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Mechanical Expansion of Steel Tubing as a Solution to Leaky Wellbores

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Published on: November 20, 2014

Generalized coupling parameter expansion: application to square well and Lennard-Jones fluids.

A Sai Venkata Ramana¹

¹Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India.

The Journal of Chemical Physics

|August 2, 2013

Summary

This study enhances thermodynamic perturbation theory for simple fluids, accurately predicting properties like radial distribution functions and phase diagrams for Square-Well and Lennard-Jones fluids. The improved method overcomes limitations of integral equation theories, especially in coexistence regions.

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Area of Science:

Thermodynamics
Statistical Mechanics
Physical Chemistry

Background:

Thermodynamic perturbation theory (TPT) is crucial for understanding fluid behavior.
Integral equation theories (IETs) have limitations, particularly in liquid-vapor coexistence regions.
Bridge functions play a key role in accurately describing fluid correlations.

Purpose of the Study:

To generalize TPT by incorporating derivatives of the bridge function with respect to the coupling parameter.
To apply this enhanced theory to Square-Well (SW) and Lennard-Jones (LJ) fluids.
To assess the accuracy and applicability of the method compared to IET and simulations.

Main Methods:

Generalized coupling parameter expansion in TPT, including bridge function derivatives.
Application of seventh-order TPT to SW and LJ fluids using the Sarkisov bridge function.
Comparison of results with integral equation theory and simulation data.

Main Results:

Accurate reproduction of radial distribution functions for SW and LJ fluids.
Successful prediction of liquid-vapor phase diagrams, even in regions where IETs fail.
Improved liquid-vapor phase diagram for SW fluids using Carnahan-Starling for the hard-sphere reference system.
Significant impact of bridge function derivatives on the liquid part of the phase diagram.
Good agreement between theoretical and simulation results for surface tension of SW fluids.
Consistent equation of state for LJ fluids compared to IET.

Conclusions:

The generalized TPT offers improved accuracy over standard IET when reference system properties are known.
The method provides a viable alternative for solving Ornstein-Zernkequations when reference system data is unavailable.
The inclusion of bridge function derivatives enhances the predictive power of TPT for fluid phase behavior.