Supercritical Water E-Book

Yizhak Marcus

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 399

Veröffentlichungsjahr: 2012

Beschreibung

Discover the many new and emerging applications of supercritical water as a green solvent Drawing from thousands of original research articles, this book reviews and summarizes what is currently known about the properties and uses of supercritical water. In particular, it focuses on new and emerging applications of supercritical water as a green solvent, including the catalytic conversion of biomass into fuels and the oxidation of hazardous materials. Supercritical Water begins with an introduction that defines supercritical fluids in general. It then defines supercritical water in particular, using the saturation curve to illustrate its relationship to regular water. Following this introduction, the book: * Describes the bulk macroscopic properties of supercritical water, using equations of state to explain temperature-pressure-density relationships * Examines supercritical water's molecular properties, setting forth the latest experimental data as well as computer simulations that shed new light on structure and dynamics * Explores the solubilities of gases, organic substances, salts, and ions in supercritical water in terms of the relevant phase equilibria * Sets forth the practical uses of supercritical water at both small scales and full industrial scales Throughout the book, the author uses tables for at-a-glance reviews of key information. Summaries at the end of each chapter reinforce core principles, and references to original research and reviews serve as a gateway and guide to the extensive literature in the field. Supercritical Water is written for students and professionals in physical chemistry, chemistry of water, chemical engineering, and organic chemistry, interested in exploring the applications and properties of supercritical water.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

List of Acronyms and Symbols

Acronyms

Symbols

Subscripts and Superscripts

Chapter 1: Introduction

1.1 Phase Diagrams of Single Fluids

1.2 The Critical Point

1.3 Supercritical Fluids as Solvents

1.4 Gaseous and Liquid Water

1.5 Near-Critical Water

1.6 Summary

References

Chapter 2: Bulk Properties of SCW

2.1 Equations of State (EoS)

2.2 Thermophysical Properties of SCW

2.3 Electrical and Optical Properties

2.4 Transport Properties

2.5 Ionic Dissociation of SCW

2.6 Properties Related to the Solvent Power of SCW

2.7 Summary

References

Chapter 3: Molecular Properties of SCW

3.1 Diffraction Studies of SCW Structure

3.2 Computer Simulations of SCW

3.3 Spectroscopic Studies of SCW

3.4 The Extent of Hydrogen Bonding in SCW

3.5 The Dynamics of Water Molecules in SCW

3.6 Summary

References

Chapter 4: SCW as a “Green” Solvent

4.1 Solutions of Gases in SCW

4.2 Solutions of Organic Substances in SCW

4.3 Solutions of Salts and Ions in SCW

4.4 Binary Mixtures of Cosolvents with SCW

4.5 Summary

References

Chapter 5: Applications of SCW

5.1 Conversion of Organic Substances to Fuel

5.2 Supercritical Water Oxidation

5.3 Uses of SCW in Organic Synthesis

5.4 Uses in Powder Technology of Inorganic Substances

5.5 Geothermal Aspects of SCW

5.6 Application of SCW in Nuclear Reactors

5.7 Corrosion Problems with SCW

5.8 Summary

References

Author Index

Subject Index

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Marcus, Y.

Supercritical water : a green solvent, properties and uses / Yizhak Marcus.

p. cm.

Includes indexes.

ISBN 978-0-470-88947-3 (hardback)

1. Solvents. 2. Green technology. I. Title.

TP247.5.M294 2012

541'.3482–dc23

2011049802

Preface

As of the summer 2011, there were more than 3000 topics dealing in detail with supercritical water (SCW) in the SciFinder literature search instrument of the American Chemical Society. However, there were more than 14,000 entries outlining this concept. In the 1980s some 100 papers and in the 1990s some 900 papers on supercritical water were published, while at present there are already more than 2000 papers. As it is impossible to compile all the published information in a book, an attempt has been made to include the maximum possible important properties and uses of supercritical water. Factual information is given in numerous tables along with suggested references for more details on the subject. Where appropriate, the reader is referred to several reviews relevant to the topics included in this book.

Prior to 1980, only a few dozen papers dealt with SCW, considering SCW mainly within the broad subject of high-pressure steam in the context of electric power generation. The papers dealt principally with the heat transfer in SCW, mineral solubilities in it, and corrosion by it. E. U. Franck, a pioneer in the study of supercritical fluids, however, published in 1968 a review (Endeavour, 22, 55) that highlighted some of the properties of this fluid and its possible uses. The properties contrasted with those of water vapor and of the liquid water at ambient condition. They included the complete miscibility of SCW with nonpolar fluids, the very high mobility of ions from electrolytes dissolved in SCW, and the water itself acquiring appreciable electrical conductivity. Knowledge of the chemical behavior of high-temperature water, in the pure state and when serving as a solvent, led to the understanding of the structural features of SCW and of hydration phenomena in it. The properties of geochemically important “hydrothermal” solutions could also be explained and possible technical applications were suggested.

The properties of dense steam or compressed hot water below the critical point and solutions in such media can be of interest, as these are able to act as “green” solvents. In the present book, the so-called near-critical water is however only cursorily dealt with, as it is mainly devoted to the properties and uses of supercritical water. SCW in itself can also be deemed to be a “green” solvent, that is, environment-friendly.

Having dealt for many years with liquids and solutions, the author's interest in SCW was raised by the proposal he received in the late 1990s from the INTAS agency for his participation in an international collaboration on this subject. During the period of 3 years of the project that involved three groups from Russia, one from Greece, one from Germany, and the present author, “experimental and theoretical studies of supercritical aqueous solutions as a medium for new environmentally friendly and energy efficient technologies of pollution control” were carried out. As a further result of this collaboration, one of the participants, A. Kalinichev, was invited together with the present author by R. Ludwig, the editor of the book Water: From Hydrogen Bonding to Dynamics and Structure, to write a chapter on SCW for it. This provided the initial impetus to the writing of the present book, seeing that none existed so far that summarized the state of the art and in view of the increasing interest in the subject as reflected by the increasing number of published papers.

The book is divided into five chapters. Chapter 1 introduces supercritical fluids in terms of the phase diagrams of the fluids and their critical points. A brief description of a variety of supercritical fluids that have been used as solvents is given. Attention is then turned toward the water substance, in its gaseous state (water vapor) and ordinary liquid water and their properties. As water is heated toward the critical point, near-critical water is reached, and a short discussion of this state of water (that has found some applications as a “green” solvent) is presented. Chapter 2 deals with the macroscopic measurable properties. Foremost of these are the temperature–pressure–density or volume (PVT) relationships described by means of equations of state. Other important thermophysical properties of SCW are the heat capacity and the enthalpy and entropy. The electrical and optical properties include the static dielectric constant, the light refraction, and the electrical conductivity of neat SCW. The transport properties involve the viscosity, the self-diffusion, and the thermal conductivity. The ionic dissociation of SCW is then discussed, and finally the properties of SCW relevant to the solubility of solutes in it are briefly described. Chapter 3 deals with the structure and dynamics as inferred from experimental data and computer simulations. Diffraction of X-rays and in particular of neutrons provides information on the molecular structure of SCW. Computer simulations provide information on both the structure (by the Monte Carlo method) and the dynamics (the molecular dynamics method). Spectroscopic studies, involving infrared light absorption, Raman light scattering, nuclear magnetic resonance, and dielectric relaxation, complement the aforementioned studies. It is shown that SCW has appreciable hydrogen bonding between its molecules and the extent of this is explored. Finally, the dynamics of the water molecules in SCW and the lifetime of various configurations in it are discussed. Chapter 4 describes the solubilities of gases, organic substances, salts, and ions in SCW in terms of the relevant phase equilibria. The interactions that take place between the water molecules and the solutes of the various categories are presented. In particular, for ions and salts, the properties of such solutions are dealt with. In case of ions, their association on the one hand and their hydration on the other determine these properties. Finally, Chapter 5 includes the current practical uses, whether on a modest or on a full industrial scale. Conversion of biomass to fuel, gaseous or liquid, is one such use. SCW oxidation (SCWO) of pollutants and hazardous materials is another important use, the problems associated with which have not so far been completely resolved. Some other uses include organic synthesis, where SCW is both a reaction medium and a reactant, nanoparticle production of inorganic substances (mainly oxides), and as a neutron moderator in nuclear power reactors and at the same time as the coolant, providing the fluid for turbine operation. Geochemistry is another field where SCW plays a role, because deep strata in the earth's crust provide the high temperature and pressure to convert any water derived from hydrous minerals to SCW. This is then evolved in thermal vents, carrying along some minerals dissolved in it. Finally, some of the corrosion problems met with in applications of SCW are briefly dealt with.

A vast amount of information is available on SCW and solutions therein; this book however provides those numerical data in tables that help the reader to appreciate the quantitative aspects of SCW and its properties. Some other tables include annotated examples of the uses of SCW, but on the whole, it is possible only to point out what various authors have studied, to summarize it, and as necessary to comment on this. This book includes references to which the readers interested in having in-depth knowledge of the topics may refer. It is hoped that the book will help understand the concept of supercritical water, its properties, and uses.

Yizhak Marcus

Jerusalem, 2011

List of Acronyms and Symbols

Acronyms

EoSEquation of statesMCMonte Carlo computer simulationMDMolecular dynamics computer simulationPVTPressure–volume–temperatureSAFTStatistical associated fluid theorySCDSupercritical carbon dioxideSCFSupercritical fluidSCWSupercritical waterSCWGSupercritical water gasificationSCWOSupercritical water oxidationVLEVapor/liquid equilibrium

Symbols

SymbolDescriptionUnitsUniversal constantseUnit electrical charge: 1.602177 × 10−19CFFaraday's constant: 9.64853 × 104C mol−1kBBoltzmann's constant: 1.380658 × 10−23J K−1NAAvogadro's number: 6.022136 × 1023mol−1RGas constant: 8.31451J K−1 mol−1ε0Permittivity of vacuum: 8.854188 × 10−12C2 J−1 m−1Physical quantitiesAHelmholtz energy, molarkJ mol−1aAttractive parameter in EoSJ2 Pa−1 mol−2BVirial coefficientm3bScattering lengthnmbCovolume parameter in EoSm3CoNumber of componentsCPHeat capacity at constant pressure, molarJ K−1 mol−1CVHeat capacity at constant volume, molarJ K−1 mol−1cConcentration, molar scalemol dm−3DDiffusion coefficientm2 s−1DfNumber of degrees of freedomdInteratomic distancenmEEnergy, molarkJ mol−1eHBEnergy of an H-bondkJ mol−1fFugacitykPafiFraction of water molecules with i H-bondsGGibbs energy, molarkJ mol−1gKirkwood dipole orientation parameterg(r)Pair correlation functionHEnthalpy, molarkJ mol−1hihydration number, ionicIIonic strengthmol dm−3IIntensity of scattered or absorbed radiationKEquilibrium constantdm3 mol−1Octanol/water partition coefficientKWIon product of waterdm6 mol−2kVariable, function of diffraction anglem−1kRate constants−1LgOstwald coefficient of gas solubilityMMass, molarkg mol−1mMass, molecularkgmMolalitymol kg−1NNumber of componentsNNumber of molecules or ionsNcoCoordination numbernRefractive index (at specified frequency)Average number of H-bonds per water moleculePPressureMPaPhNumber of coexisting phasesPiInternal pressureMPapVapor pressurekPap (event)Probability of an eventrRadial distance from a particlenmriRadius, ionicnmSEntropy, molarJ K−1 mol−1S(k)Structure factorsSolubilitymol dm−3TTemperature (absolute)KT1Spin-lattice NMR relaxation timestTemperature°CtiTransference number, ionicUConfigurational energy of system, molarkJ mol−1uSound velocitym s−1uiMobility, ionicm s−1 V−1VVolume, molarm3vSpecific volumem3 kg−1vVelocity, molecularm s−1xMole fraction of specified component or speciesYGeneralized thermodynamic functionyActivity coefficient, molar scaleZCompressibility factor PV/RTZLattice parameterzCharge number, algebraicαKamlet–Taft H-bond donation ability indexαPolarizability, molecularm−3αpExpansibility, isobaricK−1βKamlet–Taft H-bond acceptance ability indexγActivity coefficient, molal scaleδNMR chemical shiftppmδHHildebrand solubility parameterΜMPa1/2εrRelative permittivityζReciprocal of the friction coefficientηDynamic viscositymPa s−1θAngle between two dipoles or three atoms°κSCompressibility, adiabaticGPa−1κTCompressibility, isothermalGPa−1ΛConductivity, molarΩ−1 m2 mol−1λiConductivity, ionic equivalentΩ−1 m2 mol−1λthConductivity, thermalW K−1 m−1μDipole momentC mμChemical potentialkJ mol−1νWave numbercm−1ξCorrelation lengthmπ*Kamlet–Taft polarity/polarizability indexρDensitykg m−3σDiameter, molecularnmτRelaxation or correlation timepsVolume fractionχNumber of H-bonds of any given water moleculeωFrequencys−1ωPitzer's acentric factor

Subscripts and Superscripts

*Pure substance or scaling parameter°Standard state∞Infinite frequency∞Infinite dilutionassAssociationcCriticalDDielectric or Debye, or self-diffusionEExcess thermodynamic quantityfFormation (thermodynamic quantity)gGasigIdeal gasrReduced, divided by the critical quantityVVaporizationWWaterσSaturation (VLE equilibrium)

Chapter 1

Introduction

1.1 Phase Diagrams of Single Fluids

Substances appear in Nature in several states of aggregation: crystalline solids, amorphous solids, glasses, liquids, and gases. The latter two states are collectively termed “fluids” because they are subject to flow under moderate stresses (forces). A phase is a portion of space in which all the properties are homogeneous, that is, they do not depend on the precise location in the phase (except at its boundaries). Depending on the external conditions (thermodynamic states) of temperature and pressure, a substance may exist at several states of aggregation at the same time, each of which is represented as a different phase. These phases may be at equilibrium with each other, and the phase diagram, in terms of the external conditions of the temperature and pressure, represent which phases are at equilibrium with each other. These phase equilibria have several important features, governed by the phase rule of Gibbs. This rule states that number of degrees of freedom (Df) in a system is equal to 2 plus the number of components (Co) minus the number of phases that exist at equilibrium (Ph):

(1.1)

The degrees of freedom of interest in the present context are the external conditions that can be independently chosen: the pressure P, the temperature T, and the composition of mixtures. When the latter are expressed as the mole fractions of the components: x1, x2, . . ., xN for an N-component mixture, there are N − 1 independent composition variables. A component is a substance that can be added independently: water is an example of a component and a salt, such as NaCl, is another example, but each of their constituent ions (H+ or H3O+, OH−, Na+, Cl−) is not. Only neutral combinations of the ions can be considered as components, since they can be actually handled.

For a single substance Co = 1 and up to three phases can exist at equilibrium, in which case Df = 0, there remain no freely determinable external conditions (no degrees of freedom): the temperature and pressure are fixed. This invariant point (involving a solid, a liquid, and their vapor) is called the triple point of the substance. In the case of water: ice, liquid water, and water vapor are at equilibrium at 0.01°C (T = 273.16 K) and P = 0.61166 kPa [1].

Two phases of a single component at equilibrium permit according to the phase rule (1.1) a single degree of freedom: either the temperature is variable and the pressure is then fixed or for a variable pressure the temperature is fixed. This simple function determines a line in the two-dimensional phase diagram. For the water substance, at temperatures below freezing several phases of ice exist, depending on the pressure, and a pair of which can exist at equilibrium along the lines of the relevant phase diagrams. Ice may sublime to form water vapor, and again the two phases may exist at equilibrium along the sublimation line of the phase diagram of water. These aspects of the phase diagram of water are outside the scope of this book. The phase diagram of water is shown in Fig. 1.1, the phase boundaries being the coexistence lines of two phases at equilibrium. The phase diagram of water at very low temperatures and very high pressures is complicated by the existence of several ice phases of different densities and structures (not shown in Fig. 1.1), but these are of no concern in the present context.

Figure 1.1 The phase diagram of water: point corresponds to the triple point (ttr = 0.01°C, Ptr = 0.611 kPa), point to the melting point (tm = 0°C, Pm = 101.3 kPa), point to the normal boiling point (tb = 100°C, Pb = 101.3 kPa), and point to the critical (tc = 374°C, Pc = 22.1 MPa). The line between and is the saturation line, P = pσ. Various compressed ices exist above point that are of no concern in the present context.

When attention is drawn toward fluid phases, vapor–liquid equilibria (VLE) constitute a very important subject. Again, in such two-phase systems the feature of the phase diagram of water is a line, called the saturation line for VLE, and is designated by the subscript (σ). This line for water is shown in Fig. 1.1, extending from the triple point up to the critical point (see below). The fact that the normal boiling point of water at ambient pressure (1 atm = 1.01325 bar = 101.325 kPa) happens to correspond to 100°C (373.15 K), is incidental in this respect. Wagner and Pruss reported the IAPWS 1995 formulation for the thermodynamic properties of ordinary water substance [1] that appears still to be the last word on the subject. The expression for the saturation vapor pressure pσ(T) takes the following form:

(1.2)

where Pc is the critical pressure and τ = 1 − T/Tc, with Tc being the critical temperature. The values of Pc, Tc, and the coefficients ai (i = 1–6) are shown in Table 1.1.

Table 1.1 Parameters for the Saturation Vapor Pressure of Water, Eq. (1.2)

Numerical values of pσ at several temperatures are shown in Table 1.5 along with data for other properties of liquid water discussed in Section 4.

A supercritical fluid (SCF) consists of a single phase and since Co = Ph = 1 it has two degrees of freedom according to Eq. (1.1). Its temperature and the pressure can be chosen at will, provided they are larger than the critical values (see below).

1.2 The Critical Point

As the temperature and pressure of a fluid increase, a point is reached where the two phases, the liquid and the vapor, coalesce into a single phase. The density of the liquid diminishes along the saturation line whereas that of the vapor increases as its pressure increases, until finally they become equal at the critical point. This is characterized by a critical temperature Tc, a critical pressure Pc, and a critical density ρc. A liquid that is confined in a vessel in a gravitational field has a free surface with respect to its vapor, hence, being denser, lies below it. However, at the critical point the meniscus that is characteristic of this surface disappears. Slightly below Tc the fluid becomes opalescent because of the fine dispersion of minute droplets of the liquid in the vapor of almost the same density. At temperatures and pressures above the critical ones, T > Tc and P > Pc, the substance exists as a single clear phase, the supercritical fluid. According to the phase rule, Eq. (1.1), the supercritical fluid has two degrees of freedom, and the temperature and pressure can be chosen at will. These two external variables determine the properties of the supercritical fluid, such as its density, heat capacity, viscosity, relative permittivity, among many others, as are dealt with for the supercritical water (SCW) substance in Chapter 2. The critical temperature of water is Tc = 647.096 K = 373.946°C and its critical pressure is Pc = 22.064 MPa = 21.78 atm (cf. Tables 1.1 and 1.3). The critical density of water is ρc = 322 kg m−3 and its critical molar volume is Vc = 56.0 × 10−6 m3 mol−1, the latter two quantities being known to no better than ±1%.

For many purposes, and especially for the description of the properties of supercritical fluids, it is expedient to use the reduced variables: the reduced temperature, Tr = T/Tc, the reduced pressure Pr = P/Pc, the reduced density ρr = ρ/ρc, or the reduced molar volume Vr = V/Vc. In the vicinity of the critical point there are some general relationships that depend on the deviation of the temperature from the critical point: τ = 1 − Tr. As the critical point is approached from below (τ > 0) the enthalpy of vaporization tends to zero and the heat capacity of the system tends to infinity according to the proportionality relationship

(1.3)

The dependence of the density difference between the liquid and vapor phases on τ is according to Eq. (1.4):

(1.4)

The compressibility of either phase depends on the temperature as

(1.5)

At τ = 0 (at the critical point) the reduced pressure depends on the reduced density as

(1.6)

These proportionalities are described by means of the critical indices, the commonly accepted theoretical values for them being α ≈ 0, β = ½, γ = 1, and δ = 3, assumed to be universal. However, for specific substances the values of these indices differ from the universal ones, as is the case for water (Section 5).

The densities of the liquid and vapor phases of a substance approach each other as the critical point is approached. The mean specific volume along the saturation curve is a linear function of the temperature, a nearly perfect experimental fact called the “law of rectilinear diameters”:

(1.7)

The value of the temperature coefficient b is generally small and negative, the a and b values for water are presented in Section 5.

1.3 Supercritical Fluids as Solvents

Supercritical fluids have been proposed as solvents for many uses, both in the laboratory and industrially. Their properties as solvents are, therefore, of interest. The following comparison with gases and liquids (Table 1.2) are illuminating in this respect.

Table 1.2 Comparison of the Property Ranges of Supercritical Fluids with those of Gases and Liquids at Ambient Conditions.

Supercritical fluids have an advantage over ordinary gaseous fluids for many applications in having much higher densities, and an advantage over ordinary liquids in having lower viscosities and considerable higher diffusivities. SCFs are well integrated in the modern tendency toward “green” solvents for reactions and separations that are ecologically friendly. They can be employed as reaction media, for extraction, separation, and purification, and for drug formulations, among other uses. In addition to being “green,” they are tunable, so that their properties can be varied at will. The solvent power of supercritical fluids can be fine-tuned by adjustment of the temperature and pressure, hence of the density. This gives them some advantage over common solvents used at ambient conditions, although the solvent power of the latter can be tuned by mixing with cosolvents, as can also be done for SCFs, of course.

Table 1.3 reports the critical temperature, Tc, the critical pressure, Pc, and the critical density, ρc, of substances of interest in the present context.

Table 1.3 The Critical Points of Some Substances, Together with their Critical Densities, ρc

The general mode of the application of SCFs is by dissolution of the reactants or the materials to be separated in them, carrying out the reaction and separation, and then recovering the products by either one of two techniques. One is by rapid diminution of the pressure, allowing the rapid expansion of the supercritical solvent (RESS technique) and eventual formation of the gaseous solvent (for recovery) leaving liquid or solid products behind. The other is the addition of an “antisolvent” that diminishes the solubility of the product in the SCF.

Following are some examples of the uses of SCFs as solvents.

Synthesis: Diels–Alders reactions in supercritical water; polymerization of methyl methacrylate in supercritical difluoromethane; phase transfer catalysis by tetraheptylammonium bromide in supercritical carbon dioxide (SCD) modified with acetone.Pyrolysis: Conversion of biomass to fuel; complete oxidation of obnoxious materials in SCW (Chapter 5).Separations: Recovery of fat-soluble vitamins by SCD; delipidation of protein extracts; as chromatographic eluents in forensic analysis; fractionation of mono-, di- and triglycerides.Small Particle Formulations: Drug particle design, for example, for inhalable insulin; powder drying; microencapsulation.

An important issue for the use of SCFs is their solvent power. One way to describe this is in terms of the linear solvation energy relationship for a series of solutes in a given solvent or of a given solute in a series of solvents:

(1.8)

Here xsolute is the mole fraction of the solute in the saturated solution, Vsolute is its molar volume, and , αsolute, and βsolute are its Kamlet–Taft solvatochromic parameters, dealing with its polarity/polarizibility, hydrogen bond donation (or electron pair acceptance) ability, and hydrogen bond acceptance (or electron pair donation) ability [2]. The parameters p, q, s, a, b, and v characterize the SCF, the latter four depending on the reduced density, ρr. The parameter v is generally negative, solute solubilities decrease with increasing solute molar volumes. Some SCFs are apolar (e.g., SCD), that is, they are incapable of acceptance and donation of hydrogen bonds (or electron pairs), hence have a = b = 0 and their s values may be near zero or negative. Others are dipolar aprotic (like acetone) with b = 0 but have positive values for a and s, and still others are protic (like water and methanol) and have also b > 0, being capable of both acceptance and donation of hydrogen bonds.

Another way to describe the solvent power of an SCF is by means of its (Hildebrand) solubility parameter, δH[3]. For solute/solvent systems with small solute solubilities, the following expression

(1.9)

is valid. Conformal fluids, that is, SCFs conformal with a reference fluid, generally interact through central forces of the van der Waals type. Their solubility parameter can be expressed by

(1.10)

They depend on the temperature and pressure mainly through the dependence of the reduced density, ρr. The solubility parameters of the solutes are available from group contributions and are assumed to be rather independent of the temperature and pressure for estimation of the solubility via Eq. (1.9). A difference δH SCF − δH solute > 4 MPa1/2 represents a low solubility of the solute. However, water is not a conformal fluid, since it interacts by dipole and hydrogen bonding interactions beyond the van der Waals ones. Its solubility parameter is discussed in Section 2.6 and the resulting expression, Eq. (2.42), differs from Eq. (1.10).

The best-known and most widely employed supercritical fluid is SCD, used industrially on a large scale for the decaffeination of coffee. It has convenient Tc and Pc values: 30.9°C (304.1 K) and 72.4 atm (7.34 MPa), is environmentally friendly (its industrial contribution to the greenhouse gas inventory is negligible compared to that resulting from the burning of fossil fuels), is nonflammable, nontoxic (at low concentrations), and noncorrosive to common structural materials, and is cheap. Its main drawback is its low solvent power, the solubility of polar substances in it is rather small and even nonpolar substances are not very soluble in SCD. This situation can be ameliorated by the addition of modifiers, such as methanol, but a detailed discussion of SCD, its properties and uses, is outside the scope of this book.

Supercritical water has properties differing considerably from those of SCD; for some recent reviews, see Refs [4, 5]. Its critical (absolute) temperature is twice and its critical pressure almost three times those of SCD; its ranges of application are about 400–600°C and 30–100 MPa. Thus, although nontoxic, nonflammable, and environmentally friendly it involves certain technical difficulties in view of these high temperatures and pressures, and mainly also corrosion problems. Applications of SCW and problems involved with them are fully discussed in Chapter 5. Here the solvent powers are only mentioned, these being fully discussed in Chapter 4: SCW retains the hydrogen bond donation and acceptance abilities of the water molecule, and its relatively low permittivity permits dissolution of nonpolar solutes.

1.4 Gaseous and Liquid Water

Before going on to the properties of supercritical water, it is expedient to survey briefly the properties of water in the gas phase, as individual molecules and clusters, and in the liquid phase, in the latter case along the saturation curve (Fig. 1.1). Some of the properties of individual water molecules [6, 7], both H2O and D2O, are shown in Table 1.4. These properties are manifested when the water molecules are present at low pressures in the ideal gaseous state, where PV/RT = 1.

Table 1.4 Some Molecular Properties of (Light) Water, H2O and Heavy Water, D2O.

PropertyH2OD2OMolar mass, M/kg mol−10.0180150.020031O–H(D) bond length, dpm95.7295.75H–O–H angle, °104.523104.474Moment of inertia,aIA10−30 kg m−20.102200.18384Moment of inertia,aIB10−30 kg m−20.191870.38340Moment of inertia,aIC10−30 kg m−20.293760.56698Hydrogen bond length, dpm276.5276.6Dipole moment, μDb1.8341.84Electrical quadrupole moment, Θ10−39 C m21.87Polarizability, α10−30 m31.4561.536Collision diameter, σpm274Potential energy minimum, (u/kB)K732O–H(D) bond energy at 0 K, EkJ mol−144.77Proton (deuteron) affinity, EkJ mol−1762c772cSymmetrical stretching frequency, ν1cm−13656.652671.46Asymmetrical stretching frequency, ν3cm−13755.792788.05Bending frequency, ν2cm−11594.591178.33Zero point vibrational energy, kJ mol−155.31d40.44dIdeal gas heat capacity, J · K−1 · mol−133.584Ideal gas entropy, SigJ K−1 mol−1188.67a The moment of inertia IA pertains to rotation round the O–H bond and IB pertains to rotation round the axis through the oxygen atom, and IC pertains to rotation round an axis perpendicular to the latter.b 1 D = 3.33564 × 10−30 C m.c From Ref. [45].d From Ref. [46].

The nonideality of water vapor (gaseous water) at nonnegligible pressures can be expressed in terms of the compressibility factor Z and the virial expansion:

(1.11)

The temperature-dependent Bi are called the second, third, and so on, virial coefficients. The experimental B2 values from 50 to 460°C are expressed by [7]

(1.12)

It is negative (−1059 cm3 mol−1 at 20°C) but becomes less so as the temperature increases (−292 cm3 mol−1 at 150°C and −105 cm3 mol−1 at 325°C). Values of the third virial coefficient of water are less well known, B3 is zero at <150°C, it is about −5.9 × 104 cm6 mol−1 at 150°C and changes sign near 300°C [8].

Water in the gaseous phase, unless at very low pressures, tends to associate to dimers, trimers, and larger clusters. The clustering to dimers and higher oligomers can be regarded as an interpretation of the nonideality of the water vapor expressed by Eq. (1.11). Rowlinson [9] derived the equilibrium constant for the association of water molecules to dimers in terms of the partial pressures of the species as

(1.13)

This corresponds to a (temperature independent) enthalpy of dimerization of −23.9 kJ mol−1 and would lead to the presence of a mole fraction of 0.04 for the dimers at the critical point [7]. Less negative enthalpies of dimerization were consistent with the speed of ultrasound, −15.4 ± 8.7 kJ mol−1[10] and values varying from −16.3 kJ mol−1 at 0°C down to −11.4 kJ mol−1 at the critical point were derived from computer simulations by Slanina [11]. However, a more recent estimate by Sit et al. [12] of the binding energy of the dimer is −22.8 kJ mol−1. A consequence of the uncertainty in the dimerization enthalpy is an uncertainty in the mole fraction of the dimer as pressure and density of the vapor (and the temperature) increase along the saturation line. The increased total pressure should enhance the dimerization, and mole fractions of xdim = 0.276 and xtrim = 0.006 have been estimated by Slanina [13] for the dimer and trimer at the critical point.

The pressure dependence of the integrated infrared absorption intensities of the stretching modes ν1 + ν3 of water vapor (3200–4200 cm−1) at 300–450°C and up to 8 MPa is consistent with a low content of dimers. The resulting dimerization enthalpy −16.7 ± 3.8 kJ mol−1 [14] is within the range of the values quoted above.

The Raman spectra of saturated water vapor were measured by Walrafen et al. [15], showing an isosbestic point at 3648.5 cm−1 as the temperature is increased. Frequencies above this point are considered due to monomeric water, those below it, their intensities being proportional to the square of the density, are considered due to the dimers. A much higher mole fraction of dimers at the critical point results from the Raman data, namely xdim = 0.696. This interpretation was subsequently withdrawn by the authors [16], since the resulting enthalpies of dimerization had the wrong sign. The two-species equilibrium suggested by the isosbestic point was attributed to low and high rotationally excited monomeric water molecules. This does not explain the proportionality of the low frequency Raman intensities to the square of the pressure (density), however.

Dimers are not considered to contribute appreciably to the infrared absorption of dilute water vapor in the atmosphere, whereas large clusters of, say, 30 molecules do [17]. These are of consequence to cloud formation and consist of multihydrated hydrogen and hydroxide ions: H(H2O)n+ and HO(H2O)m−, or even the neutral ion pairs or zwitterions H+(H2O)pOH−. Clusters of water around other ions are found by mass spectrometry. A further consideration of these entities, important for cloud formation, is outside the scope of this book.

Turning now to liquid water along the saturation line, some of the relevant properties are collected in Table 1.5.

Table 1.5 Some Properties of Liquid Water Along the Saturation Line.

Several features of the property changes of the liquid water with increasing temperatures and diminishing densities, ρ, along the saturation line should be noted. The relative permittivity, εr, the dynamic viscosity, η, the surface tension, γ, and the molar enthalpy of vaporization, ΔVH, diminish steadily as the temperature is increased. On approaching the critical point, say above 300°C, they fall rather abruptly, the latter two quantities, γ and ΔVH vanishing at the critical point. On the other hand, the constant pressure molar heat capacity, CP, and the isothermal compressibility, κT, have a shallow minimum near 33 and 46°C, respectively, but increase with the temperature, diverging to infinity at the critical point.

Several derived quantities are of interest; for instance, the temperature and pressure derivatives of the relative permittivity have been reported by Fernandez et al. [18]. These yield according to Bradley and Pitzer [19] the limiting slopes for the Debye–Hückel theoretical expressions for the osmotic and activity coefficients and the apparent molar enthalpies and volumes of electrolytes in water up to 350°C along the saturation line as well at higher pressures. The complex permittivity of water was measured by Lyubimov and Nabokov [20, 21] up to 260°C along the saturation curve. The derived relaxation times decrease steadily from 5.82 ps at 40°C to 0.75 ps at 260°C. The corresponding values for heavy water, D2O, are 25% to 12% larger.

Other derived quantities include the isobaric expansibility, αP, or the pressure derivative of the compressibility itself (the second pressure derivative of the density), the isochoric (constant volume) molar heat capacity, CV, and the speed of sound, u. These are to be found in the Steam Tables and they can be derived from the equation of state as presented most recently by Wagner and Pruss [1]. The internal pressure, Pi = TαP/κT − pσ, has a maximum of 758 MPa near 172°C, diminishing to 473 MPa at 360°C. The cohesive energy density (ΔVH° − RT)/V decreases steadily from 2357 MPa at 0°C to 1653 MPa at 172°C to 236 MPa at 360°C. A liquid is deemed structured (“stiff”) when the cohesive energy density is larger by ≥50 MPa than the internal pressure, as suggested by Marcus [22]. Since there is a crossover between these two dependencies by 328°C, liquid water above this temperature is no longer “stiff” according to this criterion.

An interesting derived quantity is the Kirkwood–Fröhlich dipole orientation parameter g, which reflects the association of the water molecules in the liquid. For a coordination number Nco (the number of nearest neighbors), obtainable experimentally from diffraction of X-rays or neutrons, g describes the average angle, θij, between the dipoles of neighboring water molecules i and j:

(1.14)

The values of g are obtained from the measured relative permittivity according to

(1.15)

Here ε0, kB, and NA are the universal constants, M is the molar mass of water, ρ is its density (M/ρ is its molar volume, V), μ is its permanent dipole moment (Table 1.4), and ε∞ is the infinite frequency permittivity, equal to the square of the infinite frequency refractive index, . The latter quantity is obtained from the polarizibility of water, α (Table 1.4) according to the Lorenz–Lorentz relation as

(1.16)

where B = 4πNA/3. The values of g, shown in Table 1.5, are calculated according to the polynomial reported by Marcus [22]. The g values >1 show that water is associated as a liquid, though to a diminishing extent as the temperature rises. The average angle, with an assumed (not much temperature dependent) coordination number Nco = 4, increases from 61.6° at 25°C to 78.3° at 200°C and 78.6° at the critical point, showing some alignment of the dipoles even at these high temperatures (an angle of 90° corresponds to no correlation between the dipoles and to no association).

The structuredness of water has been explored by the present author [22] in terms of several measures. One of these is the ratio of the difference of the standard molar Gibbs energies of condensation of light and heavy water to the difference in the hydrogen bond energies of these two kinds of water. The resulting average number of hydrogen bonds per water molecule diminishes from 1.34 at 5°C to 0.30 at 305°C, but there are several difficulties with this interpretation of the structuredness, as discussed in the cited paper. The heat capacity density of liquid water relative to its ideal gas is another measure of the structuredness. It changes only slightly, from 2.37 to 2.20 J/K−1 cm−3 from 0 to 200°C, and remains considerably higher than for unstructured liquids, for which it is 0.6 J/K−1 cm−3. The entropy deficit of liquid water relative to its vapor (corrected for association of the latter) and normalized with regards to this quantity for the unstructured methane, ΔΔVS°/R, changes more from 8.35 at 0°C to 6.93 at 200°C and to 6.06 at 360°C, again being much larger than for unstructured liquids, for which it is 2.0. That is, water is “ordered” according to this criterion. This measure of structuredness is quite well proportional to the dipole orientation parameter through the relevant temperature range: (ΔΔVS°/R)/g = 2.83 ± 0.15, both measures pertaining to the “order” in the liquid water [22].

Another quantity of interest is the ionic dissociation constant of the water, or rather the ion product KW = [H3O+][OH−]. The recent evaluation of Chen et al. [23] let to the values of pKW (for KW on the (mol kg−1)2 scale) shown in Table 1.5. This reference provides also values for the enthalpy, entropy, heat capacity and volume changes for the ionization of water at its saturation pressure. Note that pKW decreases (ionization increases) as the temperature increases up to 250°C and increases again (ionization decreases) somewhat beyond this temperature.

Spectroscopic studies of liquid water along the saturation line reveal some interesting aspects. The overtone band of HOD shows features at 7000 and 7150 cm−1, attributed by Luck [24] to nonhydrogen bonded water molecules, a band at 6850 cm−1 attributed to weakly cooperative hydrogen bonded molecules, and one at 6400 cm−1 attributed to strongly cooperative hydrogen bonded molecules. As expected, the latter diminish sharply from 52% at 0°C to 7% at 230°C and remain near that level up to 350°C. On the other hand, the nonhydrogen bonded molecules increase from 10% at 0°C rather steadily to 65% at 350°C. The NMR chemical shifts δ were measured by Tsukahara et al. [25] in pressurized water (30 MPa) from 25°C up to and beyond the critical point. The values of δ/ppm vary substantially linearly from −1 at 25°C to −18 at 350°C and the deduced extent of hydrogen bonding, relative to that in ambient water, η, is linear with it: η = 1 + 0.0274(δ/ppm), thus diminishing to 0.51 at 350°C. The deduced reorientation relaxation times diminish sharply from 2.9 ps at 25°C to 0.6 ps at 100°C and then more gently to 0.1 ps at 350°C. These values may be compared with the dielectric relaxation times reported above.

Thermodynamic properties of heavy water, D2O, along its saturation line have been reviewed and compared to those of light (ordinary) water, H2O, by Hill and MacMillan [8] up to 325°C. The data shown are the liquid and vapor volumes (densities) and enthalpies and the specific heat of the liquid. Note that the critical point of D2O is lower than that of H2O by 3.21 K (Table 1.3).

As mentioned in Section 3, solvatochromic parameters can be used to predict the solubility of solutes in solvents according to Eq. (1.8). Lu et al. [26] reported plots of the Kamlet–Taft π*, α and β solvatochromic parameters as well as those of Reichardt's ET(30) polarity index in water along the saturation line up to 275°C. One of these parameters, π* that describes the polarity/polarizibility of the solvent, measured by means of the solvatochromic indicator 4-nitroanisole, is linear with the density of the water. Its temperature dependence curve is concave downward (π* diminishing from 1.09 at ambience to 0.69 at 275°C), whereas that of the hydrogen bond donation parameter α is concave upward (diminishing from 1.19 at ambience to 0.84 at 275°C). The hydrogen bond acceptance parameter β (for monomeric water) varies little up to 100°C, then increases by some 30% up to 150°C and remains more or less at this value up to 275°C. The polarity index ET(30) decreases linearly from 63 kcal mol−1 (264 kJ mol−1) at ambience to 53 (222 kJ mol−1) at 275°C. In pressurized (40 MPa) high temperature water [27] (up to 420°C, i.e., beyond the critical point), the values of π* were again linear with the density of the water, π* = 1.77ρ − 0.71 up to 360°C. If the pressure dependence of π* for the liquid is assumed to be negligible, the result is π* = 0.980 + 7.12 × 10−4(t /°C) − 7.40 × 10−6(t /°C)2 for water along the saturation line. The alternative probes, 4-nitro- and 4-cyano-N,N-dimethylaniline yield values consistent with these for liquid water.

1.5 Near-Critical Water

There is no clear definition of “near-critical” water, but most publications tend to use this epithet for pressurized hot liquid water at temperatures 300 ≤t /°C ≤ 375. Near-critical water has been proposed as an environmentally benign medium for chemical reactions [28, 29], biomass decomposition [30] and gasification [31], or preparation of inorganic nanoparticles [32], to cite at random some recent applications.

As the critical point is approached the differences in properties between the liquid and the vapor diminish, the fluid becomes opalescent due to the minute dispersion of liquid-like and vapor-like domains, and the meniscus separating the liquid from the vapor vanishes at the critical point. There remaining no free surface at the critical point, the surface tension γ vanishes, and since no energy is needed to convert the liquid to its vapor (these states being identical) also the enthalpy of vaporization, ΔVH, vanishes and the heat capacities CP and CV diverge to infinity (Table 1.5). Still, the properties of water near the critical point, say within 1–5 K above and below it, have been studied intensively.

The law of rectilinear diameters, Eq. (1.7) applies to water as for other fluids. For water the values of the coefficients of the mean specific volumes are a = (61.6 ± 0.6) × 10−3 m3 kg−1 and b = (90.4 ± 1.0) × 10−6 m3/kg−1 · K−1 over a considerable range of temperatures: T ≥ 600 K up to the critical point. The critical density derived from this expression is the accepted value of 322 ± 3 kg m−3.

The critical indexes (see Section 2) are supposed to have universal values, but when actual P, ρ, and T (PVT) data for water very near the critical point, at τ = 1 − T/Tc 0.01 are used somewhat different values result: α = 0.11 (instead of ≈0), β = 0.34 (instead of 0.5), γ = 1.21 (instead of 1), and δ = 4.56 (instead of 3) [33]. A slightly different set was given earlier by Watson et al. [34]: α = 0.087, β = 0.335, γ = 1.212, and δ = 4.46. With these and 13 additional parameters the equation of state is established from τ = −0.002 to 0.118 within the experimental errors of the PVT data. Also, the sound velocity u and heat capacity CP data could be modeled well around the critical density. Considerably fewer parameters (only eight) are needed when the PVT data are modeled according to the three-site associated perturbed anisotropic chain theory (APACT), with a total mean deviation of 1% for the density and 2% for the pressure for −0.27 ≤ τ ≤ 1.97 [35].

Supplementary values for V(T, P