Abstract

Equations of State (EoS) live at the heart of all thermodynamic calculations in chemical engineering applications as they allow for the determination of all related fluid properties such as vapor pressure, density, enthalpy, specific heat, and speed of sound, in an accurate and consistent way. Both macroscopic EoS models such as the classic cubic EoS models as well as models based on statistical mechanics and developed by means of perturbation theory are available. Under suitable pressure and temperature conditions, fluids of known composition may split in more than one phases, usually vapor and liquid while solids may also be present, each one exhibiting its own composition. Therefore, computational methods are utilized to calculate the number and the composition of the equilibrium phases at which a feed composition will potentially split so as to estimate their thermodynamic properties by means of the EoS. This chapter focuses on two of the most pronounced EoS models, the cubic ones and those based on statistical mechanics incorporating perturbation analysis. Subsequently, it describes the existing algorithms to solve phase behavior problems that rely on the classic rigorous thermodynamics context as well as modern trends that aim at accelerating computations.

Highlights

  • Equations of State (EoS) have been widely used in the chemical engineering industry for the calculation of process fluids phase properties

  • The ones most widely used in the chemical engineering industry are the cubic ones [1] due to their simplicity and speed of calculations, minimizing the computing time required for flow simulations in processes, porous media and pipelines

  • EoS models based on the application of statistical mechanics in conjunction to perturbation theory to describe the thermodynamic behavior of substances at a microscopic level are commonly used to estimate properties of liquids [3]

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Summary

Introduction

Equations of State (EoS) have been widely used in the chemical engineering industry for the calculation of process fluids phase properties. EoS models are algebraic expressions of the form f ðp, T, vmÞ 1⁄4 0 which relate molar volume vm to pressure and temperature. Since the derivation of the ideal gas law and following the pioneering work of Van der Waals, dozens of EoS models of various complexity and thermodynamic considerations have been presented to accurately estimate thermophysical properties. Basic and extended cubic equations of state, virial forms, EoS models with association terms and models based on statistical physics. The ones most widely used in the chemical engineering industry are the cubic ones [1] due to their simplicity and speed of calculations, minimizing the computing time required for flow simulations in processes, porous media and pipelines. Less simple but more accurate models incorporating associating theory are often used in midstream and downstream applications [2]

A Collection of Papers on Chaos Theory and Its Applications
Development of the cubic EoS models
Use of the cubic EoS models
Volume translation
EoS models in the thermodynamic perturbation theory context
The correlation function formalism to derive EoS models
Derivation of fluid properties for specific pair functions
The hard-sphere model
The pair potentials are equal between any pair of molecules
The stability test
Compute fugacity of each component of the feed f ðizÞ using the EoS model
The phase split
Using k-values from correlations and charts
Using composition dependent k-values from an EoS model
Saturation condition calculations
Negative flash calculations f ð i y
Multiphase calculations
Accelerated phase behavior calculations
Rigorous methods
The reduced variable framework
Initialize yi and β
Soft computing methods
Conclusions
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