### Abstract

Based on the generalized van der Waals theory, a cubic equation of state (the van der Waals equation) was extended to describe the behavior of pure fluids and mixtures confined in porous solids. Each pore was assumed to be a cylinder with a continuous and homogeneous surface. Fluid molecules were assumed spherical, interacting with each other and with the wall of the pore through square-well potentials. Pairwise additivity was assumed for the attractive parts of all interaction potentials. The repulsive part of the equation of state for confined fluids was modeled based on literature data for the packing of hard spheres in cylinders. The effect of pore size on fluid properties was explicitly represented in the model, allowing its application to both confined and bulk fluids thus providing a consistent description of adsorption systems for all pore sizes. The resulting equation of state has two fitting parameters for each component of the fluid, which are related to the interaction between the fluid molecules and the pore walls. Calculations of pure fluid adsorption were carried out in order to analyze the sensitivity of the model to its fitting parameters and to pore size. It was found that the model is able to describe different types of adsorption isotherms. The model correlated experimental data of pure fluid adsorption quite well and was then used to predict the adsorption of several binary mixtures and one ternary mixture with no additional fitting, with good results. The methodological framework presented here can be extended to other widely used equations of state for modeling confined fluids.

Original language | English |
---|---|

Pages (from-to) | 3088-3099 |

Number of pages | 12 |

Journal | Chemical Engineering Science |

Volume | 65 |

Issue number | 10 |

DOIs | |

Publication status | Published - 15 May 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Adsorption
- Mathematical modeling
- Porous media
- State equation
- Statistical thermodynamics

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Chemistry(all)
- Applied Mathematics
- Industrial and Manufacturing Engineering

### Cite this

*Chemical Engineering Science*,

*65*(10), 3088-3099. https://doi.org/10.1016/j.ces.2010.01.032

**Thermodynamic modeling of confined fluids using an extension of the generalized van der Waals theory.** / Travalloni, Leonardo; Castier, Marcelo; Tavares, Frederico W.; Sandler, Stanley I.

Research output: Contribution to journal › Article

*Chemical Engineering Science*, vol. 65, no. 10, pp. 3088-3099. https://doi.org/10.1016/j.ces.2010.01.032

}

TY - JOUR

T1 - Thermodynamic modeling of confined fluids using an extension of the generalized van der Waals theory

AU - Travalloni, Leonardo

AU - Castier, Marcelo

AU - Tavares, Frederico W.

AU - Sandler, Stanley I.

PY - 2010/5/15

Y1 - 2010/5/15

N2 - Based on the generalized van der Waals theory, a cubic equation of state (the van der Waals equation) was extended to describe the behavior of pure fluids and mixtures confined in porous solids. Each pore was assumed to be a cylinder with a continuous and homogeneous surface. Fluid molecules were assumed spherical, interacting with each other and with the wall of the pore through square-well potentials. Pairwise additivity was assumed for the attractive parts of all interaction potentials. The repulsive part of the equation of state for confined fluids was modeled based on literature data for the packing of hard spheres in cylinders. The effect of pore size on fluid properties was explicitly represented in the model, allowing its application to both confined and bulk fluids thus providing a consistent description of adsorption systems for all pore sizes. The resulting equation of state has two fitting parameters for each component of the fluid, which are related to the interaction between the fluid molecules and the pore walls. Calculations of pure fluid adsorption were carried out in order to analyze the sensitivity of the model to its fitting parameters and to pore size. It was found that the model is able to describe different types of adsorption isotherms. The model correlated experimental data of pure fluid adsorption quite well and was then used to predict the adsorption of several binary mixtures and one ternary mixture with no additional fitting, with good results. The methodological framework presented here can be extended to other widely used equations of state for modeling confined fluids.

AB - Based on the generalized van der Waals theory, a cubic equation of state (the van der Waals equation) was extended to describe the behavior of pure fluids and mixtures confined in porous solids. Each pore was assumed to be a cylinder with a continuous and homogeneous surface. Fluid molecules were assumed spherical, interacting with each other and with the wall of the pore through square-well potentials. Pairwise additivity was assumed for the attractive parts of all interaction potentials. The repulsive part of the equation of state for confined fluids was modeled based on literature data for the packing of hard spheres in cylinders. The effect of pore size on fluid properties was explicitly represented in the model, allowing its application to both confined and bulk fluids thus providing a consistent description of adsorption systems for all pore sizes. The resulting equation of state has two fitting parameters for each component of the fluid, which are related to the interaction between the fluid molecules and the pore walls. Calculations of pure fluid adsorption were carried out in order to analyze the sensitivity of the model to its fitting parameters and to pore size. It was found that the model is able to describe different types of adsorption isotherms. The model correlated experimental data of pure fluid adsorption quite well and was then used to predict the adsorption of several binary mixtures and one ternary mixture with no additional fitting, with good results. The methodological framework presented here can be extended to other widely used equations of state for modeling confined fluids.

KW - Adsorption

KW - Mathematical modeling

KW - Porous media

KW - State equation

KW - Statistical thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=77950595148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950595148&partnerID=8YFLogxK

U2 - 10.1016/j.ces.2010.01.032

DO - 10.1016/j.ces.2010.01.032

M3 - Article

AN - SCOPUS:77950595148

VL - 65

SP - 3088

EP - 3099

JO - Chemical Engineering Science

JF - Chemical Engineering Science

SN - 0009-2509

IS - 10

ER -