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Claire S. Adjiman - One of the best experts on this subject based on the ideXlab platform.
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on the impact of using volume as an independent variable for the solution of p t Fluid Phase Equilibrium with equations of state
Computers & Chemical Engineering, 2014Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:a b s t r a c t The constant pressure–temperature (P–T) flash plays an important role in the modelling of Fluid-Phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P–T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which a direct evaluation of the free-energy is possible. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual), introduced in Pereira et al. (2012), and GILD (Gibbs free energy Lagrangian dual), introduced here, for the Fluid-Phase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
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On the impact of using volume as an independent variable for the solution of P–T Fluid-Phase Equilibrium with equations of state
Computers & Chemical Engineering, 2014Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:a b s t r a c t The constant pressure–temperature (P–T) flash plays an important role in the modelling of Fluid-Phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P–T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which a direct evaluation of the free-energy is possible. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual), introduced in Pereira et al. (2012), and GILD (Gibbs free energy Lagrangian dual), introduced here, for the Fluid-Phase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
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SAFT-γ force field for the simulation of molecular Fluids: 3. Coarse-grained models of benzene and hetero-group models of n-decylbenzene
Molecular Physics, 2012Co-Authors: Thomas Lafitte, Claire S. Adjiman, Amparo Galindo, George Jackson, Carlos Avendaño, Vasileios Papaioannou, Erich A. MüllerAbstract:In the first paper of this series [C. Avendano, T. Lafitte, A. Galindo, C.S. Adjiman, G. Jackson, and E.A. Muller, J. Phys. Chem. B 115, 11154 (2011)] our methodology for the development of accurate coarse-grained (CG) SAFT-γ force fields for the computer simulation of molecular Fluids was introduced with carbon dioxide as a particular case study. The procedure involves the use of a molecular-based equation of state to obtain effective intermolecular parameters (from experimental Fluid Phase Equilibrium data) appropriate for molecular simulation over a wide range of Fluid conditions. We now extend the methodology to develop coarse-grained models for benzene (C6H6) that can be used in Fluid Phase simulations. Our SAFT-γ CG force fields for benzene consist of a simple single-segment spherical model, and a rigid three-segment ring structure of tangent spherical groups interacting via Mie (generalized Lennard-Jones) segment–segment interactions. The description of the Fluid Phase behaviour of benzene with our...
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A duality-based optimisation approach for the reliable solution of (P, T) Phase Equilibrium in volume-composition space
Fluid Phase Equilibria, 2010Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:Abstract A reliable algorithm for the solution of Fluid Phase Equilibrium at constant pressure and temperature (P, T flash) is presented. The approach is applicable to multi-component mixtures described with general equations of state and is based on a formulation of P, T Phase Equilibrium as a dual optimisation problem in volume-composition space, translated away from the Gibbs free energy to the Helmholtz free energy. This formulation facilitates the use of guaranteed solution algorithms, particularly in the case of sophisticated equations of state (EOSs) such as SAFT (statistical associating Fluid theory), because such representations are higher-than-cubic functions in volume and are formulated in the Helmholtz free energy. With the proposed algorithm (which is based on a combination of local and global optimisation, where the number of subproblems to be solved globally is kept at a minimum) one is guaranteed to identify the number of stable Phases present at Equilibrium, along with their properties, without any need for initial guesses, or indeed any a priori knowledge about the behaviour of the system. The method is applicable to the calculation of any kind of Fluid Phase behaviour (e.g., vapour–liquid (VLE), liquid–liquid (LLE), vapour–liquid–liquid (VLLE), etc.). Several algorithmic options are investigated and their computational performance compared. A prototype implementation is used to determine the Fluid Phase equilibria of a number of binary and ternary systems, where the thermodynamic properties are calculated through a molecular-based EOS. Examples are shown for the VLE and VLLE for mixtures modelled with an augmented van der Waals EOS, a non-cubic EOS that incorporates the Carnahan and Starling representation of the repulsive interactions. Further examples are presented for VLE and VLLE in polymer systems, modelled with an EOS of the generic SAFT form. Fluid Phase Equilibrium calculations for polymer systems are notoriously difficult, and convergence problems are often encountered, even with good initial guesses. The proposed method is found to be reliable in all cases examined.
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Integrated Modeling of Mixture Fluid Phase Equilibrium Experiments Using SAFT-VR Applied to Xenon + Diborane, Xenon + Cyclopropane, Xenon + Boron Trifluoride
Industrial & Engineering Chemistry Research, 2009Co-Authors: M. Pollock, Claire S. Adjiman, Amparo Galindo, George Jackson, Eduardo J. M. FilipeAbstract:An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid Equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor Phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid Equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating Fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the Fluid Phase Equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting Phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-Phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the Fluid Phase Equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state. © 2009 American Chemical Society.
Eduardo J. M. Filipe - One of the best experts on this subject based on the ideXlab platform.
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Integrated Modeling of Mixture Fluid Phase Equilibrium Experiments Using SAFT-VR Applied to Xenon + Diborane, Xenon + Cyclopropane, Xenon + Boron Trifluoride
Industrial & Engineering Chemistry Research, 2009Co-Authors: M. Pollock, Claire S. Adjiman, Amparo Galindo, George Jackson, Eduardo J. M. FilipeAbstract:An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid Equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor Phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid Equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating Fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the Fluid Phase Equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting Phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-Phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the Fluid Phase Equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state. © 2009 American Chemical Society.
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integrated modeling of mixture Fluid Phase Equilibrium experiments using saft vr applied to xenon diborane xenon cyclopropane xenon boron trifluoride
Industrial & Engineering Chemistry Research, 2009Co-Authors: M. Pollock, Claire S. Adjiman, Amparo Galindo, George Jackson, Eduardo J. M. FilipeAbstract:An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid Equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor Phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid Equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating Fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the Fluid Phase Equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting Phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-Phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the Fluid Phase Equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state. © 2009 American Chemical Society.
Amparo Galindo - One of the best experts on this subject based on the ideXlab platform.
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on the impact of using volume as an independent variable for the solution of p t Fluid Phase Equilibrium with equations of state
Computers & Chemical Engineering, 2014Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:a b s t r a c t The constant pressure–temperature (P–T) flash plays an important role in the modelling of Fluid-Phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P–T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which a direct evaluation of the free-energy is possible. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual), introduced in Pereira et al. (2012), and GILD (Gibbs free energy Lagrangian dual), introduced here, for the Fluid-Phase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
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On the impact of using volume as an independent variable for the solution of P–T Fluid-Phase Equilibrium with equations of state
Computers & Chemical Engineering, 2014Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:a b s t r a c t The constant pressure–temperature (P–T) flash plays an important role in the modelling of Fluid-Phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P–T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which a direct evaluation of the free-energy is possible. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual), introduced in Pereira et al. (2012), and GILD (Gibbs free energy Lagrangian dual), introduced here, for the Fluid-Phase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
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SAFT-γ force field for the simulation of molecular Fluids: 3. Coarse-grained models of benzene and hetero-group models of n-decylbenzene
Molecular Physics, 2012Co-Authors: Thomas Lafitte, Claire S. Adjiman, Amparo Galindo, George Jackson, Carlos Avendaño, Vasileios Papaioannou, Erich A. MüllerAbstract:In the first paper of this series [C. Avendano, T. Lafitte, A. Galindo, C.S. Adjiman, G. Jackson, and E.A. Muller, J. Phys. Chem. B 115, 11154 (2011)] our methodology for the development of accurate coarse-grained (CG) SAFT-γ force fields for the computer simulation of molecular Fluids was introduced with carbon dioxide as a particular case study. The procedure involves the use of a molecular-based equation of state to obtain effective intermolecular parameters (from experimental Fluid Phase Equilibrium data) appropriate for molecular simulation over a wide range of Fluid conditions. We now extend the methodology to develop coarse-grained models for benzene (C6H6) that can be used in Fluid Phase simulations. Our SAFT-γ CG force fields for benzene consist of a simple single-segment spherical model, and a rigid three-segment ring structure of tangent spherical groups interacting via Mie (generalized Lennard-Jones) segment–segment interactions. The description of the Fluid Phase behaviour of benzene with our...
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A duality-based optimisation approach for the reliable solution of (P, T) Phase Equilibrium in volume-composition space
Fluid Phase Equilibria, 2010Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:Abstract A reliable algorithm for the solution of Fluid Phase Equilibrium at constant pressure and temperature (P, T flash) is presented. The approach is applicable to multi-component mixtures described with general equations of state and is based on a formulation of P, T Phase Equilibrium as a dual optimisation problem in volume-composition space, translated away from the Gibbs free energy to the Helmholtz free energy. This formulation facilitates the use of guaranteed solution algorithms, particularly in the case of sophisticated equations of state (EOSs) such as SAFT (statistical associating Fluid theory), because such representations are higher-than-cubic functions in volume and are formulated in the Helmholtz free energy. With the proposed algorithm (which is based on a combination of local and global optimisation, where the number of subproblems to be solved globally is kept at a minimum) one is guaranteed to identify the number of stable Phases present at Equilibrium, along with their properties, without any need for initial guesses, or indeed any a priori knowledge about the behaviour of the system. The method is applicable to the calculation of any kind of Fluid Phase behaviour (e.g., vapour–liquid (VLE), liquid–liquid (LLE), vapour–liquid–liquid (VLLE), etc.). Several algorithmic options are investigated and their computational performance compared. A prototype implementation is used to determine the Fluid Phase equilibria of a number of binary and ternary systems, where the thermodynamic properties are calculated through a molecular-based EOS. Examples are shown for the VLE and VLLE for mixtures modelled with an augmented van der Waals EOS, a non-cubic EOS that incorporates the Carnahan and Starling representation of the repulsive interactions. Further examples are presented for VLE and VLLE in polymer systems, modelled with an EOS of the generic SAFT form. Fluid Phase Equilibrium calculations for polymer systems are notoriously difficult, and convergence problems are often encountered, even with good initial guesses. The proposed method is found to be reliable in all cases examined.
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Integrated Modeling of Mixture Fluid Phase Equilibrium Experiments Using SAFT-VR Applied to Xenon + Diborane, Xenon + Cyclopropane, Xenon + Boron Trifluoride
Industrial & Engineering Chemistry Research, 2009Co-Authors: M. Pollock, Claire S. Adjiman, Amparo Galindo, George Jackson, Eduardo J. M. FilipeAbstract:An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid Equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor Phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid Equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating Fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the Fluid Phase Equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting Phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-Phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the Fluid Phase Equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state. © 2009 American Chemical Society.
George Jackson - One of the best experts on this subject based on the ideXlab platform.
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on the impact of using volume as an independent variable for the solution of p t Fluid Phase Equilibrium with equations of state
Computers & Chemical Engineering, 2014Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:a b s t r a c t The constant pressure–temperature (P–T) flash plays an important role in the modelling of Fluid-Phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P–T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which a direct evaluation of the free-energy is possible. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual), introduced in Pereira et al. (2012), and GILD (Gibbs free energy Lagrangian dual), introduced here, for the Fluid-Phase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
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On the impact of using volume as an independent variable for the solution of P–T Fluid-Phase Equilibrium with equations of state
Computers & Chemical Engineering, 2014Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:a b s t r a c t The constant pressure–temperature (P–T) flash plays an important role in the modelling of Fluid-Phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P–T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which a direct evaluation of the free-energy is possible. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual), introduced in Pereira et al. (2012), and GILD (Gibbs free energy Lagrangian dual), introduced here, for the Fluid-Phase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
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SAFT-γ force field for the simulation of molecular Fluids: 3. Coarse-grained models of benzene and hetero-group models of n-decylbenzene
Molecular Physics, 2012Co-Authors: Thomas Lafitte, Claire S. Adjiman, Amparo Galindo, George Jackson, Carlos Avendaño, Vasileios Papaioannou, Erich A. MüllerAbstract:In the first paper of this series [C. Avendano, T. Lafitte, A. Galindo, C.S. Adjiman, G. Jackson, and E.A. Muller, J. Phys. Chem. B 115, 11154 (2011)] our methodology for the development of accurate coarse-grained (CG) SAFT-γ force fields for the computer simulation of molecular Fluids was introduced with carbon dioxide as a particular case study. The procedure involves the use of a molecular-based equation of state to obtain effective intermolecular parameters (from experimental Fluid Phase Equilibrium data) appropriate for molecular simulation over a wide range of Fluid conditions. We now extend the methodology to develop coarse-grained models for benzene (C6H6) that can be used in Fluid Phase simulations. Our SAFT-γ CG force fields for benzene consist of a simple single-segment spherical model, and a rigid three-segment ring structure of tangent spherical groups interacting via Mie (generalized Lennard-Jones) segment–segment interactions. The description of the Fluid Phase behaviour of benzene with our...
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A duality-based optimisation approach for the reliable solution of (P, T) Phase Equilibrium in volume-composition space
Fluid Phase Equilibria, 2010Co-Authors: Frances E. Pereira, George Jackson, Amparo Galindo, Claire S. AdjimanAbstract:Abstract A reliable algorithm for the solution of Fluid Phase Equilibrium at constant pressure and temperature (P, T flash) is presented. The approach is applicable to multi-component mixtures described with general equations of state and is based on a formulation of P, T Phase Equilibrium as a dual optimisation problem in volume-composition space, translated away from the Gibbs free energy to the Helmholtz free energy. This formulation facilitates the use of guaranteed solution algorithms, particularly in the case of sophisticated equations of state (EOSs) such as SAFT (statistical associating Fluid theory), because such representations are higher-than-cubic functions in volume and are formulated in the Helmholtz free energy. With the proposed algorithm (which is based on a combination of local and global optimisation, where the number of subproblems to be solved globally is kept at a minimum) one is guaranteed to identify the number of stable Phases present at Equilibrium, along with their properties, without any need for initial guesses, or indeed any a priori knowledge about the behaviour of the system. The method is applicable to the calculation of any kind of Fluid Phase behaviour (e.g., vapour–liquid (VLE), liquid–liquid (LLE), vapour–liquid–liquid (VLLE), etc.). Several algorithmic options are investigated and their computational performance compared. A prototype implementation is used to determine the Fluid Phase equilibria of a number of binary and ternary systems, where the thermodynamic properties are calculated through a molecular-based EOS. Examples are shown for the VLE and VLLE for mixtures modelled with an augmented van der Waals EOS, a non-cubic EOS that incorporates the Carnahan and Starling representation of the repulsive interactions. Further examples are presented for VLE and VLLE in polymer systems, modelled with an EOS of the generic SAFT form. Fluid Phase Equilibrium calculations for polymer systems are notoriously difficult, and convergence problems are often encountered, even with good initial guesses. The proposed method is found to be reliable in all cases examined.
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Integrated Modeling of Mixture Fluid Phase Equilibrium Experiments Using SAFT-VR Applied to Xenon + Diborane, Xenon + Cyclopropane, Xenon + Boron Trifluoride
Industrial & Engineering Chemistry Research, 2009Co-Authors: M. Pollock, Claire S. Adjiman, Amparo Galindo, George Jackson, Eduardo J. M. FilipeAbstract:An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid Equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor Phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid Equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating Fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the Fluid Phase Equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting Phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-Phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the Fluid Phase Equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state. © 2009 American Chemical Society.
Jean-noël Jaubert - One of the best experts on this subject based on the ideXlab platform.
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Application of the Corresponding-State Law to the Parametrization of Statistical Associating Fluid Theory (SAFT)-Type Models: Generation and Use of “Generalized Charts”
Industrial & Engineering Chemistry Research, 2019Co-Authors: Romain Privat, Edouard Moine, Baptiste Sirjean, Rafiqul Gani, Jean-noël JaubertAbstract:Most of the Statistical Associating Fluid Theory (SAFT) and cubic equations of state (EoS) for nonassociating pure components obey the three-parameter corresponding-state law, meaning that the knowledge of three component-specific properties is a prerequisite to apply an EoS to a given pure species. Here, the methodology used to attribute values to EoS parameters is called “parameterization procedure”. In this Article, it is shown that generalized charts, derived from the corresponding-state theory, can be used advantageously to parametrize SAFT models. SAFT EoS is a well-established class of models frequently used for process simulation. Depending on the EoS parameter set selected, most of SAFT EoS are likely to predict unrealistic phenomena (mainly, the presence of multiple critical points and three-Fluid Phase Equilibrium regions in pure-component Phase diagrams). Generalized charts can be used to detect whether such unrealistic phenomena affect pure-component Phase diagrams in the temperature and pres...
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Fluid-Phase-Equilibrium prediction of fluorocompound-containing binary systems with the predictive E-PPR78 model
International Journal of Refrigeration, 2017Co-Authors: Jun-wei Qian, Romain Privat, Jean-noël Jaubert, Christophe Coquelet, Deresh RamjugernathAbstract:Abstract In order to reduce the overall emissions of greenhouse gases and to be in compliance with the current environmental regulations, a new class of refrigerants has appeared. Such refrigerants are generally multi-component systems that contain a fluorocompound mixed with CO2 and/or an alkane. In order to design processes involving such blends or to implement a product-design approach aimed at identifying new refrigerant mixtures, an equation of state (EoS) able to predict the properties of fluorocompound-containing systems is required. In order to reach this goal, it was decided in this study to add six fluorinated groups to the Enhanced-PPR78 model which combines the Peng–Robinson EoS and a group contribution method aimed at estimating the binary interaction parameters, kij(T), involved in Van der Waals one-Fluid mixing rules.
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Addition of the Sulfur Dioxide Group (SO2), the Oxygen Group (O-2), and the Nitric Oxide Group (NO) to the E-PPR78 Model
Industrial and engineering chemistry research, 2015Co-Authors: Romain Privat, Jean-noël JaubertAbstract:The E-PPR78 model is a predictive version of the widely used Peng-Robinson equation of state in which the binary interaction parameters are estimated by a group-contribution method. With the 24 groups available before the writing of this paper, such a model could be used to predict Fluid Phase Equilibrium of systems containing hydrocarbons, permanent gases (CO2, N-2, H2S, H-2, CO, He, and Ar), mercaptans, alkenes, and water. During the process of the Carbon dioxide Capture and Storage (CCS), it is often necessary to know thermodynamic properties of mixtures containing carbon dioxide, water, hydrocarbons, and trace gases, such as nitrogen, argon, hydrogen, carbon monoxide, sulfur dioxide, oxygen, or nitric oxide. Basically, except sulfur dioxide, oxygen, and nitric oxide, most components encountered in systems regarding CCS processes could be modeled with the E-PPR78 model. So in order to predict the Phase behavior and estimate energetic properties (e.g., enthalpy or heat capacity changes on mixing) of such systems, the applicability range of the E-PPR78 model is extended through the addition of three new groups: "SO2," "O-2," and "NO.
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Addition of the Sulfur Dioxide Group (SO2), the Oxygen Group (O2), and the Nitric Oxide Group (NO) to the E-PPR78 Model
Industrial & Engineering Chemistry Research, 2015Co-Authors: Romain Privat, Jean-noël JaubertAbstract:The E-PPR78 model is a predictive version of the widely used Peng–Robinson equation of state in which the binary interaction parameters are estimated by a group-contribution method. With the 24 groups available before the writing of this paper, such a model could be used to predict Fluid Phase Equilibrium of systems containing hydrocarbons, permanent gases (CO2, N2, H2S, H2, CO, He, and Ar), mercaptans, alkenes, and water. During the process of the Carbon dioxide Capture and Storage (CCS), it is often necessary to know thermodynamic properties of mixtures containing carbon dioxide, water, hydrocarbons, and trace gases, such as nitrogen, argon, hydrogen, carbon monoxide, sulfur dioxide, oxygen, or nitric oxide. Basically, except sulfur dioxide, oxygen, and nitric oxide, most components encountered in systems regarding CCS processes could be modeled with the E-PPR78 model. So in order to predict the Phase behavior and estimate energetic properties (e.g., enthalpy or heat capacity changes on mixing) of such ...
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classification of global Fluid Phase Equilibrium behaviors in binary systems
Chemical Engineering Research & Design, 2013Co-Authors: Romain Privat, Jean-noël JaubertAbstract:Abstract The study of Phase equilibria is one of the most important sources of information about the nature of intermolecular forces in liquids and their mixtures and is of the highest importance for designing and optimizing processes. Many of the main features of vapor–liquid and liquid–liquid Phase behavior were well characterized experimentally during the early part of the 20th century, and many equations of state were developed to reproduce the many types of Phase diagrams observed for binary systems. In spite of the quasi-infinite number of possible configurations and rearrangements of Fluid–Fluid Equilibrium Phase diagrams, this paper presents a near-exhaustive classification scheme of Fluid Phase equilibria in binary systems. It starts from the one proposed by Van Konynenburg and Scott and brings it up-to-date by detailing the progress carried out on this topic since their classification scheme was first proposed. The second part of this paper is devoted to describing the transitions between the various types of systems.