High-Pressure Fluid Phase Equilibria

Phenomenology and Computation

Ulrich K Deiters, Thomas Kraska

• Publisher: Elsevier
• Year: 2012
• eBook ISBN: 9780444563545
• Topic: Tecnologia e ingegneria
• Subtopic: Chimica fisica e teoretica

The book begins with an overview of the phase diagrams of fluid mixtures (fluid = liquid, gas, or supercritical state), which can show an astonishing variety when elevated pressures are taken into account; phenomena like retrograde condensation (single and double) and azeotropy (normal and double) are discussed. It then gives an introduction into the relevant thermodynamic equations for fluid mixtures, including some that are rarely found in modern textbooks, and shows how they can they be used to compute phase diagrams and related properties. This chapter gives a consistent and axiomatic approach to fluid thermodynamics; it avoids using activity coefficients. Further chapters are dedicated to solid-fluid phase equilibria and global phase diagrams (systematic search for phase diagram classes). The appendix contains numerical algorithms needed for the computations. The book thus enables the reader to create or improve computer programs for the calculation of fluid phase diagrams. - introduces phase diagram classes, how to recognize them and identify their characteristic features - presents rational nomenclature of binary fluid phase diagrams - includes problems and solutions for self-testing, exercises or seminars

Supercritical Fluid Science and Technology, Vol. 2, Suppl (C), 2012

ISSN: 2212-0505

doi: 10.1016/B978-0-444-56347-7.00001-3

Chapter 1 Introduction

Ulrich K. Deiters, Thomas Kraska

Before going to the main chapters of the book, it seems advisable to describe its objectives and scope. Furthermore, we will introduce some conventions and (hopefully) provide the reader with motivation to continue.

1.1 What are Fluids?

It is a common knowledge that there are three different states of aggregation, namely solid, liquid, and gas.¹ Why is the term “fluid” needed?

In everyday life, it is easy and practical to distinguish between liquids and gases (or vapors). However, everyday life takes place at low pressures around 0.1 MPa only – for humans at least. But there are environments where high pressures naturally occur, for instance at the bottom of the oceans (up to 110 MPa), in deep geological strata, and especially in natural oil and gas reservoirs. Furthermore, there are many technical applications that involve elevated pressures, e.g., gas and oil pipelines, thermal power plants, refrigeration systems, and numerous chemical production processes. In the world of high pressures, however, it is no longer trivial to distinguish between liquids and gases. In fact, there are continuous transitions between the liquid and the gas state, i.e., gradual transitions that change one into the other without ever involving a phase transition, namely by passing through the supercritical region, where the distinction between liquid and gas is no longer meaningful.

We use the word “fluid” here as a generic term for all states of aggregation that are not solid, where “solid” indicates a state of matter with a long-distance order (periodicity of molecule locations)²: fluids have no long-distance order, and their constituent molecules can move about.³

Because of this mobility, the equilibration of fluid phases is usually rapid, unless the viscosity is very high. If a phase separation occurs, the coexisting phases separate on a macroscopic scale. Phase equilibria involving fluid phases are, therefore, the foundation of many chemical separation techniques. Important examples are distillation or extraction.

1.2 Why should You Read This Book?

What is so complicated about fluid-phase equilibria that one should write a book about this subject?

At a first glance, the subject seems simple: the most common type of equilibrium between two fluid phases is the liquid–vapor transition (boiling or condensation) of a pure compound. Of course, the boiling point of a pure compound depends on pressure. The relationship between boiling temperature and pressure is graphically represented in a phase diagram by the vapor pressure curve.

The phase diagram of a pure compound contains exactly one vapor pressure curve, which originates in a triple point and ends – if the physically accessible temperature range is not restricted by decomposition reactions – in the critical point. Here, liquid and vapor become identical. There is only one critical point, and there is only one kind of fluid-phase equilibrium, namely the vapor–liquid equilibrium.⁴

The situation is more complicated in mixtures: in a mixture of two compounds, each compound has its own vapor pressure curve, and the vapor–liquid phase behavior of the mixture depends on the locations of these vapor pressure curves relative to each other. Because a binary mixture, according to Gibbs’ phase rule, has one thermodynamical degree of freedom more than a pure compound, there are now critical curves to consider instead of merely critical points. As a further complication, a new kind of phase equilibrium can occur, namely liquid–liquid demixing. Here, the mutual miscibility of the compounds depends on the external parameters pressure and temperature. Furthermore, there can be complicated interactions between liquid–liquid and vapor–liquid phase behavior. Like the latter, liquid–liquid phase equilibria have critical curves too. Therefore, it is possible to have two or three critical curves in the phase diagram of a binary mixture; theoretically, far higher numbers are conceivable.

Now the thermodynamic conditions of phase equilibrium and phase stability have been known since the end of 19th century. Since more than 100 years, there are thermodynamic models, especially thermal equations of state and lattice gas models, which yield expressions for the Gibbs or Helmholtz energy of fluid mixtures.⁵ One might expect that, by application of the criteria for phase equilibria to these models, one should be able to derive all possible phase equilibrium phenomena in liquid or gaseous mixtures.

However, even for simple equations of state, the criteria of phase equilibrium lead to systems of nonlinear equations of such complexity that their solution has become practically feasible after the invention of electronic computers only. The earliest publications on the quantitative calculation of fluid-phase equilibria from equations of state using electronic computers date from about 1960.⁶ Nowadays, with powerful computers being available worldwide, more than 1500 different equations of state and mixing theories are used for modeling various thermodynamic properties of mixtures. In connection with modern electronic data banks, phase diagrams can be – seemingly – generated at the press of a button.

Does this mean that the theory of phase equilibria has become obsolete? This would be a dangerous conclusion: Automated computation methods may work well for some not too complicated mixtures, but seriously fail otherwise; this book contains many phase diagrams that cannot be treated as routine cases. We feel that an understanding of the principles of fluid-phase equilibria is essential.⁷ Moreover, the experimentalist constructing an apparatus for the determination of phase equilibria as well as the theoretician developing a computer program for their calculation always start with some preconception of what the outcome will be or might be. But there are pitfalls, e.g.:

• It is a common technique to determine two-phase equilibria by removing and analyzing samples from the top and bottom of an otherwise sealed vessel. But then an unexpected three-phase equilibrium may escape detection.

• A computer program for the calculation of heats of mixing will not warn its users if the input data specify a state within a two-phase region – unless the programmer had been aware of this possibility.

Evidently it is necessary that those working with thermodynamic apparatus or programs are aware of the phase-theoretical possibilities and pitfalls of their objects of study. Phase diagrams may sometimes be confusing, but they obey certain rules...

Table of contents

• Cover image
• Title page
• Table of Contents
• Series Editor
• Edited by
• Copyright page
• Dedication
• Symbols
• Foreword
• Preface
• Chapter 1: Introduction
• Chapter 2: Phenomenology of Phase Diagrams
• Chapter 3: Experimental Observation of Phase Equilibria
• Chapter 4: Thermodynamic Variables and Functions
• Chapter 5: Stability and Equilibrium
• Chapter 6: Solid–Fluid Equilibrium
• Chapter 7: Equations of State for Pure Fluids
• Chapter 8: Equations of State for Mixtures
• Chapter 9: Global Phase Diagrams
• Appendix A: Algebraic and Numeric Methods
• Appendix B: Proofs
• Appendix C: Equations of State: Auxiliary Equations for Programming
• Appendix D: Solutions of the Problems
• References
• Index