thermal separation technology principles methods process design

ConstantArea, exchange area, interfacial areaVolumetric interfacial area AmplitudeActivityBottom fraction, bottom productBottom product rate WidthMass concentrationMolar concentrationSpe

Alfons Mersmann • Matthias Kind • Johann Stichlmair

Thermal Separation Technology

Springer Heidelberg Dordrecht London New York

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e-ISBN 978-3-642-12525-6ISBN 978-3-642-12524-9

Thirty years ago the first edition of this book was published in German The source for students Today our world is characterized by high-speed developmentsand more principal approaches in comparison to the past Therefore, the authorsput the question: Is it reasonable in the Internet age to write scientific books and –

con-if yes – for whom and in which language?

This book is the answer to these questions We hope that students as well as enced engineers and scientists may find access to the representation of the topicand may gain from the lecture of the work According to the concept of the book it

experi-is assumed that the book experi-is read from the beginning to the end However, we knowvery well that there are no such readers The book may be a helpful tool for begin-ners and experts for consulting and for deepening their knowledge In spite of thefact that the concept of a large number of unit operations is widely abandoned, theoverall arrangement of the book corresponds to this structure because there are notonly intelligent and abstractively thinking readers but also others with a morepractical approach to problems of chemical engineering The contents of this bookare too extensive for students with time limitations for their studies but not suffici-ent for specialists

The notation is a compromise between internationally and nationally applied bols With respect to the literature cited, only publications necessary for a deeper ormore general study of the topic are mentioned

sym-Let us come back to the question: Is it reasonable to publish books in the modernhave been printed and read Two centuries ago Johann Wolfgang von Goethewrote:

“what you possess in black on white you can carry home.”

However, Goethe could not have any idea of computers, copy machines, and net If so, he probably would write:

Inter-world of communication and information? Since the times of Gutenberg, bookscept of the work – at that time printed in leaden letters – was a cheap information

v

“Secure is what is stored in electronic brains as many dots,

but often not in human brains with empty spots.”

We think that not the persons believing in computers but thinking persons who arelooking on black on white are in the position of getting access to problems of

separation technology

M Kind

J Stichlmair

ConstantArea, exchange area, interfacial areaVolumetric interfacial area

AmplitudeActivityBottom fraction, bottom productBottom product rate

WidthMass concentrationMolar concentrationSpecific heat capacity at constant pressureMolar heat capacity at constant pressureSpecific heat capacity at constant volumeMolar heat capacity at constant volumeFriction factor

Distillate, overhead fractionDistillate rate

Diameter (apparatus)Dispersion coefficient

Diameter (small, sphere, particle, tube, stirrer)Hydraulic diameter

Particle diameterSauter diameter Energy

Efficiency, enhancement factorExtract

Extract rateCharge of an electron Force

FeedFeed rateFree inner energyPartial molar free inner energyDegree of freedom

FugacityCross-sectional areaFrequency

Gas, G-phaseGas rate, G-phase rateFree enthalpy, Gibbs enthalpySpecific free enthalpyMolar free enthalpyPartial molar free enthalpyTotal height, distanceHeight

EnthalpySpecific enthalpyMolar enthalpyPartial molar enthalpyPartial molar enthalpy of mixingPartial molar enthalpy of bondingSpecific phase change enthalpy,latent heat of evaporationMolar phase change enthalpyMomentum

Equilibrium ratio, equilibrium constantNumber of components

Boltzmann constant Overall heat transfer coefficientMolar mass transfer coefficientMass transfer coefficientTotal length

LengthLiquid (L-phase)Liquid rate (L-phase rate)Mass

Mass rateMolar massMass fluxNumber (transfer units, molecule layers)Particles per volume

Avogadro constant or Loschmidt constantAmount of substance

Substance ratesubstance fluxNumber (stages, particles)Rate of revolutions

PowerNumber of phasesTotal pressureCritical pressure

Partial pressure of component i Vapor pressure of component i

Reduced pressurePressure difference, pressure lossHeat

Heat rateHeat fluxRadius (tube, sphere, particle)Reflux ratio

RaffinateRaffinate rateGeneral gas constant

Specific gas constant of component i

RadiusSpecific heat of evaporationMolar heat of evaporation Solid

Solid rateEntropySpecific entropyMolar entropy

Partial molar entropy of component i

ThicknessTorqueCarrier substanceCarrier substance rateAbsolute temperatureBoiling temperature at normal pressureCritical temperature

Reduced temperatureMelting temperatureTime

Inner energySpecific inner energyMolar inner energy

Partial molar inner energy of component i Velocity (x-coordinate), superficial velocity

VolumeVolumetric flow rate

Volumetric flux

Velocity (y-coordinate)

Specific volumeMolar volumePartial molar volumeWork

Power (=work per time)Specific work

Velocity (z-coordinate)

Velocity in an opening (hole, orifice, nozzle)Terminal settling or rising velocity of a single particleTerminal settling or rising velocity of a swarm of par-ticles

Mass loading of component i

(adsorbate, liquid, raffinate)

Mole loading of component i

(adsorbate, liquid, raffinate)

Mass fraction of component i

(adsorbate, liquid, raffinate)

Mole fraction of component i

(adsorbate, liquid, raffinate)Rectangular coordinate

Mass loading of component i

(adsorptive, gas, extract)

Mole loading of component i

(adsorptive, gas, extract)

Mass fraction of component i

(adsorptive, gas, extract)

Mole fraction of component i

(adsorptive, gas, extract)Rectangular coordinateCompressibility factorRectangular coordinateOverall mass fraction in a multiphase systemOverall mole fraction in a multiphase system

Greek Symbols

Relative volatilityDegree of dissociationHeat transfer coefficientMass transfer coefficientMass transfer coefficient (semipermeable interface)Cubical expansion coefficient

Activity coefficientThickness, film thicknessSpecific power inputVoidage, porosityVolume fraction of continuous phaseVolume fractioin of dispersed phaseDynamic viscosity

Celsius temperatureMean path lengthHeat conductivityChemical potentialDensity

Molar densitySurface or interfacial tensionShear stress

Residence timeFugacity coefficientRelative saturationRelative free area, volume fractionAngular velocity

Indices

AreaActivityAdsorptionAgglomerationAnhydrateAvoidance of settlingAtom

AxialBurton–Cabrera–FrankBottom lifting

Birth and spreadBoiling

Crystal, criticalCirculationCollisionDiffusionDisruption, dispersionEffective

ForeignGasGeometrical

Component i

IdealLiquidLaminarMolecule, molarMacro

Maximum valueMicro

MinimumOptimumParticlePoly nuclearRelativeSolidSettling, seedSettling of a swarmSuspensionTotalTotalTurbulentVickers, volumevan der WaalsVelocity, superficial velocityStart

End

Dimensionless Numbers

Single and Two-Phase Flow

Archimedes NumberEuler numberDispersion or Fourier numberFroude number

Modified Froude number in two-phase systemsGalilei number

Reynolds numberWeber numberBond number (in US literature)Modified number in two-phase systemsStrouhal number

Heat and Mass Transfer

Fourier number (heat transfer)Fourier number (mass transfer)Grashof number (heat transfer)Lewis number

Nusselt numberPeclet numberPhase change numberPrandtl numberSchmidt numberSherwood numberBodenstein number (continuous phase)

Bodenstein number (dispersed phase)

Dimensionless irrigation rate

Maximum diameter of fluid particles in turbulent fieldFluid number of dispersed systems

Film number

Gas-film number

Microscale of turbulenceNewton number of stirrers

Flow number of stirrersNumber of transfer unitsMixing time number Macromixing time Micromixing time

Dimensionless flow density in bubble and dropcolumns

Contents

Preface v

1 Introduction 1

2 Thermodynamic Phase Equilibrium 11

1.1 Contributions of Chemical Engineering to the Carbon Dioxide Problem 3

3 Fundamentals of Single-Phase and Multiphase Flow 117

2.1 Liquid/Gas Systems 13

2.1.1 Characteristics of Pure Substances 13

2.1.2 Behavior of Binary Mixtures 19

2.1.3 Behavior of Ideal Mixtures 32

2.1.4 Real Behavior of Liquid Mixtures 39

2.2 Liquid/Liquid Systems 60

2.3 Solid/Liquid Systems 65

2.4 Sorption Equilibria 71

2.4.1 Single Component Sorption 71

2.4.4 Calculation of Single Component Adsorption Equilibria 85

2.4.5 Prediction of Multicomponent Adsorption Equilibria 93

2.5 Enthalpy–Concentration Diagram 101

3.1 Basic Laws of Single-Phase Flow 118

3.1.1 Laws of Mass Conservation and Continuity 118

3.1.2 Irrotational and Rotational Flow 119

3.1.3 The Viscous Fluid 120

3.1.4 Navier–Stokes, Euler, and Bernoulli Equations 120

3.1.5 Laminar and Turbulent Flow in Ducts 123

3.1.6 Turbulence 127

3.1.7 Molecular Flow 128

3.1.8 Falling Film on a Vertical Wall 130

3.2 Countercurrent Flow of a Gas and a Liquid in a Circular Vertical Tube 133

Symbols vii

2.4.2 Heat of Adsorption and Bonding 77

2.4.3 Multicomponent Adsorption 79

xv

3.3 Similarity Hypothesis, Dimensional Analysis, and Dimensionless

3.6.2 Volumetric Holdup (Fluidized Beds, Spray, Bubble

Numbers 134

3.4 Particulate Systems 136

3.5 Flow in Fixed Beds 139

3.6 Disperse Systems in a Gravity Field 141

3.6.1 The Final Rising or Falling Velocity of Single Particles 144

and Drop Columns) 149

3.7 Flow in Stirred Vessels 155

3.7.1 Macro-, Meso-, and Micromixing 162

3.7.2 Suspending, Tendency of Settling 165

3.7.3 Breakup of Gases and Liquids (Bubbles and Drops) 168

3.7.4 Gas–Liquid Systems in Stirred Vessels 169

4 Balances, Kinetics of Heat and Mass Transfer 175

4.1 Introduction 175

4.2 Balances 176

4.2.1 Basics 176

4.2.2 Balancing Exercises of Processes Without Kinetic Phenomena 179

4.3 Heat and Mass Transfer 192

4.3.1 Kinetics 192

4.3.2 Heat and Mass Transfer Coefficients 196

4.3.3 Balancing Exercises of Processes with Kinetic Phenomena 211

5 Distillation, Rectification, and Absorption 231

5.1 Distillation 232

5.1.1 Fundamentals 232

5.1.2 Continuous Closed Distillation 242

5.1.3 Discontinuous Open Distillation (Batch Distillation) 246

5.2 Rectification 251

5.2.1 Fundamentals 251

5.2.2 Continuous Rectification 254

5.2.3 Batch Distillation (Multistage) 289

5.3 Absorption and Desorption 296

5.3.1 Phase Equilibrium 298

5.3.2 Physical Absorption 299

5.3.3 Chemical Absorption 306

5.4 Dimensioning of Mass Transfer Columns 310

5.4.1 Tray Columns 312

5.4.2 Packed Columns 329

Contents xvii

6 Extraction 349

6.1 Phase Equilibrium 350

6.1.1 Selection of Solvent 352

6.2 Thermodynamic Description of Extraction 354

6.2.1 Single Stage Extraction 354

6.2.2 Multistage Crossflow Extraction 356

6.2.3 Multiple Stage Countercurrent Extraction 357

6.3 Equipment 361

6.3.1 Equipment for Solvent Extraction 361

6.3.2 Selection of the Dispersed Phase 365

6.3.3 Decantation (Phase Splitting) 366

6.4 Dimensioning of Solvent Extractors 370

6.4.1 Two-Phase Flow 370

6.4.2 Mass Transfer 376

7 Evaporation and Condensation 385

7.1 Evaporators 386

7.2 Multiple Effect Evaporation 391

7.3 Condensers 399

7.4 Design of Evaporators and Condensers 401

7.5 Thermocompression 406

7.6 Evaporation Processes 409

8 Crystallization 413

8.1 Fundamentals and Equilibrium 413

8.1.1 Fundamentals 414

8.1.2 Equilibrium 417

8.2 Crystallization Processes and Devices 418

8.2.1 Cooling Crystallization 418

8.2.2 Evaporative Crystallization 419

8.2.3 Vacuum Crystallization 420

8.2.4 Drowning-Out and Reactive Crystallization 420

8.2.5 Crystallization Devices 422

8.3 Balances 432

8.3.1 Mass Balance of the Continuously Operated Crystallizer 432

8.3.2 Mass Balance of the Batch Crystallizer 436

8.3.3 Energy Balance of the Continuously Operated Crystallizer 438

8.3.4 Population Balance 441

8.4 Crystallization Kinetics 444

8.4.1 Nucleation and Metastable Zone 444

8.4.2 Crystal Growth 454

8.4.3 Aggregation and Agglomeration 460

8.4.4 Nucleation and Crystal Growth in MSMPR Crystallizers 470

8.5 Design of Crystallizers 473

9 Adsorption, Chromatography, Ion Exchange 483

9.1 Industrial Adsorbents 483

9.2 Adsorbers 487

9.3 Sorption Equilibria 493

9.4 Single and Multistage Adsorber 496

9.4.1 Single Stage 496

9.4.2 Crossflow of Stages 497

9.4.3 Countercurrent Flow 499

9.5 Adsorption Kinetics 501

9.5.1 Simplified Models of Fixed Beds 507

9.5.2 Simplified Solution for a Single Pellet 514

9.5.3 Transport Coefficients 518

9.5.4 The Adiabatic Fixed Bed Absorber 524

9.6 Regeneration of Adsorbents 530

9.7 Adsorption Processes 534

9.8 Chromatography 536

9.8.1 Equilibria 537

9.8.3 Chromatography Processes 550

9.8.4 Industrial processes 551

9.9 Ion Exchange 551

9.9.1 Capacity and Equilibrium 553

9.9.2 Kinetics and Breakthrough 554

9.9.3 Operation Modes 555

9.9.4 Industrial Application 556

10.3 The Single-Stage Apparatus in the Enthalpy–Concentration Diagram for Humid Air 572

10 Drying 56

10.1 Types of Dryers 562

10.2 Drying Goods and Desiccants 566

10.2.1 Drying Goods 567

10.2.2 Desiccants 571

10.2.3 Drying by Radiation 572

10.4 Multistage Dryer 578

10.5 Fluid Dynamics and Heat Transfer 580

10.6 Drying Periods 581

10.6.1 Constant Rate Period (I Drying Period) 582

10.6.2 Critical Moisture Content 585

10.6.3 Falling Rate Period (II Drying Period) 585

10.7 Some Further Drying Processes 590

9.8.2 Theoretical Model of the Number N of Stages 540

1

Contents xix

References 635

11 Conceptual Process Design 595

11.1 Processes for Separating Binary Mixtures 596

11.1.1 Concentration of Sulfuric Acid 596

11.1.2 Removal of Ammonia from Wastewater 598

11.1.3 Removal of Hydrogen Chloride from Inert Gases 599

11.1.4 Air separation 601

11.2 Processes for Separating Zeotropic Multicomponent Mixtures 602

11.2.1 Basic Processes for Fractionating Ternary Mixtures 603

11.2.2 Processes with Side Columns 607

11.2.3 Processes with Indirect (Thermal) Column Coupling 612

11.3 Processes for Separating Azeotropic Mixtures 617

11.3.1 Fractionation of Mixtures with Heteroazeotropes 617

11.3.2 Pressure Swing Distillation 619

11.3.3 Processes with Entrainer 620

11.4 Hybrid Processes 623

11.4.1 Azeotropic Distillation 62

11.4.2 Extractive Distillation 625

11.4.3 Processes Combining Distillation and Extraction 626

11.4.4 Processes Combining Distillation with Desorption 627

11.4.5 Processes Combining Distillation with Adsorption 627

11.4.6 Processes Combining Distillation with Permeation 629

11.5 Reactive Distillation 631

Index 661

4

Starting with natural as well as chemically or biologically produced substances theseparation of mixtures is an important task for chemical engineers This disciplinecan be subdivided into thermal, mechanical, chemical, biological, and biomedicalprocesses to effect changes of substances or to avoid such changes Today, an addi-tional objective of thermal separation technology is process engineering and pro-duct development.

A general problem of thermal separation technology is the identification of themost economical process for the separation of mixtures into pure components orspecified fractions The separation principles are based on:

• Differences of vapor pressures of the components (e.g., evaporation, tion, distillation, rectification, drying)

condensa-• Differences of solubilities (e.g., extraction, reextraction, crystallization, tion, desorption)

absorp-• Differences of sorption behavior (e.g., adsorption, desorption, chromatography,drying)

• Differences of forces (mechanical, capillary, electric, magnetic) in porous solids

or membranes (e.g., dialysis, electrolysis, electrophoresis, osmosis, reverseosmosis, pervaporation, ultrafiltration)

• Differences in chemical equilibria (e.g., chemisorption, ion exchange)

As a rule, the addition of substances to a mixture is not helpful However, there areexceptions, for instance, the addition of entrainers, desorbents, drowning-outagents, and solvents

In industry, separations effected by porous solid materials (adsorbents, membranes,ion exchange resins, special kinds of solid matrices) are seldom applied in compa-rison to separations carried out in systems with fluid phases The reason may be apoorer state of the art than in fluid systems Furthermore, the handling of fluid sys-tems is much easier than the handling of systems with solid phases On the other

© Springer-Verlag Berlin Heidelberg 2011

A Mersmann et al., Thermal Separation Technology: Principles, Methods, 1

Process Design, VDI-Buch, DOI 10.1007/978-3-642-12525-6_1,

Introduction

1

same order of magnitude in fluid/fluid and fluid/solid systems Since, at the presentstate of the art, fluid/fluid systems dominate separation technology, they are prefe-rentially presented in this book.

It is common practice to divide separation technologies into the unit operationsabsorption, adsorption, crystallization, distillation, rectification, extraction, evapo-ration, drying, etc Such an approach is no longer recommended because the readerwould have difficulties to recognize common and general items and laws of allthese separation techniques Our intention is to stress common features andmethods and to demonstrate how to proceed in solving a concrete separation prob-lem

The following complexes are the basis of all models in chemical engineering:

• Chemical and physical equilibria (or more general, thermodynamic behavior ofsubstances)

• Conservation laws of energy, mass, components, and numbers

• Single and multiphase flow (or, in general, the conservation law of momentum)

• Kinetics of changes in systems which are not at equilibrium (heat transfer, masstransfer, chemical reaction)

If the underlying laws of these complexes are well understood then separation cesses can be developed and the equipment dimensioned However, with respect tospecial features of separation technology, a gross subdivision in unit operations isindeed reasonable Therefore, some parts of the book are structured in unit opera-tions according to the principle “from the molecule to the plant.”

pro-Methods of conceptual process design are a prerequisite for the combination ofprocess steps to an integrated process which is economically and ecologicallyefficient and meets modern safety standards Special attention is paid to the ques-tion how high product qualities can be achieved This is especially important forproducts produced in crystallization and drying steps Furthermore, the purity ofdistillates or off-gases purified by absorption or desorption processes can be decis-ive in process development The authors are aware that computer-aided processsimulation is widely applied in industry In this book tools for this approach arepresented The models are based on general laws of natural sciences and simplifiedbut tolerable engineering methods

hand, there is a great potential of microporous material with respect to innovativeand tailor-made membranes The volumetric mass transfer coefficients are in the

pic mixtures) can be reduced or avoided from the very beginning Often, there is agood chance to simplify the process and to save energy and raw material.

Many examples of energy saving in thermal separation processes are presented inthe last chapter of this book In addition, energy saving is a general task for engi-neers with respect to the carbon dioxide problem Therefore, the first pages of thisbook deal with process technologies for mitigation of carbon dioxide emissionsinto the atmosphere

With respect to process optimization, at first high-efficient and selective catalysts

in a general sense (e.g., chemical and biological catalysts, algae, bacteria, fungi,and mammal cells viruses, yeasts) are very important An optimum process is cha-racterized by minimum consumption of resources (energy, raw material) and mini-mum production of waste (heat, materials without any chance on the market).Safety aspects play a big role Another goal of chemical engineering is the anticipa-tion of possible improvements of the process during its production life However,this is a difficult task in times of hectic simultaneous process development

The main concern of the climate discussion in recent years was the anthropogenicincrease of carbon dioxide in the atmosphere Let us have a look on the globalmary renewable energies (i.e., sun, water, wind, biogas, and biomass) whereas pri-mary energies from the earth crust (i.e., fossil combustibles, radioactive ores, geo-thermal heat, etc.) can be found in the circles of the lower row Nearly all energiesare consumed as thermal energy, mechanical energy, or electrical energy, finallydissipated as thermal energy in the environment These secondary energies can be

1.1 Contributions of Chemical Engineering to the Carbon Dioxide Problem

energy supply, see Fig 1.1-1 The circles at the top and in the upper row mark

pri-found in the circles of the intermediate row of Fig 1.1-1

Primary energy can be converted into secondary energy by energy converters likewater or wind turbines, solar cells, sun collectors, furnaces, combustion engines,gas and vapor turbines, generators, fuel cells, nuclear reactors, and heat pumps.Arrows mark such converters Their maximum efficiencies, e.g., how much of the

It is important to note that in biological or chemical laboratories, where novel ducts are developed, the aspects of separation technology should be taken into con-sideration since in many cases waste streams of worthless side products, largerecirculation streams, and mixture which are difficult to separate (water or azeotro-

pro-Global energy supply

Fig 1.1-1

• Replacement of fossil combustibles by other energy sources, especially by wable energies

rene-• Recovery of waste heat (e.g., heat/power generation)

• Lower energy losses of energy transportation systems

• Higher energy efficiency of equipment used by consumers (industry, traffic,household, etc.)

Since process industry is very energy consuming much information is given in thisbook about how to save or recover energy

• Higher efficiencies of the energy converters mentioned in Fig 1.1-1

energy is converted from one state into the other, are between 0.95 and 0.99 validfor electrical generators and 0.05 up to 0.18 valid for solar cells

There are many possibilities to reduce carbon dioxide emissions caused by fossilcombustibles as carbon or hydrocarbons:

mass% hydrogen content) or carbon (no hydrogen content) as fossil combustiblesare burnt with oxygen or air (the mass percentage of hydrogen of all hydrocarbons

is between 0 and 25%) Note that the production of oxygen requires the separation

pression of hydrogen (up to 70 MPa), and the liquefaction of hydrogen at a

tempe-rature of –254 C are considered in four processes Hydrogen combustion may bepromising for all kinds of vehicles Chemical reactions and heats of reaction are

°

In Fig 1.1-2 simple schemes of feasible processes starting from methane (25

of air In Fig 1.1-3 the cracking of methane, the sequestration of carbon, the

4

72 (36) H O 2 2

28 CO 6(2) H 2

dis-• Sequestration of carbon dioxide as compressed gas or liquid

• Cracking of methane or other hydrocarbons, combustion of hydrogen, andsequestration of carbon

Let us have a short look on the energy efficiencies of these processes

Schemes of four combustion processes (sequestration of carbon): Crack(ing)

Fig 1.1-3

absorption or adsorption processes when the combustion is performed with air Calculations elucidate the minimum energy demand for the separation and com-pression of carbon dioxide based on the minimum separation energy of gaseousmixtures (flue gases) and on the adiabatic compression of carbon dioxide (up to 10MPa) These minimum energy demands related to the heat of combustion of thecombustibles (C or CH4) are for

carbon dioxide vs temperature is shown

in Fig 1.1-4 Carbon dioxide has to be separated from flue gases for instance by

• The processes 1 to 4 approximately 7–8%

• The processes 5 and (5) approximately 21–23%

Note that, as a rule, compressors are driven by electrical engines, and efficiencies

of power stations are below 0.5 (conversion of chemical into electrical energy).Using such electrical engines the above minimum percentages of the processes 1–4have approximately to be doubled

Let us now have a short look on the energetic efficiency of the processes depictedproduced by the cracking of methane In the following, all energies are valid for 1kmol = 16 kg methane or 2 kmol = 4 kg hydrogen (heat of combustion = –499,400kJ) or 1 kmol = 12 kg carbon (heat of combustion = –395,800 kJ) The cracking of

of 1 kmol methane (heat of combustion = –803,500 kJ) requires 91,700 kJ, and for

in Fig 1.1-3 for the production of either compressed (70 MPa) or liquefied hydrogenlisted in Table 1.1-1 The vapor pressure of

CH4  C 2H

2

4 -+

2+2H2O 803.5 kJ

4 -–

2 –395.8 -kJ

2 -O2

2 -–

2+ +131 -kJ

2 -O2

2 -O2

2

4 -–

2 -+

1,000°C1,000°C1,000°C1,000°C

mol CHmol CHmol Cmol Hmol Cmol COmol CH

mol Cmol CHmol CO

Table 1.1-1 Chemical reactions

If compression of hydrogen is replaced by liquefaction (+50,000 kJ/kgH2), mately 85% of the heat of combustion of methane is lost as discarded carbon and

Kreysa, 2008) Since carbon is sequestered it

as 72,000 kJ (

required for cracking of methane and liquefaction of hydrogen

Vapor pressure of CO2 vs temperature

Fig 1.1-4

After this disillusioning considerations let us have a short look on concerns andrestrictions encountered in the area of primary energy sources:

• Fossil combustibles Emissions of carbon dioxide or sequestration of carbon

dioxide (availability of secure and tight caverns) or carbon

• Nuclear fuels Security and secure disposal of nuclear waste.

• Geothermal heat Upper limit of operating temperature and large heat transfer

areas because of heat flux densities < 10–4

• Biogas and biomass In the case of energy plant production competition with

human food supply

kW m 2

• Solar energy With respect to solar radiation of <0.2 , large absorptionareas (photovoltaic) or large mirrors (solar power station) are necessary.

• Water With the power , high flow rates or height ofwater column are required Availability of reservoirs and rivers

, large diameters D (>100 m) are necessary Great differences of

local and momentary wind velocities

Note that the storage of energy is difficult and the locations of energy offer and that

of energy demand can be rather distant This requires high efficiencies of tation systems and much international cooperation in the future

Thermodynamic Phase Equilibrium

In this chapter the thermodynamic behavior of single- and multiphase systems of

are described in a general way In the References

Multiphase systems are often found in machinery and apparatuses of the ing industry because most thermal separation processes are based on the transfer ofone or more components from one phase to another

process-A phase is the entirety of regions, where material properties either do not change oronly change continually, but never change abruptly However, it makes no differ-ence whether the regions are spatially coherent or not (continuous or dispersedphase) A phase can consist of one or more chemically uniform substances, whichare called components A system can contain one phase (gas, liquid, solid), twophases (e.g., liquid/gas, fluid/solid, fluid/fluid), or even more (in an evaporativecrystallizer, e.g., there are a solid, a liquid and a gaseous phase) This chapterdescribes the thermodynamic equilibrium between phases

Gibbs phase-rule states how many degrees of freedom f fully describe a

multicom-ponent and multiphase system:

state-The description of the thermodynamical equilibrium is based upon the laws of modynamics The first law of thermodynamics is the law of conservation of energy.For a resting, closed, and nonreacting system, only the conservation of the internal

ther-energy has to be considered It can only be changed by transferring heat dq and work dw across the system boundaries:

f = k p– +2

u

© Springer-Verlag Berlin Heidelberg 2011

A Mersmann et al., Thermal Separation Technology: Principles, Methods,

Process Design, VDI-Buch, DOI 10.1007/978-3-642-12525-6_2,

2

(2.0-1)

11section some general textbooks and data compilations are recommended

pure substances and their mixtures

Work dw is transferred across the system boundary by compressing the volume

of the system against its pressure :

From the definition of enthalpy,

follows

.The internal energy of a system correlates to the translational, rotational, andvibrational energy of the molecules and only depends on the temperature of thesystem:

Corresponding to the equations above, the heat capacity has to be determined in

a way that for a change in the system temperature in there is no transfer of

work dw Hence, the volume has to be kept constant:

And analogously

is to be measured at constant pressure

The thermodynamic state of a system is defined not only by its internal energy ,but also by its entropy , which is defined by

The entropy of a closed system, which is at temperature , is changed by theheat transferred across its boundary The second law of thermodynamics statesthat any process within the system enhances the entropy of the system, except ifthis process is reversible.

Furthermore, it is convenient to define the free enthalpy as a state variable

,

or in its differential form:

.With , Gibbs fundamental equation follows for reversible processes

within the system:

.This is an important relation for the description of thermodynamic equilibria as it

contains the measurable dimensions dp and dT of the system.

Liquid/Gas Systems

In this chapter important thermodynamic fundamentals will be introduced for uid/gas systems ( ) In analogy, they also apply to the other two- ( , ,) and multiphase systems

liq-Characteristics of Pure Substances

Vapor pressure

Vapor pressure is a function of temperature only The vapor pressure curvevapor pressure curves of water, benzene, and naphthalene are depicted Vapor pres-sure curves show a bend at the triple point TP and end at the critical point CP.The pressure that is reached at a given temperature of a closed, equilibrated two-phase system ( ) of a pure substance is called vapor pressure The irrevers-ible exchange processes within the system come to rest if temperature and pressure

of liquid and gas are in equilibrium Then the entropy of the entire system reachesits maximum

The pressure reached in equilibrium is denoted vapor pressure (of the pure

component) From this and with Gibbs fundamental equation, which is valid for

each of the phases, it follows that

.Sufficiently far from the critical point ( , and ) it follows that

and that the law of ideal gases

(2.1-3)

(2.1-4)

(2.1-5)

(2.1-6)

To vaporize the substance in a system at p = const., an amount of heat , which iscalled specific vaporization enthalpy , has to be added Therefore,

results, with being the sublimation enthalpy The last equation provides ple vapor pressure relations for small temperature ranges in which and only change insignificantly:

sim-

For greater temperature spans the Antoine equation provides better results:

.Today, a modified form of an equation given by Wagner (1972) is considered to bestate of the art

The VDI-Heat Atlas (2010) provides values for the coefficients of this equation for

h

0ln

A simple vapor pressure diagram with the possibility for extrapolation is given bytemperature scale obeys the relation

Here T is the absolute temperature in Kelvin.

The vapor pressure curve of each component is rendered by two straight lines Thevapor pressure curve has a sharp bend at the triple point because of the differencebetween sublimation and vaporization enthalpy The diagram offers the possibility

to extraploate measured vapor pressures

Above, it has been shown that the enthalpy of vaporization can be obtained fromthe vapor pressure curve However, an estimation of the enthalpy of vaporization can

Trouton’s rule Experience shows that for many

sub-stances and at standard conditions the molar entropy of vaporization isthe homologues of different organic compounds is plotted vs their respectivemolar mass The stronger the dipole moment of the single molecules, the strongerthe association of the molecules and the higher the entropy of vaporization Waterwith its extremely high dipole moment has an entropy of vaporization of 109

The enthalpy of vaporization decreases when approaching the cal point and vanishes at the critical point With good accuracy the enthalpy ofvaporization can be calculated by the following equation for the entire temperature

criti-Vapor pressure vs modified temperature

range between and (Watson 1943) is the boiling temperature at standardpressure.

The PPDS equation

with is suitable for correlation of data of heat of vaporization.VDI-Heat Atlas (2010) provides values for the coefficients of this equation for 275substances

After Thiesen (1923), it seems favorable to plot the enthalpy of vaporization vs thedifference of the critical temperature and the temperature in a double loga-

is not very close This diagram also shows that the enthalpy of phase transitionchanges at the triple point At the triple point the enthalpy of vaporization and theenthalpy of melting add up to the enthalpy of sublimation:

The enthalpy of melting can be calculated with the equation of Clausius–

Clapeyron and with the change of specific volume from to :

about 9.2 kJ/(kmolK) for metals, 22–29 kJ/(kmolK) for inorganic compounds, and38–58 kJ/(kmolK) for organic compounds

Vapor Pressure at Strongly Curved Liquid Surfaces

The vapor pressure at liquid surfaces with pronounced concave curvature is smallerthan that of flat surfaces In case of convex curvature, the vapor pressure of the liq-uid is greater than that of flat surfaces A concave liquid surface is found, e.g., forbubbles or in a capillary if the liquid wets the capillary’s wall Droplets on the con-trary have a convexly bent surface As prerequisite to vaporization, tiny steam bub-bles have to be formed initially while for condensation small droplets have to formfirst

The vapor pressure at strongly curved liquid surfaces with radius can becalculated from the Gibbs–Thomson equation:

,

with being the surface tension This relation is obtained if the isothermal work

of compression of a small amount of substance from vapor pressure of thebent surface to the vapor pressure is set equal to the increase of surface energy.According to this relation, the logarithm of the pressure ratio is directly propor-

Specific heat of vaporization vs the difference Tc–T for some substances

tional to the surface tension and inversely proportional to the radius At convexliquid surfaces, the radius is positive In this case the pressure is larger than that

of flat ones In contrast, for concave surfaces with a negative radius of curvature alowering of vapor pressure results These effects are only significant, if the radius

of curvature is very small

is plotted vs the radius of curvature for methylalcohol, water, and mercury, which shows surface tensions of 0.0226, 0.0727, andsurfaces deviates by more than 1% from that of flat liquid surfaces for manyorganic substances as well as for water, if the radii of bubbles and drops are smallerthan 100 nm It can be derived from this diagram that the effects are considerable

for bubbles or drops made up of only a few hundred molecules The

Gibbs–Thom-son equation is often used to explain retardation of boiling (superheating of the

liq-uid) as well as condensation–inhibiting processes (supercooling of vapor) In tion it gives information about unusual sorption isotherms of adsorbent materials or

addi-Behavior of Binary Mixtures

Process engineering often deals with multicomponent mixtures The behavior ofmulticomponent mixtures in general does not differ from the behavior of two com-ponent mixtures, which are technically and practically easier to describe There-fore, it is advantageous to acquire the basics for the behavior of binary systems.How the equations can be transferred to fit multicomponent mixtures is shown in

Vapor pressure ratio vs the radius of curvature

In Fig 2.1-5, the ratio  p

0.435 N/m, respectively at 20°C Figure 2.1-5 shows that the vapor pressure at bent

about goods with very narrow capillary tubes which have to be dried, see Chap 10

Fig 2.1-5

2.1.2

Chap 5

19