CHEMICAL ENGINEERING DEPARTMENT

Equation of State
for Confined Fluids

Documentation

The following paper contains extensive documentation of our model. Knowledge of statistical mechanics is required to fully understand it.
The model is subjected to the condition of low values of the porosity parameter (p).

Tips for using this webpage

• When trying to model behavior seen experimentally by finding the value of Γ´ best results are obtained when using low pressures (below 10 bar).
• Always check that the accuracy of the Γ´ calculation is of the order of 1e-10 or smaller.
• Always check that the value of the calculated Tc´ is positive.
• Values of Γ´ over ~20 do not return the expected VanDerWaal curves.
• The z variable is assigned a value of 4 for 2D structures and a value of 6 for 3D structures.

Nomenclature

• n_i - molecule density in lattice gas for sit i
• H - Hamiltonian function
• p - density of particles in porous matrix
• P - Pressure
• Tc - critical Temperature
• z - lattice coordination number
• ε - random variable
• μ - chemical potential
• Γ - fluid-solid coupling parameter in lattice gas
• ρ - fluid density

Paper under submission

We have submitted a paper to the Chemical Engineering Communications Journal. Here is the abstract:

   We present results showing how a new mean-field equation of state model, originally developed for predicting the critical behavior of fluids confined in porous, random structures can be used to model adsorption phenomena in light gas systems. The model is an exact mean-field equation, based upon a lattice-gas formalism, obtained from fundamental statistical mechanical arguments. It explicitly incorporates the effects of fluid confinement and is different to the well-known Bragg-Williams model in that the confining structure is treated as a quenched variable with the fluid density and annealed variable.

   In this short communication we illustrate how the model may be used to represent and predict adsorption data in porous structures. The results suggest that this equation of state approach provides a basis for developing useful, fundamentally inspired models for representing thermodynamic properties in adsorption systems.

Authors: Carla Martin, Mathew Fabrizio, Eldred H. Chimowitz

Email: cm005j@mail.rochester.edu or chim@che.rochester.edu
Any suggestions will be appreciated!

Special Thanks:

• To the National Science Foundation which provided financial support for this work through grant CTS-0104323.
• To David J. Sankel for his invaluable help with the programming aspect of this model.
• To Sandra Willison for her constant support and valuable help and advice.
• To Matt Tierney for his help developing the computational results.