Introduction to Supercritical Fluids: A Spreadsheet-based Approach

By Richard Smith, Hiroshi Inomata and Cor Peters

This text provides an introduction to supercritical fluids with easy-to-use Excel spreadsheets suitable for both specialized-discipline (chemistry or chemical engineering student) and mixed-discipline (engineering/economic student) classes. Each chapter contains worked examples, tip boxes and end-of-the-chapter problems and projects.

Part I covers web-based chemical information resources, applications and simplified theory presented in a way that allows students of all disciplines to delve into the properties of supercritical fluids and to design energy, extraction and materials formation systems for real-world processes that use supercritical water or supercritical carbon dioxide.

Part II takes a practical approach and addresses the thermodynamic framework, equations of state, fluid phase equilibria, heat and mass transfer, chemical equilibria and reaction kinetics of supercritical fluids. Spreadsheets are arranged as Visual Basic for Applications (VBA) functions and macros that are completely (source code) accessible for students who have interest in developing their own programs. Programming is not required to solve problems or to complete projects in the text.

• Property worksheets/spreadsheets that are easy to use in learning environments
• Worked examples with Excel VBA Worksheet functions allow users to design their own processes
• Fluid phase equilibria and chemical equilibria worksheets allow users to change conditions, study new solutes, co-solvents, chemical systems or reactions

• Language: English
• Publisher: Elsevier Science
• Release date: Dec 8, 2013
• ISBN: 9780080931302

Richard Smith

Richard Smith wrote his PhD thesis on China’s economic reforms and has written extensively Chinese issues for New Left Review, Monthly Review, Real-World Economics Review, and Ecologist. He has also written essays collected in Green Capitalism: The God that Failed (2016) and in The Democracy Collaborative’s Next System Project (2017). Smith is also a founding member of the US-based group System Change Not Climate Change.

Book preview

Introduction to Supercritical Fluids

A Spreadsheet-based Approach

Volume 4C

Richard Smith

Tohoku University, Sendai, Japan

Hiroshi Inomata

Tohoku University, Sendai, Japan

Cor Peters

Petroleum Institute, Abu Dhabi, United Arab Emirates

SUPERCRITICAL FLUID SCIENCE AND TECHNOLOGY SERIES

Editor

Erdogan Kiran

Table of Contents

Cover image

Title page

Copyright

List of Examples

List of Tip Boxes

Foreword

Preface

Chapter 1. Chemical Vocabulary and Essentials

1.1 Philosophy of the Text

1.2 Organization of the text

1.3 Basic Words

1.4 Some Notes on Pressure

1.5 Chapter Summary

1.6  Suggested Reading and References

Chapter 2. Systems, Devices and Processes

2.1 Material, Energy, and Entropy Balances

2.2 Analysis of Devices and Processes

2.3 Practical Process I: Transcritical CO2 System for Heating Hot Water

2.4 Practical Process II: Flavor Extraction with Supercritical CO2

2.5 Practical Process III: Fine Particle Formation with Supercritical H2O

2.6 Chapter Summary

2.7  Suggested Reading and References

Chapter 3. Chemical Information and Know-How

3.1 Sources of Chemical Information

3.2 Chemical Property Databases

3.3 Chemical Property Databases: Nonreference Substances

3.4 Chemical Literature Databases

3.5 Bibliometrics

3.6 Chapter Summary

3.7  Suggested Additional Reading and References

Chapter 4. Historical Background and Applications

4.1 Historical Background

4.2 Characteristic Properties Common to All Supercritical Fluids

4.3 Extraction with Supercritical CO2

4.4 Commercial Food Products

4.5 Methods for Improving Yield and Modifying Selectivity

4.6 Dietary Supplements

4.7 Green Chemistry with Supercritical CO2

4.8 Polymer Synthesis

4.9 Separations

4.10 Characteristic Features of Water

4.11 Commercial Chemical and Waste Recycling Processes

4.12 Commercial Hydrothermal and Supercritical Oxidation Processes

4.13 Particle Formation

4.14 Coating and Film Deposition

4.15 Polymer Processing

4.16 Food Processing

4.17 Chromatography

4.18 Gas-Expanded Liquids (GXLs)

4.19 List of Companies Involved with Supercritical Fluids

4.20 Chapter Summary

4.21 References and Suggested Reading

Chapter 5. Underlying Thermodynamics and Practical Expressions

5.1 Introduction

5.2 Thermodynamic State Functions

5.3 Material, Energy, and Entropy Balances

5.4 Thermodynamic Systems

5.5 Basic Thermodynamic Relationships

5.6 Fugacity

5.7 Phase Stability

5.8 Practical Criteria

5.9 Practical Expressions

5.10 Chapter Summary

5.11. References and Suggested Reading

Chapter 6. Equations of State and Formulations for Mixtures

6.1 Overview

6.2 Calculation of CO2 Properties with Excel VBA Functions

6.3 Calculation of H2O Properties with Excel VBA Functions

6.4 Mathematically Simple EoS

6.5 Cubic EoS

6.6 Pure Component Fugacity from a Cubic EoS

6.7 Application of Cubic EoS to Mixtures

6.8 Modern Cubic EoS Formulations

6.9 Huron–Vidal Concept of Relating EoS Constants to Solution Models

6.10 Specialized EoS

6.11 Chapter Summary

6.12  Suggested References and Reading

Chapter 7. Phase Equilibria and Mass Transfer

7.1 Overview

7.2 Solid–Vapor Equilibria

7.3 Solid–Liquid–Vapor Equilibria

7.4 Vapor–Liquid Equilibria

7.5 Numerical Solution Method for VLE

7.6 Critical Points of Mixtures

7.7 Numerical Solution Method for Critical Points of Mixtures

7.8 Visualization

7.9 van Konynenburg and Scott Classification

7.10 Mass Transfer

7.11 Chapter Summary

7.12  Selected References and Recommended Reading

Chapter 8. Heat Transfer and Finite-Difference Methods

8.1 Overview

8.2 Heat Exchangers

8.3 Equations for the Heat Transfer Modes

8.4 Fluid Physical Properties

8.5 Analysis of Shell-and-Tube Heat Exchangers

8.6 Estimation of Heat Exchanger Area

8.7 Equations of Change

8.8 Chapter Summary

8.9 Selected References and Recommended Reading

Chapter 9. Chemical Equilibria and Reaction Kinetics

9.1 Overview

9.2 Thermochemistry

9.4 Le Châtelier's Principle

9.5 Calculation of Chemical Equilibrium

9.6 Chemical Reactors

9.7 Flow Reactor at Constant P

9.8 Reaction Enthalpy from an EoS

9.9 Reaction Kinetics

9.10 Partial Oxidation of p-Xylene in Supercritical Water

9.11 Chapter Summary

9.12  Suggested Additional Reading and References

Chapter 10. Conclusions and Suggestions for Further Study

10.1 Conclusions

10.2 Suggestions for Future Study

References and Suggested Reading

Appendices

Appendix A Guide to Visual Basic for Applications (VBA) in Excel

Appendix B Guide to Importing Data into 3D Grapher

Appendix C Partial List of Excel Worksheets

Index

Copyright

Elsevier

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The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK

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List of Examples

Chapter 1  Examples - Chemical Vocabulary and Essentials

1.1 Expansion of water in a 3-L thermo hot pot

1.2 Initial and final pressure of a vessel containing CO2

1.3 Determination of the mass fraction of a mixed phase system

1.4 Liquid contained in a compressed gas cylinder

1.5 Location of paths on P–T and P–ρ phase diagrams

1.6 Visualization of paths on phase diagram

1.7 Energy requirements for heating a batch reactor

1.8 Energy requirements for heating a batch reactor with phase change

1.9 Energy required to vaporize liquid CO2 from the T–S diagram

Chapter 2  Examples - Systems, Devices and Processes

2.1 Adiabatic mixing of streams at atmospheric pressure

2.2 Entropy generation and lost work for adiabatic mixing

2.3 Energy production from a turbine

2.4 Energy requirements and temperature rise for compressing liquid CO2

2.5 Energy requirements and temperature rise for compressing vapor CO2

2.6 Depressurization of CO2 through a control valve

2.7 Depressurization of CO2 through a valve into the two-phase region

2.8 Design of an air–water heat exchanger for hot water in the home

2.9 Design of a CO2 transcritical heat exchanger for making hot water

2.10 Design of an evaporator for liquid carbon dioxide

2.11 Solubility of paprika oleoresin in supercritical CO2

2.12 Design of a process for supercritical carbon dioxide extraction of paprika oleoresin

2.13 Fine particle products from Fe(NO3)3 in supercritical water

2.14 Mixing tee conditions for a supercritical water particle formation process

2.15 Space time for a supercritical water reactor

2.16 Increase of reactor space time with pressure for a supercritical water reactor

Chapter 3  Examples - Chemical Information and Know-How

3.1 Determine the chemical structure, SMILES formula, and basic physical properties of erythromycin

3.2 Estimate the sublimation pressure of erythromycin at 60 °C

3.3 Draw an editable chemical structure of erythromycin

3.4 Tabulate the thermophysical properties of CO2 at 60 °C from 0.0 to 30 MPa in 2 MPa increments

3.5 Locate some solubility data for the system CO2 and biphenyl

3.6 Determine whether solubility data have been reported for carbon dioxide and erythromycin

3.7 For dodecylbenzene, determine whether vapor pressure data exists

3.8 Determine the data that are available for 1-butyl-3-methylimidazolium chloride, [bmim][Cl]

3.9 Determine the data that are available for 1-butyl-3-methylimidazolium chloride, [bmim][Cl], as a binary mixture with CO2

3.10 Determine the most highly-cited research paper with the keyword supercritical fluids

3.11 Tracing a research thread

Chapter 4  Examples - Historical Background and Applications

4.1 Atom efficiency for hydrogenation of butyric acid

4.2 Assignment of phases in a ternary diagram

4.3 Binary component phase behavior from a ternary phase diagram

4.4 Determination of the phases present with a ternary phase diagram

4.5 Stream flow rates for a ternary system from the inverse lever rule

4.6 Stream flow rates for a feed stream that has a composition in the three-phase region

4.7 Solvent-to-feed ratio and deasphalted oil flow rate for a residuum

Chapter 5  Examples - Underlying Thermodynamics and Practical Expressions

5.1 Calculation with departure functions and residual functions

5.2 Determination of vapor (V) and liquid (L) exiting a separator

5.3 Application of material, energy and entropy balances to a supercritical extraction apparatus

5.4 Show the phase equilibrium relationships for a pure system that has vapor and liquid phases

5.5 Show the phase equilibrium relationships for a two-component (binary) system that has vapor and liquid phases

5.6 Calculation of the Gibbs energy of mixing

5.7 Calculation of the Gibbs energy of mixing

5.8 Phase equilibrium criteria in terms of the fugacities

5.9 Phase equilibrium criteria at low (atmospheric) pressure for (i) an ideal solution and for (ii) a nonideal solution represented by an excess Gibbs energy model

5.10 Calculation of phase equilibria from excess Gibbs energy expressions and analysis of stability

Chapter 6  Examples - Equations of State and Formulations for Mixtures

6.1 Span and Wagner EoS nonanalytical term

6.2 Gibbs energy of saturated liquid and vapor phases of CO2

6.3 Reduced critical isotherm of water and CO2 with reference equations

6.4 Compressibility of CO2 with a virial equation of state

6.5 Virial coefficients from the van der Waals equation of state

6.6 Critical isotherm of CO2 with equations of state using Excel VBA functions

6.7 Subcritical isotherm with the Peng-Robinson equation of state

6.8 Determination of vapor pressure graphically with the Peng–Robinson EoS

6.9 Program for solving the Peng-Robinson equation with Deiter’s method

6.10 Phase boundary of CO2 with the Peng–Robinson equation of state

6.11 Spinodal curve of the Peng–Robinson equation of state

6.12 Molar volume of a mixture with the Peng–Robinson equation of state

6.13 Fitting of the Peng–Robinson equation of state to mixture density data

6.14 Peneloux volume translation for the Peng–Robinson equation of state

6.15 Peneloux volume translation for solid–vapor equilibria (SVE) or solid–liquid–vapor equilibria (SLVE)

6.16 Fitting of the volume–translated Peng–Robinson equation of state (VTPR EoS) to saturation data

6.17 Equation of state constants with the Huron–Vidal concept of infinite pressure

6.18 Gibbs energy of mixing for SRK EoS with Huron–Vidal mixing rules

6.19 Equation of state constants from excess Gibbs energy models

6.20 Densities of the Sanchez–Lacombe equation of state (SL EoS)

6.21 Saturation properties of n–heptane with the Sanchez–Lacombe equation of state

6.22 Intermolecular potential function that includes short-range highly directional hydrogen bonding

6.23 Supercritical isotherm of CO2 with the pc-SAFT equation of state

Chapter 7  Examples - Phase Equilibria and Mass Transfer

7.1 Solubility of naphthalene in CO2 at atmospheric pressure

7.2 Conversion of the units and base of a sublimation pressure equation

7.3 Solubility of naphthalene in supercritical CO2 with the Peng–Robinson equation of state

7.4 Solid-liquid-vapor equilibrium (SLVE) curve of the biphenyl – carbon dioxide system with the Peng–Robinson equation of state

7.5 Solubility of naphthalene in supercritical CO2. with co-solvents with the Peng–Robinson equation of state

7.6 Solubility of biphenyl in supercritical CO2. with toluene co-solvent with the Peng–Robinson equation of state

7.7 Vapor-liquid equilibrium of the CO2. – toluene system with the Peng-Robinson equation of state

7.8 Vapor-liquid equilibrium of the CO2. – biphenyl system with the Peng-Robinson equation of state

7.9 Fitting of equilibrium data of the CO2. – biphenyl system with the Peng-Robinson equation of state

7.10 Critical locus of the CO2 (1) – toluene (2) system

Chapter 8  Examples - Heat Transfer and Finite-Difference Methods

8.1 Selection of heat exchanger type for supercritical fluid processes

8.2 Temperature profiles in heat exchangers

8.3 Determination of the log mean temperature

8.4 Pseudocritical line

8.5 Prandtl number for CO2 and H2O in the supercritical critical region

8.6 Expression for the overall heat transfer coefficient

8.7 Equations for determining wall temperature

8.8 Determination of wall temperature during heating of CO2 to supercritical conditions

8.9 Determination of wall temperature during heating of CO2 to supercritical conditions with correction for viscosity at the wall

8.10 Comparison of equations to calculate Nu number

8.11 Nusselt number from the Krasnoshchekov and Protopopov (KP) correlation

8.12 Co-current heat exchanger area for heating a supercritical fluid

Chapter 9  Examples - Chemical Equilibria and Reaction Kinetics

9.1 Gas-phase formation of ammonia

9.2 Molar extent of reaction for ammonia formation

9.3 Heat of reaction for ammonia formation

9.4 Equation for the chemical equilibrium constant as a function of temperature

9.5 Equilibrium constant for ammonia formation

9.6 Functional form of contributions to the equilibrium constant

9.7 Determination of the molar extent of reaction in the synthesis of ammonia

9.8 Determination the molar extent of reaction in the synthesis of ammonia from a stoichiometric mixture of nitrogen and hydrogen at 200 °C and 400 °C at pressures from 0.1 to 30 MPa

9.9 Adiabatic reaction temperature of ammonia synthesis

9.10 Show how the temperature changes in the plug flow reactor of 9.9 along a path of Q = 0 from Tin to Tout

9.11 Ammonia cracking to produce hydrogen

9.12 Reaction and phase behavior for the hydroformylation of propene to produce butyraldehyde

9.13 Partial oxidation of p-xylene in subcritical and supercritical water

List of Tip Boxes

Chapter 1  Tip Boxes - Chemical Vocabulary and Essentials

#1 Chapter objectives

#2 The tip box

#3 Units and dimensions

#4 Common units definitions

#5 Types of systems

#6 Intensive and extensive properties

#7 Critical point of a pure substance

#8 Phase mass fractions

#9 Compressibility factor of a pure substance

Chapter 2  Tip Boxes - Systems, Devices and Processes

#1 Chapter objectives

#2 Steps for analyzing systems with balances

#3 Using excel workbooks

#4 Independent variables of devices and processes

#5 Heat exchangers

Chapter 3  Tip Boxes - Chemical Information and Know-How

#1 Chapter objectives

#2 How to use this chapter

#3 ChemSpider

#4 NIST Chemistry WebBook

#5 NIST Data Gateway

#6 Bibliometrics

#7 Tracing research threads with references and citations

#8 Self-citation

#9 Citations and downloads

Chapter 4  Tip Boxes - Historical Background and Applications

#1 Chapter objectives

#2 Seven essential points for extraction

#3 Product and by-product

#4 Steps for assigning phases on ternary diagrams

#5 Lever rule and inverse lever rule

#6 Ionic solubility in supercritical water

Chapter 5  Tip Boxes - Underlying Thermodynamics and Practical Expressions

#1 Chapter objectives

#2 Recommended texts

#3 State variables

Chapter 6  Tip Boxes - Equations of State and Formulations for Mixtures

#1 Chapter objectives

#2 Analytical and nonanalytical functions

#3 Mathematics of cubic Equation of State (EoS)

#4 Relating equation of state constants to virial coefficients

#5 Solution to a quadratic equation

#6 Heaviside's rule of partial fractions

#7 Deiters' method to solve cubic equations of state

#8 Maxwell's equal area rule

#9 Initial guess for vapor pressure Psat calculation for cubic EoS

#10 Yun's method for solving nonlinear functions without derivatives

#11 Returning multiple–values with excel VBA functions

#12 Compressibility factor of a mixture

#13 Assumptions of the Huron–Vidal concept for EoS mixing rules

#14 Sanchez–Lacombe equation of state parameter relationships

#15 Taylor and Maclaurin series

#16 Using integration tables in handbooks

#17 Application of L'Hôpital's rule to the Sanchez–Lacombe EoS

#18 Modified false position numerical method

#19 Useful texts on statistical mechanics and statistical thermodynamics

#20 Trends of the periodic table

#21 Blue shift, red shift and their meaning

#22 Using long function names in excel

Chapter 7  Tip Boxes - Phase Equilibria and Mass Transfer

#1 Chapter objectives

#2 Changing the units and base of an Antoine equation

#3 Step-by-step procedure for calculating solid-vapor equilibria (SVE)

#4 Several possible uses of the crossover region

#5 Step-by-step procedure for calculating solid-liquid-vapor equilibria (SLVE)

#6 Step-by-step procedure for calculating vapor-liquid equilibria (VLE)

#7 Topology of critical loci

#8 Step-by-step procedure for calculating critical points of mixtures

Chapter 8  Tip Boxes - Heat Transfer and Finite-Difference Methods

#1 Chapter objectives

#2 Log mean temperature difference (LMTD)

#3 Use of LMTD in heat exchanger design

#4 Thermal conductivity

#5 SAFETY FIRST

Chapter 9  Tip Boxes - Chemical Equilibria and Reaction Kinetics

#1 Chapter objectives

#2 Thermochemistry of reactions

#3 Bounds on the molar extent of reaction, X or Xlimit

#4 Heat of reaction at any temperature

#5 Using the molar extent of reaction, X

#6 Conversion, yield and selectivity

#7 Numerical solution of ordinary differential equations

Chapter 10  Tip Boxes - Conclusions and Suggestions for Further Study

#1 Chapter objectives

#2 Other texts in the series to explore!

Foreword

Erdogan Kiran, Series Editor

Blacksburg, Virginia

It is with immense pleasure that I finally introduce the book which was meant to be the first in our book series on Supercritical Fluid Science and Technology. It is now appearing as Volume 4 in the series. But I can state without any reservation and I am sure after seeing the book you will all agree that it has been worth waiting for.

This book entitled Introduction to Supercritical Fluids. A Spreadsheet-Based Approach written by Professors Richard Smith and Hiroshi Inomata of the Tohoku University, Japan, and Professor Cor Peters of Eindhoven University, The Netherlands, and the Petroleum Institute, Abu Dhabi, is unique in its format and coverage and, in my personal opinion, exceeds all expectations. It is comprehensive and thorough in its treatment of every topic, it is highly pedagogical in its approach and is extremely student-friendly in its style and format, and it is practical with clear examples and is moreover formulated in a manner that welcomes anyone with a basic science and engineering background to learn the fundamentals of supercritical fluid science and technology. The book will be an invaluable resource in the education of the next generation of scientists who through this book can readily develop a full understanding of the fundamentals and an appreciation of the present-day challenges to develop new ideas and lead to future advances in our understanding, along with potential new discoveries.

Those of us who have chemical engineering background will immediately recognize that there is something extraordinary about this volume. The enthusiasm and layout of this practically oriented volume is reminiscent of the spirit of the classical book Transport Phenomena by Bird et al., who presented a unified theoretical treatment that influenced many generations of chemical engineers. This volume in many ways brings together many practical facets of supercritical fluids and high-pressure phenomena within the context of the fundamentals of thermodynamics, transport, and kinetics as the basic pillars of this ever-expanding field of science and technology and places them in a modern format. This great achievement has been possible because of the admirable vision and commitment of Professor Smith and the immense and diverse research and teaching experience that he and his coauthors have brought to the table. Professors Smith, Inomata, and Peters have each been active in the field for nearly three decades or more and are immediately recognizable names.

The book starts with an introductory chapter that brings the reader up to speed in terms of terminology, basic physicochemical concepts, as well as the salient features and process pathway implications of pressure–density–temperature or temperature-entropy diagrams which are beautifully illustrated for carbon dioxide and water, and carbon dioxide- or water-based processes even if the reader may not have an engineering background.

Chapter 2 provides an excellent review of mass and energy balances as applied to closed and open systems with examples of variable-volume batch reactors, turbines and compressors, expansion valves, and heat exchangers as case studies, again with beautiful illustrations that help visualizations and illustrative problems that involve carbon dioxide or water as the working or process fluid. Among the worked-out examples are the design of a CO2 transcritical heat exchanger for making hot water, the design of a process for supercritical carbon dioxide extraction of natural materials, and particle formation in supercritical water.

Chapter 3 is devoted to sources of chemical information and available databases (governmental such as NIST; commercial such as Thermofluids; professional societies such as DIPPR, ChemSpider, or IUPAC databases) which I am sure will be extremely well received as it provides a rare compendium of such valuable information presented all together in one unit. This chapter provides all the links to access the information. Descriptions and the links to literature sources such as Web of Science, SciFinder, or Scopus and bibliographic information and patents are also provided along with illustrations of how to trace literature related to a topic and review citations.

Chapter 4 provides an excellent historical perspective of the supercritical fluids and supercritical fluid-based processes. This chapter provides extensive compilations of the commercial products and processes that employ near- or supercritical fluids. Classical processes, such as coffee or tea decaffeination and hops extraction, as well as more recent applications in municipal waste treatment, food processing, polymerizations, plastics recycling, polymer foaming, metal recovery from catalysts, particle formation, reactive processing, and hydrothermal synthesis are reviewed. This chapter also provides a listing of companies engaged in near- and supercritical fluid processing in 25 countries around the world from Austria to the United States.

Chapter 5 is an overview of the basic thermodynamics with a special focus on high-pressure properties, mixtures and phase equilibria, and stability. The concept of fugacity is elegantly introduced, and the fugacity calculations for vapor, liquid, and solids are illustrated in the clearest manner with phase diagrams that show the paths along which such calculations are carried out. I am sure you will all agree with me that these diagrams help to understand and demonstrate how these calculations are carried out without ambiguity. The stepwise calculation process integrated with the phase diagram is a clear illustration of the Poynting correction that one must consider for high-pressure calculations.

Chapter 6 provides the background and the utilization of various equations of state ranging from ideal gas to cubic equations of state such as the van der Waals or the Peng–Robinson, to lattice models such as the Sanchez–Lacombe, and to models based on statistical mechanics such as the SAFT equation of state and their modified forms. This chapter is rich with examples that use spreadsheet calculations. Illustrations are given on calculation and generation of P–V isotherms as well as assessment of the metastable regions and the calculation of the spinodal curve. The extension of the use of the equations of state to mixtures is presented in detail, with full discussions of the physical significances and the implementation of the mixing rules that are involved.

Chapter 7 is devoted to phase equilibria and mass transfer that are relevant to supercritical fluid-based processes with algorithms to calculate the solubility of selected solutes in fluids like carbon dioxide or carbon dioxide plus a cosolvent using selected equation of state models. This chapter is also rich with diagrams that are designed to help students to visualize phase boundaries and their importance in multiphase systems.

Chapter 8 provides a comprehensive look at heat transfer, and how the properties vary when working with supercritical fluids. Clear discussions are provided on the selection of the appropriate heat exchanger configurations for a given supercritical fluid process. This chapter describes how the properties such as density, viscosity, thermal conductivity, and heat capacity vary with temperature and pressure, and how these influence the dimensionless numbers such as the Prandtl number with examples drawn from carbon dioxide. A finite-difference method is used so that precise property variations can be considered in heat exchanger design with a simple method.

Chapter 9 is devoted to chemical equilibria and reaction kinetics. As in previous chapters, concepts are introduced in a systematic manner, using this time ammonia synthesis as a case study. How reaction pathway and phase equilibria are linked is illustrated for hydroformylation of propene in carbon dioxide as solvent. The importance of the critical locus and how it changes with reaction progress are clearly demonstrated. Examples are also drawn from reactions carried out in sub-or supercritical water.

Chapter 10 is a final chapter in which Professor Smith provides his summary of the topics that have been presented in the book and the authors’ perspectives on how students can further advance their understanding of this subject matter. The authors also offer their availability to provide further explanations and extend an invitation for suggestions for improvements.

Each chapter contains end-of-the-chapter problems and many chapters contain end-of-the-chapter projects. The text is accompanied by Microsoft Excel files that allow both casual and serious students and researchers to perform their own calculations on Windows or Mac machines to follow the examples or to explore new areas.

I do hope that you will share my enthusiasm on this volume and find it to be of great value in your future educational, research, or practical endeavors.

October 2013

Preface

Richard Smith

Sendai, Japan

The original concept for an introductory text on supercritical fluids was conceived some years ago by Erdogan Kiran, who imagined that it would be a pedagogical work with end-of-chapter exercises. After some time, I became involved in the project as the lead author. I invited Hiroshi Inomata, who is a close colleague of mine, to work with Cor and myself. All things considered, a great combination!

One of the ideas considered as an image for the final product was an example-based text that would complement authoritative monographs such as Supercritical Fluid Extraction by Mark McHugh and Val Krukonis, Dense Gases for Extraction and Refining by Egon Stahl, Karl-Werner Quirin and Dieter Gerard, The Chemistry and Technology of Supercritical Fluids (in Japanese) by Shozaburo Saito, Supercritical Fluid Extraction by Larry Taylor, and Gas Extraction by Gerd Brunner, but in truth the progress in the writing was exceedingly slow, as none of us had a clear idea on what the final product should look like or who would be its likely readers. Should the text cover our research areas and include end-of-chapter exercises or should it try to cover many topics and be broad? The tasks seemed endless!

Around the end of 2010, we had a 10-chapter outline for which there were text remnants of chemical information, history, thermodynamics, phase equilibria, and heat transfer with spreadsheet programs (Excel worksheets) for pure fluids and mixtures. The spreadsheet programs were used in special lectures to incoming fourth-year undergraduate students at Tohoku University and in a first-year graduate course on supercritical fluid engineering. At one get-together, Cor was fascinated by the Excel programs for CO2 and H2O, the simplicity of the function names, and the ease at which properties could be rapidly generated for many different sets of conditions. However, he said that he preferred the phase equilibrium programs of Michelsen (see Calculation Methods [CM1] in Chapter 5) because they just work and are fast. I agree and the present text tries to address some of those points. During this time, I was assigned to teach a problem-practice course in the Graduate School of Environmental Studies for students of mixed disciplines (economics, environmental, sociocultural, resource management). The students were mainly nonnative Japanese, nonnative English speakers, and about half of them had an engineering background. Challenging!

On a lazy Friday afternoon in March, it was snowing outside in Sendai and freezing cold. Doctoral and Master course students had completed their defenses and fourth-year undergraduate students would soon be submitting their research theses. Things were quiet. The Japanese academic year was coming to another close and the cycle would begin again in April, which is the springtime. I was working on the computer in my office at Tohoku University, on a sentence that didn’t seem to want to be written and then, an event happened that I believe that anyone in Japan will remember for the rest of their life. An abrupt 20-s (?) pre-earthquake building alarm sounded off that said unusually, Level 5 earthquake eminent. I went below the desk for protection—later finding that it was Level 6 for our area. Thankful to be alive!

A magnitude 9 earthquake struck 130 km off the coast of Aomori prefecture (38.0 long., 142.9 lat.) as shown in Fig. 1. For the next few minutes that seemed like an eternity, the floor, buildings, bridges, roads, anything, moved violently. After that, many events happened as the world knows. The reason for describing the above is to say a few things about the planned schedule and to try to express to readers that we feel that the text lacks a certain degree of continuity. Some examples and parts of the text were done previous to March 11. We’ll improve it in the future!

Figure 1 Great East Japan Earthquake, 11-March-2011. Date, time, and origin of earthquakes are shown in the first three columns of the table. The Japanese scale (0–7) is used to indicate the actual result on land, since many earthquakes that have high Richter-scale values do not always affect inhabited regions. All sea earthquakes have the potential to cause a tsunami. The first boxed value on 9-March-2011 is a possible slip. The second boxed value on 11-March-2011 is a possible slide for slip-sliding theories of earthquakes.

As we helped each other to recover, I resolved myself to finish the book project and decided to make some radical changes in the text and its management:

(i) tailor the text into two parts:

Part I: multidisciplinary instruction (Chapters 1–4)

Part II: specialized discipline instruction (Chapters 5–9)

(ii) design the text for use on portable digital devices such as those used for eBooks and use color extensively

(iii) use my coauthors for discussion and advice on topics rather than for the writing of topics in the text in an attempt to obtain better uniformity in the presentation that was still evolving.

Tip Box #1. Instruction to Multidisciplinary Classes

* Cover parts of Chapters 1 and 2

* Let students become familiar with using Excel

* Explain ρ, H, and S in simple terms as in locating points on an x–y graph

* Limit the instruction to one of the topics:

(i) Transcritical heat exchange (EcoCute)

(ii) Supercritical extraction

(iii) Supercritical hydrothermal synthesis

* Mix engineering and nonengineering students in a group project

In my experience, topic (i) works the best as students can propose many systems and study conditions based on environmental temperatures in their own countries.

In Part I, problems used in teaching multidisciplinary classes at Tohoku University associated with developing efficient hot-water heating systems with supercritical CO2 are introduced. This material is being taught to incoming graduate students who do not necessarily have an engineering degree and is given mainly in Chapters 1 and 2 of the text. In general, teaching can focus on the meaning of properties, with density being a property that is commonly understood among disciplines. Location of density on a phase diagram from a given set of conditions is important. Then, the method for locating the density on a phase diagram can be used to locate the energy variables, enthalpy and entropy on a phase diagram. In this way, students can develop confidence in evaluating the safety of a procedure or in determining the required energy for a process. After becoming comfortable with locating properties from conditions and with determining energy values, the projects give students the creative freedom to explore. The projects listed in Chapter 2 are only examples and the instructor should feel free to let student groups try something different with instructor guidance. Try something new to learn something new!

In Part II, problems used in special lectures given to incoming fourth-year undergraduate students at Tohoku University and in a first-year graduate students’ course in supercritical fluid engineering are introduced. Chapter 5 contains problems typically used for third-year undergraduate students’ chemical engineering fundamental practice. In one detailed example given, a calculation is performed by varying a constant on an excess Gibbs energy expression. Students will need guidance on determining an activity coefficient expression from an excess Gibbs energy expression, which is explained in any of the thermodynamic texts mentioned in the chapter. In the detailed example in Chapter 5 (Example 5.10), students are led to do a calculation that will produce incorrect results in one case. The original phase diagram problem (Example 5.10) is simplified and adapted from Classical Thermodynamics of Nonelectrolyte Solutions (1982) by van Ness and Abbott (see Example 6-27 that text) but our example uses the Gibbs energy of mixing to do an analysis, which is original to the problems used with our students and to this text. In our classroom implementation, we do not give the analysis, but allow students to make the incorrect calculations and to develop their own analysis with guidance. Try something the wrong way, to understand the right way! (Mark Twain: "A man who carries a cat by the tail learns something he can learn in no other way.")

Tip Box #2. Instruction to Specialized Discipline Classes (Chemical-Related Fields)

* Review supercritical technologies (Chapter 4)

* Give student groups of two the problem statement of Example 5.10 without its solution. The results and discussion will help to break the ice

* Review some problems from Chapter 1 with Excel

* Find data on a mixture and develop a sublimation pressure equation with methods in Chapter 3

* Develop any two projects in a semester:

(i) Supercritical extraction and solvent recycle (Chapters 2 and 7)

(ii) Phase equilibria of high-pressure systems and their topology in three dimensions (Chapter 7)

(iii) Transcritical cycle and detailed heat exchanger design (Chapters 2 and 8)

(iv) Synthetic chemistry (hydroformylation) under homogeneous conditions (Chapters 7 and 9)

In Chapter 6, many types of equations of state are described. We recommend to choose any of the simple cubic equations (Table 6.3) and let students plot them over the full mathematical range of molar volumes (−∞ ≤ V ≤ +∞) at given temperatures (T < Tc and T ≥ Tc) so that the relationship between pressure and volume can be clearly understood. Then, the relationship between pure component fugacity and volume can be seen. The method of Deiters (Chapter 6, Tip Box #7) is used in solving the cubic equations of state for a given temperature and pressure. Yun’s method (Chapter 6, Tip Box #10) is introduced as a highly unconventional method for solving nonlinear equations without derivatives. The pitfall of Yun’s method is the number of function evaluations required. Modified false position (Chapter 6, Tip Box #18) is introduced as a method convenient for functions that can be bracketed. A simple homotopy technique is used and is invaluable when solving problems in chemical equilibria (Chapter 9). Although application of equations of state to mixtures and fitting are covered in Chapter 6, the technique for developing expressions for the fugacity of a component i in a mixture is not covered. Rather, the thermodynamic relationships are given in Chapter 5 and the results are given in Chapter 6, namely the Peng–Robinson equation (Table 6.4) and Sanchez–Lacombe equation (Table 6.5). The instructor can choose to make development of the expressions for other equations of state a homework problem for cubic equations or a project for the pc-SAFT equation. For the pc-SAFT equation, only expressions for the compressibility factor are given. To understand it, plot it!

In Chapter 7, the calculation of solubilities, vapor–liquid equilibria, and gas–liquid critical points is introduced. Mass transfer is only given a cursory description and it is a weakness of this chapter that we hope to improve in the future. Successive substitution is the numerical method used for calculation of the solubilities and vapor–liquid equilibria, and the method of Heidemann and Khalil is used for the gas–liquid critical points. The calculations can be assembled into three-dimensional (3D) plots and we urge instructors to let students do so. Some premade ones are included with this text: (i) pure CO2, (ii) pure H2O, and (iii) CO2–biphenyl and others. Just about any software that can make engineering 3D plots can be used, but we have found that the Open GL program, 3D Grapher, to be fun and attractive because it allows real-time zooming, rotation, and the display of different traces including animation. Unfortunately, 3D Grapher is limited to Windows and the program has not been updated for quite a few years. So please consider that in the assignments. We are interested in software that can do the same provided that is simple and easy to use. Assemble it, to understand it!

In Chapter 8, detailed design of a supercritical fluid heat exchanger is shown. There are lots of combinations here, and with the Excel programs for pure component properties (CO2, H2O), the combinations are almost limitless. A finite-difference method is used for numerical solution, and Excel Goal Seek is used. There are other possibilities including the use of Solver according to instructor preference. When considering any of the processes discussed in Chapter 2, solvent recycle should be considered to examine energy use. Every calculation begins with a single step!

In Chapter 9, thermochemistry and chemical equilibria are introduced. Reaction kinetics is covered but is not linked to the chemical equilibria as a limitation of the text. The calculation method used to determine chemical equilibria is limited to a single chemical reaction that can contain practically any number of species but limited in the spreadsheet to 10 chemical species. Chemical reactions can be studied at just about any conditions with the spreadsheets, and in fact the adiabatic (Q = 0) reaction temperature of any reaction being studied in the laboratory should be calculated for safety. Safe experimentalists know the adiabatic reaction temperature for SAFE-T!

Tip Box #3. eBooks and MS Office

MS Word is famous for its jumping figures and MS Office is famous for its inconsistent interface (copy/paste, sub/superscripts) among its applications. To put text and pictures together that are attractive for eBooks, use the Drawing Canvas:

(1) Create a new drawing canvas.

(2) Select the canvas. Under format (Ribbon), select Position. Choose one position.

(3) Select the canvas again to show the anchor move it to a suitable position.

Pictures and text including equations placed into a Drawing Canvas = O.K.!

Pictures and text including equations placed into a Text Box = Disaster!

Jumping Figures is still unresolved, but the situation is manageable!

Specialized eBook software suitable for scientific manuscripts that use equation software such as MathType and bibliographic software such as EndNote does not seem to exist. In this text, we considered OpenOffice, GoogleDocs/Sheets/Slides, and other packages, but presently none of those could handle equations, tables, figures, text, and Excel-type macros sufficiently enough. Problems create opportunities!

The coauthors of the text have served as excellent sources of information and discussants on the topics. However, the errors and deficiencies in the text are solely those of the lead author. There are a number of people that the lead author would like to acknowledge who helped to make this text possible. The presence of any name below does not imply endorsement of the text or its content by that person.

To actual readers, students Atrouli Chatterjee and Keisuke Okada (Chapters 1–4, solutions manual to Chapters 1–3), Shiori Baba (Chapters 1 and 2), Yuya Hiraga (Chapter 5), and Takuya Morioka (Chapter 2), and faculty readers, Naeema Ibrahim Karam Al Darmaki (Chapters 1, 2, and 6), Gheorghe Anitescu (Chapters 3 and 9), and Erdogan Kiran (overall)

For nice discussion on topics over the years, to Shigeki Takishima (Chapter 6, Sanchez–Lacombe equation), David A. Kofke (Chapter 6, Directional hydrogen bonding), Hye Min Kim (Chapter 6, Directional hydrogen bonding), Yoshiyuki Sato (Chapters 2, 6 and 8), Taku Michael Aida (Chapter 2), Masaru Watanabe (Chapter 2), Zhen Fang (Chapter 2), David Shan-Hill Wong (Chapter 6), Masafumi Takesue (Chapter 2), Hiromichi Hayashi (Chapter 2), Masaki Ota (Chapters 2 and 4), Anneke and Jan Sengers (Chapter 6), many companies (Chapter 4), James Titmas (Chapter 4), François Cansell (Chapter 4), Youn-Woo Lee (Chapter 4), Ed Lester (Chapter 4), Joseph M. DeSimone (Chapter 4), Motonobu Goto (Chapter 4), Tadafumi Adschiri (Chapter 4), Anthony R. H. Goodwin (Chapter 3), Yusuke Shimoyama (Chapter 5, SAFT and pc-SAFT equation), Masaki Togo (Chapter 5, pc-SAFT equation verification), Masayuki Iguchi (Chapter 6), Hiroshi Machida (Chapter 6, pc-SAFT derivation), Md. Zaidul Islam Sarker (Chapter 4), Xinhua Qi (Chapter 7), Olson/Allen NIST (Problem 8.X, heat transfer data), many Japanese colleagues and SCEJ scf div.

To Tokyo Institute of Technology students (Chapter 5, Example 5.10 and Project 5.1), Tohoku University Graduate School of Environmental Studies students (Chapters 1 and 2), Applied Chemistry, Chemical Engineering and Biomolecular Engineering Students (Chapters 3, 5, 7, 8, and 9), Tohoku University, Inomata and Smith Lab students

To Inomata Lab and Smith Lab assistants, Yumi Homma, Asako Yoshioka, Emi Yoshida, Rina Yambe, and Junko Hirama "J!"

To Elsevier staff, Derek Coleman, Susan Dennis, Angela Welch (Chapter 3), and Masako Takeda (Chapter 3)

To Georgia Institute of Technology for many inspiring instructors and professors (Amyn Teja, Gary Poehlein, Jude Sommerfeld, Henderson Ward, Michael Matteson, Clay Lewis, Bill Tedder, Pradeep Agrawal, and many others!).

My special thanks, to Professor Robert A. Heidemann (Chapter 7) for discussion and helpful comments over a 25-year period

For the many different philosophies, to Professors Shozaburo Saito, Kunio Arai, Martyn Poliakoff, and John P. O’Connell

To special friends, Raganath, Yoshimi, and Priya Bharath

To my family, Azusa, Ken, Shoh, and Mari Haruhara

my gratitude forever.

October, 2013

Chapter 1

Chemical Vocabulary and Essentials

Richard Smith, Cor Peters and Hiroshi Inomata

The difference between the almost right word & the right word is really a large matter–it's the difference between the lightning bug and the lightning

Mark Twain, Samuel Langhorne Clemens (1835–1910)

Tip Box#1

Chapter objectives

(1) to provide an overview of the text arrangement

(2) to introduce chemical vocabulary and essential concepts

(3) to learn how to determine properties using phase diagrams

(4) to learn how properties are used in simple processes

1.1 Philosophy of the Text

Part I (Chapters 1–4) of the text is written with the philosophy of providing students who do not necessarily have an engineering background with an introduction to supercritical fluids. The text focuses on carbon dioxide (CO2) and water (H2O), because these are environmentally-friendly substances that can be used to develop clean and low-energy chemical processes. Part II (Chapters 4–9) of the text is written for students in chemical-related fields, who have had a course in chemical thermodynamics.

In making a chemical process, it takes many different disciplines working together to produce a final product or result. Societies decide whether the process is safe and acceptable to our environment; economics and societal needs determine whether the chemical process will survive. It is our hope that the text can convey some of the excitement of using supercritical fluids in the next-generation of clean chemical processes.

The supercritical state of a substance is the condition of temperature and pressure for which it becomes highly-compressible. Many researchers refer to supercritical fluids as being dense gases because they have a density that is between that of a gas and a liquid. The attraction of supercritical carbon dioxide and supercritical water lies not only their environmental characteristics, but also in their high-performance as chemical solvents.

In many cases, supercritical fluids provide a unique way to extract, react, foam, crystallize, separate, encapsulate, impregnate or depolymerize substances to obtain chemical products that could not otherwise be manufactured. Some very remarkable things have been achieved for CO2 and H2O in their supercritical state.

Examples for Supercritical CO2

* low-energy hot water heaters

* natural coffee and tea decaffeination

* long-shelf-life rice and vegetable oils

* functional foods and food ingredients

* natural flavors and exquisite perfumes

* environmentally friendly polymer syntheses

* analytical methods for chromatography

* micronization and encapsulation of medicines

* nutraceuticals for hay fever and allergies

* water-free dyeing of fabrics

* dry-cleaning without organic solvents

* bone scaffolds and biomaterial implants

* time-release medication heart stents

Examples for Supercritical H2O

* rapid nanoparticle production

* nanoparticles for quantum dots in biomedicals

* low-energy phosphors and lighting materials

* efficient oxidative waste-water treatment

* recycle of plastics and polymer bottles

* organic solvent-free chemical analyses

* biomass delignification

* cellulose conversion for polymeric materials

* lignocellulose processing for biofuels and chemicals

* petroleum upgrading

In fact, there is an entire scientific journal devoted to the science and technology of supercritical fluids that publishes new ideas and applications:

www.journals.elsevier.com/the-journal-of-supercritical-fluids

Tip Box#2

The tip box

Tip Boxes are given in the text on selected topics to reinforce certain concepts and to alert the reader to something that the authors feel is important. See Tip Box#1 and then read the chapter summary.

1.2 Organization of the text

The textbook is designed to introduce some of the basic vocabulary used to study supercritical fluids with an emphasis on their properties and characteristics. The text is organized around applications rather than on detailed thermodynamics. Part I, which consists of Chapters 1–4 provides an introduction for multi-disciplinary students. Part II, which consists of Chapters 5–9, contains more specialized topics for students in chemical-related fields. A selection of chapters in Part I and Part II of the text are suitable for a short-course depending on instructor emphasis.

The text makes extensive use of Microsoft Excel spreadsheets or workbooks (Figure 1.1) with Microsoft are used to show the calculated results. The green boxes (Figure 1.1) contain functions, that can be used anywhere in the spreadsheet. One can make What if? type of calculations that change a property such as temperature or pressure to see its effect on the energy consumption. The reason for using Microsoft Excel is simple: many people are familiar with the spreadsheet format and Excel is highly accessible these days. Visual Basic for Applications (VBA) is Excel's programming language that can be used to write programs or VBA functions. VBA functions are readily used by beginners and advanced-users alike so that the analysis and development of supercritical fluid processes become possible.

Figure 1.1 Spreadsheet showing functions for properties of carbon dioxide (CO2). Typing a number into a yellow field will give a calculated result in a green field. The colors tell which values on the spreadsheet can be changed by the user. Green fields contain function definitions that can be used anywhere in the spreadsheet to make your own calculations. The function =RHO_TP1(20,10E6) gives the density of CO2 (in kg/m³) as a function of temperature T (in °C) and pressure P (in Pa). The 1 in the function name denotes CO2; water is denoted as 2.

The Excel spreadsheets used in this text do not require any special knowledge of programming and the best part is that the spreadsheets do not require installation of proprietary add-ins/add-ons/DLLs or other complicated things. However, Excel Macros will need to be enabled in the Excel worksheet for the spreadsheets to work. Many results can be seen almost immediately with pre-made graphs. All of the VBA code used in the spreadsheets can be viewed and modified or corrected. A few pointers and hints for using VBA code are given in the text and in the Appendix.

In the chapter arrangement, Tip Boxes are given on selected topics to enhance the organization of the text-flow and to alert the reader to something that the authors feel is important. Examples in each chapter show how to make a calculation or analysis and are used to illustrate the use of some of the supplied spreadsheets.

1.3 Basic Words

Learning a new subject can be thought of as building one's vocabulary in a specific field. As one learns the meaning basic words, it is possible to think, reason or imagine ways to use them in different combinations. Gradually, comprehension of the basic vocabulary is attained and practice in using the terms reinforces comprehension.

Process and System

Pictures and diagrams are very useful for learning new vocabulary and they make it fun to discuss the concepts. Consider the following picture that might be used to explain the word, process, and its input (In) and output (Out):

To define the picture a little bit better, words or symbols could be added so that the arrows are associated with In and Out and the purple object is associated with Process:

Then, suppose numerical values are assigned to the In and Out:

What questions arise when considering this process?

To an economics student, the picture might make perfect sense, because numbers are frequently associated with monetary values:

The exact details of the Process do not need to be known and even the type of currency might be assumed. An Investment of 1$ gives a Return of 4$.

or ¥. Therefore, the engineering student would typically ask a question regarding the units of the input and output. See Tip Box#3 for some hints on units.

Tip Box#3

Units and dimensions

International system of units Le système international d'unités (SI units)

In engineering and physical sciences, fundamental units of mass, length and time are used to describe physical quantities. There are seven fundamental units. The dimensions of a physical quantity is some combination of fundamental units. The fundamental unit of length is meters or m. The dimensions of area is square meters or m². The dimensions of volume are cubic meters or m³. Some ratios of units describe physical quantities:

* density is mass per volume or kg/m³ or kg · s− 1 and is given the Greek symbol ρ.

* mass flow rate is mass per time or kg/s or kg · s− 1.

* force is mass times acceleration or kg · m/s² or N, which is the unit of Newton.

* energy as work is force times distance or N · m or J, which is the unit of Joule.

* power is energy per time or J/s or J · s− 1 or W, which is the unit of Watt.

* pressure is force per area or N/m² or Pa, which is the unit of Pascal.

Some numerical values have no units and so are dimensionless because they are ratios of numerical values that have the same dimension. Some special groupings of numerical values are widely used in engineering. When writing numerical values, it is important to always write their units so that the meaning of the value is clear. SI units are preferably used in science. In this text, primarily SI units are used with the exception of temperature, which is many times given in degrees Celsius (°C) due to its common everyday use.

In engineering, fundamental units and their ratios are used for describing physical quantities. Fundamental units such as kilograms (kg) for specifying mass, meters for specifying length (m), and seconds (s) for specifying time are used to describe the dimensions of physical quantities such as force in Newtons (N), energy in Joules (J) or power in Watts (W). Some numerical values do not have units since they are ratios of values that have the same units.

Returning to the process being discussed, once an engineering student knows the dimensions of the streams, then, a follow-up question would be asked to see if the process is steady-state or unsteady-state.

A steady-state process is one in which the mass flow rate and the energy rate values of the streams remain constant with time (Figure 1.2). An unsteady-state process is one in which the mass and energy values of the streams change with time.

Figure 1.2 Liquid water flowing into a tank that has a hole in the bottom. The tank initially contains water. Water can flow into the tank at the same flow rate that water is leaving the tank (steady-state) or water can flow into the tank at a rate that is either greater than or less than water leaving the tank (unsteady-state).

The difference between a steady-state process and an unsteady-state process can be seen by the graphic depicting water flowing from a faucet into a tank that has a hole in it—steady-state (Figure 1.2, left) or unsteady-state (Figure 1.2, right). If the liquid level in the tank remains constant in Figure 1.2, the process is steady-state and the water flowing into the tank is exactly equal to the water flowing out of the container.

On the other hand, if the liquid level in the tank rises, then water is flowing into the tank faster than it is flowing out of the container and so the process is unsteady-state. Similarly, if the liquid level falls, then water is flowing into the tank slower than it is flowing out of the tank. A process can be steady-state or unsteady-state and it is important in many types of analyses.

Consider the process for liquid water flowing into and out of a container. Suppose that the input were 1 g/min and the output were 4 g/min, which corresponds to 1 mL/min input and 4 mL/min output. For a steady-state process, this is not possible as it would violate the law of conservation of mass: material can neither be created nor destroyed. For an unsteady-state process, flow rates such as 1 g/min in, 4 g/min out, would be possible.

Would the liquid level be falling or rising if water flowing into the container were 1 mL/min and water flowing out of the container were 4 mL/min?

Tip Box#4

Common units definitions

Force, work, energy and power

Now consider the following process that takes action on energy (see Tip Box#4):

From the picture, 1000 W, which is energy per unit time (W = J/s), is input into a process that creates 4000 W of energy as output.

Is this possible for an unsteady-state process?

Both economists and engineers will probably answer Yes to the question, because the process could have some amount of stored energy internally that could be released.

→ The answer is yes. Portable devices are unsteady-state processes.

Is this possible for a steady-state process?

For this case, economists will tend to risk saying Yes since the picture seems similar to the case for investments and returns. On the other hand, most engineers will conclude No as they are aware of the law of conservation of energy, which says that energy can neither be created nor destroyed.

→ The answer is yes. A steady-state process that converts 1 kW of energy into 4 kW of energy is a commercial reality and is known as a heat pump. However, the forms of energy of the input and output of the process are different and an important piece of this puzzle missing from the diagram of the process is the environment. Namely, the environment can supply energy to a process.

The coefficient of performance (COP) is used to rate energy devices and is defined as ratio of useful energy output from the process to electrical energy input to the process. For an electrical resistance heater, an input of 1 kW electricity gives an output of 1 kW heat so that the COP = 1 kW/1 kW = 1. COP is a dimensionless number.

A heat pump is a process that moves heat from one place to another by using the environment to supply some of the necessary heat. In the above picture, the input from the environment is missing.

Redrawing the picture to show the system and the environment gives

The system defines the mass and energy exchange of some part of a process with the environment or surroundings. The choice of a system is for convenience of analysis. Any properly defined system must obey the law of conservation of mass and the law of conservation of energy.

For the heat pump shown in the picture, 1 kW of electrical power as input gives 4 kW of heat output and so its COP value is 4. The way that the heat pump achieves this surprising feat is by using 3 kW of heat from the environment.

The EcoCute hot water heater (Figure 1.3) is a commercial device made by many Japanese manufacturers that can achieve COP values as high as 8. The EcoCute device uses CO2 in its supercritical state so that heat exchange takes place efficiently without phase change. Students will have an opportunity to design an EcoCute type of hot water heater in Chapter 2.

Figure 1.3 Commercial CO2 heat pump for producing hot water.

Energy can be in the form of mass, work or heat and physics shows that conversion of mass (m) to energy (E) is through Einstein's relativistic relationship, E = mc². In this text, mass and energy are considered as separate quantities.

There are three types of systems summarized in Figure 1.4:

An isolated system exchanges neither mass or energy with the environment.

A closed system exchanges energy but not mass with the environment.

An open system exchanges both mass and energy with its surroundings. In the open system, the streams flows each have energy content that must be considered in the analysis.

Figure 1.4 Types of systems that have mass and energy exchanges.

Each type of system is useful for analyzing and solving problems. See Tip Box#5 for some additional guidance and ideas for the types of analyses that can be made. Thermodynamic texts and problems are also helpful [TP1].

Tip Box#5

Types of systems

The concept of an isolated system allows one to analyze the physical state and conditions of a substance in a container or vessel. The closed system can be used to determine how conditions change if the contents are heated or cooled. The open system can be used to determine conditions and energy requirements for flowing fluids.

Solids, Liquids, Gases and Vapors

Solids such as sugar or salt, liquids such as water or vegetable oil, and gases such as air that we breathe or carbon dioxide bubbles that we see in beverage, are common substances in our everyday lives. When water is boiled, it is common to see water vapor emerging from the liquid surface as steam and when bread is baked or rice is cooked, it is a common to experience the pleasant effects of the gases or vapors. We are aware of these physical states of matter through our senses of sight, smell, taste, touch or hearing even though we may not be able to see them or define them precisely.

State and Phase

In physical chemistry [PC1], the common aggregation of a substance is called a phase. One can refer to the state or condition of a substance as being in its solid phase, liquid phase or gas phase. A solid phase has a specific shape or arrangement. A liquid phase has no definite shape or arrangement, but it conforms to the shape of its container according to its available volume. A gas phase has no definite shape or arrangement, but it completely fills or expands to the volume of its container. The terms gas phase and vapor phase are almost used interchangeably, however, vapor phase carries the connotation of a vapor possibly being in the presence of a liquid.

Temperature and pressure are variables that can affect the state of a substance. An increase in temperature can cause an ice crystal to melt to form a liquid which is an example of a phase transition. A phase transition can be defined as the change in the state of aggregation through variation of one or more conditions. Some of the phase transitions that commonly occur for pure substances are:

liquid → solid: fusion of a liquid to form a solid

solid → liquid: melting of a solid to form a liquid

liquid → gas: vaporization of a liquid to form a vapor

gas → liquid: condensation of a gas to form a liquid

solid → gas: sublimation of a solid to form a gas

gas → solid: deposition of a gas to form a solid

Temperature

Temperature is defined as the hotness or coldness of an object or environment and is commonly measured in units of degrees Celsius (°C) or degrees Fahrenheit (°F). These two common temperature scales are related to thermodynamic temperature scales used in science called absolute temperature scales. The absolute temperature scale for °C is called the