in combination with the CPA equation of state. Fluid Phase Equilibria, 228, 479-485.
  • Ravagnani, S.P., D’Avila, S.G., (1985). VLE of Polar Mixtures: A New Generalized Correlation. Proceedings of IV International Chemical Engineering Conference, CHEMPOR’85, Coimbra, Portugal, 05 / 01 – 05.
  • Rosenbrock, H. H., (1960). An Automatic Method for Finding the Greatest or Least Value of a Function, Computer Journal, 3, 175-184.
  • Sadus, R. J., (2001). Equations of state for fluids: The Dieterici approach revisited. J. Chem. Phys., 115, 146014
  • Soave, G., (1972). Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27, 1197-1203.
  • Toghiani, H., Viswanath, D.S., (1986). A Cubic Equation of State for Polar and Apolar Fluids. Ind. Eng. Chem.. Process Des. Dev., 25, 531-536.
  • Trebble, M.A., Bishnoi, P.R., (1987). Development of a new four-parameter cubic equation of state. Fluid Phase Equilibria 35, 1-18.
  • Vargaftik, N.B., (1975). Handbook of Physical Properties of Liquid and Gases (Pure Substances and Mixtures), 2 nd Edition, John Willey, D.C. von Solms, N., Michelsen, M. L., Passos, C. P., Derawi, S. O., Kontogeorgis, G. M., (2006). Investigating Models for Associating Fluids Using Spectroscopy. Ind. Eng. Chem. Res., 45, 5368-5374.
  • Wei, S., Shi, Z., Castleman, A., (1991). Mixed Cluster Ions as a Structure Probe: Experimental Evidence for
  • Clathrate Structure of (H 2 O) 20 H + and (H 2 O) 21 H + . J. Chem. Phys., 94, 3268-3270.
  • Wei, Y.S., Sadus, R.J., (2000). Equations of State for Calculation of Fluid-Phase Equilibria. AIChE J., 46, 169-1
  • Wei, Y.S., Sadus, R.J., Franck, E.U., (1996). Binary mixtures of water + five noble gases: comparison of bimodal and critical curves at high pressures. Fluid Phase Equilibria 123, 1-15.
  • Wertheim, M. S., (1984a) Fluids with Highly Directional Attractive Forces. I. Statistical Thermodynamics. J. Stat. Phys., 35, 19-34.
  • Wertheim, M. S., (1984b). Fluids with Highly Directional Attractive Forces. II. Thermodynamic Perturbation Theory and Integral Equations. J. Stat. Phys., 35, 35-47. Wertheim, M. S., (1986a). Fluids with Highly Directional Attractive Forces. III. Multiple Attraction Sites. J. Stat. Phys., 42, 459-476.
  • Wertheim, M. S., (1986b). Fluids with Highly Directional Attractive Forces. IV. Equilibrium Polimerization, J. Stat. Phys., 42, 477-492.
  • Wertheim, M. S., (1986c). Fluids of Dimerizing Hard Spheres and Mixtures of Hard Spheres and Dispheres. J. Chem. Phys., 85, 2929-2936.
  • Wertheim, M. S., (1987). Thermodynamic Perturbation Theory of Polymerization, J. Chem. Phys., 87, 732373
  • Xu, Z, Sandler, S.I., (1987). Temperature dependent parameters and Peng-Robinson equation of state. Ind. Eng. Chem. Res., 26, 601-606.
  • Zhong, C., Masuoka, H., (1997). An EOS/G E type mixing rule for perturbed hard sphere equation of state and its application to calculation of solid solubility in supercritical carbon dioxide. Fluid Phase Equilibria, 141,13-23.
Year 2013, Volume: 16 Issue: 1, 20 - 27, 12.11.2012

Abstract

References

  • Abbot, M. M. (1989). Thirteen Ways of Looking at the van der Waals Equation, Chemical Engineering Progress, (2), 25-37.
  • Beaton, C. F., Ambrose, D., Brunner, E., Chase, M. W., Downey, J. R., Hobson G., Humphreys, A. E., Jamieson, D. T., Knight, S. R., Schoenberg, M., Walton, J., (1989). Ortobaric densities and molar volumes of liquids, Alcohols, Engineering Sciences Data Unit – ESDU, Eng. Sci. Data Item Nr. 89037.
  • Beaton, C. F., Ambrose, D., Foxcroft, H. J., Hobson, G., Jamieson, D. T., Knight, S. R., Rowell, G. M., Schoenberg, M., White, Jr., H. J., (1989). Vapor pressures and critical points of liquids, Alcohols, Engineering Sciences Data Unit – ESDU, Eng. Sci. Data Item Nr. 89028 Vapor Pressure Data.
  • Carnahan, N. F., Starling, K. E., (1969). Equation of State for Nonattracting Rigid Spheres. The Journal of Chemical Physics, 51, 635-636.
  • Carnahan, N. F., Starling, K. E., (1972). Intermolecular Repulsions and the Equation of State for Fluids. AIChE. J., 18, 1184-1189.
  • Coquelet, C., Chapoy, A. Richon, D., (2004). Development of a New Alpha Function for the Peng-Robinson Equation of State: Comparative Study of Alpha Function Models for Pure Gases (Natural Gas Components) and Water-Gas Systems. Int. J. Thermophys. 25, 133-158.
  • De Santis, R., Gironi, F., Marrelli, L., (1976). Vapor-Liquid Equilibrium from a Hard-Sphere Equation of State. Ind. Eng. Chem. Fundam., 15, 183-189.
  • Fuller, G.G., (1976). A Modified Redlich-Kwong-Soave Equation of State Capable of Representing the Liquid State. Ind. Eng. Chem. Fundam., 15, 254-257.
  • Haghtalab, A., Mahmoodi, P., Mazloumi, S. H., (2011). A modified Peng-Robinson equation of state for phase equilibrium calculation of liquefied, synthetic natural gas, and gas condensate mixtures. Can. J. of Chem. Eng., 89, 1376-1387.
  • Hamam, S. E. M., Chung, W. K., Elshayal, I. M, Lu, B. CY., (1977). Generalized
  • Temperature-Dependent Parameters of the Redlich-Kwong Equation of State for Vapor-Liquid Equilibrium Calculations. Ind. Eng. Chem. Process Des. Dev., 16, 51-59. Huang, S. H., Radosz, M., (1990). Equation of State for
  • Small, Large, Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res., 29, 2284-2294.
  • Koh, C. A., Tanaka, H., Walsh, J. M., Cubbins, K. E., Zollweg, J. A., (1993). Thermodynamic and structural properties of methanol-water mixtures: experiment, theory and molecular simulation. Fluid Phase Equilibria, 83, 51-58.
  • Kontogeorgis, G. M., Michelsen, M. L., Folas, G. K., Derawi, S., von Solms, N., Stenby, E. H., (2006). Ten
  • Years with the CPA (Cubic-Plus-Association) Equation of State. Part 1. Pure Compounds and Self-Associating Systems. Ind. Eng. Chem. Res., 45, 4855-4868.
  • Kontogeorgis, G. M., Voutsas, E. C., Yakoumis, I. V., Tassios, D. P., (1996). An Equation of State for
  • Associating Fluids, Ind. Eng. Chem. Res., 35, 431043
  • Kontogeorgis, G. M., Yakoumis, I. V., Meijer, H., Hendriks, E. M., Moorwood, T., (1999).
  • Multicomponent phase equilibrium calculations for water-methanol-alkane mixtures. Fluid Phase Equilibria, 158, 201-209. Kuester, J. L., Mize, J. H., (1973). Optimization
  • Techniques, McGraw-Hill, USA. Kutney, M.C., Dodd, V.S., Smith, K.A., Herzog, H.J., Tester, J.W., (1997). A hard-sphere volume translated van der Waals equation of state for supercritical process modeling 1. Pure components. Fluid Phase Equilibria, 128, 149-171.
  • Mathias, P. M., Copeman, T. W., (1983). Extension of the Peng-Robinson Equations of State to Complex
  • Mixtures: Evaluation of the Various Forms of the Local Composition Concept. Fluid Phase Equilibria, 13, 91 Nasrifar, K., Moshfeghian, M., (2001). A new cubic equation of state for simple fluids: pure and mixture.
  • Fluid Phase Equilibria, 190, 73-88. Nath, A., Bender, E., (1981). On the thermodynamics of associated solutions. I. An analytical method for determining the enyhalpy and entropy of association and equilibrium constant for pure liquid substances.
  • Fluid Phase Equilibria, 7, 275-287. Sassi, P., Paolantoni, M., Morresi, A., Cataliotti, R. S., (2006). Comparison of Hydrogen Bonding in 1-Octanol and 2-Octanol as Probed by Spectroscopic Techniques. J. Phys. Chem. B, 110, 18017-18025.
  • Peng, D-Y, Robinson, D.B., (1976). A New Two-Constant
  • Equation of State. Ind. Eng. Chem. Fundam., 15, 59-64. Perakis, C. A., Voutsas, E. C., Magoulas, K. G., Tassios, D. P., (2007). Thermodynamic Modeling of the Water +
  • Acetic Acid + CO 2 System: The Importance of the Number of Association Sites of Water and of the Nonassociation Contribution for the CPA and SAFTType Models. Ind. Eng. Chem. Res., 46, 932-938. Queimada, A. J., Miqueu, C., Marrucho, I. M., Kontogeorgis, G. M., Coutinho, J. A. P., (2005). Modeling vapor-liquid interfaces with the gradient theory in combination with the CPA equation of state. Fluid Phase Equilibria, 228, 479-485.
  • Ravagnani, S.P., D’Avila, S.G., (1985). VLE of Polar Mixtures: A New Generalized Correlation. Proceedings of IV International Chemical Engineering Conference, CHEMPOR’85, Coimbra, Portugal, 05 / 01 – 05.
  • Rosenbrock, H. H., (1960). An Automatic Method for Finding the Greatest or Least Value of a Function, Computer Journal, 3, 175-184.
  • Sadus, R. J., (2001). Equations of state for fluids: The Dieterici approach revisited. J. Chem. Phys., 115, 146014
  • Soave, G., (1972). Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27, 1197-1203.
  • Toghiani, H., Viswanath, D.S., (1986). A Cubic Equation of State for Polar and Apolar Fluids. Ind. Eng. Chem.. Process Des. Dev., 25, 531-536.
  • Trebble, M.A., Bishnoi, P.R., (1987). Development of a new four-parameter cubic equation of state. Fluid Phase Equilibria 35, 1-18.
  • Vargaftik, N.B., (1975). Handbook of Physical Properties of Liquid and Gases (Pure Substances and Mixtures), 2 nd Edition, John Willey, D.C. von Solms, N., Michelsen, M. L., Passos, C. P., Derawi, S. O., Kontogeorgis, G. M., (2006). Investigating Models for Associating Fluids Using Spectroscopy. Ind. Eng. Chem. Res., 45, 5368-5374.
  • Wei, S., Shi, Z., Castleman, A., (1991). Mixed Cluster Ions as a Structure Probe: Experimental Evidence for
  • Clathrate Structure of (H 2 O) 20 H + and (H 2 O) 21 H + . J. Chem. Phys., 94, 3268-3270.
  • Wei, Y.S., Sadus, R.J., (2000). Equations of State for Calculation of Fluid-Phase Equilibria. AIChE J., 46, 169-1
  • Wei, Y.S., Sadus, R.J., Franck, E.U., (1996). Binary mixtures of water + five noble gases: comparison of bimodal and critical curves at high pressures. Fluid Phase Equilibria 123, 1-15.
  • Wertheim, M. S., (1984a) Fluids with Highly Directional Attractive Forces. I. Statistical Thermodynamics. J. Stat. Phys., 35, 19-34.
  • Wertheim, M. S., (1984b). Fluids with Highly Directional Attractive Forces. II. Thermodynamic Perturbation Theory and Integral Equations. J. Stat. Phys., 35, 35-47. Wertheim, M. S., (1986a). Fluids with Highly Directional Attractive Forces. III. Multiple Attraction Sites. J. Stat. Phys., 42, 459-476.
  • Wertheim, M. S., (1986b). Fluids with Highly Directional Attractive Forces. IV. Equilibrium Polimerization, J. Stat. Phys., 42, 477-492.
  • Wertheim, M. S., (1986c). Fluids of Dimerizing Hard Spheres and Mixtures of Hard Spheres and Dispheres. J. Chem. Phys., 85, 2929-2936.
  • Wertheim, M. S., (1987). Thermodynamic Perturbation Theory of Polymerization, J. Chem. Phys., 87, 732373
  • Xu, Z, Sandler, S.I., (1987). Temperature dependent parameters and Peng-Robinson equation of state. Ind. Eng. Chem. Res., 26, 601-606.
  • Zhong, C., Masuoka, H., (1997). An EOS/G E type mixing rule for perturbed hard sphere equation of state and its application to calculation of solid solubility in supercritical carbon dioxide. Fluid Phase Equilibria, 141,13-23.
There are 45 citations in total.

Details

Primary Language En
Journal Section Regular Original Research Article
Authors

Ricardo Checoni

S. P. Ravagnani This is me

Publication Date November 12, 2012
Published in Issue Year 2013 Volume: 16 Issue: 1

Cite

APA Checoni, R., & Ravagnani, S. P. (2012). Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term. International Journal of Thermodynamics, 16(1), 20-27.
AMA Checoni R, Ravagnani SP. Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term. International Journal of Thermodynamics. December 2012;16(1):20-27.
Chicago Checoni, Ricardo, and S. P. Ravagnani. “Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term”. International Journal of Thermodynamics 16, no. 1 (December 2012): 20-27.
EndNote Checoni R, Ravagnani SP (December 1, 2012) Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term. International Journal of Thermodynamics 16 1 20–27.
IEEE R. Checoni and S. P. Ravagnani, “Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term”, International Journal of Thermodynamics, vol. 16, no. 1, pp. 20–27, 2012.
ISNAD Checoni, Ricardo - Ravagnani, S. P. “Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term”. International Journal of Thermodynamics 16/1 (December 2012), 20-27.
JAMA Checoni R, Ravagnani SP. Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term. International Journal of Thermodynamics. 2012;16:20–27.
MLA Checoni, Ricardo and S. P. Ravagnani. “Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term”. International Journal of Thermodynamics, vol. 16, no. 1, 2012, pp. 20-27.
Vancouver Checoni R, Ravagnani SP. Studies about an Equation of State for Pure Associated Fluids: Temperature Dependent Co-Volume Accounting a Physically Consistent Repulsive Term. International Journal of Thermodynamics. 2012;16(1):20-7.